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Add csg boolean operators using elalish/manifold.

Browse source 
Uses MeshGL64 for more floating point precision.

Co-Authored-By: 31 <31eee384@gmail.com>
Co-Authored-By: Claudio Z <120678869+cloudofoz@users.noreply.github.com>
This commit is contained in:
K. S. Ernest (iFire) Lee 2022-08-03 12:14:42 -07:00
parent d09d82d433
commit fda444bb01
45 changed files with 20005 additions and 1628 deletions
Download patch file Download diff file Expand all files Collapse all files

5
COPYRIGHT.txt
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@ -334,6 +334,11 @@ Comment: WebP codec
Copyright: 2010, Google Inc.
License: BSD-3-clause
Files: ./thirdparty/manifold/
Comment: Manifold
Copyright: 2020-2024, The Manifold Authors
License: Apache-2.0
Files: ./thirdparty/mbedtls/
Comment: Mbed TLS
Copyright: The Mbed TLS Contributors

37
modules/csg/SCsub
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@ -6,7 +6,42 @@ Import("env_modules")
env_csg = env_modules.Clone()
# Godot source files
env_csg.Append(CPPDEFINES=("MANIFOLD_PAR", "-1"))
# Thirdparty source files
thirdparty_obj = []
thirdparty_dir = "#thirdparty/manifold/"
thirdparty_sources = [
"src/boolean_result.cpp",
"src/boolean3.cpp",
"src/constructors.cpp",
"src/csg_tree.cpp",
"src/edge_op.cpp",
"src/face_op.cpp",
"src/impl.cpp",
"src/manifold.cpp",
"src/polygon.cpp",
"src/properties.cpp",
"src/quickhull.cpp",
"src/smoothing.cpp",
"src/sort.cpp",
"src/subdivision.cpp",
]
thirdparty_sources = [thirdparty_dir + file for file in thirdparty_sources]
env_csg.Prepend(
CPPPATH=[
thirdparty_dir + "include",
]
)
env_thirdparty = env_csg.Clone()
env_thirdparty.disable_warnings()
env_thirdparty.add_source_files(thirdparty_obj, thirdparty_sources)
env.modules_sources += thirdparty_obj
# Godot's own source files
env_csg.add_source_files(env.modules_sources, "*.cpp")
if env.editor_build:
env_csg.add_source_files(env.modules_sources, "editor/*.cpp")

1428
modules/csg/csg.cpp
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File diff suppressed because it is too large Load diff

148
modules/csg/csg.h
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@ -55,150 +55,18 @@ struct CSGBrush {
Vector<Face> faces;
Vector<Ref<Material>> materials;
inline void _regen_face_aabbs();
inline void _regen_face_aabbs() {
for (int i = 0; i < faces.size(); i++) {
faces.write[i].aabb = AABB();
faces.write[i].aabb.position = faces[i].vertices[0];
faces.write[i].aabb.expand_to(faces[i].vertices[1]);
faces.write[i].aabb.expand_to(faces[i].vertices[2]);
}
}
// Create a brush from faces.
void build_from_faces(const Vector<Vector3> &p_vertices, const Vector<Vector2> &p_uvs, const Vector<bool> &p_smooth, const Vector<Ref<Material>> &p_materials, const Vector<bool> &p_invert_faces);
void copy_from(const CSGBrush &p_brush, const Transform3D &p_xform);
};
struct CSGBrushOperation {
enum Operation {
OPERATION_UNION,
OPERATION_INTERSECTION,
OPERATION_SUBTRACTION,
};
void merge_brushes(Operation p_operation, const CSGBrush &p_brush_a, const CSGBrush &p_brush_b, CSGBrush &r_merged_brush, float p_vertex_snap);
struct MeshMerge {
struct Face {
bool from_b = false;
bool inside = false;
int points[3] = {};
Vector2 uvs[3];
bool smooth = false;
bool invert = false;
int material_idx = 0;
};
struct FaceBVH {
int face = 0;
int left = 0;
int right = 0;
int next = 0;
Vector3 center;
AABB aabb;
};
struct FaceBVHCmpX {
_FORCE_INLINE_ bool operator()(const FaceBVH *p_left, const FaceBVH *p_right) const {
return p_left->center.x < p_right->center.x;
}
};
struct FaceBVHCmpY {
_FORCE_INLINE_ bool operator()(const FaceBVH *p_left, const FaceBVH *p_right) const {
return p_left->center.y < p_right->center.y;
}
};
struct FaceBVHCmpZ {
_FORCE_INLINE_ bool operator()(const FaceBVH *p_left, const FaceBVH *p_right) const {
return p_left->center.z < p_right->center.z;
}
};
struct VertexKey {
int32_t x, y, z;
_FORCE_INLINE_ bool operator<(const VertexKey &p_key) const {
if (x == p_key.x) {
if (y == p_key.y) {
return z < p_key.z;
} else {
return y < p_key.y;
}
} else {
return x < p_key.x;
}
}
_FORCE_INLINE_ bool operator==(const VertexKey &p_key) const {
return (x == p_key.x && y == p_key.y && z == p_key.z);
}
};
struct VertexKeyHash {
static _FORCE_INLINE_ uint32_t hash(const VertexKey &p_vk) {
uint32_t h = hash_murmur3_one_32(p_vk.x);
h = hash_murmur3_one_32(p_vk.y, h);
h = hash_murmur3_one_32(p_vk.z, h);
return h;
}
};
struct Intersection {
bool found = false;
real_t conormal = FLT_MAX;
real_t distance_squared = FLT_MAX;
real_t origin_angle = FLT_MAX;
};
struct IntersectionDistance {
bool is_conormal;
real_t distance_squared;
};
Vector<Vector3> points;
Vector<Face> faces;
HashMap<Ref<Material>, int> materials;
HashMap<Vector3, int> vertex_map;
OAHashMap<VertexKey, int, VertexKeyHash> snap_cache;
float vertex_snap = 0.0;
inline void _add_distance(List<IntersectionDistance> &r_intersectionsA, List<IntersectionDistance> &r_intersectionsB, bool p_from_B, real_t p_distance, bool p_is_conormal) const;
inline bool _bvh_inside(FaceBVH *r_facebvhptr, int p_max_depth, int p_bvh_first, int p_face_idx) const;
inline int _create_bvh(FaceBVH *r_facebvhptr, FaceBVH **r_facebvhptrptr, int p_from, int p_size, int p_depth, int &r_max_depth, int &r_max_alloc);
void add_face(const Vector3 p_points[3], const Vector2 p_uvs[3], bool p_smooth, bool p_invert, const Ref<Material> &p_material, bool p_from_b);
void mark_inside_faces();
};
struct Build2DFaces {
struct Vertex2D {
Vector2 point;
Vector2 uv;
};
struct Face2D {
int vertex_idx[3] = {};
};
Vector<Vertex2D> vertices;
Vector<Face2D> faces;
Plane plane;
Transform3D to_2D;
Transform3D to_3D;
float vertex_snap2 = 0.0;
inline int _get_point_idx(const Vector2 &p_point);
inline int _add_vertex(const Vertex2D &p_vertex);
inline void _add_vertex_idx_sorted(Vector<int> &r_vertex_indices, int p_new_vertex_index);
inline void _merge_faces(const Vector<int> &p_segment_indices);
inline void _find_edge_intersections(const Vector2 p_segment_points[2], Vector<int> &r_segment_indices);
inline int _insert_point(const Vector2 &p_point);
void insert(const CSGBrush &p_brush, int p_brush_face);
void addFacesToMesh(MeshMerge &r_mesh_merge, bool p_smooth, bool p_invert, const Ref<Material> &p_material, bool p_from_b);
Build2DFaces() {}
Build2DFaces(const CSGBrush &p_brush, int p_brush_face, float p_vertex_snap2);
};
struct Build2DFaceCollection {
HashMap<int, Build2DFaces> build2DFacesA;
HashMap<int, Build2DFaces> build2DFacesB;
};
void update_faces(const CSGBrush &p_brush_a, const int p_face_idx_a, const CSGBrush &p_brush_b, const int p_face_idx_b, Build2DFaceCollection &p_collection, float p_vertex_snap);
};
#endif // CSG_H

261
modules/csg/csg_shape.cpp
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@ -32,6 +32,8 @@
#include "core/math/geometry_2d.h"
#include <manifold/manifold.h>
void CSGShape3D::set_use_collision(bool p_enable) {
if (use_collision == p_enable) {
return;
@ -167,78 +169,213 @@ void CSGShape3D::_make_dirty(bool p_parent_removing) {
dirty = true;
}
CSGBrush *CSGShape3D::_get_brush() {
if (dirty) {
if (brush) {
memdelete(brush);
}
brush = nullptr;
enum ManifoldProperty {
MANIFOLD_PROPERTY_POSITION_X = 0,
MANIFOLD_PROPERTY_POSITION_Y,
MANIFOLD_PROPERTY_POSITION_Z,
MANIFOLD_PROPERTY_INVERT,
MANIFOLD_PROPERTY_SMOOTH_GROUP,
MANIFOLD_PROPERTY_UV_X_0,
MANIFOLD_PROPERTY_UV_Y_0,
MANIFOLD_PROPERTY_MAX
};
CSGBrush *n = _build_brush();
static void _unpack_manifold(
const manifold::Manifold &p_manifold,
const HashMap<int32_t, Ref<Material>> &p_mesh_materials,
CSGBrush *r_mesh_merge) {
manifold::MeshGL64 mesh = p_manifold.GetMeshGL64();
for (int i = 0; i < get_child_count(); i++) {
CSGShape3D *child = Object::cast_to<CSGShape3D>(get_child(i));
if (!child) {
continue;
}
if (!child->is_visible()) {
continue;
}
constexpr int32_t order[3] = { 0, 2, 1 };
CSGBrush *n2 = child->_get_brush();
if (!n2) {
continue;
}
if (!n) {
n = memnew(CSGBrush);
n->copy_from(*n2, child->get_transform());
} else {
CSGBrush *nn = memnew(CSGBrush);
CSGBrush *nn2 = memnew(CSGBrush);
nn2->copy_from(*n2, child->get_transform());
CSGBrushOperation bop;
switch (child->get_operation()) {
case CSGShape3D::OPERATION_UNION:
bop.merge_brushes(CSGBrushOperation::OPERATION_UNION, *n, *nn2, *nn, snap);
break;
case CSGShape3D::OPERATION_INTERSECTION:
bop.merge_brushes(CSGBrushOperation::OPERATION_INTERSECTION, *n, *nn2, *nn, snap);
break;
case CSGShape3D::OPERATION_SUBTRACTION:
bop.merge_brushes(CSGBrushOperation::OPERATION_SUBTRACTION, *n, *nn2, *nn, snap);
break;
}
memdelete(n);
memdelete(nn2);
n = nn;
}
for (size_t run_i = 0; run_i < mesh.runIndex.size() - 1; run_i++) {
uint32_t original_id = -1;
if (run_i < mesh.runOriginalID.size()) {
original_id = mesh.runOriginalID[run_i];
}
if (n) {
AABB aabb;
for (int i = 0; i < n->faces.size(); i++) {
for (int j = 0; j < 3; j++) {
if (i == 0 && j == 0) {
aabb.position = n->faces[i].vertices[j];
} else {
aabb.expand_to(n->faces[i].vertices[j]);
}
}
}
node_aabb = aabb;
} else {
node_aabb = AABB();
Ref<Material> material;
if (p_mesh_materials.has(original_id)) {
material = p_mesh_materials[original_id];
}
// Find or reserve a material ID in the brush.
int32_t material_id = r_mesh_merge->materials.find(material);
if (material_id == -1) {
material_id = r_mesh_merge->materials.size();
r_mesh_merge->materials.push_back(material);
}
brush = n;
size_t begin = mesh.runIndex[run_i];
size_t end = mesh.runIndex[run_i + 1];
for (size_t vert_i = begin; vert_i < end; vert_i += 3) {
CSGBrush::Face face;
face.material = material_id;
int32_t first_property_index = mesh.triVerts[vert_i + order[0]];
face.smooth = mesh.vertProperties[first_property_index * mesh.numProp + MANIFOLD_PROPERTY_SMOOTH_GROUP] > 0.5f;
face.invert = mesh.vertProperties[first_property_index * mesh.numProp + MANIFOLD_PROPERTY_INVERT] > 0.5f;
dirty = false;
for (int32_t tri_order_i = 0; tri_order_i < 3; tri_order_i++) {
int32_t property_i = mesh.triVerts[vert_i + order[tri_order_i]];
ERR_FAIL_COND_MSG(property_i * mesh.numProp >= mesh.vertProperties.size(), "Invalid index into vertex properties");
face.vertices[tri_order_i] = Vector3(
mesh.vertProperties[property_i * mesh.numProp + MANIFOLD_PROPERTY_POSITION_X],
mesh.vertProperties[property_i * mesh.numProp + MANIFOLD_PROPERTY_POSITION_Y],
mesh.vertProperties[property_i * mesh.numProp + MANIFOLD_PROPERTY_POSITION_Z]);
face.uvs[tri_order_i] = Vector2(
mesh.vertProperties[property_i * mesh.numProp + MANIFOLD_PROPERTY_UV_X_0],
mesh.vertProperties[property_i * mesh.numProp + MANIFOLD_PROPERTY_UV_Y_0]);
}
r_mesh_merge->faces.push_back(face);
}
}
r_mesh_merge->_regen_face_aabbs();
}
static void _pack_manifold(
const CSGBrush *const p_mesh_merge,
manifold::Manifold &r_manifold,
HashMap<int32_t, Ref<Material>> &p_mesh_materials,
float p_snap) {
ERR_FAIL_NULL_MSG(p_mesh_merge, "p_mesh_merge is null");
HashMap<uint32_t, Vector<CSGBrush::Face>> faces_by_material;
for (int face_i = 0; face_i < p_mesh_merge->faces.size(); face_i++) {
const CSGBrush::Face &face = p_mesh_merge->faces[face_i];
faces_by_material[face.material].push_back(face);
}
manifold::MeshGL64 mesh;
mesh.tolerance = p_snap;
mesh.numProp = MANIFOLD_PROPERTY_MAX;
mesh.runOriginalID.reserve(faces_by_material.size());
mesh.runIndex.reserve(faces_by_material.size() + 1);
mesh.vertProperties.reserve(p_mesh_merge->faces.size() * 3 * MANIFOLD_PROPERTY_MAX);
// Make a run of triangles for each material.
for (const KeyValue<uint32_t, Vector<CSGBrush::Face>> &E : faces_by_material) {
const uint32_t material_id = E.key;
const Vector<CSGBrush::Face> &faces = E.value;
mesh.runIndex.push_back(mesh.triVerts.size());
// Associate the material with an ID.
uint32_t reserved_id = r_manifold.ReserveIDs(1);
mesh.runOriginalID.push_back(reserved_id);
Ref<Material> material;
if (material_id < p_mesh_merge->materials.size()) {
material = p_mesh_merge->materials[material_id];
}
p_mesh_materials.insert(reserved_id, material);
for (const CSGBrush::Face &face : faces) {
for (int32_t tri_order_i = 0; tri_order_i < 3; tri_order_i++) {
constexpr int32_t order[3] = { 0, 2, 1 };
int i = order[tri_order_i];
mesh.triVerts.push_back(mesh.vertProperties.size() / MANIFOLD_PROPERTY_MAX);
size_t begin = mesh.vertProperties.size();
mesh.vertProperties.resize(mesh.vertProperties.size() + MANIFOLD_PROPERTY_MAX);
// Add the vertex properties.
// Use CSGBrush constants rather than push_back for clarity.
double *vert = &mesh.vertProperties[begin];
vert[MANIFOLD_PROPERTY_POSITION_X] = face.vertices[i].x;
vert[MANIFOLD_PROPERTY_POSITION_Y] = face.vertices[i].y;
vert[MANIFOLD_PROPERTY_POSITION_Z] = face.vertices[i].z;
vert[MANIFOLD_PROPERTY_UV_X_0] = face.uvs[i].x;
vert[MANIFOLD_PROPERTY_UV_Y_0] = face.uvs[i].y;
vert[MANIFOLD_PROPERTY_SMOOTH_GROUP] = face.smooth ? 1.0f : 0.0f;
vert[MANIFOLD_PROPERTY_INVERT] = face.invert ? 1.0f : 0.0f;
}
}
}
// runIndex needs an explicit end value.
mesh.runIndex.push_back(mesh.triVerts.size());
ERR_FAIL_COND_MSG(mesh.vertProperties.size() % mesh.numProp != 0, "Invalid vertex properties size.");
mesh.Merge();
r_manifold = manifold::Manifold(mesh);
manifold::Manifold::Error err = r_manifold.Status();
if (err != manifold::Manifold::Error::NoError) {
print_error(String("Manifold creation from mesh failed:" + itos((int)err)));
}
}
struct ManifoldOperation {
manifold::Manifold manifold;
manifold::OpType operation;
static manifold::OpType convert_csg_op(CSGShape3D::Operation op) {
switch (op) {
case CSGShape3D::OPERATION_SUBTRACTION:
return manifold::OpType::Subtract;
case CSGShape3D::OPERATION_INTERSECTION:
return manifold::OpType::Intersect;
default:
return manifold::OpType::Add;
}
}
ManifoldOperation() :
operation(manifold::OpType::Add) {}
ManifoldOperation(const manifold::Manifold &m, manifold::OpType op) :
manifold(m), operation(op) {}
};
CSGBrush *CSGShape3D::_get_brush() {
if (!dirty) {
return brush;
}
if (brush) {
memdelete(brush);
}
brush = nullptr;
CSGBrush *n = _build_brush();
HashMap<int32_t, Ref<Material>> mesh_materials;
manifold::Manifold root_manifold;
_pack_manifold(n, root_manifold, mesh_materials, get_snap());
manifold::OpType current_op = ManifoldOperation::convert_csg_op(get_operation());
std::vector<manifold::Manifold> manifolds;
manifolds.push_back(root_manifold);
for (int i = 0; i < get_child_count(); i++) {
CSGShape3D *child = Object::cast_to<CSGShape3D>(get_child(i));
if (!child || !child->is_visible()) {
continue;
}
CSGBrush *child_brush = child->_get_brush();
if (!child_brush) {
continue;
}
CSGBrush transformed_brush;
transformed_brush.copy_from(*child_brush, child->get_transform());
manifold::Manifold child_manifold;
_pack_manifold(&transformed_brush, child_manifold, mesh_materials, get_snap());
manifold::OpType child_operation = ManifoldOperation::convert_csg_op(child->get_operation());
if (child_operation != current_op) {
manifold::Manifold result = manifold::Manifold::BatchBoolean(manifolds, current_op);
manifolds.clear();
manifolds.push_back(result);
current_op = child_operation;
}
manifolds.push_back(child_manifold);
}
if (!manifolds.empty()) {
manifold::Manifold manifold_result = manifold::Manifold::BatchBoolean(manifolds, current_op);
if (n) {
memdelete(n);
}
n = memnew(CSGBrush);
_unpack_manifold(manifold_result, mesh_materials, n);
}
AABB aabb;
if (n && !n->faces.is_empty()) {
aabb.position = n->faces[0].vertices[0];
for (const CSGBrush::Face &face : n->faces) {
for (int i = 0; i < 3; ++i) {
aabb.expand_to(face.vertices[i]);
}
}
}
node_aabb = aabb;
brush = n;
dirty = false;
return brush;
}

12
thirdparty/README.md vendored
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@ -546,6 +546,18 @@ Patch `godot-node-debug-fix.patch` workarounds shadowing of Godot's Node class
in the MSVC debugger.
## manifold
- Upstream: https://github.com/elalish/manifold
- Version: 3.0.0 (5d127e57fbfb89225a8e905d0d914ccc86c139c8, 2024)
- License: Apache 2.0
File extracted from upstream source:
- `src/`
- `AUTHORS`, `LICENSE`
## mbedtls
- Upstream: https://github.com/Mbed-TLS/mbedtls

10
thirdparty/manifold/AUTHORS vendored Normal file
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@ -0,0 +1,10 @@
# This is the list of Manifold's significant contributors.
#
# This does not necessarily list everyone who has contributed code,
# especially since many employees of one corporation may be contributing.
# To see the full list of contributors, see the revision history in
# source control.
Emmett Lalish <elalish>
Chun Kit LAM <pca006132>
Geoff deRosenroll <geoffder>
Google LLC

201
thirdparty/manifold/LICENSE vendored Normal file
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@ -0,0 +1,201 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/
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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <limits>
#include <vector>
#ifdef MANIFOLD_DEBUG
#include <chrono>
#endif
#include "manifold/linalg.h"
namespace manifold {
/** @addtogroup Math
* @ingroup Core
* @brief Simple math operations.
* */
/** @addtogroup LinAlg
* @{
*/
namespace la = linalg;
using vec2 = la::vec<double, 2>;
using vec3 = la::vec<double, 3>;
using vec4 = la::vec<double, 4>;
using bvec4 = la::vec<bool, 4>;
using mat2 = la::mat<double, 2, 2>;
using mat3x2 = la::mat<double, 3, 2>;
using mat4x2 = la::mat<double, 4, 2>;
using mat2x3 = la::mat<double, 2, 3>;
using mat3 = la::mat<double, 3, 3>;
using mat4x3 = la::mat<double, 4, 3>;
using mat3x4 = la::mat<double, 3, 4>;
using mat4 = la::mat<double, 4, 4>;
using ivec2 = la::vec<int, 2>;
using ivec3 = la::vec<int, 3>;
using ivec4 = la::vec<int, 4>;
using quat = la::vec<double, 4>;
/** @} */
/** @addtogroup Scalar
* @ingroup Math
* @brief Simple scalar operations.
* @{
*/
constexpr double kPi = 3.14159265358979323846264338327950288;
constexpr double kTwoPi = 6.28318530717958647692528676655900576;
constexpr double kHalfPi = 1.57079632679489661923132169163975144;
/**
* Convert degrees to radians.
*
* @param a Angle in degrees.
*/
constexpr double radians(double a) { return a * kPi / 180; }
/**
* Convert radians to degrees.
*
* @param a Angle in radians.
*/
constexpr double degrees(double a) { return a * 180 / kPi; }
/**
* Performs smooth Hermite interpolation between 0 and 1 when edge0 < x < edge1.
*
* @param edge0 Specifies the value of the lower edge of the Hermite function.
* @param edge1 Specifies the value of the upper edge of the Hermite function.
* @param a Specifies the source value for interpolation.
*/
constexpr double smoothstep(double edge0, double edge1, double a) {
const double x = la::clamp((a - edge0) / (edge1 - edge0), 0, 1);
return x * x * (3 - 2 * x);
}
/**
* Sine function where multiples of 90 degrees come out exact.
*
* @param x Angle in degrees.
*/
inline double sind(double x) {
if (!la::isfinite(x)) return sin(x);
if (x < 0.0) return -sind(-x);
int quo;
x = remquo(fabs(x), 90.0, &quo);
switch (quo % 4) {
case 0:
return sin(radians(x));
case 1:
return cos(radians(x));
case 2:
return -sin(radians(x));
case 3:
return -cos(radians(x));
}
return 0.0;
}
/**
* Cosine function where multiples of 90 degrees come out exact.
*
* @param x Angle in degrees.
*/
inline double cosd(double x) { return sind(x + 90.0); }
/** @} */
/** @addtogroup Structs
* @ingroup Core
* @brief Miscellaneous data structures for interfacing with this library.
* @{
*/
/**
* @brief Single polygon contour, wound CCW. First and last point are implicitly
* connected. Should ensure all input is
* [&epsilon;-valid](https://github.com/elalish/manifold/wiki/Manifold-Library#definition-of-%CE%B5-valid).
*/
using SimplePolygon = std::vector<vec2>;
/**
* @brief Set of polygons with holes. Order of contours is arbitrary. Can
* contain any depth of nested holes and any number of separate polygons. Should
* ensure all input is
* [&epsilon;-valid](https://github.com/elalish/manifold/wiki/Manifold-Library#definition-of-%CE%B5-valid).
*/
using Polygons = std::vector<SimplePolygon>;
/**
* @brief Defines which edges to sharpen and how much for the Manifold.Smooth()
* constructor.
*/
struct Smoothness {
/// The halfedge index = 3 * tri + i, referring to Mesh.triVerts[tri][i].
size_t halfedge;
/// A value between 0 and 1, where 0 is sharp and 1 is the default and the
/// curvature is interpolated between these values. The two paired halfedges
/// can have different values while maintaining C-1 continuity (except for 0).
double smoothness;
};
/**
* @brief Axis-aligned 3D box, primarily for bounding.
*/
struct Box {
vec3 min = vec3(std::numeric_limits<double>::infinity());
vec3 max = vec3(-std::numeric_limits<double>::infinity());
/**
* Default constructor is an infinite box that contains all space.
*/
constexpr Box() {}
/**
* Creates a box that contains the two given points.
*/
constexpr Box(const vec3 p1, const vec3 p2) {
min = la::min(p1, p2);
max = la::max(p1, p2);
}
/**
* Returns the dimensions of the Box.
*/
constexpr vec3 Size() const { return max - min; }
/**
* Returns the center point of the Box.
*/
constexpr vec3 Center() const { return 0.5 * (max + min); }
/**
* Returns the absolute-largest coordinate value of any contained
* point.
*/
constexpr double Scale() const {
vec3 absMax = la::max(la::abs(min), la::abs(max));
return la::max(absMax.x, la::max(absMax.y, absMax.z));
}
/**
* Does this box contain (includes equal) the given point?
*/
constexpr bool Contains(const vec3& p) const {
return la::all(la::gequal(p, min)) && la::all(la::gequal(max, p));
}
/**
* Does this box contain (includes equal) the given box?
*/
constexpr bool Contains(const Box& box) const {
return la::all(la::gequal(box.min, min)) &&
la::all(la::gequal(max, box.max));
}
/**
* Expand this box to include the given point.
*/
void Union(const vec3 p) {
min = la::min(min, p);
max = la::max(max, p);
}
/**
* Expand this box to include the given box.
*/
constexpr Box Union(const Box& box) const {
Box out;
out.min = la::min(min, box.min);
out.max = la::max(max, box.max);
return out;
}
/**
* Transform the given box by the given axis-aligned affine transform.
*
* Ensure the transform passed in is axis-aligned (rotations are all
* multiples of 90 degrees), or else the resulting bounding box will no longer
* bound properly.
*/
constexpr Box Transform(const mat3x4& transform) const {
Box out;
vec3 minT = transform * vec4(min, 1.0);
vec3 maxT = transform * vec4(max, 1.0);
out.min = la::min(minT, maxT);
out.max = la::max(minT, maxT);
return out;
}
/**
* Shift this box by the given vector.
*/
constexpr Box operator+(vec3 shift) const {
Box out;
out.min = min + shift;
out.max = max + shift;
return out;
}
/**
* Shift this box in-place by the given vector.
*/
Box& operator+=(vec3 shift) {
min += shift;
max += shift;
return *this;
}
/**
* Scale this box by the given vector.
*/
constexpr Box operator*(vec3 scale) const {
Box out;
out.min = min * scale;
out.max = max * scale;
return out;
}
/**
* Scale this box in-place by the given vector.
*/
Box& operator*=(vec3 scale) {
min *= scale;
max *= scale;
return *this;
}
/**
* Does this box overlap the one given (including equality)?
*/
constexpr bool DoesOverlap(const Box& box) const {
return min.x <= box.max.x && min.y <= box.max.y && min.z <= box.max.z &&
max.x >= box.min.x && max.y >= box.min.y && max.z >= box.min.z;
}
/**
* Does the given point project within the XY extent of this box
* (including equality)?
*/
constexpr bool DoesOverlap(vec3 p) const { // projected in z
return p.x <= max.x && p.x >= min.x && p.y <= max.y && p.y >= min.y;
}
/**
* Does this box have finite bounds?
*/
constexpr bool IsFinite() const {
return la::all(la::isfinite(min)) && la::all(la::isfinite(max));
}
};
/**
* @brief Axis-aligned 2D box, primarily for bounding.
*/
struct Rect {
vec2 min = vec2(std::numeric_limits<double>::infinity());
vec2 max = vec2(-std::numeric_limits<double>::infinity());
/**
* Default constructor is an empty rectangle..
*/
constexpr Rect() {}
/**
* Create a rectangle that contains the two given points.
*/
constexpr Rect(const vec2 a, const vec2 b) {
min = la::min(a, b);
max = la::max(a, b);
}
/** @name Information
* Details of the rectangle
*/
///@{
/**
* Return the dimensions of the rectangle.
*/
constexpr vec2 Size() const { return max - min; }
/**
* Return the area of the rectangle.
*/
constexpr double Area() const {
auto sz = Size();
return sz.x * sz.y;
}
/**
* Returns the absolute-largest coordinate value of any contained
* point.
*/
constexpr double Scale() const {
vec2 absMax = la::max(la::abs(min), la::abs(max));
return la::max(absMax.x, absMax.y);
}
/**
* Returns the center point of the rectangle.
*/
constexpr vec2 Center() const { return 0.5 * (max + min); }
/**
* Does this rectangle contain (includes on border) the given point?
*/
constexpr bool Contains(const vec2& p) const {
return la::all(la::gequal(p, min)) && la::all(la::gequal(max, p));
}
/**
* Does this rectangle contain (includes equal) the given rectangle?
*/
constexpr bool Contains(const Rect& rect) const {
return la::all(la::gequal(rect.min, min)) &&
la::all(la::gequal(max, rect.max));
}
/**
* Does this rectangle overlap the one given (including equality)?
*/
constexpr bool DoesOverlap(const Rect& rect) const {
return min.x <= rect.max.x && min.y <= rect.max.y && max.x >= rect.min.x &&
max.y >= rect.min.y;
}
/**
* Is the rectangle empty (containing no space)?
*/
constexpr bool IsEmpty() const { return max.y <= min.y || max.x <= min.x; };
/**
* Does this recangle have finite bounds?
*/
constexpr bool IsFinite() const {
return la::all(la::isfinite(min)) && la::all(la::isfinite(max));
}
///@}
/** @name Modification
*/
///@{
/**
* Expand this rectangle (in place) to include the given point.
*/
void Union(const vec2 p) {
min = la::min(min, p);
max = la::max(max, p);
}
/**
* Expand this rectangle to include the given Rect.
*/
constexpr Rect Union(const Rect& rect) const {
Rect out;
out.min = la::min(min, rect.min);
out.max = la::max(max, rect.max);
return out;
}
/**
* Shift this rectangle by the given vector.
*/
constexpr Rect operator+(const vec2 shift) const {
Rect out;
out.min = min + shift;
out.max = max + shift;
return out;
}
/**
* Shift this rectangle in-place by the given vector.
*/
Rect& operator+=(const vec2 shift) {
min += shift;
max += shift;
return *this;
}
/**
* Scale this rectangle by the given vector.
*/
constexpr Rect operator*(const vec2 scale) const {
Rect out;
out.min = min * scale;
out.max = max * scale;
return out;
}
/**
* Scale this rectangle in-place by the given vector.
*/
Rect& operator*=(const vec2 scale) {
min *= scale;
max *= scale;
return *this;
}
/**
* Transform the rectangle by the given axis-aligned affine transform.
*
* Ensure the transform passed in is axis-aligned (rotations are all
* multiples of 90 degrees), or else the resulting rectangle will no longer
* bound properly.
*/
constexpr Rect Transform(const mat2x3& m) const {
Rect rect;
rect.min = m * vec3(min, 1);
rect.max = m * vec3(max, 1);
return rect;
}
///@}
};
/**
* @brief Boolean operation type: Add (Union), Subtract (Difference), and
* Intersect.
*/
enum class OpType { Add, Subtract, Intersect };
constexpr int DEFAULT_SEGMENTS = 0;
constexpr double DEFAULT_ANGLE = 10.0;
constexpr double DEFAULT_LENGTH = 1.0;
/**
* @brief These static properties control how circular shapes are quantized by
* default on construction.
*
* If circularSegments is specified, it takes
* precedence. If it is zero, then instead the minimum is used of the segments
* calculated based on edge length and angle, rounded up to the nearest
* multiple of four. To get numbers not divisible by four, circularSegments
* must be specified.
*/
class Quality {
private:
inline static int circularSegments_ = DEFAULT_SEGMENTS;
inline static double circularAngle_ = DEFAULT_ANGLE;
inline static double circularEdgeLength_ = DEFAULT_LENGTH;
public:
/**
* Sets an angle constraint the default number of circular segments for the
* CrossSection::Circle(), Manifold::Cylinder(), Manifold::Sphere(), and
* Manifold::Revolve() constructors. The number of segments will be rounded up
* to the nearest factor of four.
*
* @param angle The minimum angle in degrees between consecutive segments. The
* angle will increase if the the segments hit the minimum edge length.
* Default is 10 degrees.
*/
static void SetMinCircularAngle(double angle) {
if (angle <= 0) return;
circularAngle_ = angle;
}
/**
* Sets a length constraint the default number of circular segments for the
* CrossSection::Circle(), Manifold::Cylinder(), Manifold::Sphere(), and
* Manifold::Revolve() constructors. The number of segments will be rounded up
* to the nearest factor of four.
*
* @param length The minimum length of segments. The length will
* increase if the the segments hit the minimum angle. Default is 1.0.
*/
static void SetMinCircularEdgeLength(double length) {
if (length <= 0) return;
circularEdgeLength_ = length;
}
/**
* Sets the default number of circular segments for the
* CrossSection::Circle(), Manifold::Cylinder(), Manifold::Sphere(), and
* Manifold::Revolve() constructors. Overrides the edge length and angle
* constraints and sets the number of segments to exactly this value.
*
* @param number Number of circular segments. Default is 0, meaning no
* constraint is applied.
*/
static void SetCircularSegments(int number) {
if (number < 3 && number != 0) return;
circularSegments_ = number;
}
/**
* Determine the result of the SetMinCircularAngle(),
* SetMinCircularEdgeLength(), and SetCircularSegments() defaults.
*
* @param radius For a given radius of circle, determine how many default
* segments there will be.
*/
static int GetCircularSegments(double radius) {
if (circularSegments_ > 0) return circularSegments_;
int nSegA = 360.0 / circularAngle_;
int nSegL = 2.0 * radius * kPi / circularEdgeLength_;
int nSeg = fmin(nSegA, nSegL) + 3;
nSeg -= nSeg % 4;
return std::max(nSeg, 3);
}
/**
* Resets the circular construction parameters to their defaults if
* SetMinCircularAngle, SetMinCircularEdgeLength, or SetCircularSegments have
* been called.
*/
static void ResetToDefaults() {
circularSegments_ = DEFAULT_SEGMENTS;
circularAngle_ = DEFAULT_ANGLE;
circularEdgeLength_ = DEFAULT_LENGTH;
}
};
/** @} */
/** @addtogroup Debug
* @ingroup Optional
* @{
*/
/**
* @brief Global parameters that control debugging output. Only has an
* effect when compiled with the MANIFOLD_DEBUG flag.
*/
struct ExecutionParams {
/// Perform extra sanity checks and assertions on the intermediate data
/// structures.
bool intermediateChecks = false;
/// Verbose output primarily of the Boolean, including timing info and vector
/// sizes.
bool verbose = false;
/// If processOverlaps is false, a geometric check will be performed to assert
/// all triangles are CCW.
bool processOverlaps = true;
/// Suppresses printed errors regarding CW triangles. Has no effect if
/// processOverlaps is true.
bool suppressErrors = false;
/// Perform optional but recommended triangle cleanups in SimplifyTopology()
bool cleanupTriangles = true;
};
/** @} */
#ifdef MANIFOLD_DEBUG
inline std::ostream& operator<<(std::ostream& stream, const Box& box) {
return stream << "min: " << box.min << ", "
<< "max: " << box.max;
}
inline std::ostream& operator<<(std::ostream& stream, const Rect& box) {
return stream << "min: " << box.min << ", "
<< "max: " << box.max;
}
/**
* Print the contents of this vector to standard output. Only exists if compiled
* with MANIFOLD_DEBUG flag.
*/
template <typename T>
void Dump(const std::vector<T>& vec) {
std::cout << "Vec = " << std::endl;
for (size_t i = 0; i < vec.size(); ++i) {
std::cout << i << ", " << vec[i] << ", " << std::endl;
}
std::cout << std::endl;
}
template <typename T>
void Diff(const std::vector<T>& a, const std::vector<T>& b) {
std::cout << "Diff = " << std::endl;
if (a.size() != b.size()) {
std::cout << "a and b must have the same length, aborting Diff"
<< std::endl;
return;
}
for (size_t i = 0; i < a.size(); ++i) {
if (a[i] != b[i])
std::cout << i << ": " << a[i] << ", " << b[i] << std::endl;
}
std::cout << std::endl;
}
struct Timer {
std::chrono::high_resolution_clock::time_point start, end;
void Start() { start = std::chrono::high_resolution_clock::now(); }
void Stop() { end = std::chrono::high_resolution_clock::now(); }
float Elapsed() {
return std::chrono::duration_cast<std::chrono::milliseconds>(end - start)
.count();
}
void Print(std::string message) {
std::cout << "----------- " << std::round(Elapsed()) << " ms for "
<< message << std::endl;
}
};
#endif
} // namespace manifold

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// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <iterator>
#include <type_traits>
namespace manifold {
template <typename F, typename Iter>
struct TransformIterator {
private:
Iter iter;
F f;
public:
using pointer = void;
using reference = std::invoke_result_t<
F, typename std::iterator_traits<std::remove_const_t<Iter>>::value_type>;
using difference_type =
typename std::iterator_traits<std::remove_const_t<Iter>>::difference_type;
using value_type = reference;
using iterator_category = typename std::iterator_traits<
std::remove_const_t<Iter>>::iterator_category;
constexpr TransformIterator(Iter iter, F f) : iter(iter), f(f) {}
TransformIterator& operator=(const TransformIterator& other) {
if (this == &other) return *this;
// don't copy function, should be the same
iter = other.iter;
return *this;
}
constexpr reference operator*() const { return f(*iter); }
constexpr reference operator[](size_t i) const { return f(iter[i]); }
// prefix increment
TransformIterator& operator++() {
iter += 1;
return *this;
}
// postfix
TransformIterator operator++(int) {
auto old = *this;
operator++();
return old;
}
// prefix increment
TransformIterator& operator--() {
iter -= 1;
return *this;
}
// postfix
TransformIterator operator--(int) {
auto old = *this;
operator--();
return old;
}
constexpr TransformIterator operator+(size_t n) const {
return TransformIterator(iter + n, f);
}
TransformIterator& operator+=(size_t n) {
iter += n;
return *this;
}
constexpr TransformIterator operator-(size_t n) const {
return TransformIterator(iter - n, f);
}
TransformIterator& operator-=(size_t n) {
iter -= n;
return *this;
}
constexpr bool operator==(TransformIterator other) const {
return iter == other.iter;
}
constexpr bool operator!=(TransformIterator other) const {
return !(iter == other.iter);
}
constexpr bool operator<(TransformIterator other) const {
return iter < other.iter;
}
constexpr difference_type operator-(TransformIterator other) const {
return iter - other.iter;
}
constexpr operator TransformIterator<F, const Iter>() const {
return TransformIterator(f, iter);
}
};
template <typename T>
struct CountingIterator {
private:
T counter;
public:
using pointer = void;
using reference = T;
using difference_type = std::make_signed_t<T>;
using value_type = T;
using iterator_category = std::random_access_iterator_tag;
constexpr CountingIterator(T counter) : counter(counter) {}
constexpr value_type operator*() const { return counter; }
constexpr value_type operator[](T i) const { return counter + i; }
// prefix increment
CountingIterator& operator++() {
counter += 1;
return *this;
}
// postfix
CountingIterator operator++(int) {
auto old = *this;
operator++();
return old;
}
// prefix increment
CountingIterator& operator--() {
counter -= 1;
return *this;
}
// postfix
CountingIterator operator--(int) {
auto old = *this;
operator--();
return old;
}
constexpr CountingIterator operator+(T n) const {
return CountingIterator(counter + n);
}
CountingIterator& operator+=(T n) {
counter += n;
return *this;
}
constexpr CountingIterator operator-(T n) const {
return CountingIterator(counter - n);
}
CountingIterator& operator-=(T n) {
counter -= n;
return *this;
}
constexpr friend bool operator==(CountingIterator a, CountingIterator b) {
return a.counter == b.counter;
}
constexpr friend bool operator!=(CountingIterator a, CountingIterator b) {
return a.counter != b.counter;
}
constexpr friend bool operator<(CountingIterator a, CountingIterator b) {
return a.counter < b.counter;
}
constexpr friend difference_type operator-(CountingIterator a,
CountingIterator b) {
return a.counter - b.counter;
}
constexpr operator CountingIterator<const T>() const {
return CountingIterator(counter);
}
};
constexpr CountingIterator<size_t> countAt(size_t i) {
return CountingIterator(i);
}
template <typename Iter>
struct StridedRange {
private:
struct StridedRangeIter {
private:
Iter iter;
size_t stride;
public:
using pointer =
typename std::iterator_traits<std::remove_const_t<Iter>>::pointer;
using reference =
typename std::iterator_traits<std::remove_const_t<Iter>>::reference;
using difference_type = typename std::iterator_traits<
std::remove_const_t<Iter>>::difference_type;
using value_type =
typename std::iterator_traits<std::remove_const_t<Iter>>::value_type;
using iterator_category = typename std::iterator_traits<
std::remove_const_t<Iter>>::iterator_category;
constexpr StridedRangeIter(Iter iter, int stride)
: iter(iter), stride(stride) {}
constexpr reference operator*() { return *iter; }
constexpr std::add_const_t<reference> operator*() const { return *iter; }
constexpr reference operator[](size_t i) { return iter[i * stride]; }
constexpr std::add_const_t<reference> operator[](size_t i) const {
return iter[i * stride];
}
// prefix increment
StridedRangeIter& operator++() {
iter += stride;
return *this;
}
// postfix
StridedRangeIter operator++(int) {
auto old = *this;
operator++();
return old;
}
// prefix increment
StridedRangeIter& operator--() {
iter -= stride;
return *this;
}
// postfix
StridedRangeIter operator--(int) {
auto old = *this;
operator--();
return old;
}
constexpr StridedRangeIter operator+(size_t n) const {
return StridedRangeIter(iter + n * stride, stride);
}
StridedRangeIter& operator+=(size_t n) {
iter += n * stride;
return *this;
}
constexpr StridedRangeIter operator-(size_t n) const {
return StridedRangeIter(iter - n * stride, stride);
}
StridedRangeIter& operator-=(size_t n) {
iter -= n * stride;
return *this;
}
constexpr friend bool operator==(StridedRangeIter a, StridedRangeIter b) {
return a.iter == b.iter;
}
constexpr friend bool operator!=(StridedRangeIter a, StridedRangeIter b) {
return !(a.iter == b.iter);
}
constexpr friend bool operator<(StridedRangeIter a, StridedRangeIter b) {
return a.iter < b.iter;
}
constexpr friend difference_type operator-(StridedRangeIter a,
StridedRangeIter b) {
// note that this is not well-defined if a.stride != b.stride...
return (a.iter - b.iter) / a.stride;
}
};
Iter _start, _end;
const size_t stride;
public:
constexpr StridedRange(Iter start, Iter end, size_t stride)
: _start(start), _end(end), stride(stride) {}
constexpr StridedRangeIter begin() const {
return StridedRangeIter(_start, stride);
}
constexpr StridedRangeIter end() const {
return StridedRangeIter(_start, stride) +
((std::distance(_start, _end) + (stride - 1)) / stride);
}
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <functional>
#include <memory>
#include "manifold/common.h"
#include "manifold/vec_view.h"
namespace manifold {
/**
* @ingroup Debug
*
* Allows modification of the assertions checked in MANIFOLD_DEBUG mode.
*
* @return ExecutionParams&
*/
ExecutionParams& ManifoldParams();
class CsgNode;
class CsgLeafNode;
/** @addtogroup Core
* @brief The central classes of the library
* @{
*/
/**
* @brief Mesh input/output suitable for pushing directly into graphics
* libraries.
*
* This may not be manifold since the verts are duplicated along property
* boundaries that do not match. The additional merge vectors store this missing
* information, allowing the manifold to be reconstructed. MeshGL is an alias
* for the standard single-precision version. Use MeshGL64 to output the full
* double precision that Manifold uses internally.
*/
template <typename Precision, typename I = uint32_t>
struct MeshGLP {
/// Number of property vertices
I NumVert() const { return vertProperties.size() / numProp; };
/// Number of triangles
I NumTri() const { return triVerts.size() / 3; };
/// Number of properties per vertex, always >= 3.
I numProp = 3;
/// Flat, GL-style interleaved list of all vertex properties: propVal =
/// vertProperties[vert * numProp + propIdx]. The first three properties are
/// always the position x, y, z.
std::vector<Precision> vertProperties;
/// The vertex indices of the three triangle corners in CCW (from the outside)
/// order, for each triangle.
std::vector<I> triVerts;
/// Optional: A list of only the vertex indicies that need to be merged to
/// reconstruct the manifold.
std::vector<I> mergeFromVert;
/// Optional: The same length as mergeFromVert, and the corresponding value
/// contains the vertex to merge with. It will have an identical position, but
/// the other properties may differ.
std::vector<I> mergeToVert;
/// Optional: Indicates runs of triangles that correspond to a particular
/// input mesh instance. The runs encompass all of triVerts and are sorted
/// by runOriginalID. Run i begins at triVerts[runIndex[i]] and ends at
/// triVerts[runIndex[i+1]]. All runIndex values are divisible by 3. Returned
/// runIndex will always be 1 longer than runOriginalID, but same length is
/// also allowed as input: triVerts.size() will be automatically appended in
/// this case.
std::vector<I> runIndex;
/// Optional: The OriginalID of the mesh this triangle run came from. This ID
/// is ideal for reapplying materials to the output mesh. Multiple runs may
/// have the same ID, e.g. representing different copies of the same input
/// mesh. If you create an input MeshGL that you want to be able to reference
/// as one or more originals, be sure to set unique values from ReserveIDs().
std::vector<uint32_t> runOriginalID;
/// Optional: For each run, a 3x4 transform is stored representing how the
/// corresponding original mesh was transformed to create this triangle run.
/// This matrix is stored in column-major order and the length of the overall
/// vector is 12 * runOriginalID.size().
std::vector<Precision> runTransform;
/// Optional: Length NumTri, contains the source face ID this
/// triangle comes from. When auto-generated, this ID will be a triangle index
/// into the original mesh. This index/ID is purely for external use (e.g.
/// recreating polygonal faces) and will not affect Manifold's algorithms.
std::vector<I> faceID;
/// Optional: The X-Y-Z-W weighted tangent vectors for smooth Refine(). If
/// non-empty, must be exactly four times as long as Mesh.triVerts. Indexed
/// as 4 * (3 * tri + i) + j, i < 3, j < 4, representing the tangent value
/// Mesh.triVerts[tri][i] along the CCW edge. If empty, mesh is faceted.
std::vector<Precision> halfedgeTangent;
/// Tolerance for mesh simplification. When creating a Manifold, the tolerance
/// used will be the maximum of this and a baseline tolerance from the size of
/// the bounding box. Any edge shorter than tolerance may be collapsed.
/// Tolerance may be enlarged when floating point error accumulates.
Precision tolerance = 0;
MeshGLP() = default;
/**
* Updates the mergeFromVert and mergeToVert vectors in order to create a
* manifold solid. If the MeshGL is already manifold, no change will occur and
* the function will return false. Otherwise, this will merge verts along open
* edges within tolerance (the maximum of the MeshGL tolerance and the
* baseline bounding-box tolerance), keeping any from the existing merge
* vectors, and return true.
*
* There is no guarantee the result will be manifold - this is a best-effort
* helper function designed primarily to aid in the case where a manifold
* multi-material MeshGL was produced, but its merge vectors were lost due to
* a round-trip through a file format. Constructing a Manifold from the result
* will report an error status if it is not manifold.
*/
bool Merge();
/**
* Returns the x, y, z position of the ith vertex.
*
* @param v vertex index.
*/
la::vec<Precision, 3> GetVertPos(size_t v) const {
size_t offset = v * numProp;
return la::vec<Precision, 3>(vertProperties[offset],
vertProperties[offset + 1],
vertProperties[offset + 2]);
}
/**
* Returns the three vertex indices of the ith triangle.
*
* @param t triangle index.
*/
la::vec<I, 3> GetTriVerts(size_t t) const {
size_t offset = 3 * t;
return la::vec<I, 3>(triVerts[offset], triVerts[offset + 1],
triVerts[offset + 2]);
}
/**
* Returns the x, y, z, w tangent of the ith halfedge.
*
* @param h halfedge index (3 * triangle_index + [0|1|2]).
*/
la::vec<Precision, 4> GetTangent(size_t h) const {
size_t offset = 4 * h;
return la::vec<Precision, 4>(
halfedgeTangent[offset], halfedgeTangent[offset + 1],
halfedgeTangent[offset + 2], halfedgeTangent[offset + 3]);
}
};
/**
* @brief Single-precision - ideal for most uses, especially graphics.
*/
using MeshGL = MeshGLP<float>;
/**
* @brief Double-precision, 64-bit indices - best for huge meshes.
*/
using MeshGL64 = MeshGLP<double, uint64_t>;
/**
* @brief This library's internal representation of an oriented, 2-manifold,
* triangle mesh - a simple boundary-representation of a solid object. Use this
* class to store and operate on solids, and use MeshGL for input and output.
*
* In addition to storing geometric data, a Manifold can also store an arbitrary
* number of vertex properties. These could be anything, e.g. normals, UV
* coordinates, colors, etc, but this library is completely agnostic. All
* properties are merely float values indexed by channel number. It is up to the
* user to associate channel numbers with meaning.
*
* Manifold allows vertex properties to be shared for efficient storage, or to
* have multiple property verts associated with a single geometric vertex,
* allowing sudden property changes, e.g. at Boolean intersections, without
* sacrificing manifoldness.
*
* Manifolds also keep track of their relationships to their inputs, via
* OriginalIDs and the faceIDs and transforms accessible through MeshGL. This
* allows object-level properties to be re-associated with the output after many
* operations, particularly useful for materials. Since separate object's
* properties are not mixed, there is no requirement that channels have
* consistent meaning between different inputs.
*/
class Manifold {
public:
/** @name Basics
* Copy / move / assignment
*/
///@{
Manifold();
~Manifold();
Manifold(const Manifold& other);
Manifold& operator=(const Manifold& other);
Manifold(Manifold&&) noexcept;
Manifold& operator=(Manifold&&) noexcept;
///@}
/** @name Input & Output
* Create and retrieve arbitrary manifolds
*/
///@{
Manifold(const MeshGL&);
Manifold(const MeshGL64&);
MeshGL GetMeshGL(int normalIdx = -1) const;
MeshGL64 GetMeshGL64(int normalIdx = -1) const;
///@}
/** @name Constructors
* Topological ops, primitives, and SDF
*/
///@{
std::vector<Manifold> Decompose() const;
static Manifold Compose(const std::vector<Manifold>&);
static Manifold Tetrahedron();
static Manifold Cube(vec3 size = vec3(1.0), bool center = false);
static Manifold Cylinder(double height, double radiusLow,
double radiusHigh = -1.0, int circularSegments = 0,
bool center = false);
static Manifold Sphere(double radius, int circularSegments = 0);
static Manifold LevelSet(std::function<double(vec3)> sdf, Box bounds,
double edgeLength, double level = 0,
double tolerance = -1, bool canParallel = true);
///@}
/** @name Polygons
* 3D to 2D and 2D to 3D
*/
///@{
Polygons Slice(double height = 0) const;
Polygons Project() const;
static Manifold Extrude(const Polygons& crossSection, double height,
int nDivisions = 0, double twistDegrees = 0.0,
vec2 scaleTop = vec2(1.0));
static Manifold Revolve(const Polygons& crossSection,
int circularSegments = 0,
double revolveDegrees = 360.0f);
///@}
enum class Error {
NoError,
NonFiniteVertex,
NotManifold,
VertexOutOfBounds,
PropertiesWrongLength,
MissingPositionProperties,
MergeVectorsDifferentLengths,
MergeIndexOutOfBounds,
TransformWrongLength,
RunIndexWrongLength,
FaceIDWrongLength,
InvalidConstruction,
};
/** @name Information
* Details of the manifold
*/
///@{
Error Status() const;
bool IsEmpty() const;
size_t NumVert() const;
size_t NumEdge() const;
size_t NumTri() const;
size_t NumProp() const;
size_t NumPropVert() const;
Box BoundingBox() const;
int Genus() const;
double GetTolerance() const;
///@}
/** @name Measurement
*/
///@{
double SurfaceArea() const;
double Volume() const;
double MinGap(const Manifold& other, double searchLength) const;
///@}
/** @name Mesh ID
* Details of the manifold's relation to its input meshes, for the purposes
* of reapplying mesh properties.
*/
///@{
int OriginalID() const;
Manifold AsOriginal() const;
static uint32_t ReserveIDs(uint32_t);
///@}
/** @name Transformations
*/
///@{
Manifold Translate(vec3) const;
Manifold Scale(vec3) const;
Manifold Rotate(double xDegrees, double yDegrees = 0.0,
double zDegrees = 0.0) const;
Manifold Mirror(vec3) const;
Manifold Transform(const mat3x4&) const;
Manifold Warp(std::function<void(vec3&)>) const;
Manifold WarpBatch(std::function<void(VecView<vec3>)>) const;
Manifold SetTolerance(double) const;
///@}
/** @name Boolean
* Combine two manifolds
*/
///@{
Manifold Boolean(const Manifold& second, OpType op) const;
static Manifold BatchBoolean(const std::vector<Manifold>& manifolds,
OpType op);
// Boolean operation shorthand
Manifold operator+(const Manifold&) const; // Add (Union)
Manifold& operator+=(const Manifold&);
Manifold operator-(const Manifold&) const; // Subtract (Difference)
Manifold& operator-=(const Manifold&);
Manifold operator^(const Manifold&) const; // Intersect
Manifold& operator^=(const Manifold&);
std::pair<Manifold, Manifold> Split(const Manifold&) const;
std::pair<Manifold, Manifold> SplitByPlane(vec3 normal,
double originOffset) const;
Manifold TrimByPlane(vec3 normal, double originOffset) const;
///@}
/** @name Properties
* Create and modify vertex properties.
*/
///@{
Manifold SetProperties(
int numProp,
std::function<void(double*, vec3, const double*)> propFunc) const;
Manifold CalculateCurvature(int gaussianIdx, int meanIdx) const;
Manifold CalculateNormals(int normalIdx, double minSharpAngle = 60) const;
///@}
/** @name Smoothing
* Smooth meshes by calculating tangent vectors and refining to a higher
* triangle count.
*/
///@{
Manifold Refine(int) const;
Manifold RefineToLength(double) const;
Manifold RefineToTolerance(double) const;
Manifold SmoothByNormals(int normalIdx) const;
Manifold SmoothOut(double minSharpAngle = 60, double minSmoothness = 0) const;
static Manifold Smooth(const MeshGL&,
const std::vector<Smoothness>& sharpenedEdges = {});
static Manifold Smooth(const MeshGL64&,
const std::vector<Smoothness>& sharpenedEdges = {});
///@}
/** @name Convex Hull
*/
///@{
Manifold Hull() const;
static Manifold Hull(const std::vector<Manifold>& manifolds);
static Manifold Hull(const std::vector<vec3>& pts);
///@}
/** @name Testing Hooks
* These are just for internal testing.
*/
///@{
bool MatchesTriNormals() const;
size_t NumDegenerateTris() const;
size_t NumOverlaps(const Manifold& second) const;
double GetEpsilon() const;
///@}
struct Impl;
private:
Manifold(std::shared_ptr<CsgNode> pNode_);
Manifold(std::shared_ptr<Impl> pImpl_);
static Manifold Invalid();
mutable std::shared_ptr<CsgNode> pNode_;
CsgLeafNode& GetCsgLeafNode() const;
};
/** @} */
/** @addtogroup Debug
* @ingroup Optional
* @brief Debugging features
*
* The features require compiler flags to be enabled. Assertions are enabled
* with the MANIFOLD_DEBUG flag and then controlled with ExecutionParams.
* @{
*/
#ifdef MANIFOLD_DEBUG
inline std::string ToString(const Manifold::Error& error) {
switch (error) {
case Manifold::Error::NoError:
return "No Error";
case Manifold::Error::NonFiniteVertex:
return "Non Finite Vertex";
case Manifold::Error::NotManifold:
return "Not Manifold";
case Manifold::Error::VertexOutOfBounds:
return "Vertex Out Of Bounds";
case Manifold::Error::PropertiesWrongLength:
return "Properties Wrong Length";
case Manifold::Error::MissingPositionProperties:
return "Missing Position Properties";
case Manifold::Error::MergeVectorsDifferentLengths:
return "Merge Vectors Different Lengths";
case Manifold::Error::MergeIndexOutOfBounds:
return "Merge Index Out Of Bounds";
case Manifold::Error::TransformWrongLength:
return "Transform Wrong Length";
case Manifold::Error::RunIndexWrongLength:
return "Run Index Wrong Length";
case Manifold::Error::FaceIDWrongLength:
return "Face ID Wrong Length";
case Manifold::Error::InvalidConstruction:
return "Invalid Construction";
default:
return "Unknown Error";
};
}
inline std::ostream& operator<<(std::ostream& stream,
const Manifold::Error& error) {
return stream << ToString(error);
}
#endif
/** @} */
} // namespace manifold

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// Copyright 2022 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#ifdef MANIFOLD_DEBUG
#include <iostream>
#include <sstream>
#include <stdexcept>
#include <string>
/** @addtogroup Debug
* @{
*/
struct userErr : public virtual std::runtime_error {
using std::runtime_error::runtime_error;
};
struct topologyErr : public virtual std::runtime_error {
using std::runtime_error::runtime_error;
};
struct geometryErr : public virtual std::runtime_error {
using std::runtime_error::runtime_error;
};
using logicErr = std::logic_error;
template <typename Ex>
void AssertFail(const char* file, int line, const char* cond, const char* msg) {
std::ostringstream output;
output << "Error in file: " << file << " (" << line << "): \'" << cond
<< "\' is false: " << msg;
throw Ex(output.str());
}
template <typename Ex>
void AssertFail(const char* file, int line, const std::string& cond,
const std::string& msg) {
std::ostringstream output;
output << "Error in file: " << file << " (" << line << "): \'" << cond
<< "\' is false: " << msg;
throw Ex(output.str());
}
// DEBUG_ASSERT is slightly slower due to the function call, but gives more
// detailed info.
#define DEBUG_ASSERT(condition, EX, msg) \
if (!(condition)) AssertFail<EX>(__FILE__, __LINE__, #condition, msg);
// ASSERT has almost no overhead, so better to use for frequent calls like
// vector bounds checking.
#define ASSERT(condition, EX) \
if (!(condition)) throw(EX);
#else
#define DEBUG_ASSERT(condition, EX, msg)
#define ASSERT(condition, EX)
#endif
/** @} */

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "manifold/common.h"
namespace manifold {
/** @addtogroup Structs
* @{
*/
/**
* @brief Polygon vertex.
*/
struct PolyVert {
/// X-Y position
vec2 pos;
/// ID or index into another vertex vector
int idx;
};
/**
* @brief Single polygon contour, wound CCW, with indices. First and last point
* are implicitly connected. Should ensure all input is
* [&epsilon;-valid](https://github.com/elalish/manifold/wiki/Manifold-Library#definition-of-%CE%B5-valid).
*/
using SimplePolygonIdx = std::vector<PolyVert>;
/**
* @brief Set of indexed polygons with holes. Order of contours is arbitrary.
* Can contain any depth of nested holes and any number of separate polygons.
* Should ensure all input is
* [&epsilon;-valid](https://github.com/elalish/manifold/wiki/Manifold-Library#definition-of-%CE%B5-valid).
*/
using PolygonsIdx = std::vector<SimplePolygonIdx>;
/** @} */
/** @addtogroup Triangulation
* @ingroup Core
* @brief Polygon triangulation
* @{
*/
std::vector<ivec3> TriangulateIdx(const PolygonsIdx &polys,
double epsilon = -1);
std::vector<ivec3> Triangulate(const Polygons &polygons, double epsilon = -1);
ExecutionParams &PolygonParams();
/** @} */
} // namespace manifold

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// Copyright 2023 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <cstddef>
#include <limits>
#include <type_traits>
#include <vector>
#include "manifold/optional_assert.h"
namespace manifold {
/**
* View for Vec, can perform offset operation.
* This will be invalidated when the original vector is dropped or changes
* length. Roughly equivalent to std::span<T> from c++20
*/
template <typename T>
class VecView {
public:
using Iter = T *;
using IterC = const T *;
VecView() : ptr_(nullptr), size_(0) {}
VecView(T *ptr, size_t size) : ptr_(ptr), size_(size) {}
VecView(const std::vector<std::remove_cv_t<T>> &v)
: ptr_(v.data()), size_(v.size()) {}
VecView(const VecView &other) {
ptr_ = other.ptr_;
size_ = other.size_;
}
VecView &operator=(const VecView &other) {
ptr_ = other.ptr_;
size_ = other.size_;
return *this;
}
// allows conversion to a const VecView
operator VecView<const T>() const { return {ptr_, size_}; }
inline const T &operator[](size_t i) const {
ASSERT(i < size_, std::out_of_range("Vec out of range"));
return ptr_[i];
}
inline T &operator[](size_t i) {
ASSERT(i < size_, std::out_of_range("Vec out of range"));
return ptr_[i];
}
IterC cbegin() const { return ptr_; }
IterC cend() const { return ptr_ + size_; }
IterC begin() const { return cbegin(); }
IterC end() const { return cend(); }
Iter begin() { return ptr_; }
Iter end() { return ptr_ + size_; }
const T &front() const {
ASSERT(size_ != 0,
std::out_of_range("Attempt to take the front of an empty vector"));
return ptr_[0];
}
const T &back() const {
ASSERT(size_ != 0,
std::out_of_range("Attempt to take the back of an empty vector"));
return ptr_[size_ - 1];
}
T &front() {
ASSERT(size_ != 0,
std::out_of_range("Attempt to take the front of an empty vector"));
return ptr_[0];
}
T &back() {
ASSERT(size_ != 0,
std::out_of_range("Attempt to take the back of an empty vector"));
return ptr_[size_ - 1];
}
size_t size() const { return size_; }
bool empty() const { return size_ == 0; }
VecView<T> view(size_t offset = 0,
size_t length = std::numeric_limits<size_t>::max()) {
if (length == std::numeric_limits<size_t>::max())
length = this->size_ - offset;
ASSERT(length >= 0, std::out_of_range("Vec::view out of range"));
ASSERT(offset + length <= this->size_ && offset >= 0,
std::out_of_range("Vec::view out of range"));
return VecView<T>(this->ptr_ + offset, length);
}
VecView<const T> cview(
size_t offset = 0,
size_t length = std::numeric_limits<size_t>::max()) const {
if (length == std::numeric_limits<size_t>::max())
length = this->size_ - offset;
ASSERT(length >= 0, std::out_of_range("Vec::cview out of range"));
ASSERT(offset + length <= this->size_ && offset >= 0,
std::out_of_range("Vec::cview out of range"));
return VecView<const T>(this->ptr_ + offset, length);
}
VecView<const T> view(
size_t offset = 0,
size_t length = std::numeric_limits<size_t>::max()) const {
return cview(offset, length);
}
T *data() { return this->ptr_; }
const T *data() const { return this->ptr_; }
#ifdef MANIFOLD_DEBUG
void Dump() const {
std::cout << "Vec = " << std::endl;
for (size_t i = 0; i < size(); ++i) {
std::cout << i << ", " << ptr_[i] << ", " << std::endl;
}
std::cout << std::endl;
}
#endif
protected:
T *ptr_ = nullptr;
size_t size_ = 0;
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./boolean3.h"
#include <limits>
#include "./parallel.h"
using namespace manifold;
namespace {
// These two functions (Interpolate and Intersect) are the only places where
// floating-point operations take place in the whole Boolean function. These
// are carefully designed to minimize rounding error and to eliminate it at edge
// cases to ensure consistency.
vec2 Interpolate(vec3 pL, vec3 pR, double x) {
const double dxL = x - pL.x;
const double dxR = x - pR.x;
DEBUG_ASSERT(dxL * dxR <= 0, logicErr,
"Boolean manifold error: not in domain");
const bool useL = fabs(dxL) < fabs(dxR);
const vec3 dLR = pR - pL;
const double lambda = (useL ? dxL : dxR) / dLR.x;
if (!std::isfinite(lambda) || !std::isfinite(dLR.y) || !std::isfinite(dLR.z))
return vec2(pL.y, pL.z);
vec2 yz;
yz[0] = fma(lambda, dLR.y, useL ? pL.y : pR.y);
yz[1] = fma(lambda, dLR.z, useL ? pL.z : pR.z);
return yz;
}
vec4 Intersect(const vec3 &pL, const vec3 &pR, const vec3 &qL, const vec3 &qR) {
const double dyL = qL.y - pL.y;
const double dyR = qR.y - pR.y;
DEBUG_ASSERT(dyL * dyR <= 0, logicErr,
"Boolean manifold error: no intersection");
const bool useL = fabs(dyL) < fabs(dyR);
const double dx = pR.x - pL.x;
double lambda = (useL ? dyL : dyR) / (dyL - dyR);
if (!std::isfinite(lambda)) lambda = 0.0;
vec4 xyzz;
xyzz.x = fma(lambda, dx, useL ? pL.x : pR.x);
const double pDy = pR.y - pL.y;
const double qDy = qR.y - qL.y;
const bool useP = fabs(pDy) < fabs(qDy);
xyzz.y = fma(lambda, useP ? pDy : qDy,
useL ? (useP ? pL.y : qL.y) : (useP ? pR.y : qR.y));
xyzz.z = fma(lambda, pR.z - pL.z, useL ? pL.z : pR.z);
xyzz.w = fma(lambda, qR.z - qL.z, useL ? qL.z : qR.z);
return xyzz;
}
template <const bool inverted>
struct CopyFaceEdges {
const SparseIndices &p1q1;
// x can be either vert or edge (0 or 1).
SparseIndices &pXq1;
VecView<const Halfedge> halfedgesQ;
const size_t offset;
void operator()(const size_t i) {
int idx = 3 * (i + offset);
int pX = p1q1.Get(i, inverted);
int q2 = p1q1.Get(i, !inverted);
for (const int j : {0, 1, 2}) {
const int q1 = 3 * q2 + j;
const Halfedge edge = halfedgesQ[q1];
int a = pX;
int b = edge.IsForward() ? q1 : edge.pairedHalfedge;
if (inverted) std::swap(a, b);
pXq1.Set(idx + static_cast<size_t>(j), a, b);
}
}
};
SparseIndices Filter11(const Manifold::Impl &inP, const Manifold::Impl &inQ,
const SparseIndices &p1q2, const SparseIndices &p2q1) {
ZoneScoped;
SparseIndices p1q1(3 * p1q2.size() + 3 * p2q1.size());
for_each_n(autoPolicy(p1q2.size(), 1e5), countAt(0_uz), p1q2.size(),
CopyFaceEdges<false>({p1q2, p1q1, inQ.halfedge_, 0_uz}));
for_each_n(autoPolicy(p2q1.size(), 1e5), countAt(0_uz), p2q1.size(),
CopyFaceEdges<true>({p2q1, p1q1, inP.halfedge_, p1q2.size()}));
p1q1.Unique();
return p1q1;
}
inline bool Shadows(double p, double q, double dir) {
return p == q ? dir < 0 : p < q;
}
inline std::pair<int, vec2> Shadow01(
const int p0, const int q1, VecView<const vec3> vertPosP,
VecView<const vec3> vertPosQ, VecView<const Halfedge> halfedgeQ,
const double expandP, VecView<const vec3> normalP, const bool reverse) {
const int q1s = halfedgeQ[q1].startVert;
const int q1e = halfedgeQ[q1].endVert;
const double p0x = vertPosP[p0].x;
const double q1sx = vertPosQ[q1s].x;
const double q1ex = vertPosQ[q1e].x;
int s01 = reverse ? Shadows(q1sx, p0x, expandP * normalP[q1s].x) -
Shadows(q1ex, p0x, expandP * normalP[q1e].x)
: Shadows(p0x, q1ex, expandP * normalP[p0].x) -
Shadows(p0x, q1sx, expandP * normalP[p0].x);
vec2 yz01(NAN);
if (s01 != 0) {
yz01 = Interpolate(vertPosQ[q1s], vertPosQ[q1e], vertPosP[p0].x);
if (reverse) {
vec3 diff = vertPosQ[q1s] - vertPosP[p0];
const double start2 = la::dot(diff, diff);
diff = vertPosQ[q1e] - vertPosP[p0];
const double end2 = la::dot(diff, diff);
const double dir = start2 < end2 ? normalP[q1s].y : normalP[q1e].y;
if (!Shadows(yz01[0], vertPosP[p0].y, expandP * dir)) s01 = 0;
} else {
if (!Shadows(vertPosP[p0].y, yz01[0], expandP * normalP[p0].y)) s01 = 0;
}
}
return std::make_pair(s01, yz01);
}
// https://github.com/scandum/binary_search/blob/master/README.md
// much faster than standard binary search on large arrays
size_t monobound_quaternary_search(VecView<const int64_t> array, int64_t key) {
if (array.size() == 0) {
return std::numeric_limits<size_t>::max();
}
size_t bot = 0;
size_t top = array.size();
while (top >= 65536) {
size_t mid = top / 4;
top -= mid * 3;
if (key < array[bot + mid * 2]) {
if (key >= array[bot + mid]) {
bot += mid;
}
} else {
bot += mid * 2;
if (key >= array[bot + mid]) {
bot += mid;
}
}
}
while (top > 3) {
size_t mid = top / 2;
if (key >= array[bot + mid]) {
bot += mid;
}
top -= mid;
}
while (top--) {
if (key == array[bot + top]) {
return bot + top;
}
}
return -1;
}
struct Kernel11 {
VecView<vec4> xyzz;
VecView<int> s;
VecView<const vec3> vertPosP;
VecView<const vec3> vertPosQ;
VecView<const Halfedge> halfedgeP;
VecView<const Halfedge> halfedgeQ;
const double expandP;
VecView<const vec3> normalP;
const SparseIndices &p1q1;
void operator()(const size_t idx) {
const int p1 = p1q1.Get(idx, false);
const int q1 = p1q1.Get(idx, true);
vec4 &xyzz11 = xyzz[idx];
int &s11 = s[idx];
// For pRL[k], qRL[k], k==0 is the left and k==1 is the right.
int k = 0;
vec3 pRL[2], qRL[2];
// Either the left or right must shadow, but not both. This ensures the
// intersection is between the left and right.
bool shadows = false;
s11 = 0;
const int p0[2] = {halfedgeP[p1].startVert, halfedgeP[p1].endVert};
for (int i : {0, 1}) {
const auto syz01 = Shadow01(p0[i], q1, vertPosP, vertPosQ, halfedgeQ,
expandP, normalP, false);
const int s01 = syz01.first;
const vec2 yz01 = syz01.second;
// If the value is NaN, then these do not overlap.
if (std::isfinite(yz01[0])) {
s11 += s01 * (i == 0 ? -1 : 1);
if (k < 2 && (k == 0 || (s01 != 0) != shadows)) {
shadows = s01 != 0;
pRL[k] = vertPosP[p0[i]];
qRL[k] = vec3(pRL[k].x, yz01.x, yz01.y);
++k;
}
}
}
const int q0[2] = {halfedgeQ[q1].startVert, halfedgeQ[q1].endVert};
for (int i : {0, 1}) {
const auto syz10 = Shadow01(q0[i], p1, vertPosQ, vertPosP, halfedgeP,
expandP, normalP, true);
const int s10 = syz10.first;
const vec2 yz10 = syz10.second;
// If the value is NaN, then these do not overlap.
if (std::isfinite(yz10[0])) {
s11 += s10 * (i == 0 ? -1 : 1);
if (k < 2 && (k == 0 || (s10 != 0) != shadows)) {
shadows = s10 != 0;
qRL[k] = vertPosQ[q0[i]];
pRL[k] = vec3(qRL[k].x, yz10.x, yz10.y);
++k;
}
}
}
if (s11 == 0) { // No intersection
xyzz11 = vec4(NAN);
} else {
DEBUG_ASSERT(k == 2, logicErr, "Boolean manifold error: s11");
xyzz11 = Intersect(pRL[0], pRL[1], qRL[0], qRL[1]);
const int p1s = halfedgeP[p1].startVert;
const int p1e = halfedgeP[p1].endVert;
vec3 diff = vertPosP[p1s] - vec3(xyzz11);
const double start2 = la::dot(diff, diff);
diff = vertPosP[p1e] - vec3(xyzz11);
const double end2 = la::dot(diff, diff);
const double dir = start2 < end2 ? normalP[p1s].z : normalP[p1e].z;
if (!Shadows(xyzz11.z, xyzz11.w, expandP * dir)) s11 = 0;
}
}
};
std::tuple<Vec<int>, Vec<vec4>> Shadow11(SparseIndices &p1q1,
const Manifold::Impl &inP,
const Manifold::Impl &inQ,
double expandP) {
ZoneScoped;
Vec<int> s11(p1q1.size());
Vec<vec4> xyzz11(p1q1.size());
for_each_n(autoPolicy(p1q1.size(), 1e4), countAt(0_uz), p1q1.size(),
Kernel11({xyzz11, s11, inP.vertPos_, inQ.vertPos_, inP.halfedge_,
inQ.halfedge_, expandP, inP.vertNormal_, p1q1}));
p1q1.KeepFinite(xyzz11, s11);
return std::make_tuple(s11, xyzz11);
};
struct Kernel02 {
VecView<int> s;
VecView<double> z;
VecView<const vec3> vertPosP;
VecView<const Halfedge> halfedgeQ;
VecView<const vec3> vertPosQ;
const double expandP;
VecView<const vec3> vertNormalP;
const SparseIndices &p0q2;
const bool forward;
void operator()(const size_t idx) {
const int p0 = p0q2.Get(idx, !forward);
const int q2 = p0q2.Get(idx, forward);
int &s02 = s[idx];
double &z02 = z[idx];
// For yzzLR[k], k==0 is the left and k==1 is the right.
int k = 0;
vec3 yzzRL[2];
// Either the left or right must shadow, but not both. This ensures the
// intersection is between the left and right.
bool shadows = false;
int closestVert = -1;
double minMetric = std::numeric_limits<double>::infinity();
s02 = 0;
const vec3 posP = vertPosP[p0];
for (const int i : {0, 1, 2}) {
const int q1 = 3 * q2 + i;
const Halfedge edge = halfedgeQ[q1];
const int q1F = edge.IsForward() ? q1 : edge.pairedHalfedge;
if (!forward) {
const int qVert = halfedgeQ[q1F].startVert;
const vec3 diff = posP - vertPosQ[qVert];
const double metric = la::dot(diff, diff);
if (metric < minMetric) {
minMetric = metric;
closestVert = qVert;
}
}
const auto syz01 = Shadow01(p0, q1F, vertPosP, vertPosQ, halfedgeQ,
expandP, vertNormalP, !forward);
const int s01 = syz01.first;
const vec2 yz01 = syz01.second;
// If the value is NaN, then these do not overlap.
if (std::isfinite(yz01[0])) {
s02 += s01 * (forward == edge.IsForward() ? -1 : 1);
if (k < 2 && (k == 0 || (s01 != 0) != shadows)) {
shadows = s01 != 0;
yzzRL[k++] = vec3(yz01[0], yz01[1], yz01[1]);
}
}
}
if (s02 == 0) { // No intersection
z02 = NAN;
} else {
DEBUG_ASSERT(k == 2, logicErr, "Boolean manifold error: s02");
vec3 vertPos = vertPosP[p0];
z02 = Interpolate(yzzRL[0], yzzRL[1], vertPos.y)[1];
if (forward) {
if (!Shadows(vertPos.z, z02, expandP * vertNormalP[p0].z)) s02 = 0;
} else {
// DEBUG_ASSERT(closestVert != -1, topologyErr, "No closest vert");
if (!Shadows(z02, vertPos.z, expandP * vertNormalP[closestVert].z))
s02 = 0;
}
}
}
};
std::tuple<Vec<int>, Vec<double>> Shadow02(const Manifold::Impl &inP,
const Manifold::Impl &inQ,
SparseIndices &p0q2, bool forward,
double expandP) {
ZoneScoped;
Vec<int> s02(p0q2.size());
Vec<double> z02(p0q2.size());
auto vertNormalP = forward ? inP.vertNormal_ : inQ.vertNormal_;
for_each_n(autoPolicy(p0q2.size(), 1e4), countAt(0_uz), p0q2.size(),
Kernel02({s02, z02, inP.vertPos_, inQ.halfedge_, inQ.vertPos_,
expandP, vertNormalP, p0q2, forward}));
p0q2.KeepFinite(z02, s02);
return std::make_tuple(s02, z02);
};
struct Kernel12 {
VecView<int> x;
VecView<vec3> v;
VecView<const int64_t> p0q2;
VecView<const int> s02;
VecView<const double> z02;
VecView<const int64_t> p1q1;
VecView<const int> s11;
VecView<const vec4> xyzz11;
VecView<const Halfedge> halfedgesP;
VecView<const Halfedge> halfedgesQ;
VecView<const vec3> vertPosP;
const bool forward;
const SparseIndices &p1q2;
void operator()(const size_t idx) {
int p1 = p1q2.Get(idx, !forward);
int q2 = p1q2.Get(idx, forward);
int &x12 = x[idx];
vec3 &v12 = v[idx];
// For xzyLR-[k], k==0 is the left and k==1 is the right.
int k = 0;
vec3 xzyLR0[2];
vec3 xzyLR1[2];
// Either the left or right must shadow, but not both. This ensures the
// intersection is between the left and right.
bool shadows = false;
x12 = 0;
const Halfedge edge = halfedgesP[p1];
for (int vert : {edge.startVert, edge.endVert}) {
const int64_t key = forward ? SparseIndices::EncodePQ(vert, q2)
: SparseIndices::EncodePQ(q2, vert);
const size_t idx = monobound_quaternary_search(p0q2, key);
if (idx != std::numeric_limits<size_t>::max()) {
const int s = s02[idx];
x12 += s * ((vert == edge.startVert) == forward ? 1 : -1);
if (k < 2 && (k == 0 || (s != 0) != shadows)) {
shadows = s != 0;
xzyLR0[k] = vertPosP[vert];
std::swap(xzyLR0[k].y, xzyLR0[k].z);
xzyLR1[k] = xzyLR0[k];
xzyLR1[k][1] = z02[idx];
k++;
}
}
}
for (const int i : {0, 1, 2}) {
const int q1 = 3 * q2 + i;
const Halfedge edge = halfedgesQ[q1];
const int q1F = edge.IsForward() ? q1 : edge.pairedHalfedge;
const int64_t key = forward ? SparseIndices::EncodePQ(p1, q1F)
: SparseIndices::EncodePQ(q1F, p1);
const size_t idx = monobound_quaternary_search(p1q1, key);
if (idx !=
std::numeric_limits<size_t>::max()) { // s is implicitly zero for
// anything not found
const int s = s11[idx];
x12 -= s * (edge.IsForward() ? 1 : -1);
if (k < 2 && (k == 0 || (s != 0) != shadows)) {
shadows = s != 0;
const vec4 xyzz = xyzz11[idx];
xzyLR0[k][0] = xyzz.x;
xzyLR0[k][1] = xyzz.z;
xzyLR0[k][2] = xyzz.y;
xzyLR1[k] = xzyLR0[k];
xzyLR1[k][1] = xyzz.w;
if (!forward) std::swap(xzyLR0[k][1], xzyLR1[k][1]);
k++;
}
}
}
if (x12 == 0) { // No intersection
v12 = vec3(NAN);
} else {
DEBUG_ASSERT(k == 2, logicErr, "Boolean manifold error: v12");
const vec4 xzyy = Intersect(xzyLR0[0], xzyLR0[1], xzyLR1[0], xzyLR1[1]);
v12.x = xzyy[0];
v12.y = xzyy[2];
v12.z = xzyy[1];
}
}
};
std::tuple<Vec<int>, Vec<vec3>> Intersect12(
const Manifold::Impl &inP, const Manifold::Impl &inQ, const Vec<int> &s02,
const SparseIndices &p0q2, const Vec<int> &s11, const SparseIndices &p1q1,
const Vec<double> &z02, const Vec<vec4> &xyzz11, SparseIndices &p1q2,
bool forward) {
ZoneScoped;
Vec<int> x12(p1q2.size());
Vec<vec3> v12(p1q2.size());
for_each_n(
autoPolicy(p1q2.size(), 1e4), countAt(0_uz), p1q2.size(),
Kernel12({x12, v12, p0q2.AsVec64(), s02, z02, p1q1.AsVec64(), s11, xyzz11,
inP.halfedge_, inQ.halfedge_, inP.vertPos_, forward, p1q2}));
p1q2.KeepFinite(v12, x12);
return std::make_tuple(x12, v12);
};
Vec<int> Winding03(const Manifold::Impl &inP, Vec<int> &vertices, Vec<int> &s02,
bool reverse) {
ZoneScoped;
// verts that are not shadowed (not in p0q2) have winding number zero.
Vec<int> w03(inP.NumVert(), 0);
if (vertices.size() <= 1e5) {
for_each_n(ExecutionPolicy::Seq, countAt(0), s02.size(),
[&w03, &vertices, &s02, reverse](const int i) {
w03[vertices[i]] += s02[i] * (reverse ? -1 : 1);
});
} else {
for_each_n(ExecutionPolicy::Par, countAt(0), s02.size(),
[&w03, &vertices, &s02, reverse](const int i) {
AtomicAdd(w03[vertices[i]], s02[i] * (reverse ? -1 : 1));
});
}
return w03;
};
} // namespace
namespace manifold {
Boolean3::Boolean3(const Manifold::Impl &inP, const Manifold::Impl &inQ,
OpType op)
: inP_(inP), inQ_(inQ), expandP_(op == OpType::Add ? 1.0 : -1.0) {
// Symbolic perturbation:
// Union -> expand inP
// Difference, Intersection -> contract inP
#ifdef MANIFOLD_DEBUG
Timer broad;
broad.Start();
#endif
if (inP.IsEmpty() || inQ.IsEmpty() || !inP.bBox_.DoesOverlap(inQ.bBox_)) {
PRINT("No overlap, early out");
w03_.resize(inP.NumVert(), 0);
w30_.resize(inQ.NumVert(), 0);
return;
}
// Level 3
// Find edge-triangle overlaps (broad phase)
p1q2_ = inQ_.EdgeCollisions(inP_);
p2q1_ = inP_.EdgeCollisions(inQ_, true); // inverted
p1q2_.Sort();
PRINT("p1q2 size = " << p1q2_.size());
p2q1_.Sort();
PRINT("p2q1 size = " << p2q1_.size());
// Level 2
// Find vertices that overlap faces in XY-projection
SparseIndices p0q2 = inQ.VertexCollisionsZ(inP.vertPos_);
p0q2.Sort();
PRINT("p0q2 size = " << p0q2.size());
SparseIndices p2q0 = inP.VertexCollisionsZ(inQ.vertPos_, true); // inverted
p2q0.Sort();
PRINT("p2q0 size = " << p2q0.size());
// Find involved edge pairs from Level 3
SparseIndices p1q1 = Filter11(inP_, inQ_, p1q2_, p2q1_);
PRINT("p1q1 size = " << p1q1.size());
#ifdef MANIFOLD_DEBUG
broad.Stop();
Timer intersections;
intersections.Start();
#endif
// Level 2
// Build up XY-projection intersection of two edges, including the z-value for
// each edge, keeping only those whose intersection exists.
Vec<int> s11;
Vec<vec4> xyzz11;
std::tie(s11, xyzz11) = Shadow11(p1q1, inP, inQ, expandP_);
PRINT("s11 size = " << s11.size());
// Build up Z-projection of vertices onto triangles, keeping only those that
// fall inside the triangle.
Vec<int> s02;
Vec<double> z02;
std::tie(s02, z02) = Shadow02(inP, inQ, p0q2, true, expandP_);
PRINT("s02 size = " << s02.size());
Vec<int> s20;
Vec<double> z20;
std::tie(s20, z20) = Shadow02(inQ, inP, p2q0, false, expandP_);
PRINT("s20 size = " << s20.size());
// Level 3
// Build up the intersection of the edges and triangles, keeping only those
// that intersect, and record the direction the edge is passing through the
// triangle.
std::tie(x12_, v12_) =
Intersect12(inP, inQ, s02, p0q2, s11, p1q1, z02, xyzz11, p1q2_, true);
PRINT("x12 size = " << x12_.size());
std::tie(x21_, v21_) =
Intersect12(inQ, inP, s20, p2q0, s11, p1q1, z20, xyzz11, p2q1_, false);
PRINT("x21 size = " << x21_.size());
s11.clear();
xyzz11.clear();
z02.clear();
z20.clear();
Vec<int> p0 = p0q2.Copy(false);
p0q2.Resize(0);
Vec<int> q0 = p2q0.Copy(true);
p2q0.Resize(0);
// Sum up the winding numbers of all vertices.
w03_ = Winding03(inP, p0, s02, false);
w30_ = Winding03(inQ, q0, s20, true);
#ifdef MANIFOLD_DEBUG
intersections.Stop();
if (ManifoldParams().verbose) {
broad.Print("Broad phase");
intersections.Print("Intersections");
}
#endif
}
} // namespace manifold

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// Copyright 2020 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./impl.h"
#ifdef MANIFOLD_DEBUG
#define PRINT(msg) \
if (ManifoldParams().verbose) std::cout << msg << std::endl;
#else
#define PRINT(msg)
#endif
/**
* The notation in these files is abbreviated due to the complexity of the
* functions involved. The key is that the input manifolds are P and Q, while
* the output is R, and these letters in both upper and lower case refer to
* these objects. Operations are based on dimensionality: vert: 0, edge: 1,
* face: 2, solid: 3. X denotes a winding-number type quantity from the source
* paper of this algorithm, while S is closely related but includes only the
* subset of X values which "shadow" (are on the correct side of).
*
* Nearly everything here are sparse arrays, where for instance each pair in
* p2q1 refers to a face index of P interacting with a halfedge index of Q.
* Adjacent arrays like x21 refer to the values of X corresponding to each
* sparse index pair.
*
* Note many functions are designed to work symmetrically, for instance for both
* p2q1 and p1q2. Inside of these functions P and Q are marked as though the
* function is forwards, but it may include a Boolean "reverse" that indicates P
* and Q have been swapped.
*/
namespace manifold {
/** @ingroup Private */
class Boolean3 {
public:
Boolean3(const Manifold::Impl& inP, const Manifold::Impl& inQ, OpType op);
Manifold::Impl Result(OpType op) const;
private:
const Manifold::Impl &inP_, &inQ_;
const double expandP_;
SparseIndices p1q2_, p2q1_;
Vec<int> x12_, x21_, w03_, w30_;
Vec<vec3> v12_, v21_;
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <algorithm>
#include <array>
#include <map>
#include "./boolean3.h"
#include "./parallel.h"
#include "./utils.h"
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_map.h>)
#define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
#include <tbb/concurrent_map.h>
#include <tbb/parallel_for.h>
template <typename K, typename V>
using concurrent_map = tbb::concurrent_map<K, V>;
#else
template <typename K, typename V>
// not really concurrent when tbb is disabled
using concurrent_map = std::map<K, V>;
#endif
using namespace manifold;
template <>
struct std::hash<std::pair<int, int>> {
size_t operator()(const std::pair<int, int> &p) const {
return std::hash<int>()(p.first) ^ std::hash<int>()(p.second);
}
};
namespace {
constexpr int kParallelThreshold = 128;
struct AbsSum {
int operator()(int a, int b) const { return abs(a) + abs(b); }
};
struct DuplicateVerts {
VecView<vec3> vertPosR;
VecView<const int> inclusion;
VecView<const int> vertR;
VecView<const vec3> vertPosP;
void operator()(const int vert) {
const int n = std::abs(inclusion[vert]);
for (int i = 0; i < n; ++i) {
vertPosR[vertR[vert] + i] = vertPosP[vert];
}
}
};
template <bool atomic>
struct CountVerts {
VecView<Halfedge> halfedges;
VecView<int> count;
VecView<const int> inclusion;
void operator()(size_t i) {
if (atomic)
AtomicAdd(count[i / 3], std::abs(inclusion[halfedges[i].startVert]));
else
count[i / 3] += std::abs(inclusion[halfedges[i].startVert]);
}
};
template <const bool inverted, const bool atomic>
struct CountNewVerts {
VecView<int> countP;
VecView<int> countQ;
VecView<const int> i12;
const SparseIndices &pq;
VecView<const Halfedge> halfedges;
void operator()(const int idx) {
int edgeP = pq.Get(idx, inverted);
int faceQ = pq.Get(idx, !inverted);
int inclusion = std::abs(i12[idx]);
if (atomic) {
AtomicAdd(countQ[faceQ], inclusion);
const Halfedge half = halfedges[edgeP];
AtomicAdd(countP[edgeP / 3], inclusion);
AtomicAdd(countP[half.pairedHalfedge / 3], inclusion);
} else {
countQ[faceQ] += inclusion;
const Halfedge half = halfedges[edgeP];
countP[edgeP / 3] += inclusion;
countP[half.pairedHalfedge / 3] += inclusion;
}
}
};
std::tuple<Vec<int>, Vec<int>> SizeOutput(
Manifold::Impl &outR, const Manifold::Impl &inP, const Manifold::Impl &inQ,
const Vec<int> &i03, const Vec<int> &i30, const Vec<int> &i12,
const Vec<int> &i21, const SparseIndices &p1q2, const SparseIndices &p2q1,
bool invertQ) {
ZoneScoped;
Vec<int> sidesPerFacePQ(inP.NumTri() + inQ.NumTri(), 0);
// note: numFaceR <= facePQ2R.size() = sidesPerFacePQ.size() + 1
auto sidesPerFaceP = sidesPerFacePQ.view(0, inP.NumTri());
auto sidesPerFaceQ = sidesPerFacePQ.view(inP.NumTri(), inQ.NumTri());
if (inP.halfedge_.size() >= 1e5) {
for_each(ExecutionPolicy::Par, countAt(0_uz), countAt(inP.halfedge_.size()),
CountVerts<true>({inP.halfedge_, sidesPerFaceP, i03}));
for_each(ExecutionPolicy::Par, countAt(0_uz), countAt(inQ.halfedge_.size()),
CountVerts<true>({inQ.halfedge_, sidesPerFaceQ, i30}));
} else {
for_each(ExecutionPolicy::Seq, countAt(0_uz), countAt(inP.halfedge_.size()),
CountVerts<false>({inP.halfedge_, sidesPerFaceP, i03}));
for_each(ExecutionPolicy::Seq, countAt(0_uz), countAt(inQ.halfedge_.size()),
CountVerts<false>({inQ.halfedge_, sidesPerFaceQ, i30}));
}
if (i12.size() >= 1e5) {
for_each_n(ExecutionPolicy::Par, countAt(0), i12.size(),
CountNewVerts<false, true>(
{sidesPerFaceP, sidesPerFaceQ, i12, p1q2, inP.halfedge_}));
for_each_n(ExecutionPolicy::Par, countAt(0), i21.size(),
CountNewVerts<true, true>(
{sidesPerFaceQ, sidesPerFaceP, i21, p2q1, inQ.halfedge_}));
} else {
for_each_n(ExecutionPolicy::Seq, countAt(0), i12.size(),
CountNewVerts<false, false>(
{sidesPerFaceP, sidesPerFaceQ, i12, p1q2, inP.halfedge_}));
for_each_n(ExecutionPolicy::Seq, countAt(0), i21.size(),
CountNewVerts<true, false>(
{sidesPerFaceQ, sidesPerFaceP, i21, p2q1, inQ.halfedge_}));
}
Vec<int> facePQ2R(inP.NumTri() + inQ.NumTri() + 1, 0);
auto keepFace = TransformIterator(sidesPerFacePQ.begin(),
[](int x) { return x > 0 ? 1 : 0; });
inclusive_scan(keepFace, keepFace + sidesPerFacePQ.size(),
facePQ2R.begin() + 1);
int numFaceR = facePQ2R.back();
facePQ2R.resize(inP.NumTri() + inQ.NumTri());
outR.faceNormal_.resize(numFaceR);
Vec<size_t> tmpBuffer(outR.faceNormal_.size());
auto faceIds = TransformIterator(countAt(0_uz), [&sidesPerFacePQ](size_t i) {
if (sidesPerFacePQ[i] > 0) return i;
return std::numeric_limits<size_t>::max();
});
auto next =
copy_if(faceIds, faceIds + inP.faceNormal_.size(), tmpBuffer.begin(),
[](size_t v) { return v != std::numeric_limits<size_t>::max(); });
gather(tmpBuffer.begin(), next, inP.faceNormal_.begin(),
outR.faceNormal_.begin());
auto faceIdsQ =
TransformIterator(countAt(0_uz), [&sidesPerFacePQ, &inP](size_t i) {
if (sidesPerFacePQ[i + inP.faceNormal_.size()] > 0) return i;
return std::numeric_limits<size_t>::max();
});
auto end =
copy_if(faceIdsQ, faceIdsQ + inQ.faceNormal_.size(), next,
[](size_t v) { return v != std::numeric_limits<size_t>::max(); });
if (invertQ) {
gather(next, end,
TransformIterator(inQ.faceNormal_.begin(), Negate<vec3>()),
outR.faceNormal_.begin() + std::distance(tmpBuffer.begin(), next));
} else {
gather(next, end, inQ.faceNormal_.begin(),
outR.faceNormal_.begin() + std::distance(tmpBuffer.begin(), next));
}
auto newEnd = remove(sidesPerFacePQ.begin(), sidesPerFacePQ.end(), 0);
Vec<int> faceEdge(newEnd - sidesPerFacePQ.begin() + 1, 0);
inclusive_scan(sidesPerFacePQ.begin(), newEnd, faceEdge.begin() + 1);
outR.halfedge_.resize(faceEdge.back());
return std::make_tuple(faceEdge, facePQ2R);
}
struct EdgePos {
int vert;
double edgePos;
bool isStart;
};
// thread sanitizer doesn't really know how to check when there are too many
// mutex
#if defined(__has_feature)
#if __has_feature(thread_sanitizer)
__attribute__((no_sanitize("thread")))
#endif
#endif
void AddNewEdgeVerts(
// we need concurrent_map because we will be adding things concurrently
concurrent_map<int, std::vector<EdgePos>> &edgesP,
concurrent_map<std::pair<int, int>, std::vector<EdgePos>> &edgesNew,
const SparseIndices &p1q2, const Vec<int> &i12, const Vec<int> &v12R,
const Vec<Halfedge> &halfedgeP, bool forward) {
ZoneScoped;
// For each edge of P that intersects a face of Q (p1q2), add this vertex to
// P's corresponding edge vector and to the two new edges, which are
// intersections between the face of Q and the two faces of P attached to the
// edge. The direction and duplicity are given by i12, while v12R remaps to
// the output vert index. When forward is false, all is reversed.
auto process = [&](std::function<void(size_t)> lock,
std::function<void(size_t)> unlock, size_t i) {
const int edgeP = p1q2.Get(i, !forward);
const int faceQ = p1q2.Get(i, forward);
const int vert = v12R[i];
const int inclusion = i12[i];
Halfedge halfedge = halfedgeP[edgeP];
std::pair<int, int> keyRight = {halfedge.pairedHalfedge / 3, faceQ};
if (!forward) std::swap(keyRight.first, keyRight.second);
std::pair<int, int> keyLeft = {edgeP / 3, faceQ};
if (!forward) std::swap(keyLeft.first, keyLeft.second);
bool direction = inclusion < 0;
std::hash<std::pair<int, int>> pairHasher;
std::array<std::tuple<bool, size_t, std::vector<EdgePos> *>, 3> edges = {
std::make_tuple(direction, std::hash<int>{}(edgeP), &edgesP[edgeP]),
std::make_tuple(direction ^ !forward, // revert if not forward
pairHasher(keyRight), &edgesNew[keyRight]),
std::make_tuple(direction ^ forward, // revert if forward
pairHasher(keyLeft), &edgesNew[keyLeft])};
for (const auto &tuple : edges) {
lock(std::get<1>(tuple));
for (int j = 0; j < std::abs(inclusion); ++j)
std::get<2>(tuple)->push_back({vert + j, 0.0, std::get<0>(tuple)});
unlock(std::get<1>(tuple));
direction = !direction;
}
};
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
// parallelize operations, requires concurrent_map so we can only enable this
// with tbb
if (p1q2.size() > kParallelThreshold) {
// ideally we should have 1 mutex per key, but kParallelThreshold is enough
// to avoid contention for most of the cases
std::array<std::mutex, kParallelThreshold> mutexes;
static tbb::affinity_partitioner ap;
auto processFun = std::bind(
process, [&](size_t hash) { mutexes[hash % mutexes.size()].lock(); },
[&](size_t hash) { mutexes[hash % mutexes.size()].unlock(); },
std::placeholders::_1);
tbb::parallel_for(
tbb::blocked_range<size_t>(0_uz, p1q2.size(), 32),
[&](const tbb::blocked_range<size_t> &range) {
for (size_t i = range.begin(); i != range.end(); i++) processFun(i);
},
ap);
return;
}
#endif
auto processFun = std::bind(
process, [](size_t _) {}, [](size_t _) {}, std::placeholders::_1);
for (size_t i = 0; i < p1q2.size(); ++i) processFun(i);
}
std::vector<Halfedge> PairUp(std::vector<EdgePos> &edgePos) {
// Pair start vertices with end vertices to form edges. The choice of pairing
// is arbitrary for the manifoldness guarantee, but must be ordered to be
// geometrically valid. If the order does not go start-end-start-end... then
// the input and output are not geometrically valid and this algorithm becomes
// a heuristic.
DEBUG_ASSERT(edgePos.size() % 2 == 0, topologyErr,
"Non-manifold edge! Not an even number of points.");
size_t nEdges = edgePos.size() / 2;
auto middle = std::partition(edgePos.begin(), edgePos.end(),
[](EdgePos x) { return x.isStart; });
DEBUG_ASSERT(static_cast<size_t>(middle - edgePos.begin()) == nEdges,
topologyErr, "Non-manifold edge!");
auto cmp = [](EdgePos a, EdgePos b) { return a.edgePos < b.edgePos; };
std::stable_sort(edgePos.begin(), middle, cmp);
std::stable_sort(middle, edgePos.end(), cmp);
std::vector<Halfedge> edges;
for (size_t i = 0; i < nEdges; ++i)
edges.push_back({edgePos[i].vert, edgePos[i + nEdges].vert, -1});
return edges;
}
void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
Vec<int> &facePtrR,
concurrent_map<int, std::vector<EdgePos>> &edgesP,
Vec<TriRef> &halfedgeRef, const Manifold::Impl &inP,
const Vec<int> &i03, const Vec<int> &vP2R,
const Vec<int>::IterC faceP2R, bool forward) {
ZoneScoped;
// Each edge in the map is partially retained; for each of these, look up
// their original verts and include them based on their winding number (i03),
// while remapping them to the output using vP2R. Use the verts position
// projected along the edge vector to pair them up, then distribute these
// edges to their faces.
Vec<Halfedge> &halfedgeR = outR.halfedge_;
const Vec<vec3> &vertPosP = inP.vertPos_;
const Vec<Halfedge> &halfedgeP = inP.halfedge_;
for (auto &value : edgesP) {
const int edgeP = value.first;
std::vector<EdgePos> &edgePosP = value.second;
const Halfedge &halfedge = halfedgeP[edgeP];
wholeHalfedgeP[edgeP] = false;
wholeHalfedgeP[halfedge.pairedHalfedge] = false;
const int vStart = halfedge.startVert;
const int vEnd = halfedge.endVert;
const vec3 edgeVec = vertPosP[vEnd] - vertPosP[vStart];
// Fill in the edge positions of the old points.
for (EdgePos &edge : edgePosP) {
edge.edgePos = la::dot(outR.vertPos_[edge.vert], edgeVec);
}
int inclusion = i03[vStart];
EdgePos edgePos = {vP2R[vStart],
la::dot(outR.vertPos_[vP2R[vStart]], edgeVec),
inclusion > 0};
for (int j = 0; j < std::abs(inclusion); ++j) {
edgePosP.push_back(edgePos);
++edgePos.vert;
}
inclusion = i03[vEnd];
edgePos = {vP2R[vEnd], la::dot(outR.vertPos_[vP2R[vEnd]], edgeVec),
inclusion < 0};
for (int j = 0; j < std::abs(inclusion); ++j) {
edgePosP.push_back(edgePos);
++edgePos.vert;
}
// sort edges into start/end pairs along length
std::vector<Halfedge> edges = PairUp(edgePosP);
// add halfedges to result
const int faceLeftP = edgeP / 3;
const int faceLeft = faceP2R[faceLeftP];
const int faceRightP = halfedge.pairedHalfedge / 3;
const int faceRight = faceP2R[faceRightP];
// Negative inclusion means the halfedges are reversed, which means our
// reference is now to the endVert instead of the startVert, which is one
// position advanced CCW. This is only valid if this is a retained vert; it
// will be ignored later if the vert is new.
const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP};
const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP};
for (Halfedge e : edges) {
const int forwardEdge = facePtrR[faceLeft]++;
const int backwardEdge = facePtrR[faceRight]++;
e.pairedHalfedge = backwardEdge;
halfedgeR[forwardEdge] = e;
halfedgeRef[forwardEdge] = forwardRef;
std::swap(e.startVert, e.endVert);
e.pairedHalfedge = forwardEdge;
halfedgeR[backwardEdge] = e;
halfedgeRef[backwardEdge] = backwardRef;
}
}
}
void AppendNewEdges(
Manifold::Impl &outR, Vec<int> &facePtrR,
concurrent_map<std::pair<int, int>, std::vector<EdgePos>> &edgesNew,
Vec<TriRef> &halfedgeRef, const Vec<int> &facePQ2R, const int numFaceP) {
ZoneScoped;
// Pair up each edge's verts and distribute to faces based on indices in key.
Vec<Halfedge> &halfedgeR = outR.halfedge_;
Vec<vec3> &vertPosR = outR.vertPos_;
for (auto &value : edgesNew) {
const int faceP = value.first.first;
const int faceQ = value.first.second;
std::vector<EdgePos> &edgePos = value.second;
Box bbox;
for (auto edge : edgePos) {
bbox.Union(vertPosR[edge.vert]);
}
const vec3 size = bbox.Size();
// Order the points along their longest dimension.
const int i = (size.x > size.y && size.x > size.z) ? 0
: size.y > size.z ? 1
: 2;
for (auto &edge : edgePos) {
edge.edgePos = vertPosR[edge.vert][i];
}
// sort edges into start/end pairs along length.
std::vector<Halfedge> edges = PairUp(edgePos);
// add halfedges to result
const int faceLeft = facePQ2R[faceP];
const int faceRight = facePQ2R[numFaceP + faceQ];
const TriRef forwardRef = {0, -1, faceP};
const TriRef backwardRef = {1, -1, faceQ};
for (Halfedge e : edges) {
const int forwardEdge = facePtrR[faceLeft]++;
const int backwardEdge = facePtrR[faceRight]++;
e.pairedHalfedge = backwardEdge;
halfedgeR[forwardEdge] = e;
halfedgeRef[forwardEdge] = forwardRef;
std::swap(e.startVert, e.endVert);
e.pairedHalfedge = forwardEdge;
halfedgeR[backwardEdge] = e;
halfedgeRef[backwardEdge] = backwardRef;
}
}
}
struct DuplicateHalfedges {
VecView<Halfedge> halfedgesR;
VecView<TriRef> halfedgeRef;
VecView<int> facePtr;
VecView<const char> wholeHalfedgeP;
VecView<const Halfedge> halfedgesP;
VecView<const int> i03;
VecView<const int> vP2R;
VecView<const int> faceP2R;
const bool forward;
void operator()(const int idx) {
if (!wholeHalfedgeP[idx]) return;
Halfedge halfedge = halfedgesP[idx];
if (!halfedge.IsForward()) return;
const int inclusion = i03[halfedge.startVert];
if (inclusion == 0) return;
if (inclusion < 0) { // reverse
std::swap(halfedge.startVert, halfedge.endVert);
}
halfedge.startVert = vP2R[halfedge.startVert];
halfedge.endVert = vP2R[halfedge.endVert];
const int faceLeftP = idx / 3;
const int newFace = faceP2R[faceLeftP];
const int faceRightP = halfedge.pairedHalfedge / 3;
const int faceRight = faceP2R[faceRightP];
// Negative inclusion means the halfedges are reversed, which means our
// reference is now to the endVert instead of the startVert, which is one
// position advanced CCW.
const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP};
const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP};
for (int i = 0; i < std::abs(inclusion); ++i) {
int forwardEdge = AtomicAdd(facePtr[newFace], 1);
int backwardEdge = AtomicAdd(facePtr[faceRight], 1);
halfedge.pairedHalfedge = backwardEdge;
halfedgesR[forwardEdge] = halfedge;
halfedgesR[backwardEdge] = {halfedge.endVert, halfedge.startVert,
forwardEdge};
halfedgeRef[forwardEdge] = forwardRef;
halfedgeRef[backwardEdge] = backwardRef;
++halfedge.startVert;
++halfedge.endVert;
}
}
};
void AppendWholeEdges(Manifold::Impl &outR, Vec<int> &facePtrR,
Vec<TriRef> &halfedgeRef, const Manifold::Impl &inP,
const Vec<char> wholeHalfedgeP, const Vec<int> &i03,
const Vec<int> &vP2R, VecView<const int> faceP2R,
bool forward) {
ZoneScoped;
for_each_n(
autoPolicy(inP.halfedge_.size()), countAt(0), inP.halfedge_.size(),
DuplicateHalfedges({outR.halfedge_, halfedgeRef, facePtrR, wholeHalfedgeP,
inP.halfedge_, i03, vP2R, faceP2R, forward}));
}
struct MapTriRef {
VecView<const TriRef> triRefP;
VecView<const TriRef> triRefQ;
const int offsetQ;
void operator()(TriRef &triRef) {
const int tri = triRef.tri;
const bool PQ = triRef.meshID == 0;
triRef = PQ ? triRefP[tri] : triRefQ[tri];
if (!PQ) triRef.meshID += offsetQ;
}
};
void UpdateReference(Manifold::Impl &outR, const Manifold::Impl &inP,
const Manifold::Impl &inQ, bool invertQ) {
const int offsetQ = Manifold::Impl::meshIDCounter_;
for_each_n(
autoPolicy(outR.NumTri(), 1e5), outR.meshRelation_.triRef.begin(),
outR.NumTri(),
MapTriRef({inP.meshRelation_.triRef, inQ.meshRelation_.triRef, offsetQ}));
for (const auto &pair : inP.meshRelation_.meshIDtransform) {
outR.meshRelation_.meshIDtransform[pair.first] = pair.second;
}
for (const auto &pair : inQ.meshRelation_.meshIDtransform) {
outR.meshRelation_.meshIDtransform[pair.first + offsetQ] = pair.second;
outR.meshRelation_.meshIDtransform[pair.first + offsetQ].backSide ^=
invertQ;
}
}
struct Barycentric {
VecView<vec3> uvw;
VecView<const TriRef> ref;
VecView<const vec3> vertPosP;
VecView<const vec3> vertPosQ;
VecView<const vec3> vertPosR;
VecView<const Halfedge> halfedgeP;
VecView<const Halfedge> halfedgeQ;
VecView<const Halfedge> halfedgeR;
const double epsilon;
void operator()(const int tri) {
const TriRef refPQ = ref[tri];
if (halfedgeR[3 * tri].startVert < 0) return;
const int triPQ = refPQ.tri;
const bool PQ = refPQ.meshID == 0;
const auto &vertPos = PQ ? vertPosP : vertPosQ;
const auto &halfedge = PQ ? halfedgeP : halfedgeQ;
mat3 triPos;
for (const int j : {0, 1, 2})
triPos[j] = vertPos[halfedge[3 * triPQ + j].startVert];
for (const int i : {0, 1, 2}) {
const int vert = halfedgeR[3 * tri + i].startVert;
uvw[3 * tri + i] = GetBarycentric(vertPosR[vert], triPos, epsilon);
}
}
};
void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
const Manifold::Impl &inQ) {
ZoneScoped;
const int numPropP = inP.NumProp();
const int numPropQ = inQ.NumProp();
const int numProp = std::max(numPropP, numPropQ);
outR.meshRelation_.numProp = numProp;
if (numProp == 0) return;
const int numTri = outR.NumTri();
outR.meshRelation_.triProperties.resize(numTri);
Vec<vec3> bary(outR.halfedge_.size());
for_each_n(autoPolicy(numTri, 1e4), countAt(0), numTri,
Barycentric({bary, outR.meshRelation_.triRef, inP.vertPos_,
inQ.vertPos_, outR.vertPos_, inP.halfedge_,
inQ.halfedge_, outR.halfedge_, outR.epsilon_}));
using Entry = std::pair<ivec3, int>;
int idMissProp = outR.NumVert();
std::vector<std::vector<Entry>> propIdx(outR.NumVert() + 1);
std::vector<int> propMissIdx[2];
propMissIdx[0].resize(inQ.NumPropVert(), -1);
propMissIdx[1].resize(inP.NumPropVert(), -1);
outR.meshRelation_.properties.reserve(outR.NumVert() * numProp);
int idx = 0;
for (int tri = 0; tri < numTri; ++tri) {
// Skip collapsed triangles
if (outR.halfedge_[3 * tri].startVert < 0) continue;
const TriRef ref = outR.meshRelation_.triRef[tri];
const bool PQ = ref.meshID == 0;
const int oldNumProp = PQ ? numPropP : numPropQ;
const auto &properties =
PQ ? inP.meshRelation_.properties : inQ.meshRelation_.properties;
const ivec3 &triProp = oldNumProp == 0 ? ivec3(-1)
: PQ ? inP.meshRelation_.triProperties[ref.tri]
: inQ.meshRelation_.triProperties[ref.tri];
for (const int i : {0, 1, 2}) {
const int vert = outR.halfedge_[3 * tri + i].startVert;
const vec3 &uvw = bary[3 * tri + i];
ivec4 key(PQ, idMissProp, -1, -1);
if (oldNumProp > 0) {
int edge = -2;
for (const int j : {0, 1, 2}) {
if (uvw[j] == 1) {
// On a retained vert, the propVert must also match
key[2] = triProp[j];
edge = -1;
break;
}
if (uvw[j] == 0) edge = j;
}
if (edge >= 0) {
// On an edge, both propVerts must match
const int p0 = triProp[Next3(edge)];
const int p1 = triProp[Prev3(edge)];
key[1] = vert;
key[2] = std::min(p0, p1);
key[3] = std::max(p0, p1);
} else if (edge == -2) {
key[1] = vert;
}
}
if (key.y == idMissProp && key.z >= 0) {
// only key.x/key.z matters
auto &entry = propMissIdx[key.x][key.z];
if (entry >= 0) {
outR.meshRelation_.triProperties[tri][i] = entry;
continue;
}
entry = idx;
} else {
auto &bin = propIdx[key.y];
bool bFound = false;
for (const auto &b : bin) {
if (b.first == ivec3(key.x, key.z, key.w)) {
bFound = true;
outR.meshRelation_.triProperties[tri][i] = b.second;
break;
}
}
if (bFound) continue;
bin.push_back(std::make_pair(ivec3(key.x, key.z, key.w), idx));
}
outR.meshRelation_.triProperties[tri][i] = idx++;
for (int p = 0; p < numProp; ++p) {
if (p < oldNumProp) {
vec3 oldProps;
for (const int j : {0, 1, 2})
oldProps[j] = properties[oldNumProp * triProp[j] + p];
outR.meshRelation_.properties.push_back(la::dot(uvw, oldProps));
} else {
outR.meshRelation_.properties.push_back(0);
}
}
}
}
}
} // namespace
namespace manifold {
Manifold::Impl Boolean3::Result(OpType op) const {
#ifdef MANIFOLD_DEBUG
Timer assemble;
assemble.Start();
#endif
DEBUG_ASSERT((expandP_ > 0) == (op == OpType::Add), logicErr,
"Result op type not compatible with constructor op type.");
const int c1 = op == OpType::Intersect ? 0 : 1;
const int c2 = op == OpType::Add ? 1 : 0;
const int c3 = op == OpType::Intersect ? 1 : -1;
if (inP_.status_ != Manifold::Error::NoError) {
auto impl = Manifold::Impl();
impl.status_ = inP_.status_;
return impl;
}
if (inQ_.status_ != Manifold::Error::NoError) {
auto impl = Manifold::Impl();
impl.status_ = inQ_.status_;
return impl;
}
if (inP_.IsEmpty()) {
if (!inQ_.IsEmpty() && op == OpType::Add) {
return inQ_;
}
return Manifold::Impl();
} else if (inQ_.IsEmpty()) {
if (op == OpType::Intersect) {
return Manifold::Impl();
}
return inP_;
}
const bool invertQ = op == OpType::Subtract;
// Convert winding numbers to inclusion values based on operation type.
Vec<int> i12(x12_.size());
Vec<int> i21(x21_.size());
Vec<int> i03(w03_.size());
Vec<int> i30(w30_.size());
transform(x12_.begin(), x12_.end(), i12.begin(),
[c3](int v) { return c3 * v; });
transform(x21_.begin(), x21_.end(), i21.begin(),
[c3](int v) { return c3 * v; });
transform(w03_.begin(), w03_.end(), i03.begin(),
[c1, c3](int v) { return c1 + c3 * v; });
transform(w30_.begin(), w30_.end(), i30.begin(),
[c2, c3](int v) { return c2 + c3 * v; });
Vec<int> vP2R(inP_.NumVert());
exclusive_scan(i03.begin(), i03.end(), vP2R.begin(), 0, AbsSum());
int numVertR = AbsSum()(vP2R.back(), i03.back());
const int nPv = numVertR;
Vec<int> vQ2R(inQ_.NumVert());
exclusive_scan(i30.begin(), i30.end(), vQ2R.begin(), numVertR, AbsSum());
numVertR = AbsSum()(vQ2R.back(), i30.back());
const int nQv = numVertR - nPv;
Vec<int> v12R(v12_.size());
if (v12_.size() > 0) {
exclusive_scan(i12.begin(), i12.end(), v12R.begin(), numVertR, AbsSum());
numVertR = AbsSum()(v12R.back(), i12.back());
}
const int n12 = numVertR - nPv - nQv;
Vec<int> v21R(v21_.size());
if (v21_.size() > 0) {
exclusive_scan(i21.begin(), i21.end(), v21R.begin(), numVertR, AbsSum());
numVertR = AbsSum()(v21R.back(), i21.back());
}
const int n21 = numVertR - nPv - nQv - n12;
// Create the output Manifold
Manifold::Impl outR;
if (numVertR == 0) return outR;
outR.epsilon_ = std::max(inP_.epsilon_, inQ_.epsilon_);
outR.tolerance_ = std::max(inP_.tolerance_, inQ_.tolerance_);
outR.vertPos_.resize(numVertR);
// Add vertices, duplicating for inclusion numbers not in [-1, 1].
// Retained vertices from P and Q:
for_each_n(autoPolicy(inP_.NumVert(), 1e4), countAt(0), inP_.NumVert(),
DuplicateVerts({outR.vertPos_, i03, vP2R, inP_.vertPos_}));
for_each_n(autoPolicy(inQ_.NumVert(), 1e4), countAt(0), inQ_.NumVert(),
DuplicateVerts({outR.vertPos_, i30, vQ2R, inQ_.vertPos_}));
// New vertices created from intersections:
for_each_n(autoPolicy(i12.size(), 1e4), countAt(0), i12.size(),
DuplicateVerts({outR.vertPos_, i12, v12R, v12_}));
for_each_n(autoPolicy(i21.size(), 1e4), countAt(0), i21.size(),
DuplicateVerts({outR.vertPos_, i21, v21R, v21_}));
PRINT(nPv << " verts from inP");
PRINT(nQv << " verts from inQ");
PRINT(n12 << " new verts from edgesP -> facesQ");
PRINT(n21 << " new verts from facesP -> edgesQ");
// Build up new polygonal faces from triangle intersections. At this point the
// calculation switches from parallel to serial.
// Level 3
// This key is the forward halfedge index of P or Q. Only includes intersected
// edges.
concurrent_map<int, std::vector<EdgePos>> edgesP, edgesQ;
// This key is the face index of <P, Q>
concurrent_map<std::pair<int, int>, std::vector<EdgePos>> edgesNew;
AddNewEdgeVerts(edgesP, edgesNew, p1q2_, i12, v12R, inP_.halfedge_, true);
AddNewEdgeVerts(edgesQ, edgesNew, p2q1_, i21, v21R, inQ_.halfedge_, false);
v12R.clear();
v21R.clear();
// Level 4
Vec<int> faceEdge;
Vec<int> facePQ2R;
std::tie(faceEdge, facePQ2R) =
SizeOutput(outR, inP_, inQ_, i03, i30, i12, i21, p1q2_, p2q1_, invertQ);
i12.clear();
i21.clear();
// This gets incremented for each halfedge that's added to a face so that the
// next one knows where to slot in.
Vec<int> facePtrR = faceEdge;
// Intersected halfedges are marked false.
Vec<char> wholeHalfedgeP(inP_.halfedge_.size(), true);
Vec<char> wholeHalfedgeQ(inQ_.halfedge_.size(), true);
// The halfedgeRef contains the data that will become triRef once the faces
// are triangulated.
Vec<TriRef> halfedgeRef(2 * outR.NumEdge());
AppendPartialEdges(outR, wholeHalfedgeP, facePtrR, edgesP, halfedgeRef, inP_,
i03, vP2R, facePQ2R.begin(), true);
AppendPartialEdges(outR, wholeHalfedgeQ, facePtrR, edgesQ, halfedgeRef, inQ_,
i30, vQ2R, facePQ2R.begin() + inP_.NumTri(), false);
edgesP.clear();
edgesQ.clear();
AppendNewEdges(outR, facePtrR, edgesNew, halfedgeRef, facePQ2R,
inP_.NumTri());
edgesNew.clear();
AppendWholeEdges(outR, facePtrR, halfedgeRef, inP_, wholeHalfedgeP, i03, vP2R,
facePQ2R.cview(0, inP_.NumTri()), true);
AppendWholeEdges(outR, facePtrR, halfedgeRef, inQ_, wholeHalfedgeQ, i30, vQ2R,
facePQ2R.cview(inP_.NumTri(), inQ_.NumTri()), false);
wholeHalfedgeP.clear();
wholeHalfedgeQ.clear();
facePtrR.clear();
facePQ2R.clear();
i03.clear();
i30.clear();
vP2R.clear();
vQ2R.clear();
#ifdef MANIFOLD_DEBUG
assemble.Stop();
Timer triangulate;
triangulate.Start();
#endif
// Level 6
if (ManifoldParams().intermediateChecks)
DEBUG_ASSERT(outR.IsManifold(), logicErr, "polygon mesh is not manifold!");
outR.Face2Tri(faceEdge, halfedgeRef);
halfedgeRef.clear();
faceEdge.clear();
#ifdef MANIFOLD_DEBUG
triangulate.Stop();
Timer simplify;
simplify.Start();
#endif
if (ManifoldParams().intermediateChecks)
DEBUG_ASSERT(outR.IsManifold(), logicErr,
"triangulated mesh is not manifold!");
CreateProperties(outR, inP_, inQ_);
UpdateReference(outR, inP_, inQ_, invertQ);
outR.SimplifyTopology();
if (ManifoldParams().intermediateChecks)
DEBUG_ASSERT(outR.Is2Manifold(), logicErr,
"simplified mesh is not 2-manifold!");
#ifdef MANIFOLD_DEBUG
simplify.Stop();
Timer sort;
sort.Start();
#endif
outR.Finish();
outR.IncrementMeshIDs();
#ifdef MANIFOLD_DEBUG
sort.Stop();
if (ManifoldParams().verbose) {
assemble.Print("Assembly");
triangulate.Print("Triangulation");
simplify.Print("Simplification");
sort.Print("Sorting");
std::cout << outR.NumVert() << " verts and " << outR.NumTri() << " tris"
<< std::endl;
}
#endif
return outR;
}
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./parallel.h"
#include "./sparse.h"
#include "./utils.h"
#include "./vec.h"
#include "manifold/common.h"
#ifdef _MSC_VER
#include <intrin.h>
#endif
#if (MANIFOLD_PAR == 1)
#include <tbb/combinable.h>
#endif
namespace manifold {
namespace collider_internal {
// Adjustable parameters
constexpr int kInitialLength = 128;
constexpr int kLengthMultiple = 4;
constexpr int kSequentialThreshold = 512;
// Fundamental constants
constexpr int kRoot = 1;
#ifdef _MSC_VER
#ifndef _WINDEF_
typedef unsigned long DWORD;
#endif
uint32_t inline ctz(uint32_t value) {
DWORD trailing_zero = 0;
if (_BitScanForward(&trailing_zero, value)) {
return trailing_zero;
} else {
// This is undefined, I better choose 32 than 0
return 32;
}
}
uint32_t inline clz(uint32_t value) {
DWORD leading_zero = 0;
if (_BitScanReverse(&leading_zero, value)) {
return 31 - leading_zero;
} else {
// Same remarks as above
return 32;
}
}
#endif
constexpr inline bool IsLeaf(int node) { return node % 2 == 0; }
constexpr inline bool IsInternal(int node) { return node % 2 == 1; }
constexpr inline int Node2Internal(int node) { return (node - 1) / 2; }
constexpr inline int Internal2Node(int internal) { return internal * 2 + 1; }
constexpr inline int Node2Leaf(int node) { return node / 2; }
constexpr inline int Leaf2Node(int leaf) { return leaf * 2; }
struct CreateRadixTree {
VecView<int> nodeParent_;
VecView<std::pair<int, int>> internalChildren_;
const VecView<const uint32_t> leafMorton_;
int PrefixLength(uint32_t a, uint32_t b) const {
// count-leading-zeros is used to find the number of identical highest-order
// bits
#ifdef _MSC_VER
// return __lzcnt(a ^ b);
return clz(a ^ b);
#else
return __builtin_clz(a ^ b);
#endif
}
int PrefixLength(int i, int j) const {
if (j < 0 || j >= static_cast<int>(leafMorton_.size())) {
return -1;
} else {
int out;
if (leafMorton_[i] == leafMorton_[j])
// use index to disambiguate
out = 32 +
PrefixLength(static_cast<uint32_t>(i), static_cast<uint32_t>(j));
else
out = PrefixLength(leafMorton_[i], leafMorton_[j]);
return out;
}
}
int RangeEnd(int i) const {
// Determine direction of range (+1 or -1)
int dir = PrefixLength(i, i + 1) - PrefixLength(i, i - 1);
dir = (dir > 0) - (dir < 0);
// Compute conservative range length with exponential increase
int commonPrefix = PrefixLength(i, i - dir);
int max_length = kInitialLength;
while (PrefixLength(i, i + dir * max_length) > commonPrefix)
max_length *= kLengthMultiple;
// Compute precise range length with binary search
int length = 0;
for (int step = max_length / 2; step > 0; step /= 2) {
if (PrefixLength(i, i + dir * (length + step)) > commonPrefix)
length += step;
}
return i + dir * length;
}
int FindSplit(int first, int last) const {
int commonPrefix = PrefixLength(first, last);
// Find the furthest object that shares more than commonPrefix bits with the
// first one, using binary search.
int split = first;
int step = last - first;
do {
step = (step + 1) >> 1; // divide by 2, rounding up
int newSplit = split + step;
if (newSplit < last) {
int splitPrefix = PrefixLength(first, newSplit);
if (splitPrefix > commonPrefix) split = newSplit;
}
} while (step > 1);
return split;
}
void operator()(int internal) {
int first = internal;
// Find the range of objects with a common prefix
int last = RangeEnd(first);
if (first > last) std::swap(first, last);
// Determine where the next-highest difference occurs
int split = FindSplit(first, last);
int child1 = split == first ? Leaf2Node(split) : Internal2Node(split);
++split;
int child2 = split == last ? Leaf2Node(split) : Internal2Node(split);
// Record parent_child relationships.
internalChildren_[internal].first = child1;
internalChildren_[internal].second = child2;
int node = Internal2Node(internal);
nodeParent_[child1] = node;
nodeParent_[child2] = node;
}
};
template <typename T, const bool selfCollision, typename Recorder>
struct FindCollision {
VecView<const T> queries;
VecView<const Box> nodeBBox_;
VecView<const std::pair<int, int>> internalChildren_;
Recorder recorder;
inline int RecordCollision(int node, const int queryIdx, SparseIndices& ind) {
bool overlaps = nodeBBox_[node].DoesOverlap(queries[queryIdx]);
if (overlaps && IsLeaf(node)) {
int leafIdx = Node2Leaf(node);
if (!selfCollision || leafIdx != queryIdx) {
recorder.record(queryIdx, leafIdx, ind);
}
}
return overlaps && IsInternal(node); // Should traverse into node
}
void operator()(const int queryIdx) {
// stack cannot overflow because radix tree has max depth 30 (Morton code) +
// 32 (index).
int stack[64];
int top = -1;
// Depth-first search
int node = kRoot;
SparseIndices& ind = recorder.local();
while (1) {
int internal = Node2Internal(node);
int child1 = internalChildren_[internal].first;
int child2 = internalChildren_[internal].second;
int traverse1 = RecordCollision(child1, queryIdx, ind);
int traverse2 = RecordCollision(child2, queryIdx, ind);
if (!traverse1 && !traverse2) {
if (top < 0) break; // done
node = stack[top--]; // get a saved node
} else {
node = traverse1 ? child1 : child2; // go here next
if (traverse1 && traverse2) {
stack[++top] = child2; // save the other for later
}
}
}
}
};
template <const bool inverted>
struct SeqCollisionRecorder {
SparseIndices& queryTri_;
inline void record(int queryIdx, int leafIdx, SparseIndices& ind) const {
if (inverted)
ind.Add(leafIdx, queryIdx);
else
ind.Add(queryIdx, leafIdx);
}
SparseIndices& local() { return queryTri_; }
};
#if (MANIFOLD_PAR == 1)
template <const bool inverted>
struct ParCollisionRecorder {
tbb::combinable<SparseIndices>& store;
inline void record(int queryIdx, int leafIdx, SparseIndices& ind) const {
// Add may invoke something in parallel, and it may return in
// another thread, making thread local unsafe
// we need to explicitly forbid parallelization by passing a flag
if (inverted)
ind.Add(leafIdx, queryIdx, true);
else
ind.Add(queryIdx, leafIdx, true);
}
SparseIndices& local() { return store.local(); }
};
#endif
struct BuildInternalBoxes {
VecView<Box> nodeBBox_;
VecView<int> counter_;
const VecView<int> nodeParent_;
const VecView<std::pair<int, int>> internalChildren_;
void operator()(int leaf) {
int node = Leaf2Node(leaf);
do {
node = nodeParent_[node];
int internal = Node2Internal(node);
if (AtomicAdd(counter_[internal], 1) == 0) return;
nodeBBox_[node] = nodeBBox_[internalChildren_[internal].first].Union(
nodeBBox_[internalChildren_[internal].second]);
} while (node != kRoot);
}
};
struct TransformBox {
const mat3x4 transform;
void operator()(Box& box) { box = box.Transform(transform); }
};
constexpr inline uint32_t SpreadBits3(uint32_t v) {
v = 0xFF0000FFu & (v * 0x00010001u);
v = 0x0F00F00Fu & (v * 0x00000101u);
v = 0xC30C30C3u & (v * 0x00000011u);
v = 0x49249249u & (v * 0x00000005u);
return v;
}
} // namespace collider_internal
/** @ingroup Private */
class Collider {
public:
Collider() {};
Collider(const VecView<const Box>& leafBB,
const VecView<const uint32_t>& leafMorton) {
ZoneScoped;
DEBUG_ASSERT(leafBB.size() == leafMorton.size(), userErr,
"vectors must be the same length");
int num_nodes = 2 * leafBB.size() - 1;
// assign and allocate members
nodeBBox_.resize(num_nodes);
nodeParent_.resize(num_nodes, -1);
internalChildren_.resize(leafBB.size() - 1, std::make_pair(-1, -1));
// organize tree
for_each_n(autoPolicy(NumInternal(), 1e4), countAt(0), NumInternal(),
collider_internal::CreateRadixTree(
{nodeParent_, internalChildren_, leafMorton}));
UpdateBoxes(leafBB);
}
bool Transform(mat3x4 transform) {
ZoneScoped;
bool axisAligned = true;
for (int row : {0, 1, 2}) {
int count = 0;
for (int col : {0, 1, 2}) {
if (transform[col][row] == 0.0) ++count;
}
if (count != 2) axisAligned = false;
}
if (axisAligned) {
for_each(autoPolicy(nodeBBox_.size(), 1e5), nodeBBox_.begin(),
nodeBBox_.end(),
[transform](Box& box) { box = box.Transform(transform); });
}
return axisAligned;
}
void UpdateBoxes(const VecView<const Box>& leafBB) {
ZoneScoped;
DEBUG_ASSERT(leafBB.size() == NumLeaves(), userErr,
"must have the same number of updated boxes as original");
// copy in leaf node Boxes
auto leaves = StridedRange(nodeBBox_.begin(), nodeBBox_.end(), 2);
copy(leafBB.cbegin(), leafBB.cend(), leaves.begin());
// create global counters
Vec<int> counter(NumInternal(), 0);
// kernel over leaves to save internal Boxes
for_each_n(autoPolicy(NumInternal(), 1e3), countAt(0), NumLeaves(),
collider_internal::BuildInternalBoxes(
{nodeBBox_, counter, nodeParent_, internalChildren_}));
}
template <const bool selfCollision = false, const bool inverted = false,
typename T>
void Collisions(const VecView<const T>& queriesIn,
SparseIndices& queryTri) const {
ZoneScoped;
using collider_internal::FindCollision;
#if (MANIFOLD_PAR == 1)
if (queriesIn.size() > collider_internal::kSequentialThreshold) {
tbb::combinable<SparseIndices> store;
for_each_n(
ExecutionPolicy::Par, countAt(0), queriesIn.size(),
FindCollision<T, selfCollision,
collider_internal::ParCollisionRecorder<inverted>>{
queriesIn, nodeBBox_, internalChildren_, {store}});
std::vector<SparseIndices> tmp;
store.combine_each(
[&](SparseIndices& ind) { tmp.emplace_back(std::move(ind)); });
queryTri.FromIndices(tmp);
return;
}
#endif
for_each_n(ExecutionPolicy::Seq, countAt(0), queriesIn.size(),
FindCollision<T, selfCollision,
collider_internal::SeqCollisionRecorder<inverted>>{
queriesIn, nodeBBox_, internalChildren_, {queryTri}});
}
template <const bool selfCollision = false, const bool inverted = false,
typename T>
SparseIndices Collisions(const VecView<const T>& queriesIn) const {
SparseIndices result;
Collisions<selfCollision, inverted, T>(queriesIn, result);
return result;
}
static uint32_t MortonCode(vec3 position, Box bBox) {
using collider_internal::SpreadBits3;
vec3 xyz = (position - bBox.min) / (bBox.max - bBox.min);
xyz = la::min(vec3(1023.0), la::max(vec3(0.0), 1024.0 * xyz));
uint32_t x = SpreadBits3(static_cast<uint32_t>(xyz.x));
uint32_t y = SpreadBits3(static_cast<uint32_t>(xyz.y));
uint32_t z = SpreadBits3(static_cast<uint32_t>(xyz.z));
return x * 4 + y * 2 + z;
}
private:
Vec<Box> nodeBBox_;
Vec<int> nodeParent_;
// even nodes are leaves, odd nodes are internal, root is 1
Vec<std::pair<int, int>> internalChildren_;
size_t NumInternal() const { return internalChildren_.size(); };
size_t NumLeaves() const {
return internalChildren_.empty() ? 0 : (NumInternal() + 1);
};
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./csg_tree.h"
#include "./impl.h"
#include "./parallel.h"
#include "manifold/polygon.h"
namespace manifold {
/**
* Constructs a smooth version of the input mesh by creating tangents; this
* method will throw if you have supplied tangents with your mesh already. The
* actual triangle resolution is unchanged; use the Refine() method to
* interpolate to a higher-resolution curve.
*
* By default, every edge is calculated for maximum smoothness (very much
* approximately), attempting to minimize the maximum mean Curvature magnitude.
* No higher-order derivatives are considered, as the interpolation is
* independent per triangle, only sharing constraints on their boundaries.
*
* @param meshGL input MeshGL.
* @param sharpenedEdges If desired, you can supply a vector of sharpened
* halfedges, which should in general be a small subset of all halfedges. Order
* of entries doesn't matter, as each one specifies the desired smoothness
* (between zero and one, with one the default for all unspecified halfedges)
* and the halfedge index (3 * triangle index + [0,1,2] where 0 is the edge
* between triVert 0 and 1, etc).
*
* At a smoothness value of zero, a sharp crease is made. The smoothness is
* interpolated along each edge, so the specified value should be thought of as
* an average. Where exactly two sharpened edges meet at a vertex, their
* tangents are rotated to be colinear so that the sharpened edge can be
* continuous. Vertices with only one sharpened edge are completely smooth,
* allowing sharpened edges to smoothly vanish at termination. A single vertex
* can be sharpened by sharping all edges that are incident on it, allowing
* cones to be formed.
*/
Manifold Manifold::Smooth(const MeshGL& meshGL,
const std::vector<Smoothness>& sharpenedEdges) {
DEBUG_ASSERT(meshGL.halfedgeTangent.empty(), std::runtime_error,
"when supplying tangents, the normal constructor should be used "
"rather than Smooth().");
std::shared_ptr<Impl> impl = std::make_shared<Impl>(meshGL);
impl->CreateTangents(impl->UpdateSharpenedEdges(sharpenedEdges));
return Manifold(impl);
}
/**
* Constructs a smooth version of the input mesh by creating tangents; this
* method will throw if you have supplied tangents with your mesh already. The
* actual triangle resolution is unchanged; use the Refine() method to
* interpolate to a higher-resolution curve.
*
* By default, every edge is calculated for maximum smoothness (very much
* approximately), attempting to minimize the maximum mean Curvature magnitude.
* No higher-order derivatives are considered, as the interpolation is
* independent per triangle, only sharing constraints on their boundaries.
*
* @param meshGL64 input MeshGL64.
* @param sharpenedEdges If desired, you can supply a vector of sharpened
* halfedges, which should in general be a small subset of all halfedges. Order
* of entries doesn't matter, as each one specifies the desired smoothness
* (between zero and one, with one the default for all unspecified halfedges)
* and the halfedge index (3 * triangle index + [0,1,2] where 0 is the edge
* between triVert 0 and 1, etc).
*
* At a smoothness value of zero, a sharp crease is made. The smoothness is
* interpolated along each edge, so the specified value should be thought of as
* an average. Where exactly two sharpened edges meet at a vertex, their
* tangents are rotated to be colinear so that the sharpened edge can be
* continuous. Vertices with only one sharpened edge are completely smooth,
* allowing sharpened edges to smoothly vanish at termination. A single vertex
* can be sharpened by sharping all edges that are incident on it, allowing
* cones to be formed.
*/
Manifold Manifold::Smooth(const MeshGL64& meshGL64,
const std::vector<Smoothness>& sharpenedEdges) {
DEBUG_ASSERT(meshGL64.halfedgeTangent.empty(), std::runtime_error,
"when supplying tangents, the normal constructor should be used "
"rather than Smooth().");
std::shared_ptr<Impl> impl = std::make_shared<Impl>(meshGL64);
impl->CreateTangents(impl->UpdateSharpenedEdges(sharpenedEdges));
return Manifold(impl);
}
/**
* Constructs a tetrahedron centered at the origin with one vertex at (1,1,1)
* and the rest at similarly symmetric points.
*/
Manifold Manifold::Tetrahedron() {
return Manifold(std::make_shared<Impl>(Impl::Shape::Tetrahedron));
}
/**
* Constructs a unit cube (edge lengths all one), by default in the first
* octant, touching the origin. If any dimensions in size are negative, or if
* all are zero, an empty Manifold will be returned.
*
* @param size The X, Y, and Z dimensions of the box.
* @param center Set to true to shift the center to the origin.
*/
Manifold Manifold::Cube(vec3 size, bool center) {
if (size.x < 0.0 || size.y < 0.0 || size.z < 0.0 || la::length(size) == 0.) {
return Invalid();
}
mat3x4 m({{size.x, 0.0, 0.0}, {0.0, size.y, 0.0}, {0.0, 0.0, size.z}},
center ? (-size / 2.0) : vec3(0.0));
return Manifold(std::make_shared<Impl>(Manifold::Impl::Shape::Cube, m));
}
/**
* A convenience constructor for the common case of extruding a circle. Can also
* form cones if both radii are specified.
*
* @param height Z-extent
* @param radiusLow Radius of bottom circle. Must be positive.
* @param radiusHigh Radius of top circle. Can equal zero. Default is equal to
* radiusLow.
* @param circularSegments How many line segments to use around the circle.
* Default is calculated by the static Defaults.
* @param center Set to true to shift the center to the origin. Default is
* origin at the bottom.
*/
Manifold Manifold::Cylinder(double height, double radiusLow, double radiusHigh,
int circularSegments, bool center) {
if (height <= 0.0 || radiusLow <= 0.0) {
return Invalid();
}
const double scale = radiusHigh >= 0.0 ? radiusHigh / radiusLow : 1.0;
const double radius = fmax(radiusLow, radiusHigh);
const int n = circularSegments > 2 ? circularSegments
: Quality::GetCircularSegments(radius);
SimplePolygon circle(n);
const double dPhi = 360.0 / n;
for (int i = 0; i < n; ++i) {
circle[i] = {radiusLow * cosd(dPhi * i), radiusLow * sind(dPhi * i)};
}
Manifold cylinder = Manifold::Extrude({circle}, height, 0, 0.0, vec2(scale));
if (center)
cylinder = cylinder.Translate(vec3(0.0, 0.0, -height / 2.0)).AsOriginal();
return cylinder;
}
/**
* Constructs a geodesic sphere of a given radius.
*
* @param radius Radius of the sphere. Must be positive.
* @param circularSegments Number of segments along its
* diameter. This number will always be rounded up to the nearest factor of
* four, as this sphere is constructed by refining an octahedron. This means
* there are a circle of vertices on all three of the axis planes. Default is
* calculated by the static Defaults.
*/
Manifold Manifold::Sphere(double radius, int circularSegments) {
if (radius <= 0.0) {
return Invalid();
}
int n = circularSegments > 0 ? (circularSegments + 3) / 4
: Quality::GetCircularSegments(radius) / 4;
auto pImpl_ = std::make_shared<Impl>(Impl::Shape::Octahedron);
pImpl_->Subdivide(
[n](vec3 edge, vec4 tangentStart, vec4 tangentEnd) { return n - 1; });
for_each_n(autoPolicy(pImpl_->NumVert(), 1e5), pImpl_->vertPos_.begin(),
pImpl_->NumVert(), [radius](vec3& v) {
v = la::cos(kHalfPi * (1.0 - v));
v = radius * la::normalize(v);
if (std::isnan(v.x)) v = vec3(0.0);
});
pImpl_->Finish();
// Ignore preceding octahedron.
pImpl_->InitializeOriginal();
return Manifold(pImpl_);
}
/**
* Constructs a manifold from a set of polygons by extruding them along the
* Z-axis.
* Note that high twistDegrees with small nDivisions may cause
* self-intersection. This is not checked here and it is up to the user to
* choose the correct parameters.
*
* @param crossSection A set of non-overlapping polygons to extrude.
* @param height Z-extent of extrusion.
* @param nDivisions Number of extra copies of the crossSection to insert into
* the shape vertically; especially useful in combination with twistDegrees to
* avoid interpolation artifacts. Default is none.
* @param twistDegrees Amount to twist the top crossSection relative to the
* bottom, interpolated linearly for the divisions in between.
* @param scaleTop Amount to scale the top (independently in X and Y). If the
* scale is {0, 0}, a pure cone is formed with only a single vertex at the top.
* Note that scale is applied after twist.
* Default {1, 1}.
*/
Manifold Manifold::Extrude(const Polygons& crossSection, double height,
int nDivisions, double twistDegrees, vec2 scaleTop) {
ZoneScoped;
if (crossSection.size() == 0 || height <= 0.0) {
return Invalid();
}
scaleTop.x = std::max(scaleTop.x, 0.0);
scaleTop.y = std::max(scaleTop.y, 0.0);
auto pImpl_ = std::make_shared<Impl>();
++nDivisions;
auto& vertPos = pImpl_->vertPos_;
Vec<ivec3> triVertsDH;
auto& triVerts = triVertsDH;
int nCrossSection = 0;
bool isCone = scaleTop.x == 0.0 && scaleTop.y == 0.0;
size_t idx = 0;
PolygonsIdx polygonsIndexed;
for (auto& poly : crossSection) {
nCrossSection += poly.size();
SimplePolygonIdx simpleIndexed;
for (const vec2& polyVert : poly) {
vertPos.push_back({polyVert.x, polyVert.y, 0.0});
simpleIndexed.push_back({polyVert, static_cast<int>(idx++)});
}
polygonsIndexed.push_back(simpleIndexed);
}
for (int i = 1; i < nDivisions + 1; ++i) {
double alpha = i / double(nDivisions);
double phi = alpha * twistDegrees;
vec2 scale = la::lerp(vec2(1.0), scaleTop, alpha);
mat2 rotation({cosd(phi), sind(phi)}, {-sind(phi), cosd(phi)});
mat2 transform = mat2({scale.x, 0.0}, {0.0, scale.y}) * rotation;
size_t j = 0;
size_t idx = 0;
for (const auto& poly : crossSection) {
for (size_t vert = 0; vert < poly.size(); ++vert) {
size_t offset = idx + nCrossSection * i;
size_t thisVert = vert + offset;
size_t lastVert = (vert == 0 ? poly.size() : vert) - 1 + offset;
if (i == nDivisions && isCone) {
triVerts.push_back(ivec3(nCrossSection * i + j,
lastVert - nCrossSection,
thisVert - nCrossSection));
} else {
vec2 pos = transform * poly[vert];
vertPos.push_back({pos.x, pos.y, height * alpha});
triVerts.push_back(
ivec3(thisVert, lastVert, thisVert - nCrossSection));
triVerts.push_back(ivec3(lastVert, lastVert - nCrossSection,
thisVert - nCrossSection));
}
}
++j;
idx += poly.size();
}
}
if (isCone)
for (size_t j = 0; j < crossSection.size();
++j) // Duplicate vertex for Genus
vertPos.push_back({0.0, 0.0, height});
std::vector<ivec3> top = TriangulateIdx(polygonsIndexed);
for (const ivec3& tri : top) {
triVerts.push_back({tri[0], tri[2], tri[1]});
if (!isCone) triVerts.push_back(tri + nCrossSection * nDivisions);
}
pImpl_->CreateHalfedges(triVertsDH);
pImpl_->Finish();
pImpl_->InitializeOriginal();
pImpl_->CreateFaces();
return Manifold(pImpl_);
}
/**
* Constructs a manifold from a set of polygons by revolving this cross-section
* around its Y-axis and then setting this as the Z-axis of the resulting
* manifold. If the polygons cross the Y-axis, only the part on the positive X
* side is used. Geometrically valid input will result in geometrically valid
* output.
*
* @param crossSection A set of non-overlapping polygons to revolve.
* @param circularSegments Number of segments along its diameter. Default is
* calculated by the static Defaults.
* @param revolveDegrees Number of degrees to revolve. Default is 360 degrees.
*/
Manifold Manifold::Revolve(const Polygons& crossSection, int circularSegments,
double revolveDegrees) {
ZoneScoped;
Polygons polygons;
double radius = 0;
for (const SimplePolygon& poly : crossSection) {
size_t i = 0;
while (i < poly.size() && poly[i].x < 0) {
++i;
}
if (i == poly.size()) {
continue;
}
polygons.push_back({});
const size_t start = i;
do {
if (poly[i].x >= 0) {
polygons.back().push_back(poly[i]);
radius = std::max(radius, poly[i].x);
}
const size_t next = i + 1 == poly.size() ? 0 : i + 1;
if ((poly[next].x < 0) != (poly[i].x < 0)) {
const double y = poly[next].y + poly[next].x *
(poly[i].y - poly[next].y) /
(poly[i].x - poly[next].x);
polygons.back().push_back({0, y});
}
i = next;
} while (i != start);
}
if (polygons.empty()) {
return Invalid();
}
if (revolveDegrees > 360.0) {
revolveDegrees = 360.0;
}
const bool isFullRevolution = revolveDegrees == 360.0;
const int nDivisions =
circularSegments > 2
? circularSegments
: Quality::GetCircularSegments(radius) * revolveDegrees / 360;
auto pImpl_ = std::make_shared<Impl>();
auto& vertPos = pImpl_->vertPos_;
Vec<ivec3> triVertsDH;
auto& triVerts = triVertsDH;
std::vector<int> startPoses;
std::vector<int> endPoses;
const double dPhi = revolveDegrees / nDivisions;
// first and last slice are distinguished if not a full revolution.
const int nSlices = isFullRevolution ? nDivisions : nDivisions + 1;
for (const auto& poly : polygons) {
std::size_t nPosVerts = 0;
std::size_t nRevolveAxisVerts = 0;
for (auto& pt : poly) {
if (pt.x > 0) {
nPosVerts++;
} else {
nRevolveAxisVerts++;
}
}
for (size_t polyVert = 0; polyVert < poly.size(); ++polyVert) {
const size_t startPosIndex = vertPos.size();
if (!isFullRevolution) startPoses.push_back(startPosIndex);
const vec2 currPolyVertex = poly[polyVert];
const vec2 prevPolyVertex =
poly[polyVert == 0 ? poly.size() - 1 : polyVert - 1];
const int prevStartPosIndex =
startPosIndex +
(polyVert == 0 ? nRevolveAxisVerts + (nSlices * nPosVerts) : 0) +
(prevPolyVertex.x == 0.0 ? -1 : -nSlices);
for (int slice = 0; slice < nSlices; ++slice) {
const double phi = slice * dPhi;
if (slice == 0 || currPolyVertex.x > 0) {
vertPos.push_back({currPolyVertex.x * cosd(phi),
currPolyVertex.x * sind(phi), currPolyVertex.y});
}
if (isFullRevolution || slice > 0) {
const int lastSlice = (slice == 0 ? nDivisions : slice) - 1;
if (currPolyVertex.x > 0.0) {
triVerts.push_back(ivec3(
startPosIndex + slice, startPosIndex + lastSlice,
// "Reuse" vertex of first slice if it lies on the revolve axis
(prevPolyVertex.x == 0.0 ? prevStartPosIndex
: prevStartPosIndex + lastSlice)));
}
if (prevPolyVertex.x > 0.0) {
triVerts.push_back(
ivec3(prevStartPosIndex + lastSlice, prevStartPosIndex + slice,
(currPolyVertex.x == 0.0 ? startPosIndex
: startPosIndex + slice)));
}
}
}
if (!isFullRevolution) endPoses.push_back(vertPos.size() - 1);
}
}
// Add front and back triangles if not a full revolution.
if (!isFullRevolution) {
std::vector<ivec3> frontTriangles = Triangulate(polygons, pImpl_->epsilon_);
for (auto& t : frontTriangles) {
triVerts.push_back({startPoses[t.x], startPoses[t.y], startPoses[t.z]});
}
for (auto& t : frontTriangles) {
triVerts.push_back({endPoses[t.z], endPoses[t.y], endPoses[t.x]});
}
}
pImpl_->CreateHalfedges(triVertsDH);
pImpl_->Finish();
pImpl_->InitializeOriginal();
pImpl_->CreateFaces();
return Manifold(pImpl_);
}
/**
* Constructs a new manifold from a vector of other manifolds. This is a purely
* topological operation, so care should be taken to avoid creating
* overlapping results. It is the inverse operation of Decompose().
*
* @param manifolds A vector of Manifolds to lazy-union together.
*/
Manifold Manifold::Compose(const std::vector<Manifold>& manifolds) {
std::vector<std::shared_ptr<CsgLeafNode>> children;
for (const auto& manifold : manifolds) {
children.push_back(manifold.pNode_->ToLeafNode());
}
return Manifold(std::make_shared<Impl>(CsgLeafNode::Compose(children)));
}
/**
* This operation returns a vector of Manifolds that are topologically
* disconnected. If everything is connected, the vector is length one,
* containing a copy of the original. It is the inverse operation of Compose().
*/
std::vector<Manifold> Manifold::Decompose() const {
ZoneScoped;
UnionFind<> uf(NumVert());
// Graph graph;
auto pImpl_ = GetCsgLeafNode().GetImpl();
for (const Halfedge& halfedge : pImpl_->halfedge_) {
if (halfedge.IsForward()) uf.unionXY(halfedge.startVert, halfedge.endVert);
}
std::vector<int> componentIndices;
const int numComponents = uf.connectedComponents(componentIndices);
if (numComponents == 1) {
std::vector<Manifold> meshes(1);
meshes[0] = *this;
return meshes;
}
Vec<int> vertLabel(componentIndices);
const int numVert = NumVert();
std::vector<Manifold> meshes;
for (int i = 0; i < numComponents; ++i) {
auto impl = std::make_shared<Impl>();
// inherit original object's precision
impl->epsilon_ = pImpl_->epsilon_;
impl->tolerance_ = pImpl_->tolerance_;
Vec<int> vertNew2Old(numVert);
const int nVert =
copy_if(countAt(0), countAt(numVert), vertNew2Old.begin(),
[i, &vertLabel](int v) { return vertLabel[v] == i; }) -
vertNew2Old.begin();
impl->vertPos_.resize(nVert);
vertNew2Old.resize(nVert);
gather(vertNew2Old.begin(), vertNew2Old.end(), pImpl_->vertPos_.begin(),
impl->vertPos_.begin());
Vec<int> faceNew2Old(NumTri());
const auto& halfedge = pImpl_->halfedge_;
const int nFace =
copy_if(countAt(0_uz), countAt(NumTri()), faceNew2Old.begin(),
[i, &vertLabel, &halfedge](int face) {
return vertLabel[halfedge[3 * face].startVert] == i;
}) -
faceNew2Old.begin();
if (nFace == 0) continue;
faceNew2Old.resize(nFace);
impl->GatherFaces(*pImpl_, faceNew2Old);
impl->ReindexVerts(vertNew2Old, pImpl_->NumVert());
impl->Finish();
meshes.push_back(Manifold(impl));
}
return meshes;
}
} // namespace manifold

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// Copyright 2023 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "manifold/cross_section.h"
#include "../utils.h"
#include "clipper2/clipper.core.h"
#include "clipper2/clipper.h"
#include "clipper2/clipper.offset.h"
namespace C2 = Clipper2Lib;
using namespace manifold;
namespace manifold {
struct PathImpl {
PathImpl(const C2::PathsD paths_) : paths_(paths_) {}
operator const C2::PathsD&() const { return paths_; }
const C2::PathsD paths_;
};
} // namespace manifold
namespace {
const int precision_ = 8;
C2::ClipType cliptype_of_op(OpType op) {
C2::ClipType ct = C2::ClipType::Union;
switch (op) {
case OpType::Add:
break;
case OpType::Subtract:
ct = C2::ClipType::Difference;
break;
case OpType::Intersect:
ct = C2::ClipType::Intersection;
break;
};
return ct;
}
C2::FillRule fr(CrossSection::FillRule fillrule) {
C2::FillRule fr = C2::FillRule::EvenOdd;
switch (fillrule) {
case CrossSection::FillRule::EvenOdd:
break;
case CrossSection::FillRule::NonZero:
fr = C2::FillRule::NonZero;
break;
case CrossSection::FillRule::Positive:
fr = C2::FillRule::Positive;
break;
case CrossSection::FillRule::Negative:
fr = C2::FillRule::Negative;
break;
};
return fr;
}
C2::JoinType jt(CrossSection::JoinType jointype) {
C2::JoinType jt = C2::JoinType::Square;
switch (jointype) {
case CrossSection::JoinType::Square:
break;
case CrossSection::JoinType::Round:
jt = C2::JoinType::Round;
break;
case CrossSection::JoinType::Miter:
jt = C2::JoinType::Miter;
break;
};
return jt;
}
vec2 v2_of_pd(const C2::PointD p) { return {p.x, p.y}; }
C2::PointD v2_to_pd(const vec2 v) { return C2::PointD(v.x, v.y); }
C2::PathD pathd_of_contour(const SimplePolygon& ctr) {
auto p = C2::PathD();
p.reserve(ctr.size());
for (auto v : ctr) {
p.push_back(v2_to_pd(v));
}
return p;
}
C2::PathsD transform(const C2::PathsD ps, const mat2x3 m) {
const bool invert = la::determinant(mat2(m)) < 0;
auto transformed = C2::PathsD();
transformed.reserve(ps.size());
for (auto path : ps) {
auto sz = path.size();
auto s = C2::PathD(sz);
for (size_t i = 0; i < sz; ++i) {
auto idx = invert ? sz - 1 - i : i;
s[idx] = v2_to_pd(m * vec3(path[i].x, path[i].y, 1));
}
transformed.push_back(s);
}
return transformed;
}
std::shared_ptr<const PathImpl> shared_paths(const C2::PathsD& ps) {
return std::make_shared<const PathImpl>(ps);
}
// forward declaration for mutual recursion
void decompose_hole(const C2::PolyTreeD* outline,
std::vector<C2::PathsD>& polys, C2::PathsD& poly,
size_t n_holes, size_t j);
void decompose_outline(const C2::PolyTreeD* tree,
std::vector<C2::PathsD>& polys, size_t i) {
auto n_outlines = tree->Count();
if (i < n_outlines) {
auto outline = tree->Child(i);
auto n_holes = outline->Count();
auto poly = C2::PathsD(n_holes + 1);
poly[0] = outline->Polygon();
decompose_hole(outline, polys, poly, n_holes, 0);
polys.push_back(poly);
if (i < n_outlines - 1) {
decompose_outline(tree, polys, i + 1);
}
}
}
void decompose_hole(const C2::PolyTreeD* outline,
std::vector<C2::PathsD>& polys, C2::PathsD& poly,
size_t n_holes, size_t j) {
if (j < n_holes) {
auto child = outline->Child(j);
decompose_outline(child, polys, 0);
poly[j + 1] = child->Polygon();
decompose_hole(outline, polys, poly, n_holes, j + 1);
}
}
void flatten(const C2::PolyTreeD* tree, C2::PathsD& polys, size_t i) {
auto n_outlines = tree->Count();
if (i < n_outlines) {
auto outline = tree->Child(i);
flatten(outline, polys, 0);
polys.push_back(outline->Polygon());
if (i < n_outlines - 1) {
flatten(tree, polys, i + 1);
}
}
}
bool V2Lesser(vec2 a, vec2 b) {
if (a.x == b.x) return a.y < b.y;
return a.x < b.x;
}
void HullBacktrack(const vec2& pt, std::vector<vec2>& stack) {
auto sz = stack.size();
while (sz >= 2 && CCW(stack[sz - 2], stack[sz - 1], pt, 0.0) <= 0.0) {
stack.pop_back();
sz = stack.size();
}
}
// Based on method described here:
// https://www.hackerearth.com/practice/math/geometry/line-sweep-technique/tutorial/
// Changed to follow:
// https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
// This is the same algorithm (Andrew, also called Montone Chain).
C2::PathD HullImpl(SimplePolygon& pts) {
size_t len = pts.size();
if (len < 3) return C2::PathD(); // not enough points to create a polygon
std::sort(pts.begin(), pts.end(), V2Lesser);
auto lower = std::vector<vec2>{};
for (auto& pt : pts) {
HullBacktrack(pt, lower);
lower.push_back(pt);
}
auto upper = std::vector<vec2>{};
for (auto pt_iter = pts.rbegin(); pt_iter != pts.rend(); pt_iter++) {
HullBacktrack(*pt_iter, upper);
upper.push_back(*pt_iter);
}
upper.pop_back();
lower.pop_back();
auto path = C2::PathD();
path.reserve(lower.size() + upper.size());
for (const auto& l : lower) path.push_back(v2_to_pd(l));
for (const auto& u : upper) path.push_back(v2_to_pd(u));
return path;
}
} // namespace
namespace manifold {
/**
* The default constructor is an empty cross-section (containing no contours).
*/
CrossSection::CrossSection() {
paths_ = std::make_shared<const PathImpl>(C2::PathsD());
}
CrossSection::~CrossSection() = default;
CrossSection::CrossSection(CrossSection&&) noexcept = default;
CrossSection& CrossSection::operator=(CrossSection&&) noexcept = default;
/**
* The copy constructor avoids copying the underlying paths vector (sharing
* with its parent via shared_ptr), however subsequent transformations, and
* their application will not be shared. It is generally recommended to avoid
* this, opting instead to simply create CrossSections with the available
* const methods.
*/
CrossSection::CrossSection(const CrossSection& other) {
paths_ = other.paths_;
transform_ = other.transform_;
}
CrossSection& CrossSection::operator=(const CrossSection& other) {
if (this != &other) {
paths_ = other.paths_;
transform_ = other.transform_;
}
return *this;
};
// Private, skips unioning.
CrossSection::CrossSection(std::shared_ptr<const PathImpl> ps) { paths_ = ps; }
/**
* Create a 2d cross-section from a single contour. A boolean union operation
* (with Positive filling rule by default) is performed to ensure the
* resulting CrossSection is free of self-intersections.
*
* @param contour A closed path outlining the desired cross-section.
* @param fillrule The filling rule used to interpret polygon sub-regions
* created by self-intersections in contour.
*/
CrossSection::CrossSection(const SimplePolygon& contour, FillRule fillrule) {
auto ps = C2::PathsD{(pathd_of_contour(contour))};
paths_ = shared_paths(C2::Union(ps, fr(fillrule), precision_));
}
/**
* Create a 2d cross-section from a set of contours (complex polygons). A
* boolean union operation (with Positive filling rule by default) is
* performed to combine overlapping polygons and ensure the resulting
* CrossSection is free of intersections.
*
* @param contours A set of closed paths describing zero or more complex
* polygons.
* @param fillrule The filling rule used to interpret polygon sub-regions in
* contours.
*/
CrossSection::CrossSection(const Polygons& contours, FillRule fillrule) {
auto ps = C2::PathsD();
ps.reserve(contours.size());
for (auto ctr : contours) {
ps.push_back(pathd_of_contour(ctr));
}
paths_ = shared_paths(C2::Union(ps, fr(fillrule), precision_));
}
/**
* Create a 2d cross-section from an axis-aligned rectangle (bounding box).
*
* @param rect An axis-aligned rectangular bounding box.
*/
CrossSection::CrossSection(const Rect& rect) {
C2::PathD p(4);
p[0] = C2::PointD(rect.min.x, rect.min.y);
p[1] = C2::PointD(rect.max.x, rect.min.y);
p[2] = C2::PointD(rect.max.x, rect.max.y);
p[3] = C2::PointD(rect.min.x, rect.max.y);
paths_ = shared_paths(C2::PathsD{p});
}
// Private
// All access to paths_ should be done through the GetPaths() method, which
// applies the accumulated transform_
std::shared_ptr<const PathImpl> CrossSection::GetPaths() const {
if (transform_ == mat2x3(la::identity)) {
return paths_;
}
paths_ = shared_paths(::transform(paths_->paths_, transform_));
transform_ = mat2x3(la::identity);
return paths_;
}
/**
* Constructs a square with the given XY dimensions. By default it is
* positioned in the first quadrant, touching the origin. If any dimensions in
* size are negative, or if all are zero, an empty Manifold will be returned.
*
* @param size The X, and Y dimensions of the square.
* @param center Set to true to shift the center to the origin.
*/
CrossSection CrossSection::Square(const vec2 size, bool center) {
if (size.x < 0.0 || size.y < 0.0 || la::length(size) == 0.0) {
return CrossSection();
}
auto p = C2::PathD(4);
if (center) {
const auto w = size.x / 2;
const auto h = size.y / 2;
p[0] = C2::PointD(w, h);
p[1] = C2::PointD(-w, h);
p[2] = C2::PointD(-w, -h);
p[3] = C2::PointD(w, -h);
} else {
const double x = size.x;
const double y = size.y;
p[0] = C2::PointD(0.0, 0.0);
p[1] = C2::PointD(x, 0.0);
p[2] = C2::PointD(x, y);
p[3] = C2::PointD(0.0, y);
}
return CrossSection(shared_paths(C2::PathsD{p}));
}
/**
* Constructs a circle of a given radius.
*
* @param radius Radius of the circle. Must be positive.
* @param circularSegments Number of segments along its diameter. Default is
* calculated by the static Quality defaults according to the radius.
*/
CrossSection CrossSection::Circle(double radius, int circularSegments) {
if (radius <= 0.0) {
return CrossSection();
}
int n = circularSegments > 2 ? circularSegments
: Quality::GetCircularSegments(radius);
double dPhi = 360.0 / n;
auto circle = C2::PathD(n);
for (int i = 0; i < n; ++i) {
circle[i] = C2::PointD(radius * cosd(dPhi * i), radius * sind(dPhi * i));
}
return CrossSection(shared_paths(C2::PathsD{circle}));
}
/**
* Perform the given boolean operation between this and another CrossSection.
*/
CrossSection CrossSection::Boolean(const CrossSection& second,
OpType op) const {
auto ct = cliptype_of_op(op);
auto res = C2::BooleanOp(ct, C2::FillRule::Positive, GetPaths()->paths_,
second.GetPaths()->paths_, precision_);
return CrossSection(shared_paths(res));
}
/**
* Perform the given boolean operation on a list of CrossSections. In case of
* Subtract, all CrossSections in the tail are differenced from the head.
*/
CrossSection CrossSection::BatchBoolean(
const std::vector<CrossSection>& crossSections, OpType op) {
if (crossSections.size() == 0)
return CrossSection();
else if (crossSections.size() == 1)
return crossSections[0];
auto subjs = crossSections[0].GetPaths();
int n_clips = 0;
for (size_t i = 1; i < crossSections.size(); ++i) {
n_clips += crossSections[i].GetPaths()->paths_.size();
}
auto clips = C2::PathsD();
clips.reserve(n_clips);
for (size_t i = 1; i < crossSections.size(); ++i) {
auto ps = crossSections[i].GetPaths();
clips.insert(clips.end(), ps->paths_.begin(), ps->paths_.end());
}
auto ct = cliptype_of_op(op);
auto res = C2::BooleanOp(ct, C2::FillRule::Positive, subjs->paths_, clips,
precision_);
return CrossSection(shared_paths(res));
}
/**
* Compute the boolean union between two cross-sections.
*/
CrossSection CrossSection::operator+(const CrossSection& Q) const {
return Boolean(Q, OpType::Add);
}
/**
* Compute the boolean union between two cross-sections, assigning the result
* to the first.
*/
CrossSection& CrossSection::operator+=(const CrossSection& Q) {
*this = *this + Q;
return *this;
}
/**
* Compute the boolean difference of a (clip) cross-section from another
* (subject).
*/
CrossSection CrossSection::operator-(const CrossSection& Q) const {
return Boolean(Q, OpType::Subtract);
}
/**
* Compute the boolean difference of a (clip) cross-section from a another
* (subject), assigning the result to the subject.
*/
CrossSection& CrossSection::operator-=(const CrossSection& Q) {
*this = *this - Q;
return *this;
}
/**
* Compute the boolean intersection between two cross-sections.
*/
CrossSection CrossSection::operator^(const CrossSection& Q) const {
return Boolean(Q, OpType::Intersect);
}
/**
* Compute the boolean intersection between two cross-sections, assigning the
* result to the first.
*/
CrossSection& CrossSection::operator^=(const CrossSection& Q) {
*this = *this ^ Q;
return *this;
}
/**
* Construct a CrossSection from a vector of other CrossSections (batch
* boolean union).
*/
CrossSection CrossSection::Compose(std::vector<CrossSection>& crossSections) {
return BatchBoolean(crossSections, OpType::Add);
}
/**
* This operation returns a vector of CrossSections that are topologically
* disconnected, each containing one outline contour with zero or more
* holes.
*/
std::vector<CrossSection> CrossSection::Decompose() const {
if (NumContour() < 2) {
return std::vector<CrossSection>{CrossSection(*this)};
}
C2::PolyTreeD tree;
C2::BooleanOp(C2::ClipType::Union, C2::FillRule::Positive, GetPaths()->paths_,
C2::PathsD(), tree, precision_);
auto polys = std::vector<C2::PathsD>();
decompose_outline(&tree, polys, 0);
auto comps = std::vector<CrossSection>();
comps.reserve(polys.size());
// reverse the stack while wrapping
for (auto poly = polys.rbegin(); poly != polys.rend(); ++poly)
comps.emplace_back(CrossSection(shared_paths(*poly)));
return comps;
}
/**
* Move this CrossSection in space. This operation can be chained. Transforms
* are combined and applied lazily.
*
* @param v The vector to add to every vertex.
*/
CrossSection CrossSection::Translate(const vec2 v) const {
mat2x3 m({1.0, 0.0}, //
{0.0, 1.0}, //
{v.x, v.y});
return Transform(m);
}
/**
* Applies a (Z-axis) rotation to the CrossSection, in degrees. This operation
* can be chained. Transforms are combined and applied lazily.
*
* @param degrees degrees about the Z-axis to rotate.
*/
CrossSection CrossSection::Rotate(double degrees) const {
auto s = sind(degrees);
auto c = cosd(degrees);
mat2x3 m({c, s}, //
{-s, c}, //
{0.0, 0.0});
return Transform(m);
}
/**
* Scale this CrossSection in space. This operation can be chained. Transforms
* are combined and applied lazily.
*
* @param scale The vector to multiply every vertex by per component.
*/
CrossSection CrossSection::Scale(const vec2 scale) const {
mat2x3 m({scale.x, 0.0}, //
{0.0, scale.y}, //
{0.0, 0.0});
return Transform(m);
}
/**
* Mirror this CrossSection over the arbitrary axis described by the unit form
* of the given vector. If the length of the vector is zero, an empty
* CrossSection is returned. This operation can be chained. Transforms are
* combined and applied lazily.
*
* @param ax the axis to be mirrored over
*/
CrossSection CrossSection::Mirror(const vec2 ax) const {
if (la::length(ax) == 0.) {
return CrossSection();
}
auto n = la::normalize(la::abs(ax));
auto m = mat2x3(mat2(la::identity) - 2.0 * la::outerprod(n, n), vec2(0.0));
return Transform(m);
}
/**
* Transform this CrossSection in space. The first two columns form a 2x2
* matrix transform and the last is a translation vector. This operation can
* be chained. Transforms are combined and applied lazily.
*
* @param m The affine transform matrix to apply to all the vertices.
*/
CrossSection CrossSection::Transform(const mat2x3& m) const {
auto transformed = CrossSection();
transformed.transform_ = m * Mat3(transform_);
transformed.paths_ = paths_;
return transformed;
}
/**
* Move the vertices of this CrossSection (creating a new one) according to
* any arbitrary input function, followed by a union operation (with a
* Positive fill rule) that ensures any introduced intersections are not
* included in the result.
*
* @param warpFunc A function that modifies a given vertex position.
*/
CrossSection CrossSection::Warp(std::function<void(vec2&)> warpFunc) const {
return WarpBatch([&warpFunc](VecView<vec2> vecs) {
for (vec2& p : vecs) {
warpFunc(p);
}
});
}
/**
* Same as CrossSection::Warp but calls warpFunc with
* a VecView which is roughly equivalent to std::span
* pointing to all vec2 elements to be modified in-place
*
* @param warpFunc A function that modifies multiple vertex positions.
*/
CrossSection CrossSection::WarpBatch(
std::function<void(VecView<vec2>)> warpFunc) const {
std::vector<vec2> tmp_verts;
C2::PathsD paths = GetPaths()->paths_; // deep copy
for (C2::PathD const& path : paths) {
for (C2::PointD const& p : path) {
tmp_verts.push_back(v2_of_pd(p));
}
}
warpFunc(VecView<vec2>(tmp_verts.data(), tmp_verts.size()));
auto cursor = tmp_verts.begin();
for (C2::PathD& path : paths) {
for (C2::PointD& p : path) {
p = v2_to_pd(*cursor);
++cursor;
}
}
return CrossSection(
shared_paths(C2::Union(paths, C2::FillRule::Positive, precision_)));
}
/**
* Remove vertices from the contours in this CrossSection that are less than
* the specified distance epsilon from an imaginary line that passes through
* its two adjacent vertices. Near duplicate vertices and collinear points
* will be removed at lower epsilons, with elimination of line segments
* becoming increasingly aggressive with larger epsilons.
*
* It is recommended to apply this function following Offset, in order to
* clean up any spurious tiny line segments introduced that do not improve
* quality in any meaningful way. This is particularly important if further
* offseting operations are to be performed, which would compound the issue.
*/
CrossSection CrossSection::Simplify(double epsilon) const {
C2::PolyTreeD tree;
C2::BooleanOp(C2::ClipType::Union, C2::FillRule::Positive, GetPaths()->paths_,
C2::PathsD(), tree, precision_);
C2::PathsD polys;
flatten(&tree, polys, 0);
// Filter out contours less than epsilon wide.
C2::PathsD filtered;
for (C2::PathD poly : polys) {
auto area = C2::Area(poly);
Rect box;
for (auto vert : poly) {
box.Union(vec2(vert.x, vert.y));
}
vec2 size = box.Size();
if (std::abs(area) > std::max(size.x, size.y) * epsilon) {
filtered.push_back(poly);
}
}
auto ps = SimplifyPaths(filtered, epsilon, true);
return CrossSection(shared_paths(ps));
}
/**
* Inflate the contours in CrossSection by the specified delta, handling
* corners according to the given JoinType.
*
* @param delta Positive deltas will cause the expansion of outlining contours
* to expand, and retraction of inner (hole) contours. Negative deltas will
* have the opposite effect.
* @param jointype The join type specifying the treatment of contour joins
* (corners).
* @param miter_limit The maximum distance in multiples of delta that vertices
* can be offset from their original positions with before squaring is
* applied, <B>when the join type is Miter</B> (default is 2, which is the
* minimum allowed). See the [Clipper2
* MiterLimit](http://www.angusj.com/clipper2/Docs/Units/Clipper.Offset/Classes/ClipperOffset/Properties/MiterLimit.htm)
* page for a visual example.
* @param circularSegments Number of segments per 360 degrees of
* <B>JoinType::Round</B> corners (roughly, the number of vertices that
* will be added to each contour). Default is calculated by the static Quality
* defaults according to the radius.
*/
CrossSection CrossSection::Offset(double delta, JoinType jointype,
double miter_limit,
int circularSegments) const {
double arc_tol = 0.;
if (jointype == JoinType::Round) {
int n = circularSegments > 2 ? circularSegments
: Quality::GetCircularSegments(delta);
// This calculates tolerance as a function of circular segments and delta
// (radius) in order to get back the same number of segments in Clipper2:
// steps_per_360 = PI / acos(1 - arc_tol / abs_delta)
const double abs_delta = std::fabs(delta);
const double scaled_delta = abs_delta * std::pow(10, precision_);
arc_tol = (std::cos(Clipper2Lib::PI / n) - 1) * -scaled_delta;
}
auto ps =
C2::InflatePaths(GetPaths()->paths_, delta, jt(jointype),
C2::EndType::Polygon, miter_limit, precision_, arc_tol);
return CrossSection(shared_paths(ps));
}
/**
* Compute the convex hull enveloping a set of cross-sections.
*
* @param crossSections A vector of cross-sections over which to compute a
* convex hull.
*/
CrossSection CrossSection::Hull(
const std::vector<CrossSection>& crossSections) {
int n = 0;
for (auto cs : crossSections) n += cs.NumVert();
SimplePolygon pts;
pts.reserve(n);
for (auto cs : crossSections) {
auto paths = cs.GetPaths()->paths_;
for (auto path : paths) {
for (auto p : path) {
pts.push_back(v2_of_pd(p));
}
}
}
return CrossSection(shared_paths(C2::PathsD{HullImpl(pts)}));
}
/**
* Compute the convex hull of this cross-section.
*/
CrossSection CrossSection::Hull() const {
return Hull(std::vector<CrossSection>{*this});
}
/**
* Compute the convex hull of a set of points. If the given points are fewer
* than 3, an empty CrossSection will be returned.
*
* @param pts A vector of 2-dimensional points over which to compute a convex
* hull.
*/
CrossSection CrossSection::Hull(SimplePolygon pts) {
return CrossSection(shared_paths(C2::PathsD{HullImpl(pts)}));
}
/**
* Compute the convex hull of a set of points/polygons. If the given points are
* fewer than 3, an empty CrossSection will be returned.
*
* @param polys A vector of vectors of 2-dimensional points over which to
* compute a convex hull.
*/
CrossSection CrossSection::Hull(const Polygons polys) {
SimplePolygon pts;
for (auto poly : polys) {
for (auto p : poly) {
pts.push_back(p);
}
}
return Hull(pts);
}
/**
* Return the total area covered by complex polygons making up the
* CrossSection.
*/
double CrossSection::Area() const { return C2::Area(GetPaths()->paths_); }
/**
* Return the number of vertices in the CrossSection.
*/
int CrossSection::NumVert() const {
int n = 0;
auto paths = GetPaths()->paths_;
for (auto p : paths) {
n += p.size();
}
return n;
}
/**
* Return the number of contours (both outer and inner paths) in the
* CrossSection.
*/
int CrossSection::NumContour() const { return GetPaths()->paths_.size(); }
/**
* Does the CrossSection contain any contours?
*/
bool CrossSection::IsEmpty() const { return GetPaths()->paths_.empty(); }
/**
* Returns the axis-aligned bounding rectangle of all the CrossSections'
* vertices.
*/
Rect CrossSection::Bounds() const {
auto r = C2::GetBounds(GetPaths()->paths_);
return Rect({r.left, r.bottom}, {r.right, r.top});
}
/**
* Return the contours of this CrossSection as a Polygons.
*/
Polygons CrossSection::ToPolygons() const {
auto polys = Polygons();
auto paths = GetPaths()->paths_;
polys.reserve(paths.size());
for (auto p : paths) {
auto sp = SimplePolygon();
sp.reserve(p.size());
for (auto v : p) {
sp.push_back({v.x, v.y});
}
polys.push_back(sp);
}
return polys;
}
} // namespace manifold

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// Copyright 2022 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_priority_queue.h>)
#include <tbb/tbb.h>
#define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
#include <tbb/concurrent_priority_queue.h>
#endif
#include <algorithm>
#include <variant>
#include "./boolean3.h"
#include "./csg_tree.h"
#include "./impl.h"
#include "./mesh_fixes.h"
#include "./parallel.h"
constexpr int kParallelThreshold = 4096;
namespace {
using namespace manifold;
struct Transform4x3 {
mat3x4 transform;
vec3 operator()(vec3 position) const {
return transform * vec4(position, 1.0);
}
};
struct UpdateHalfedge {
const int nextVert;
const int nextEdge;
const int nextFace;
Halfedge operator()(Halfedge edge) {
edge.startVert += nextVert;
edge.endVert += nextVert;
edge.pairedHalfedge += nextEdge;
return edge;
}
};
struct UpdateTriProp {
const int nextProp;
ivec3 operator()(ivec3 tri) {
tri += nextProp;
return tri;
}
};
struct UpdateMeshIDs {
const int offset;
TriRef operator()(TriRef ref) {
ref.meshID += offset;
return ref;
}
};
struct CheckOverlap {
VecView<const Box> boxes;
const size_t i;
bool operator()(size_t j) { return boxes[i].DoesOverlap(boxes[j]); }
};
using SharedImpl = std::variant<std::shared_ptr<const Manifold::Impl>,
std::shared_ptr<Manifold::Impl>>;
struct GetImplPtr {
const Manifold::Impl *operator()(const SharedImpl &p) {
if (std::holds_alternative<std::shared_ptr<const Manifold::Impl>>(p)) {
return std::get_if<std::shared_ptr<const Manifold::Impl>>(&p)->get();
} else {
return std::get_if<std::shared_ptr<Manifold::Impl>>(&p)->get();
}
};
};
struct MeshCompare {
bool operator()(const SharedImpl &a, const SharedImpl &b) {
return GetImplPtr()(a)->NumVert() < GetImplPtr()(b)->NumVert();
}
};
} // namespace
namespace manifold {
std::shared_ptr<CsgNode> CsgNode::Boolean(
const std::shared_ptr<CsgNode> &second, OpType op) {
if (auto opNode = std::dynamic_pointer_cast<CsgOpNode>(second)) {
// "this" is not a CsgOpNode (which overrides Boolean), but if "second" is
// and the operation is commutative, we let it built the tree.
if ((op == OpType::Add || op == OpType::Intersect)) {
return opNode->Boolean(shared_from_this(), op);
}
}
std::vector<std::shared_ptr<CsgNode>> children({shared_from_this(), second});
return std::make_shared<CsgOpNode>(children, op);
}
std::shared_ptr<CsgNode> CsgNode::Translate(const vec3 &t) const {
mat3x4 transform = la::identity;
transform[3] += t;
return Transform(transform);
}
std::shared_ptr<CsgNode> CsgNode::Scale(const vec3 &v) const {
mat3x4 transform;
for (int i : {0, 1, 2}) transform[i][i] = v[i];
return Transform(transform);
}
std::shared_ptr<CsgNode> CsgNode::Rotate(double xDegrees, double yDegrees,
double zDegrees) const {
mat3 rX({1.0, 0.0, 0.0}, //
{0.0, cosd(xDegrees), sind(xDegrees)}, //
{0.0, -sind(xDegrees), cosd(xDegrees)});
mat3 rY({cosd(yDegrees), 0.0, -sind(yDegrees)}, //
{0.0, 1.0, 0.0}, //
{sind(yDegrees), 0.0, cosd(yDegrees)});
mat3 rZ({cosd(zDegrees), sind(zDegrees), 0.0}, //
{-sind(zDegrees), cosd(zDegrees), 0.0}, //
{0.0, 0.0, 1.0});
mat3x4 transform(rZ * rY * rX, vec3());
return Transform(transform);
}
CsgLeafNode::CsgLeafNode() : pImpl_(std::make_shared<Manifold::Impl>()) {}
CsgLeafNode::CsgLeafNode(std::shared_ptr<const Manifold::Impl> pImpl_)
: pImpl_(pImpl_) {}
CsgLeafNode::CsgLeafNode(std::shared_ptr<const Manifold::Impl> pImpl_,
mat3x4 transform_)
: pImpl_(pImpl_), transform_(transform_) {}
std::shared_ptr<const Manifold::Impl> CsgLeafNode::GetImpl() const {
if (transform_ == mat3x4(la::identity)) return pImpl_;
pImpl_ =
std::make_shared<const Manifold::Impl>(pImpl_->Transform(transform_));
transform_ = la::identity;
return pImpl_;
}
mat3x4 CsgLeafNode::GetTransform() const { return transform_; }
std::shared_ptr<CsgLeafNode> CsgLeafNode::ToLeafNode() const {
return std::make_shared<CsgLeafNode>(*this);
}
std::shared_ptr<CsgNode> CsgLeafNode::Transform(const mat3x4 &m) const {
return std::make_shared<CsgLeafNode>(pImpl_, m * Mat4(transform_));
}
CsgNodeType CsgLeafNode::GetNodeType() const { return CsgNodeType::Leaf; }
/**
* Efficient union of a set of pairwise disjoint meshes.
*/
Manifold::Impl CsgLeafNode::Compose(
const std::vector<std::shared_ptr<CsgLeafNode>> &nodes) {
ZoneScoped;
double epsilon = -1;
double tolerance = -1;
int numVert = 0;
int numEdge = 0;
int numTri = 0;
int numPropVert = 0;
std::vector<int> vertIndices;
std::vector<int> edgeIndices;
std::vector<int> triIndices;
std::vector<int> propVertIndices;
int numPropOut = 0;
for (auto &node : nodes) {
if (node->pImpl_->status_ != Manifold::Error::NoError) {
Manifold::Impl impl;
impl.status_ = node->pImpl_->status_;
return impl;
}
double nodeOldScale = node->pImpl_->bBox_.Scale();
double nodeNewScale =
node->pImpl_->bBox_.Transform(node->transform_).Scale();
double nodeEpsilon = node->pImpl_->epsilon_;
nodeEpsilon *= std::max(1.0, nodeNewScale / nodeOldScale);
nodeEpsilon = std::max(nodeEpsilon, kPrecision * nodeNewScale);
if (!std::isfinite(nodeEpsilon)) nodeEpsilon = -1;
epsilon = std::max(epsilon, nodeEpsilon);
tolerance = std::max(tolerance, node->pImpl_->tolerance_);
vertIndices.push_back(numVert);
edgeIndices.push_back(numEdge * 2);
triIndices.push_back(numTri);
propVertIndices.push_back(numPropVert);
numVert += node->pImpl_->NumVert();
numEdge += node->pImpl_->NumEdge();
numTri += node->pImpl_->NumTri();
const int numProp = node->pImpl_->NumProp();
numPropOut = std::max(numPropOut, numProp);
numPropVert +=
numProp == 0 ? 1
: node->pImpl_->meshRelation_.properties.size() / numProp;
}
Manifold::Impl combined;
combined.epsilon_ = epsilon;
combined.tolerance_ = tolerance;
combined.vertPos_.resize(numVert);
combined.halfedge_.resize(2 * numEdge);
combined.faceNormal_.resize(numTri);
combined.halfedgeTangent_.resize(2 * numEdge);
combined.meshRelation_.triRef.resize(numTri);
if (numPropOut > 0) {
combined.meshRelation_.numProp = numPropOut;
combined.meshRelation_.properties.resize(numPropOut * numPropVert, 0);
combined.meshRelation_.triProperties.resize(numTri);
}
auto policy = autoPolicy(numTri);
// if we are already parallelizing for each node, do not perform multithreaded
// copying as it will slightly hurt performance
if (nodes.size() > 1 && policy == ExecutionPolicy::Par)
policy = ExecutionPolicy::Seq;
for_each_n(
nodes.size() > 1 ? ExecutionPolicy::Par : ExecutionPolicy::Seq,
countAt(0), nodes.size(),
[&nodes, &vertIndices, &edgeIndices, &triIndices, &propVertIndices,
numPropOut, &combined, policy](int i) {
auto &node = nodes[i];
copy(node->pImpl_->halfedgeTangent_.begin(),
node->pImpl_->halfedgeTangent_.end(),
combined.halfedgeTangent_.begin() + edgeIndices[i]);
transform(
node->pImpl_->halfedge_.begin(), node->pImpl_->halfedge_.end(),
combined.halfedge_.begin() + edgeIndices[i],
UpdateHalfedge({vertIndices[i], edgeIndices[i], triIndices[i]}));
if (numPropOut > 0) {
auto start =
combined.meshRelation_.triProperties.begin() + triIndices[i];
if (node->pImpl_->NumProp() > 0) {
auto &triProp = node->pImpl_->meshRelation_.triProperties;
transform(triProp.begin(), triProp.end(), start,
UpdateTriProp({propVertIndices[i]}));
const int numProp = node->pImpl_->NumProp();
auto &oldProp = node->pImpl_->meshRelation_.properties;
auto &newProp = combined.meshRelation_.properties;
for (int p = 0; p < numProp; ++p) {
auto oldRange =
StridedRange(oldProp.cbegin() + p, oldProp.cend(), numProp);
auto newRange = StridedRange(
newProp.begin() + numPropOut * propVertIndices[i] + p,
newProp.end(), numPropOut);
copy(oldRange.begin(), oldRange.end(), newRange.begin());
}
} else {
// point all triangles at single new property of zeros.
fill(start, start + node->pImpl_->NumTri(),
ivec3(propVertIndices[i]));
}
}
if (node->transform_ == mat3x4(la::identity)) {
copy(node->pImpl_->vertPos_.begin(), node->pImpl_->vertPos_.end(),
combined.vertPos_.begin() + vertIndices[i]);
copy(node->pImpl_->faceNormal_.begin(),
node->pImpl_->faceNormal_.end(),
combined.faceNormal_.begin() + triIndices[i]);
} else {
// no need to apply the transform to the node, just copy the vertices
// and face normals and apply transform on the fly
auto vertPosBegin = TransformIterator(
node->pImpl_->vertPos_.begin(), Transform4x3({node->transform_}));
mat3 normalTransform =
la::inverse(la::transpose(mat3(node->transform_)));
auto faceNormalBegin =
TransformIterator(node->pImpl_->faceNormal_.begin(),
TransformNormals({normalTransform}));
copy_n(vertPosBegin, node->pImpl_->vertPos_.size(),
combined.vertPos_.begin() + vertIndices[i]);
copy_n(faceNormalBegin, node->pImpl_->faceNormal_.size(),
combined.faceNormal_.begin() + triIndices[i]);
const bool invert = la::determinant(mat3(node->transform_)) < 0;
for_each_n(policy, countAt(0), node->pImpl_->halfedgeTangent_.size(),
TransformTangents{combined.halfedgeTangent_,
edgeIndices[i], mat3(node->transform_),
invert, node->pImpl_->halfedgeTangent_,
node->pImpl_->halfedge_});
if (invert)
for_each_n(policy, countAt(triIndices[i]), node->pImpl_->NumTri(),
FlipTris({combined.halfedge_}));
}
// Since the nodes may be copies containing the same meshIDs, it is
// important to add an offset so that each node instance gets
// unique meshIDs.
const int offset = i * Manifold::Impl::meshIDCounter_;
transform(node->pImpl_->meshRelation_.triRef.begin(),
node->pImpl_->meshRelation_.triRef.end(),
combined.meshRelation_.triRef.begin() + triIndices[i],
UpdateMeshIDs({offset}));
});
for (size_t i = 0; i < nodes.size(); i++) {
auto &node = nodes[i];
const int offset = i * Manifold::Impl::meshIDCounter_;
for (const auto &pair : node->pImpl_->meshRelation_.meshIDtransform) {
combined.meshRelation_.meshIDtransform[pair.first + offset] = pair.second;
}
}
// required to remove parts that are smaller than the tolerance
combined.SimplifyTopology();
combined.Finish();
combined.IncrementMeshIDs();
return combined;
}
CsgOpNode::CsgOpNode() {}
CsgOpNode::CsgOpNode(const std::vector<std::shared_ptr<CsgNode>> &children,
OpType op)
: impl_(Impl{}) {
auto impl = impl_.GetGuard();
impl->children_ = children;
SetOp(op);
}
CsgOpNode::CsgOpNode(std::vector<std::shared_ptr<CsgNode>> &&children,
OpType op)
: impl_(Impl{}) {
auto impl = impl_.GetGuard();
impl->children_ = children;
SetOp(op);
}
std::shared_ptr<CsgNode> CsgOpNode::Boolean(
const std::shared_ptr<CsgNode> &second, OpType op) {
std::vector<std::shared_ptr<CsgNode>> children;
auto isReused = [](const auto &node) { return node->impl_.UseCount() > 1; };
auto copyChildren = [&](const auto &list, const mat3x4 &transform) {
for (const auto &child : list) {
children.push_back(child->Transform(transform));
}
};
auto self = std::dynamic_pointer_cast<CsgOpNode>(shared_from_this());
if (IsOp(op) && !isReused(self)) {
auto impl = impl_.GetGuard();
copyChildren(impl->children_, transform_);
} else {
children.push_back(self);
}
auto secondOp = std::dynamic_pointer_cast<CsgOpNode>(second);
auto canInlineSecondOp = [&]() {
switch (op) {
case OpType::Add:
case OpType::Intersect:
return secondOp->IsOp(op);
case OpType::Subtract:
return secondOp->IsOp(OpType::Add);
default:
return false;
}
};
if (secondOp && canInlineSecondOp() && !isReused(secondOp)) {
auto secondImpl = secondOp->impl_.GetGuard();
copyChildren(secondImpl->children_, secondOp->transform_);
} else {
children.push_back(second);
}
return std::make_shared<CsgOpNode>(children, op);
}
std::shared_ptr<CsgNode> CsgOpNode::Transform(const mat3x4 &m) const {
auto node = std::make_shared<CsgOpNode>();
node->impl_ = impl_;
node->transform_ = m * Mat4(transform_);
node->op_ = op_;
return node;
}
std::shared_ptr<CsgLeafNode> CsgOpNode::ToLeafNode() const {
if (cache_ != nullptr) return cache_;
// turn the children into leaf nodes
GetChildren();
auto impl = impl_.GetGuard();
auto &children_ = impl->children_;
if (children_.size() > 1) {
switch (op_) {
case CsgNodeType::Union:
BatchUnion();
break;
case CsgNodeType::Intersection: {
std::vector<std::shared_ptr<const Manifold::Impl>> impls;
for (auto &child : children_) {
impls.push_back(
std::dynamic_pointer_cast<CsgLeafNode>(child)->GetImpl());
}
children_.clear();
children_.push_back(std::make_shared<CsgLeafNode>(
BatchBoolean(OpType::Intersect, impls)));
break;
};
case CsgNodeType::Difference: {
// take the lhs out and treat the remaining nodes as the rhs, perform
// union optimization for them
auto lhs = std::dynamic_pointer_cast<CsgLeafNode>(children_.front());
children_.erase(children_.begin());
BatchUnion();
auto rhs = std::dynamic_pointer_cast<CsgLeafNode>(children_.front());
children_.clear();
Boolean3 boolean(*lhs->GetImpl(), *rhs->GetImpl(), OpType::Subtract);
children_.push_back(
std::make_shared<CsgLeafNode>(std::make_shared<Manifold::Impl>(
boolean.Result(OpType::Subtract))));
};
case CsgNodeType::Leaf:
// unreachable
break;
}
} else if (children_.size() == 0) {
return nullptr;
}
// children_ must contain only one CsgLeafNode now, and its Transform will
// give CsgLeafNode as well
cache_ = std::dynamic_pointer_cast<CsgLeafNode>(
children_.front()->Transform(transform_));
return cache_;
}
/**
* Efficient boolean operation on a set of nodes utilizing commutativity of the
* operation. Only supports union and intersection.
*/
std::shared_ptr<Manifold::Impl> CsgOpNode::BatchBoolean(
OpType operation,
std::vector<std::shared_ptr<const Manifold::Impl>> &results) {
ZoneScoped;
auto getImplPtr = GetImplPtr();
DEBUG_ASSERT(operation != OpType::Subtract, logicErr,
"BatchBoolean doesn't support Difference.");
// common cases
if (results.size() == 0) return std::make_shared<Manifold::Impl>();
if (results.size() == 1)
return std::make_shared<Manifold::Impl>(*results.front());
if (results.size() == 2) {
Boolean3 boolean(*results[0], *results[1], operation);
return std::make_shared<Manifold::Impl>(boolean.Result(operation));
}
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
tbb::task_group group;
tbb::concurrent_priority_queue<SharedImpl, MeshCompare> queue(results.size());
for (auto result : results) {
queue.emplace(result);
}
results.clear();
std::function<void()> process = [&]() {
while (queue.size() > 1) {
SharedImpl a, b;
if (!queue.try_pop(a)) continue;
if (!queue.try_pop(b)) {
queue.push(a);
continue;
}
group.run([&, a, b]() {
Boolean3 boolean(*getImplPtr(a), *getImplPtr(b), operation);
queue.emplace(
std::make_shared<Manifold::Impl>(boolean.Result(operation)));
return group.run(process);
});
}
};
group.run_and_wait(process);
SharedImpl r;
queue.try_pop(r);
return *std::get_if<std::shared_ptr<Manifold::Impl>>(&r);
#endif
// apply boolean operations starting from smaller meshes
// the assumption is that boolean operations on smaller meshes is faster,
// due to less data being copied and processed
auto cmpFn = MeshCompare();
std::make_heap(results.begin(), results.end(), cmpFn);
while (results.size() > 1) {
std::pop_heap(results.begin(), results.end(), cmpFn);
auto a = std::move(results.back());
results.pop_back();
std::pop_heap(results.begin(), results.end(), cmpFn);
auto b = std::move(results.back());
results.pop_back();
// boolean operation
Boolean3 boolean(*a, *b, operation);
auto result = std::make_shared<Manifold::Impl>(boolean.Result(operation));
if (results.size() == 0) {
return result;
}
results.push_back(result);
std::push_heap(results.begin(), results.end(), cmpFn);
}
return std::make_shared<Manifold::Impl>(*results.front());
}
/**
* Efficient union operation on a set of nodes by doing Compose as much as
* possible.
* Note: Due to some unknown issues with `Compose`, we are now doing
* `BatchBoolean` instead of using `Compose` for non-intersecting manifolds.
*/
void CsgOpNode::BatchUnion() const {
ZoneScoped;
// INVARIANT: children_ is a vector of leaf nodes
// this kMaxUnionSize is a heuristic to avoid the pairwise disjoint check
// with O(n^2) complexity to take too long.
// If the number of children exceeded this limit, we will operate on chunks
// with size kMaxUnionSize.
constexpr size_t kMaxUnionSize = 1000;
auto impl = impl_.GetGuard();
auto &children_ = impl->children_;
while (children_.size() > 1) {
const size_t start = (children_.size() > kMaxUnionSize)
? (children_.size() - kMaxUnionSize)
: 0;
Vec<Box> boxes;
boxes.reserve(children_.size() - start);
for (size_t i = start; i < children_.size(); i++) {
boxes.push_back(std::dynamic_pointer_cast<CsgLeafNode>(children_[i])
->GetImpl()
->bBox_);
}
// partition the children into a set of disjoint sets
// each set contains a set of children that are pairwise disjoint
std::vector<Vec<size_t>> disjointSets;
for (size_t i = 0; i < boxes.size(); i++) {
auto lambda = [&boxes, i](const Vec<size_t> &set) {
return std::find_if(set.begin(), set.end(), CheckOverlap({boxes, i})) ==
set.end();
};
auto it = std::find_if(disjointSets.begin(), disjointSets.end(), lambda);
if (it == disjointSets.end()) {
disjointSets.push_back(std::vector<size_t>{i});
} else {
it->push_back(i);
}
}
// compose each set of disjoint children
std::vector<std::shared_ptr<const Manifold::Impl>> impls;
for (auto &set : disjointSets) {
if (set.size() == 1) {
impls.push_back(
std::dynamic_pointer_cast<CsgLeafNode>(children_[start + set[0]])
->GetImpl());
} else {
std::vector<std::shared_ptr<CsgLeafNode>> tmp;
for (size_t j : set) {
tmp.push_back(
std::dynamic_pointer_cast<CsgLeafNode>(children_[start + j]));
}
impls.push_back(
std::make_shared<const Manifold::Impl>(CsgLeafNode::Compose(tmp)));
}
}
children_.erase(children_.begin() + start, children_.end());
children_.push_back(
std::make_shared<CsgLeafNode>(BatchBoolean(OpType::Add, impls)));
// move it to the front as we process from the back, and the newly added
// child should be quite complicated
std::swap(children_.front(), children_.back());
}
}
/**
* Flatten the children to a list of leaf nodes and return them.
* If forceToLeafNodes is true, the list will be guaranteed to be a list of leaf
* nodes (i.e. no ops). Otherwise, the list may contain ops. Note that this
* function will not apply the transform to children, as they may be shared with
* other nodes.
*/
std::vector<std::shared_ptr<CsgNode>> &CsgOpNode::GetChildren(
bool forceToLeafNodes) const {
auto impl = impl_.GetGuard();
if (forceToLeafNodes && !impl->forcedToLeafNodes_) {
impl->forcedToLeafNodes_ = true;
for_each(ExecutionPolicy::Par, impl->children_.begin(),
impl->children_.end(), [](auto &child) {
if (child->GetNodeType() != CsgNodeType::Leaf) {
child = child->ToLeafNode();
}
});
}
return impl->children_;
}
void CsgOpNode::SetOp(OpType op) {
switch (op) {
case OpType::Add:
op_ = CsgNodeType::Union;
break;
case OpType::Subtract:
op_ = CsgNodeType::Difference;
break;
case OpType::Intersect:
op_ = CsgNodeType::Intersection;
break;
}
}
bool CsgOpNode::IsOp(OpType op) {
switch (op) {
case OpType::Add:
return op_ == CsgNodeType::Union;
case OpType::Subtract:
return op_ == CsgNodeType::Difference;
case OpType::Intersect:
return op_ == CsgNodeType::Intersection;
default:
return false;
}
}
mat3x4 CsgOpNode::GetTransform() const { return transform_; }
} // namespace manifold

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// Copyright 2022 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./utils.h"
#include "manifold/manifold.h"
namespace manifold {
enum class CsgNodeType { Union, Intersection, Difference, Leaf };
class CsgLeafNode;
class CsgNode : public std::enable_shared_from_this<CsgNode> {
public:
virtual std::shared_ptr<CsgLeafNode> ToLeafNode() const = 0;
virtual std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const = 0;
virtual CsgNodeType GetNodeType() const = 0;
virtual mat3x4 GetTransform() const = 0;
virtual std::shared_ptr<CsgNode> Boolean(
const std::shared_ptr<CsgNode> &second, OpType op);
std::shared_ptr<CsgNode> Translate(const vec3 &t) const;
std::shared_ptr<CsgNode> Scale(const vec3 &s) const;
std::shared_ptr<CsgNode> Rotate(double xDegrees = 0, double yDegrees = 0,
double zDegrees = 0) const;
};
class CsgLeafNode final : public CsgNode {
public:
CsgLeafNode();
CsgLeafNode(std::shared_ptr<const Manifold::Impl> pImpl_);
CsgLeafNode(std::shared_ptr<const Manifold::Impl> pImpl_, mat3x4 transform_);
std::shared_ptr<const Manifold::Impl> GetImpl() const;
std::shared_ptr<CsgLeafNode> ToLeafNode() const override;
std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const override;
CsgNodeType GetNodeType() const override;
mat3x4 GetTransform() const override;
static Manifold::Impl Compose(
const std::vector<std::shared_ptr<CsgLeafNode>> &nodes);
private:
mutable std::shared_ptr<const Manifold::Impl> pImpl_;
mutable mat3x4 transform_ = la::identity;
};
class CsgOpNode final : public CsgNode {
public:
CsgOpNode();
CsgOpNode(const std::vector<std::shared_ptr<CsgNode>> &children, OpType op);
CsgOpNode(std::vector<std::shared_ptr<CsgNode>> &&children, OpType op);
std::shared_ptr<CsgNode> Boolean(const std::shared_ptr<CsgNode> &second,
OpType op) override;
std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const override;
std::shared_ptr<CsgLeafNode> ToLeafNode() const override;
CsgNodeType GetNodeType() const override { return op_; }
mat3x4 GetTransform() const override;
private:
struct Impl {
std::vector<std::shared_ptr<CsgNode>> children_;
bool forcedToLeafNodes_ = false;
};
mutable ConcurrentSharedPtr<Impl> impl_ = ConcurrentSharedPtr<Impl>(Impl{});
CsgNodeType op_;
mat3x4 transform_ = la::identity;
// the following fields are for lazy evaluation, so they are mutable
mutable std::shared_ptr<CsgLeafNode> cache_ = nullptr;
void SetOp(OpType);
bool IsOp(OpType op);
static std::shared_ptr<Manifold::Impl> BatchBoolean(
OpType operation,
std::vector<std::shared_ptr<const Manifold::Impl>> &results);
void BatchUnion() const;
std::vector<std::shared_ptr<CsgNode>> &GetChildren(
bool forceToLeafNodes = true) const;
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./impl.h"
#include "./parallel.h"
namespace {
using namespace manifold;
ivec3 TriOf(int edge) {
ivec3 triEdge;
triEdge[0] = edge;
triEdge[1] = NextHalfedge(triEdge[0]);
triEdge[2] = NextHalfedge(triEdge[1]);
return triEdge;
}
bool Is01Longest(vec2 v0, vec2 v1, vec2 v2) {
const vec2 e[3] = {v1 - v0, v2 - v1, v0 - v2};
double l[3];
for (int i : {0, 1, 2}) l[i] = la::dot(e[i], e[i]);
return l[0] > l[1] && l[0] > l[2];
}
struct DuplicateEdge {
const Halfedge* sortedHalfedge;
bool operator()(int edge) {
const Halfedge& halfedge = sortedHalfedge[edge];
const Halfedge& nextHalfedge = sortedHalfedge[edge + 1];
return halfedge.startVert == nextHalfedge.startVert &&
halfedge.endVert == nextHalfedge.endVert;
}
};
struct ShortEdge {
VecView<const Halfedge> halfedge;
VecView<const vec3> vertPos;
const double tolerance;
bool operator()(int edge) const {
if (halfedge[edge].pairedHalfedge < 0) return false;
// Flag short edges
const vec3 delta =
vertPos[halfedge[edge].endVert] - vertPos[halfedge[edge].startVert];
return la::dot(delta, delta) < tolerance * tolerance;
}
};
struct FlagEdge {
VecView<const Halfedge> halfedge;
VecView<const TriRef> triRef;
bool operator()(int edge) const {
if (halfedge[edge].pairedHalfedge < 0) return false;
// Flag redundant edges - those where the startVert is surrounded by only
// two original triangles.
const TriRef ref0 = triRef[edge / 3];
int current = NextHalfedge(halfedge[edge].pairedHalfedge);
const TriRef ref1 = triRef[current / 3];
while (current != edge) {
current = NextHalfedge(halfedge[current].pairedHalfedge);
int tri = current / 3;
const TriRef ref = triRef[tri];
if (!ref.SameFace(ref0) && !ref.SameFace(ref1)) return false;
}
return true;
}
};
struct SwappableEdge {
VecView<const Halfedge> halfedge;
VecView<const vec3> vertPos;
VecView<const vec3> triNormal;
const double tolerance;
bool operator()(int edge) const {
if (halfedge[edge].pairedHalfedge < 0) return false;
int tri = edge / 3;
ivec3 triEdge = TriOf(edge);
mat2x3 projection = GetAxisAlignedProjection(triNormal[tri]);
vec2 v[3];
for (int i : {0, 1, 2})
v[i] = projection * vertPos[halfedge[triEdge[i]].startVert];
if (CCW(v[0], v[1], v[2], tolerance) > 0 || !Is01Longest(v[0], v[1], v[2]))
return false;
// Switch to neighbor's projection.
edge = halfedge[edge].pairedHalfedge;
tri = edge / 3;
triEdge = TriOf(edge);
projection = GetAxisAlignedProjection(triNormal[tri]);
for (int i : {0, 1, 2})
v[i] = projection * vertPos[halfedge[triEdge[i]].startVert];
return CCW(v[0], v[1], v[2], tolerance) > 0 ||
Is01Longest(v[0], v[1], v[2]);
}
};
struct SortEntry {
int start;
int end;
size_t index;
inline bool operator<(const SortEntry& other) const {
return start == other.start ? end < other.end : start < other.start;
}
};
} // namespace
namespace manifold {
/**
* Duplicates just enough verts to covert an even-manifold to a proper
* 2-manifold, splitting non-manifold verts and edges with too many triangles.
*/
void Manifold::Impl::CleanupTopology() {
if (!halfedge_.size()) return;
// In the case of a very bad triangulation, it is possible to create pinched
// verts. They must be removed before edge collapse.
SplitPinchedVerts();
while (1) {
ZoneScopedN("DedupeEdge");
const size_t nbEdges = halfedge_.size();
size_t numFlagged = 0;
Vec<SortEntry> entries;
entries.reserve(nbEdges / 2);
for (size_t i = 0; i < nbEdges; ++i) {
if (halfedge_[i].IsForward()) {
entries.push_back({halfedge_[i].startVert, halfedge_[i].endVert, i});
}
}
stable_sort(entries.begin(), entries.end());
for (size_t i = 0; i < entries.size() - 1; ++i) {
const int h0 = entries[i].index;
const int h1 = entries[i + 1].index;
if (halfedge_[h0].startVert == halfedge_[h1].startVert &&
halfedge_[h0].endVert == halfedge_[h1].endVert) {
DedupeEdge(entries[i].index);
numFlagged++;
}
}
if (numFlagged == 0) break;
#ifdef MANIFOLD_DEBUG
if (ManifoldParams().verbose) {
std::cout << "found " << numFlagged << " duplicate edges to split"
<< std::endl;
}
#endif
}
}
/**
* Collapses degenerate triangles by removing edges shorter than tolerance_ and
* any edge that is preceeded by an edge that joins the same two face relations.
* It also performs edge swaps on the long edges of degenerate triangles, though
* there are some configurations of degenerates that cannot be removed this way.
*
* Before collapsing edges, the mesh is checked for duplicate edges (more than
* one pair of triangles sharing the same edge), which are removed by
* duplicating one vert and adding two triangles. These degenerate triangles are
* likely to be collapsed again in the subsequent simplification.
*
* Note when an edge collapse would result in something non-manifold, the
* vertices are duplicated in such a way as to remove handles or separate
* meshes, thus decreasing the Genus(). It only increases when meshes that have
* collapsed to just a pair of triangles are removed entirely.
*
* Rather than actually removing the edges, this step merely marks them for
* removal, by setting vertPos to NaN and halfedge to {-1, -1, -1, -1}.
*/
void Manifold::Impl::SimplifyTopology() {
if (!halfedge_.size()) return;
CleanupTopology();
if (!ManifoldParams().cleanupTriangles) {
return;
}
const size_t nbEdges = halfedge_.size();
auto policy = autoPolicy(nbEdges, 1e5);
size_t numFlagged = 0;
Vec<uint8_t> bFlags(nbEdges);
std::vector<int> scratchBuffer;
scratchBuffer.reserve(10);
{
ZoneScopedN("CollapseShortEdge");
numFlagged = 0;
ShortEdge se{halfedge_, vertPos_, epsilon_};
for_each_n(policy, countAt(0_uz), nbEdges,
[&](size_t i) { bFlags[i] = se(i); });
for (size_t i = 0; i < nbEdges; ++i) {
if (bFlags[i]) {
CollapseEdge(i, scratchBuffer);
scratchBuffer.resize(0);
numFlagged++;
}
}
}
#ifdef MANIFOLD_DEBUG
if (ManifoldParams().verbose && numFlagged > 0) {
std::cout << "found " << numFlagged << " short edges to collapse"
<< std::endl;
}
#endif
{
ZoneScopedN("CollapseFlaggedEdge");
numFlagged = 0;
FlagEdge se{halfedge_, meshRelation_.triRef};
for_each_n(policy, countAt(0_uz), nbEdges,
[&](size_t i) { bFlags[i] = se(i); });
for (size_t i = 0; i < nbEdges; ++i) {
if (bFlags[i]) {
CollapseEdge(i, scratchBuffer);
scratchBuffer.resize(0);
numFlagged++;
}
}
}
#ifdef MANIFOLD_DEBUG
if (ManifoldParams().verbose && numFlagged > 0) {
std::cout << "found " << numFlagged << " colinear edges to collapse"
<< std::endl;
}
#endif
{
ZoneScopedN("RecursiveEdgeSwap");
numFlagged = 0;
SwappableEdge se{halfedge_, vertPos_, faceNormal_, tolerance_};
for_each_n(policy, countAt(0_uz), nbEdges,
[&](size_t i) { bFlags[i] = se(i); });
std::vector<int> edgeSwapStack;
std::vector<int> visited(halfedge_.size(), -1);
int tag = 0;
for (size_t i = 0; i < nbEdges; ++i) {
if (bFlags[i]) {
numFlagged++;
tag++;
RecursiveEdgeSwap(i, tag, visited, edgeSwapStack, scratchBuffer);
while (!edgeSwapStack.empty()) {
int last = edgeSwapStack.back();
edgeSwapStack.pop_back();
RecursiveEdgeSwap(last, tag, visited, edgeSwapStack, scratchBuffer);
}
}
}
}
#ifdef MANIFOLD_DEBUG
if (ManifoldParams().verbose && numFlagged > 0) {
std::cout << "found " << numFlagged << " edges to swap" << std::endl;
}
#endif
}
// Deduplicate the given 4-manifold edge by duplicating endVert, thus making the
// edges distinct. Also duplicates startVert if it becomes pinched.
void Manifold::Impl::DedupeEdge(const int edge) {
// Orbit endVert
const int startVert = halfedge_[edge].startVert;
const int endVert = halfedge_[edge].endVert;
int current = halfedge_[NextHalfedge(edge)].pairedHalfedge;
while (current != edge) {
const int vert = halfedge_[current].startVert;
if (vert == startVert) {
// Single topological unit needs 2 faces added to be split
const int newVert = vertPos_.size();
vertPos_.push_back(vertPos_[endVert]);
if (vertNormal_.size() > 0) vertNormal_.push_back(vertNormal_[endVert]);
current = halfedge_[NextHalfedge(current)].pairedHalfedge;
const int opposite = halfedge_[NextHalfedge(edge)].pairedHalfedge;
UpdateVert(newVert, current, opposite);
int newHalfedge = halfedge_.size();
int newFace = newHalfedge / 3;
int oldFace = current / 3;
int outsideVert = halfedge_[current].startVert;
halfedge_.push_back({endVert, newVert, -1});
halfedge_.push_back({newVert, outsideVert, -1});
halfedge_.push_back({outsideVert, endVert, -1});
PairUp(newHalfedge + 2, halfedge_[current].pairedHalfedge);
PairUp(newHalfedge + 1, current);
if (meshRelation_.triRef.size() > 0)
meshRelation_.triRef.push_back(meshRelation_.triRef[oldFace]);
if (meshRelation_.triProperties.size() > 0)
meshRelation_.triProperties.push_back(
meshRelation_.triProperties[oldFace]);
if (faceNormal_.size() > 0) faceNormal_.push_back(faceNormal_[oldFace]);
newHalfedge += 3;
++newFace;
oldFace = opposite / 3;
outsideVert = halfedge_[opposite].startVert;
halfedge_.push_back({newVert, endVert, -1});
halfedge_.push_back({endVert, outsideVert, -1});
halfedge_.push_back({outsideVert, newVert, -1});
PairUp(newHalfedge + 2, halfedge_[opposite].pairedHalfedge);
PairUp(newHalfedge + 1, opposite);
PairUp(newHalfedge, newHalfedge - 3);
if (meshRelation_.triRef.size() > 0)
meshRelation_.triRef.push_back(meshRelation_.triRef[oldFace]);
if (meshRelation_.triProperties.size() > 0)
meshRelation_.triProperties.push_back(
meshRelation_.triProperties[oldFace]);
if (faceNormal_.size() > 0) faceNormal_.push_back(faceNormal_[oldFace]);
break;
}
current = halfedge_[NextHalfedge(current)].pairedHalfedge;
}
if (current == edge) {
// Separate topological unit needs no new faces to be split
const int newVert = vertPos_.size();
vertPos_.push_back(vertPos_[endVert]);
if (vertNormal_.size() > 0) vertNormal_.push_back(vertNormal_[endVert]);
ForVert(NextHalfedge(current), [this, newVert](int e) {
halfedge_[e].startVert = newVert;
halfedge_[halfedge_[e].pairedHalfedge].endVert = newVert;
});
}
// Orbit startVert
const int pair = halfedge_[edge].pairedHalfedge;
current = halfedge_[NextHalfedge(pair)].pairedHalfedge;
while (current != pair) {
const int vert = halfedge_[current].startVert;
if (vert == endVert) {
break; // Connected: not a pinched vert
}
current = halfedge_[NextHalfedge(current)].pairedHalfedge;
}
if (current == pair) {
// Split the pinched vert the previous split created.
const int newVert = vertPos_.size();
vertPos_.push_back(vertPos_[endVert]);
if (vertNormal_.size() > 0) vertNormal_.push_back(vertNormal_[endVert]);
ForVert(NextHalfedge(current), [this, newVert](int e) {
halfedge_[e].startVert = newVert;
halfedge_[halfedge_[e].pairedHalfedge].endVert = newVert;
});
}
}
void Manifold::Impl::PairUp(int edge0, int edge1) {
halfedge_[edge0].pairedHalfedge = edge1;
halfedge_[edge1].pairedHalfedge = edge0;
}
// Traverses CW around startEdge.endVert from startEdge to endEdge
// (edgeEdge.endVert must == startEdge.endVert), updating each edge to point
// to vert instead.
void Manifold::Impl::UpdateVert(int vert, int startEdge, int endEdge) {
int current = startEdge;
while (current != endEdge) {
halfedge_[current].endVert = vert;
current = NextHalfedge(current);
halfedge_[current].startVert = vert;
current = halfedge_[current].pairedHalfedge;
DEBUG_ASSERT(current != startEdge, logicErr, "infinite loop in decimator!");
}
}
// In the event that the edge collapse would create a non-manifold edge,
// instead we duplicate the two verts and attach the manifolds the other way
// across this edge.
void Manifold::Impl::FormLoop(int current, int end) {
int startVert = vertPos_.size();
vertPos_.push_back(vertPos_[halfedge_[current].startVert]);
int endVert = vertPos_.size();
vertPos_.push_back(vertPos_[halfedge_[current].endVert]);
int oldMatch = halfedge_[current].pairedHalfedge;
int newMatch = halfedge_[end].pairedHalfedge;
UpdateVert(startVert, oldMatch, newMatch);
UpdateVert(endVert, end, current);
halfedge_[current].pairedHalfedge = newMatch;
halfedge_[newMatch].pairedHalfedge = current;
halfedge_[end].pairedHalfedge = oldMatch;
halfedge_[oldMatch].pairedHalfedge = end;
RemoveIfFolded(end);
}
void Manifold::Impl::CollapseTri(const ivec3& triEdge) {
if (halfedge_[triEdge[1]].pairedHalfedge == -1) return;
int pair1 = halfedge_[triEdge[1]].pairedHalfedge;
int pair2 = halfedge_[triEdge[2]].pairedHalfedge;
halfedge_[pair1].pairedHalfedge = pair2;
halfedge_[pair2].pairedHalfedge = pair1;
for (int i : {0, 1, 2}) {
halfedge_[triEdge[i]] = {-1, -1, -1};
}
}
void Manifold::Impl::RemoveIfFolded(int edge) {
const ivec3 tri0edge = TriOf(edge);
const ivec3 tri1edge = TriOf(halfedge_[edge].pairedHalfedge);
if (halfedge_[tri0edge[1]].pairedHalfedge == -1) return;
if (halfedge_[tri0edge[1]].endVert == halfedge_[tri1edge[1]].endVert) {
if (halfedge_[tri0edge[1]].pairedHalfedge == tri1edge[2]) {
if (halfedge_[tri0edge[2]].pairedHalfedge == tri1edge[1]) {
for (int i : {0, 1, 2})
vertPos_[halfedge_[tri0edge[i]].startVert] = vec3(NAN);
} else {
vertPos_[halfedge_[tri0edge[1]].startVert] = vec3(NAN);
}
} else {
if (halfedge_[tri0edge[2]].pairedHalfedge == tri1edge[1]) {
vertPos_[halfedge_[tri1edge[1]].startVert] = vec3(NAN);
}
}
PairUp(halfedge_[tri0edge[1]].pairedHalfedge,
halfedge_[tri1edge[2]].pairedHalfedge);
PairUp(halfedge_[tri0edge[2]].pairedHalfedge,
halfedge_[tri1edge[1]].pairedHalfedge);
for (int i : {0, 1, 2}) {
halfedge_[tri0edge[i]] = {-1, -1, -1};
halfedge_[tri1edge[i]] = {-1, -1, -1};
}
}
}
// Collapses the given edge by removing startVert. May split the mesh
// topologically if the collapse would have resulted in a 4-manifold edge. Do
// not collapse an edge if startVert is pinched - the vert will be marked NaN,
// but other edges may still be pointing to it.
void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
Vec<TriRef>& triRef = meshRelation_.triRef;
Vec<ivec3>& triProp = meshRelation_.triProperties;
const Halfedge toRemove = halfedge_[edge];
if (toRemove.pairedHalfedge < 0) return;
const int endVert = toRemove.endVert;
const ivec3 tri0edge = TriOf(edge);
const ivec3 tri1edge = TriOf(toRemove.pairedHalfedge);
const vec3 pNew = vertPos_[endVert];
const vec3 pOld = vertPos_[toRemove.startVert];
const vec3 delta = pNew - pOld;
const bool shortEdge = la::dot(delta, delta) < tolerance_ * tolerance_;
// Orbit endVert
int current = halfedge_[tri0edge[1]].pairedHalfedge;
while (current != tri1edge[2]) {
current = NextHalfedge(current);
edges.push_back(current);
current = halfedge_[current].pairedHalfedge;
}
// Orbit startVert
int start = halfedge_[tri1edge[1]].pairedHalfedge;
if (!shortEdge) {
current = start;
TriRef refCheck = triRef[toRemove.pairedHalfedge / 3];
vec3 pLast = vertPos_[halfedge_[tri1edge[1]].endVert];
while (current != tri0edge[2]) {
current = NextHalfedge(current);
vec3 pNext = vertPos_[halfedge_[current].endVert];
const int tri = current / 3;
const TriRef ref = triRef[tri];
const mat2x3 projection = GetAxisAlignedProjection(faceNormal_[tri]);
// Don't collapse if the edge is not redundant (this may have changed due
// to the collapse of neighbors).
if (!ref.SameFace(refCheck)) {
refCheck = triRef[edge / 3];
if (!ref.SameFace(refCheck)) {
return;
} else {
// Don't collapse if the edges separating the faces are not colinear
// (can happen when the two faces are coplanar).
if (CCW(projection * pOld, projection * pLast, projection * pNew,
epsilon_) != 0)
return;
}
}
// Don't collapse edge if it would cause a triangle to invert.
if (CCW(projection * pNext, projection * pLast, projection * pNew,
epsilon_) < 0)
return;
pLast = pNext;
current = halfedge_[current].pairedHalfedge;
}
}
// Remove toRemove.startVert and replace with endVert.
vertPos_[toRemove.startVert] = vec3(NAN);
CollapseTri(tri1edge);
// Orbit startVert
const int tri0 = edge / 3;
const int tri1 = toRemove.pairedHalfedge / 3;
const int triVert0 = (edge + 1) % 3;
const int triVert1 = toRemove.pairedHalfedge % 3;
current = start;
while (current != tri0edge[2]) {
current = NextHalfedge(current);
if (triProp.size() > 0) {
// Update the shifted triangles to the vertBary of endVert
const int tri = current / 3;
const int vIdx = current - 3 * tri;
if (triRef[tri].SameFace(triRef[tri0])) {
triProp[tri][vIdx] = triProp[tri0][triVert0];
} else if (triRef[tri].SameFace(triRef[tri1])) {
triProp[tri][vIdx] = triProp[tri1][triVert1];
}
}
const int vert = halfedge_[current].endVert;
const int next = halfedge_[current].pairedHalfedge;
for (size_t i = 0; i < edges.size(); ++i) {
if (vert == halfedge_[edges[i]].endVert) {
FormLoop(edges[i], current);
start = next;
edges.resize(i);
break;
}
}
current = next;
}
UpdateVert(endVert, start, tri0edge[2]);
CollapseTri(tri0edge);
RemoveIfFolded(start);
}
void Manifold::Impl::RecursiveEdgeSwap(const int edge, int& tag,
std::vector<int>& visited,
std::vector<int>& edgeSwapStack,
std::vector<int>& edges) {
Vec<TriRef>& triRef = meshRelation_.triRef;
if (edge < 0) return;
const int pair = halfedge_[edge].pairedHalfedge;
if (pair < 0) return;
// avoid infinite recursion
if (visited[edge] == tag && visited[pair] == tag) return;
const ivec3 tri0edge = TriOf(edge);
const ivec3 tri1edge = TriOf(pair);
const ivec3 perm0 = TriOf(edge % 3);
const ivec3 perm1 = TriOf(pair % 3);
mat2x3 projection = GetAxisAlignedProjection(faceNormal_[edge / 3]);
vec2 v[4];
for (int i : {0, 1, 2})
v[i] = projection * vertPos_[halfedge_[tri0edge[i]].startVert];
// Only operate on the long edge of a degenerate triangle.
if (CCW(v[0], v[1], v[2], tolerance_) > 0 || !Is01Longest(v[0], v[1], v[2]))
return;
// Switch to neighbor's projection.
projection = GetAxisAlignedProjection(faceNormal_[pair / 3]);
for (int i : {0, 1, 2})
v[i] = projection * vertPos_[halfedge_[tri0edge[i]].startVert];
v[3] = projection * vertPos_[halfedge_[tri1edge[2]].startVert];
auto SwapEdge = [&]() {
// The 0-verts are swapped to the opposite 2-verts.
const int v0 = halfedge_[tri0edge[2]].startVert;
const int v1 = halfedge_[tri1edge[2]].startVert;
halfedge_[tri0edge[0]].startVert = v1;
halfedge_[tri0edge[2]].endVert = v1;
halfedge_[tri1edge[0]].startVert = v0;
halfedge_[tri1edge[2]].endVert = v0;
PairUp(tri0edge[0], halfedge_[tri1edge[2]].pairedHalfedge);
PairUp(tri1edge[0], halfedge_[tri0edge[2]].pairedHalfedge);
PairUp(tri0edge[2], tri1edge[2]);
// Both triangles are now subsets of the neighboring triangle.
const int tri0 = tri0edge[0] / 3;
const int tri1 = tri1edge[0] / 3;
faceNormal_[tri0] = faceNormal_[tri1];
triRef[tri0] = triRef[tri1];
const double l01 = la::length(v[1] - v[0]);
const double l02 = la::length(v[2] - v[0]);
const double a = std::max(0.0, std::min(1.0, l02 / l01));
// Update properties if applicable
if (meshRelation_.properties.size() > 0) {
Vec<ivec3>& triProp = meshRelation_.triProperties;
Vec<double>& prop = meshRelation_.properties;
triProp[tri0] = triProp[tri1];
triProp[tri0][perm0[1]] = triProp[tri1][perm1[0]];
triProp[tri0][perm0[0]] = triProp[tri1][perm1[2]];
const int numProp = NumProp();
const int newProp = prop.size() / numProp;
const int propIdx0 = triProp[tri1][perm1[0]];
const int propIdx1 = triProp[tri1][perm1[1]];
for (int p = 0; p < numProp; ++p) {
prop.push_back(a * prop[numProp * propIdx0 + p] +
(1 - a) * prop[numProp * propIdx1 + p]);
}
triProp[tri1][perm1[0]] = newProp;
triProp[tri0][perm0[2]] = newProp;
}
// if the new edge already exists, duplicate the verts and split the mesh.
int current = halfedge_[tri1edge[0]].pairedHalfedge;
const int endVert = halfedge_[tri1edge[1]].endVert;
while (current != tri0edge[1]) {
current = NextHalfedge(current);
if (halfedge_[current].endVert == endVert) {
FormLoop(tri0edge[2], current);
RemoveIfFolded(tri0edge[2]);
return;
}
current = halfedge_[current].pairedHalfedge;
}
};
// Only operate if the other triangles are not degenerate.
if (CCW(v[1], v[0], v[3], tolerance_) <= 0) {
if (!Is01Longest(v[1], v[0], v[3])) return;
// Two facing, long-edge degenerates can swap.
SwapEdge();
const vec2 e23 = v[3] - v[2];
if (la::dot(e23, e23) < tolerance_ * tolerance_) {
tag++;
CollapseEdge(tri0edge[2], edges);
edges.resize(0);
} else {
visited[edge] = tag;
visited[pair] = tag;
edgeSwapStack.insert(edgeSwapStack.end(), {tri1edge[1], tri1edge[0],
tri0edge[1], tri0edge[0]});
}
return;
} else if (CCW(v[0], v[3], v[2], tolerance_) <= 0 ||
CCW(v[1], v[2], v[3], tolerance_) <= 0) {
return;
}
// Normal path
SwapEdge();
visited[edge] = tag;
visited[pair] = tag;
edgeSwapStack.insert(edgeSwapStack.end(),
{halfedge_[tri1edge[0]].pairedHalfedge,
halfedge_[tri0edge[1]].pairedHalfedge});
}
void Manifold::Impl::SplitPinchedVerts() {
ZoneScoped;
std::vector<bool> vertProcessed(NumVert(), false);
std::vector<bool> halfedgeProcessed(halfedge_.size(), false);
for (size_t i = 0; i < halfedge_.size(); ++i) {
if (halfedgeProcessed[i]) continue;
int vert = halfedge_[i].startVert;
if (vertProcessed[vert]) {
vertPos_.push_back(vertPos_[vert]);
vert = NumVert() - 1;
} else {
vertProcessed[vert] = true;
}
ForVert(i, [this, &halfedgeProcessed, vert](int current) {
halfedgeProcessed[current] = true;
halfedge_[current].startVert = vert;
halfedge_[halfedge_[current].pairedHalfedge].endVert = vert;
});
}
}
} // namespace manifold

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@ -0,0 +1,319 @@
// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_map.h>)
#include <tbb/tbb.h>
#define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
#include <tbb/concurrent_map.h>
#endif
#include <unordered_set>
#include "./impl.h"
#include "./parallel.h"
#include "manifold/polygon.h"
namespace manifold {
using GeneralTriangulation = std::function<std::vector<ivec3>(int)>;
using AddTriangle = std::function<void(int, ivec3, vec3, TriRef)>;
/**
* Triangulates the faces. In this case, the halfedge_ vector is not yet a set
* of triangles as required by this data structure, but is instead a set of
* general faces with the input faceEdge vector having length of the number of
* faces + 1. The values are indicies into the halfedge_ vector for the first
* edge of each face, with the final value being the length of the halfedge_
* vector itself. Upon return, halfedge_ has been lengthened and properly
* represents the mesh as a set of triangles as usual. In this process the
* faceNormal_ values are retained, repeated as necessary.
*/
void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
const Vec<TriRef>& halfedgeRef) {
ZoneScoped;
Vec<ivec3> triVerts;
Vec<vec3> triNormal;
Vec<TriRef>& triRef = meshRelation_.triRef;
triRef.resize(0);
auto processFace = [&](GeneralTriangulation general, AddTriangle addTri,
int face) {
const int firstEdge = faceEdge[face];
const int lastEdge = faceEdge[face + 1];
const int numEdge = lastEdge - firstEdge;
DEBUG_ASSERT(numEdge >= 3, topologyErr, "face has less than three edges.");
const vec3 normal = faceNormal_[face];
if (numEdge == 3) { // Single triangle
int mapping[3] = {halfedge_[firstEdge].startVert,
halfedge_[firstEdge + 1].startVert,
halfedge_[firstEdge + 2].startVert};
ivec3 tri(halfedge_[firstEdge].startVert,
halfedge_[firstEdge + 1].startVert,
halfedge_[firstEdge + 2].startVert);
ivec3 ends(halfedge_[firstEdge].endVert, halfedge_[firstEdge + 1].endVert,
halfedge_[firstEdge + 2].endVert);
if (ends[0] == tri[2]) {
std::swap(tri[1], tri[2]);
std::swap(ends[1], ends[2]);
}
DEBUG_ASSERT(ends[0] == tri[1] && ends[1] == tri[2] && ends[2] == tri[0],
topologyErr, "These 3 edges do not form a triangle!");
addTri(face, tri, normal, halfedgeRef[firstEdge]);
} else if (numEdge == 4) { // Pair of triangles
int mapping[4] = {halfedge_[firstEdge].startVert,
halfedge_[firstEdge + 1].startVert,
halfedge_[firstEdge + 2].startVert,
halfedge_[firstEdge + 3].startVert};
const mat2x3 projection = GetAxisAlignedProjection(normal);
auto triCCW = [&projection, this](const ivec3 tri) {
return CCW(projection * this->vertPos_[tri[0]],
projection * this->vertPos_[tri[1]],
projection * this->vertPos_[tri[2]], epsilon_) >= 0;
};
ivec3 tri0(halfedge_[firstEdge].startVert, halfedge_[firstEdge].endVert,
-1);
ivec3 tri1(-1, -1, tri0[0]);
for (const int i : {1, 2, 3}) {
if (halfedge_[firstEdge + i].startVert == tri0[1]) {
tri0[2] = halfedge_[firstEdge + i].endVert;
tri1[0] = tri0[2];
}
if (halfedge_[firstEdge + i].endVert == tri0[0]) {
tri1[1] = halfedge_[firstEdge + i].startVert;
}
}
DEBUG_ASSERT(la::all(la::gequal(tri0, ivec3(0))) &&
la::all(la::gequal(tri1, ivec3(0))),
topologyErr, "non-manifold quad!");
bool firstValid = triCCW(tri0) && triCCW(tri1);
tri0[2] = tri1[1];
tri1[2] = tri0[1];
bool secondValid = triCCW(tri0) && triCCW(tri1);
if (!secondValid) {
tri0[2] = tri1[0];
tri1[2] = tri0[0];
} else if (firstValid) {
vec3 firstCross = vertPos_[tri0[0]] - vertPos_[tri1[0]];
vec3 secondCross = vertPos_[tri0[1]] - vertPos_[tri1[1]];
if (la::dot(firstCross, firstCross) <
la::dot(secondCross, secondCross)) {
tri0[2] = tri1[0];
tri1[2] = tri0[0];
}
}
for (const auto& tri : {tri0, tri1}) {
addTri(face, tri, normal, halfedgeRef[firstEdge]);
}
} else { // General triangulation
for (const auto& tri : general(face)) {
addTri(face, tri, normal, halfedgeRef[firstEdge]);
}
}
};
auto generalTriangulation = [&](int face) {
const vec3 normal = faceNormal_[face];
const mat2x3 projection = GetAxisAlignedProjection(normal);
const PolygonsIdx polys =
Face2Polygons(halfedge_.cbegin() + faceEdge[face],
halfedge_.cbegin() + faceEdge[face + 1], projection);
return TriangulateIdx(polys, epsilon_);
};
#if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
tbb::task_group group;
// map from face to triangle
tbb::concurrent_unordered_map<int, std::vector<ivec3>> results;
Vec<size_t> triCount(faceEdge.size());
triCount.back() = 0;
// precompute number of triangles per face, and launch async tasks to
// triangulate complex faces
for_each(autoPolicy(faceEdge.size(), 1e5), countAt(0_uz),
countAt(faceEdge.size() - 1), [&](size_t face) {
triCount[face] = faceEdge[face + 1] - faceEdge[face] - 2;
DEBUG_ASSERT(triCount[face] >= 1, topologyErr,
"face has less than three edges.");
if (triCount[face] > 2)
group.run([&, face] {
std::vector<ivec3> newTris = generalTriangulation(face);
triCount[face] = newTris.size();
results[face] = std::move(newTris);
});
});
group.wait();
// prefix sum computation (assign unique index to each face) and preallocation
exclusive_scan(triCount.begin(), triCount.end(), triCount.begin(), 0_uz);
triVerts.resize(triCount.back());
triNormal.resize(triCount.back());
triRef.resize(triCount.back());
auto processFace2 = std::bind(
processFace, [&](size_t face) { return std::move(results[face]); },
[&](size_t face, ivec3 tri, vec3 normal, TriRef r) {
triVerts[triCount[face]] = tri;
triNormal[triCount[face]] = normal;
triRef[triCount[face]] = r;
triCount[face]++;
},
std::placeholders::_1);
// set triangles in parallel
for_each(autoPolicy(faceEdge.size(), 1e4), countAt(0_uz),
countAt(faceEdge.size() - 1), processFace2);
#else
triVerts.reserve(faceEdge.size());
triNormal.reserve(faceEdge.size());
triRef.reserve(faceEdge.size());
auto processFace2 = std::bind(
processFace, generalTriangulation,
[&](size_t _face, ivec3 tri, vec3 normal, TriRef r) {
triVerts.push_back(tri);
triNormal.push_back(normal);
triRef.push_back(r);
},
std::placeholders::_1);
for (size_t face = 0; face < faceEdge.size() - 1; ++face) {
processFace2(face);
}
#endif
faceNormal_ = std::move(triNormal);
CreateHalfedges(triVerts);
}
/**
* Returns a set of 2D polygons formed by the input projection of the vertices
* of the list of Halfedges, which must be an even-manifold, meaning each vert
* must be referenced the same number of times as a startVert and endVert.
*/
PolygonsIdx Manifold::Impl::Face2Polygons(VecView<Halfedge>::IterC start,
VecView<Halfedge>::IterC end,
mat2x3 projection) const {
std::multimap<int, int> vert_edge;
for (auto edge = start; edge != end; ++edge) {
vert_edge.emplace(
std::make_pair(edge->startVert, static_cast<int>(edge - start)));
}
PolygonsIdx polys;
int startEdge = 0;
int thisEdge = startEdge;
while (1) {
if (thisEdge == startEdge) {
if (vert_edge.empty()) break;
startEdge = vert_edge.begin()->second;
thisEdge = startEdge;
polys.push_back({});
}
int vert = (start + thisEdge)->startVert;
polys.back().push_back({projection * vertPos_[vert], vert});
const auto result = vert_edge.find((start + thisEdge)->endVert);
DEBUG_ASSERT(result != vert_edge.end(), topologyErr, "non-manifold edge");
thisEdge = result->second;
vert_edge.erase(result);
}
return polys;
}
Polygons Manifold::Impl::Slice(double height) const {
Box plane = bBox_;
plane.min.z = plane.max.z = height;
Vec<Box> query;
query.push_back(plane);
const SparseIndices collisions =
collider_.Collisions<false, false>(query.cview());
std::unordered_set<int> tris;
for (size_t i = 0; i < collisions.size(); ++i) {
const int tri = collisions.Get(i, 1);
double min = std::numeric_limits<double>::infinity();
double max = -std::numeric_limits<double>::infinity();
for (const int j : {0, 1, 2}) {
const double z = vertPos_[halfedge_[3 * tri + j].startVert].z;
min = std::min(min, z);
max = std::max(max, z);
}
if (min <= height && max > height) {
tris.insert(tri);
}
}
Polygons polys;
while (!tris.empty()) {
const int startTri = *tris.begin();
SimplePolygon poly;
int k = 0;
for (const int j : {0, 1, 2}) {
if (vertPos_[halfedge_[3 * startTri + j].startVert].z > height &&
vertPos_[halfedge_[3 * startTri + Next3(j)].startVert].z <= height) {
k = Next3(j);
break;
}
}
int tri = startTri;
do {
tris.erase(tris.find(tri));
if (vertPos_[halfedge_[3 * tri + k].endVert].z <= height) {
k = Next3(k);
}
Halfedge up = halfedge_[3 * tri + k];
const vec3 below = vertPos_[up.startVert];
const vec3 above = vertPos_[up.endVert];
const double a = (height - below.z) / (above.z - below.z);
poly.push_back(vec2(la::lerp(below, above, a)));
const int pair = up.pairedHalfedge;
tri = pair / 3;
k = Next3(pair % 3);
} while (tri != startTri);
polys.push_back(poly);
}
return polys;
}
Polygons Manifold::Impl::Project() const {
const mat2x3 projection = GetAxisAlignedProjection({0, 0, 1});
Vec<Halfedge> cusps(NumEdge());
cusps.resize(
copy_if(
halfedge_.cbegin(), halfedge_.cend(), cusps.begin(),
[&](Halfedge edge) {
return faceNormal_[halfedge_[edge.pairedHalfedge].pairedHalfedge /
3]
.z >= 0 &&
faceNormal_[edge.pairedHalfedge / 3].z < 0;
}) -
cusps.begin());
PolygonsIdx polysIndexed =
Face2Polygons(cusps.cbegin(), cusps.cend(), projection);
Polygons polys;
for (const auto& poly : polysIndexed) {
SimplePolygon simple;
for (const PolyVert& polyVert : poly) {
simple.push_back(polyVert.pos);
}
polys.push_back(simple);
}
return polys;
}
} // namespace manifold

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// Copyright 2022 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <stdint.h>
#include <atomic>
#include "./utils.h"
#include "./vec.h"
namespace {
typedef unsigned long long int Uint64;
typedef Uint64 (*hash_fun_t)(Uint64);
inline constexpr Uint64 kOpen = std::numeric_limits<Uint64>::max();
template <typename T>
T AtomicCAS(T& target, T compare, T val) {
std::atomic<T>& tar = reinterpret_cast<std::atomic<T>&>(target);
tar.compare_exchange_strong(compare, val, std::memory_order_acq_rel);
return compare;
}
template <typename T>
void AtomicStore(T& target, T val) {
std::atomic<T>& tar = reinterpret_cast<std::atomic<T>&>(target);
// release is good enough, although not really something general
tar.store(val, std::memory_order_release);
}
template <typename T>
T AtomicLoad(const T& target) {
const std::atomic<T>& tar = reinterpret_cast<const std::atomic<T>&>(target);
// acquire is good enough, although not general
return tar.load(std::memory_order_acquire);
}
// https://stackoverflow.com/questions/664014/what-integer-hash-function-are-good-that-accepts-an-integer-hash-key
inline Uint64 hash64bit(Uint64 x) {
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9ull;
x = (x ^ (x >> 27)) * 0x94d049bb133111ebull;
x = x ^ (x >> 31);
return x;
}
} // namespace
namespace manifold {
template <typename V, hash_fun_t H = hash64bit>
class HashTableD {
public:
HashTableD(Vec<Uint64>& keys, Vec<V>& values, std::atomic<size_t>& used,
uint32_t step = 1)
: step_{step}, keys_{keys}, values_{values}, used_{used} {}
int Size() const { return keys_.size(); }
bool Full() const {
return used_.load(std::memory_order_relaxed) * 2 >
static_cast<size_t>(Size());
}
void Insert(Uint64 key, const V& val) {
uint32_t idx = H(key) & (Size() - 1);
while (1) {
if (Full()) return;
Uint64& k = keys_[idx];
const Uint64 found = AtomicCAS(k, kOpen, key);
if (found == kOpen) {
used_.fetch_add(1, std::memory_order_relaxed);
values_[idx] = val;
return;
}
if (found == key) return;
idx = (idx + step_) & (Size() - 1);
}
}
V& operator[](Uint64 key) {
uint32_t idx = H(key) & (Size() - 1);
while (1) {
const Uint64 k = AtomicLoad(keys_[idx]);
if (k == key || k == kOpen) {
return values_[idx];
}
idx = (idx + step_) & (Size() - 1);
}
}
const V& operator[](Uint64 key) const {
uint32_t idx = H(key) & (Size() - 1);
while (1) {
const Uint64 k = AtomicLoad(keys_[idx]);
if (k == key || k == kOpen) {
return values_[idx];
}
idx = (idx + step_) & (Size() - 1);
}
}
Uint64 KeyAt(int idx) const { return AtomicLoad(keys_[idx]); }
V& At(int idx) { return values_[idx]; }
const V& At(int idx) const { return values_[idx]; }
private:
uint32_t step_;
VecView<Uint64> keys_;
VecView<V> values_;
std::atomic<size_t>& used_;
};
template <typename V, hash_fun_t H = hash64bit>
class HashTable {
public:
HashTable(size_t size, uint32_t step = 1)
: keys_{size == 0 ? 0 : 1_uz << (int)ceil(log2(size)), kOpen},
values_{size == 0 ? 0 : 1_uz << (int)ceil(log2(size)), {}},
step_(step) {}
HashTable(const HashTable& other)
: keys_(other.keys_), values_(other.values_), step_(other.step_) {
used_.store(other.used_.load());
}
HashTable& operator=(const HashTable& other) {
if (this == &other) return *this;
keys_ = other.keys_;
values_ = other.values_;
used_.store(other.used_.load());
step_ = other.step_;
return *this;
}
HashTableD<V, H> D() { return {keys_, values_, used_, step_}; }
int Entries() const { return used_.load(std::memory_order_relaxed); }
size_t Size() const { return keys_.size(); }
bool Full() const {
return used_.load(std::memory_order_relaxed) * 2 > Size();
}
double FilledFraction() const {
return static_cast<double>(used_.load(std::memory_order_relaxed)) / Size();
}
Vec<V>& GetValueStore() { return values_; }
static Uint64 Open() { return kOpen; }
private:
Vec<Uint64> keys_;
Vec<V> values_;
std::atomic<size_t> used_ = 0;
uint32_t step_;
};
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./impl.h"
#include <algorithm>
#include <atomic>
#include <map>
#include "./hashtable.h"
#include "./mesh_fixes.h"
#include "./parallel.h"
#include "./svd.h"
namespace {
using namespace manifold;
constexpr uint64_t kRemove = std::numeric_limits<uint64_t>::max();
void AtomicAddVec3(vec3& target, const vec3& add) {
for (int i : {0, 1, 2}) {
std::atomic<double>& tar =
reinterpret_cast<std::atomic<double>&>(target[i]);
double old_val = tar.load(std::memory_order_relaxed);
while (!tar.compare_exchange_weak(old_val, old_val + add[i],
std::memory_order_relaxed)) {
}
}
}
struct Transform4x3 {
const mat3x4 transform;
vec3 operator()(vec3 position) { return transform * vec4(position, 1.0); }
};
template <bool calculateTriNormal>
struct AssignNormals {
VecView<vec3> faceNormal;
VecView<vec3> vertNormal;
VecView<const vec3> vertPos;
VecView<const Halfedge> halfedges;
void operator()(const int face) {
vec3& triNormal = faceNormal[face];
ivec3 triVerts;
for (int i : {0, 1, 2}) triVerts[i] = halfedges[3 * face + i].startVert;
vec3 edge[3];
for (int i : {0, 1, 2}) {
const int j = (i + 1) % 3;
edge[i] = la::normalize(vertPos[triVerts[j]] - vertPos[triVerts[i]]);
}
if (calculateTriNormal) {
triNormal = la::normalize(la::cross(edge[0], edge[1]));
if (std::isnan(triNormal.x)) triNormal = vec3(0, 0, 1);
}
// corner angles
vec3 phi;
double dot = -la::dot(edge[2], edge[0]);
phi[0] = dot >= 1 ? 0 : (dot <= -1 ? kPi : std::acos(dot));
dot = -la::dot(edge[0], edge[1]);
phi[1] = dot >= 1 ? 0 : (dot <= -1 ? kPi : std::acos(dot));
phi[2] = kPi - phi[0] - phi[1];
// assign weighted sum
for (int i : {0, 1, 2}) {
AtomicAddVec3(vertNormal[triVerts[i]], phi[i] * triNormal);
}
}
};
struct UpdateMeshID {
const HashTableD<uint32_t> meshIDold2new;
void operator()(TriRef& ref) { ref.meshID = meshIDold2new[ref.meshID]; }
};
struct CoplanarEdge {
VecView<std::pair<int, int>> face2face;
VecView<double> triArea;
VecView<const Halfedge> halfedge;
VecView<const vec3> vertPos;
VecView<const TriRef> triRef;
VecView<const ivec3> triProp;
const int numProp;
const double epsilon;
const double tolerance;
void operator()(const int edgeIdx) {
const Halfedge edge = halfedge[edgeIdx];
const Halfedge pair = halfedge[edge.pairedHalfedge];
const int edgeFace = edgeIdx / 3;
const int pairFace = edge.pairedHalfedge / 3;
if (triRef[edgeFace].meshID != triRef[pairFace].meshID) return;
const vec3 base = vertPos[edge.startVert];
const int baseNum = edgeIdx - 3 * edgeFace;
const int jointNum = edge.pairedHalfedge - 3 * pairFace;
if (numProp > 0) {
if (triProp[edgeFace][baseNum] != triProp[pairFace][Next3(jointNum)] ||
triProp[edgeFace][Next3(baseNum)] != triProp[pairFace][jointNum])
return;
}
if (!edge.IsForward()) return;
const int edgeNum = baseNum == 0 ? 2 : baseNum - 1;
const int pairNum = jointNum == 0 ? 2 : jointNum - 1;
const vec3 jointVec = vertPos[pair.startVert] - base;
const vec3 edgeVec =
vertPos[halfedge[3 * edgeFace + edgeNum].startVert] - base;
const vec3 pairVec =
vertPos[halfedge[3 * pairFace + pairNum].startVert] - base;
const double length = std::max(la::length(jointVec), la::length(edgeVec));
const double lengthPair =
std::max(la::length(jointVec), la::length(pairVec));
vec3 normal = la::cross(jointVec, edgeVec);
const double area = la::length(normal);
const double areaPair = la::length(la::cross(pairVec, jointVec));
// make sure we only write this once
if (edgeIdx % 3 == 0) triArea[edgeFace] = area;
// Don't link degenerate triangles
if (area < length * epsilon || areaPair < lengthPair * epsilon) return;
const double volume = std::abs(la::dot(normal, pairVec));
// Only operate on coplanar triangles
if (volume > std::max(area, areaPair) * tolerance) return;
face2face[edgeIdx] = std::make_pair(edgeFace, pairFace);
}
};
struct CheckCoplanarity {
VecView<int> comp2tri;
VecView<const Halfedge> halfedge;
VecView<const vec3> vertPos;
std::vector<int>* components;
const double tolerance;
void operator()(int tri) {
const int component = (*components)[tri];
const int referenceTri =
reinterpret_cast<std::atomic<int>*>(&comp2tri[component])
->load(std::memory_order_relaxed);
if (referenceTri < 0 || referenceTri == tri) return;
const vec3 origin = vertPos[halfedge[3 * referenceTri].startVert];
const vec3 normal = la::normalize(
la::cross(vertPos[halfedge[3 * referenceTri + 1].startVert] - origin,
vertPos[halfedge[3 * referenceTri + 2].startVert] - origin));
for (const int i : {0, 1, 2}) {
const vec3 vert = vertPos[halfedge[3 * tri + i].startVert];
// If any component vertex is not coplanar with the component's reference
// triangle, unmark the entire component so that none of its triangles are
// marked coplanar.
if (std::abs(la::dot(normal, vert - origin)) > tolerance) {
reinterpret_cast<std::atomic<int>*>(&comp2tri[component])
->store(-1, std::memory_order_relaxed);
break;
}
}
}
};
int GetLabels(std::vector<int>& components,
const Vec<std::pair<int, int>>& edges, int numNodes) {
UnionFind<> uf(numNodes);
for (auto edge : edges) {
if (edge.first == -1 || edge.second == -1) continue;
uf.unionXY(edge.first, edge.second);
}
return uf.connectedComponents(components);
}
void DedupePropVerts(manifold::Vec<ivec3>& triProp,
const Vec<std::pair<int, int>>& vert2vert) {
ZoneScoped;
std::vector<int> vertLabels;
const int numLabels = GetLabels(vertLabels, vert2vert, vert2vert.size());
std::vector<int> label2vert(numLabels);
for (size_t v = 0; v < vert2vert.size(); ++v) label2vert[vertLabels[v]] = v;
for (auto& prop : triProp)
for (int i : {0, 1, 2}) prop[i] = label2vert[vertLabels[prop[i]]];
}
} // namespace
namespace manifold {
std::atomic<uint32_t> Manifold::Impl::meshIDCounter_(1);
uint32_t Manifold::Impl::ReserveIDs(uint32_t n) {
return Manifold::Impl::meshIDCounter_.fetch_add(n, std::memory_order_relaxed);
}
/**
* Create either a unit tetrahedron, cube or octahedron. The cube is in the
* first octant, while the others are symmetric about the origin.
*/
Manifold::Impl::Impl(Shape shape, const mat3x4 m) {
std::vector<vec3> vertPos;
std::vector<ivec3> triVerts;
switch (shape) {
case Shape::Tetrahedron:
vertPos = {{-1.0, -1.0, 1.0},
{-1.0, 1.0, -1.0},
{1.0, -1.0, -1.0},
{1.0, 1.0, 1.0}};
triVerts = {{2, 0, 1}, {0, 3, 1}, {2, 3, 0}, {3, 2, 1}};
break;
case Shape::Cube:
vertPos = {{0.0, 0.0, 0.0}, //
{0.0, 0.0, 1.0}, //
{0.0, 1.0, 0.0}, //
{0.0, 1.0, 1.0}, //
{1.0, 0.0, 0.0}, //
{1.0, 0.0, 1.0}, //
{1.0, 1.0, 0.0}, //
{1.0, 1.0, 1.0}};
triVerts = {{1, 0, 4}, {2, 4, 0}, //
{1, 3, 0}, {3, 1, 5}, //
{3, 2, 0}, {3, 7, 2}, //
{5, 4, 6}, {5, 1, 4}, //
{6, 4, 2}, {7, 6, 2}, //
{7, 3, 5}, {7, 5, 6}};
break;
case Shape::Octahedron:
vertPos = {{1.0, 0.0, 0.0}, //
{-1.0, 0.0, 0.0}, //
{0.0, 1.0, 0.0}, //
{0.0, -1.0, 0.0}, //
{0.0, 0.0, 1.0}, //
{0.0, 0.0, -1.0}};
triVerts = {{0, 2, 4}, {1, 5, 3}, //
{2, 1, 4}, {3, 5, 0}, //
{1, 3, 4}, {0, 5, 2}, //
{3, 0, 4}, {2, 5, 1}};
break;
}
vertPos_ = vertPos;
for (auto& v : vertPos_) v = m * vec4(v, 1.0);
CreateHalfedges(triVerts);
Finish();
InitializeOriginal();
CreateFaces();
}
void Manifold::Impl::RemoveUnreferencedVerts() {
ZoneScoped;
Vec<int> vertOld2New(NumVert(), 0);
auto policy = autoPolicy(NumVert(), 1e5);
for_each(policy, halfedge_.cbegin(), halfedge_.cend(),
[&vertOld2New](Halfedge h) {
reinterpret_cast<std::atomic<int>*>(&vertOld2New[h.startVert])
->store(1, std::memory_order_relaxed);
});
const Vec<vec3> oldVertPos = vertPos_;
Vec<size_t> tmpBuffer(oldVertPos.size());
auto vertIdIter = TransformIterator(countAt(0_uz), [&vertOld2New](size_t i) {
if (vertOld2New[i] > 0) return i;
return std::numeric_limits<size_t>::max();
});
auto next =
copy_if(vertIdIter, vertIdIter + tmpBuffer.size(), tmpBuffer.begin(),
[](size_t v) { return v != std::numeric_limits<size_t>::max(); });
if (next == tmpBuffer.end()) return;
gather(tmpBuffer.begin(), next, oldVertPos.begin(), vertPos_.begin());
vertPos_.resize(std::distance(tmpBuffer.begin(), next));
exclusive_scan(vertOld2New.begin(), vertOld2New.end(), vertOld2New.begin());
for_each(policy, halfedge_.begin(), halfedge_.end(),
[&vertOld2New](Halfedge& h) {
h.startVert = vertOld2New[h.startVert];
h.endVert = vertOld2New[h.endVert];
});
}
void Manifold::Impl::InitializeOriginal(bool keepFaceID) {
const int meshID = ReserveIDs(1);
meshRelation_.originalID = meshID;
auto& triRef = meshRelation_.triRef;
triRef.resize(NumTri());
for_each_n(autoPolicy(NumTri(), 1e5), countAt(0), NumTri(),
[meshID, keepFaceID, &triRef](const int tri) {
triRef[tri] = {meshID, meshID, tri,
keepFaceID ? triRef[tri].faceID : tri};
});
meshRelation_.meshIDtransform.clear();
meshRelation_.meshIDtransform[meshID] = {meshID};
}
void Manifold::Impl::CreateFaces() {
ZoneScoped;
Vec<std::pair<int, int>> face2face(halfedge_.size(), {-1, -1});
Vec<std::pair<int, int>> vert2vert(halfedge_.size(), {-1, -1});
Vec<double> triArea(NumTri());
const size_t numProp = NumProp();
if (numProp > 0) {
for_each_n(
autoPolicy(halfedge_.size(), 1e4), countAt(0), halfedge_.size(),
[&vert2vert, numProp, this](const int edgeIdx) {
const Halfedge edge = halfedge_[edgeIdx];
const Halfedge pair = halfedge_[edge.pairedHalfedge];
const int edgeFace = edgeIdx / 3;
const int pairFace = edge.pairedHalfedge / 3;
if (meshRelation_.triRef[edgeFace].meshID !=
meshRelation_.triRef[pairFace].meshID)
return;
const int baseNum = edgeIdx - 3 * edgeFace;
const int jointNum = edge.pairedHalfedge - 3 * pairFace;
const int prop0 = meshRelation_.triProperties[edgeFace][baseNum];
const int prop1 =
meshRelation_
.triProperties[pairFace][jointNum == 2 ? 0 : jointNum + 1];
bool propEqual = true;
for (size_t p = 0; p < numProp; ++p) {
if (meshRelation_.properties[numProp * prop0 + p] !=
meshRelation_.properties[numProp * prop1 + p]) {
propEqual = false;
break;
}
}
if (propEqual) {
vert2vert[edgeIdx] = std::make_pair(prop0, prop1);
}
});
DedupePropVerts(meshRelation_.triProperties, vert2vert);
}
for_each_n(autoPolicy(halfedge_.size(), 1e4), countAt(0), halfedge_.size(),
CoplanarEdge({face2face, triArea, halfedge_, vertPos_,
meshRelation_.triRef, meshRelation_.triProperties,
meshRelation_.numProp, epsilon_, tolerance_}));
std::vector<int> components;
const int numComponent = GetLabels(components, face2face, NumTri());
Vec<int> comp2tri(numComponent, -1);
for (size_t tri = 0; tri < NumTri(); ++tri) {
const int comp = components[tri];
const int current = comp2tri[comp];
if (current < 0 || triArea[tri] > triArea[current]) {
comp2tri[comp] = tri;
triArea[comp] = triArea[tri];
}
}
for_each_n(autoPolicy(halfedge_.size(), 1e4), countAt(0), NumTri(),
CheckCoplanarity(
{comp2tri, halfedge_, vertPos_, &components, tolerance_}));
Vec<TriRef>& triRef = meshRelation_.triRef;
for (size_t tri = 0; tri < NumTri(); ++tri) {
const int referenceTri = comp2tri[components[tri]];
if (referenceTri >= 0) {
triRef[tri].faceID = referenceTri;
}
}
}
/**
* Create the halfedge_ data structure from an input triVerts array like Mesh.
*/
void Manifold::Impl::CreateHalfedges(const Vec<ivec3>& triVerts) {
ZoneScoped;
const size_t numTri = triVerts.size();
const int numHalfedge = 3 * numTri;
// drop the old value first to avoid copy
halfedge_.resize(0);
halfedge_.resize(numHalfedge);
Vec<uint64_t> edge(numHalfedge);
Vec<int> ids(numHalfedge);
auto policy = autoPolicy(numTri, 1e5);
sequence(ids.begin(), ids.end());
for_each_n(policy, countAt(0), numTri,
[this, &edge, &triVerts](const int tri) {
const ivec3& verts = triVerts[tri];
for (const int i : {0, 1, 2}) {
const int j = (i + 1) % 3;
const int e = 3 * tri + i;
halfedge_[e] = {verts[i], verts[j], -1};
// Sort the forward halfedges in front of the backward ones
// by setting the highest-order bit.
edge[e] = uint64_t(verts[i] < verts[j] ? 1 : 0) << 63 |
((uint64_t)std::min(verts[i], verts[j])) << 32 |
std::max(verts[i], verts[j]);
}
});
// Stable sort is required here so that halfedges from the same face are
// paired together (the triangles were created in face order). In some
// degenerate situations the triangulator can add the same internal edge in
// two different faces, causing this edge to not be 2-manifold. These are
// fixed by duplicating verts in SimplifyTopology.
stable_sort(ids.begin(), ids.end(), [&edge](const int& a, const int& b) {
return edge[a] < edge[b];
});
// Mark opposed triangles for removal
const int numEdge = numHalfedge / 2;
for (int i = 0; i < numEdge; ++i) {
const int pair0 = ids[i];
Halfedge h0 = halfedge_[pair0];
int k = i + numEdge;
while (1) {
const int pair1 = ids[k];
Halfedge h1 = halfedge_[pair1];
if (h0.startVert != h1.endVert || h0.endVert != h1.startVert) break;
if (halfedge_[NextHalfedge(pair0)].endVert ==
halfedge_[NextHalfedge(pair1)].endVert) {
// Reorder so that remaining edges pair up
if (k != i + numEdge) std::swap(ids[i + numEdge], ids[k]);
break;
}
++k;
if (k >= numHalfedge) break;
}
}
// Once sorted, the first half of the range is the forward halfedges, which
// correspond to their backward pair at the same offset in the second half
// of the range.
for_each_n(policy, countAt(0), numEdge, [this, &ids, numEdge](int i) {
const int pair0 = ids[i];
const int pair1 = ids[i + numEdge];
halfedge_[pair0].pairedHalfedge = pair1;
halfedge_[pair1].pairedHalfedge = pair0;
});
// When opposed triangles are removed, they may strand unreferenced verts.
RemoveUnreferencedVerts();
}
/**
* Does a full recalculation of the face bounding boxes, including updating
* the collider, but does not resort the faces.
*/
void Manifold::Impl::Update() {
CalculateBBox();
Vec<Box> faceBox;
Vec<uint32_t> faceMorton;
GetFaceBoxMorton(faceBox, faceMorton);
collider_.UpdateBoxes(faceBox);
}
void Manifold::Impl::MarkFailure(Error status) {
bBox_ = Box();
vertPos_.resize(0);
halfedge_.resize(0);
vertNormal_.resize(0);
faceNormal_.resize(0);
halfedgeTangent_.resize(0);
meshRelation_ = MeshRelationD();
status_ = status;
}
void Manifold::Impl::Warp(std::function<void(vec3&)> warpFunc) {
WarpBatch([&warpFunc](VecView<vec3> vecs) {
for_each(ExecutionPolicy::Seq, vecs.begin(), vecs.end(), warpFunc);
});
}
void Manifold::Impl::WarpBatch(std::function<void(VecView<vec3>)> warpFunc) {
warpFunc(vertPos_.view());
CalculateBBox();
if (!IsFinite()) {
MarkFailure(Error::NonFiniteVertex);
return;
}
Update();
faceNormal_.resize(0); // force recalculation of triNormal
CalculateNormals();
SetEpsilon();
Finish();
CreateFaces();
meshRelation_.originalID = -1;
}
Manifold::Impl Manifold::Impl::Transform(const mat3x4& transform_) const {
ZoneScoped;
if (transform_ == mat3x4(la::identity)) return *this;
auto policy = autoPolicy(NumVert());
Impl result;
if (status_ != Manifold::Error::NoError) {
result.status_ = status_;
return result;
}
if (!all(la::isfinite(transform_))) {
result.MarkFailure(Error::NonFiniteVertex);
return result;
}
result.collider_ = collider_;
result.meshRelation_ = meshRelation_;
result.epsilon_ = epsilon_;
result.tolerance_ = tolerance_;
result.bBox_ = bBox_;
result.halfedge_ = halfedge_;
result.halfedgeTangent_.resize(halfedgeTangent_.size());
result.meshRelation_.originalID = -1;
for (auto& m : result.meshRelation_.meshIDtransform) {
m.second.transform = transform_ * Mat4(m.second.transform);
}
result.vertPos_.resize(NumVert());
result.faceNormal_.resize(faceNormal_.size());
result.vertNormal_.resize(vertNormal_.size());
transform(vertPos_.begin(), vertPos_.end(), result.vertPos_.begin(),
Transform4x3({transform_}));
mat3 normalTransform = NormalTransform(transform_);
transform(faceNormal_.begin(), faceNormal_.end(), result.faceNormal_.begin(),
TransformNormals({normalTransform}));
transform(vertNormal_.begin(), vertNormal_.end(), result.vertNormal_.begin(),
TransformNormals({normalTransform}));
const bool invert = la::determinant(mat3(transform_)) < 0;
if (halfedgeTangent_.size() > 0) {
for_each_n(policy, countAt(0), halfedgeTangent_.size(),
TransformTangents({result.halfedgeTangent_, 0, mat3(transform_),
invert, halfedgeTangent_, halfedge_}));
}
if (invert) {
for_each_n(policy, countAt(0), result.NumTri(),
FlipTris({result.halfedge_}));
}
// This optimization does a cheap collider update if the transform is
// axis-aligned.
if (!result.collider_.Transform(transform_)) result.Update();
result.CalculateBBox();
// Scale epsilon by the norm of the 3x3 portion of the transform.
result.epsilon_ *= SpectralNorm(mat3(transform_));
// Maximum of inherited epsilon loss and translational epsilon loss.
result.SetEpsilon(result.epsilon_);
return result;
}
/**
* Sets epsilon based on the bounding box, and limits its minimum value
* by the optional input.
*/
void Manifold::Impl::SetEpsilon(double minEpsilon, bool useSingle) {
epsilon_ = MaxEpsilon(minEpsilon, bBox_);
double minTol = epsilon_;
if (useSingle)
minTol =
std::max(minTol, std::numeric_limits<float>::epsilon() * bBox_.Scale());
tolerance_ = std::max(tolerance_, minTol);
}
/**
* If face normals are already present, this function uses them to compute
* vertex normals (angle-weighted pseudo-normals); otherwise it also computes
* the face normals. Face normals are only calculated when needed because
* nearly degenerate faces will accrue rounding error, while the Boolean can
* retain their original normal, which is more accurate and can help with
* merging coplanar faces.
*
* If the face normals have been invalidated by an operation like Warp(),
* ensure you do faceNormal_.resize(0) before calling this function to force
* recalculation.
*/
void Manifold::Impl::CalculateNormals() {
ZoneScoped;
vertNormal_.resize(NumVert());
auto policy = autoPolicy(NumTri(), 1e4);
fill(vertNormal_.begin(), vertNormal_.end(), vec3(0.0));
bool calculateTriNormal = false;
if (faceNormal_.size() != NumTri()) {
faceNormal_.resize(NumTri());
calculateTriNormal = true;
}
if (calculateTriNormal)
for_each_n(
policy, countAt(0), NumTri(),
AssignNormals<true>({faceNormal_, vertNormal_, vertPos_, halfedge_}));
else
for_each_n(
policy, countAt(0), NumTri(),
AssignNormals<false>({faceNormal_, vertNormal_, vertPos_, halfedge_}));
for_each(policy, vertNormal_.begin(), vertNormal_.end(),
[](vec3& v) { v = SafeNormalize(v); });
}
/**
* Remaps all the contained meshIDs to new unique values to represent new
* instances of these meshes.
*/
void Manifold::Impl::IncrementMeshIDs() {
HashTable<uint32_t> meshIDold2new(meshRelation_.meshIDtransform.size() * 2);
// Update keys of the transform map
std::map<int, Relation> oldTransforms;
std::swap(meshRelation_.meshIDtransform, oldTransforms);
const int numMeshIDs = oldTransforms.size();
int nextMeshID = ReserveIDs(numMeshIDs);
for (const auto& pair : oldTransforms) {
meshIDold2new.D().Insert(pair.first, nextMeshID);
meshRelation_.meshIDtransform[nextMeshID++] = pair.second;
}
const size_t numTri = NumTri();
for_each_n(autoPolicy(numTri, 1e5), meshRelation_.triRef.begin(), numTri,
UpdateMeshID({meshIDold2new.D()}));
}
/**
* Returns a sparse array of the bounding box overlaps between the edges of
* the input manifold, Q and the faces of this manifold. Returned indices only
* point to forward halfedges.
*/
SparseIndices Manifold::Impl::EdgeCollisions(const Impl& Q,
bool inverted) const {
ZoneScoped;
Vec<TmpEdge> edges = CreateTmpEdges(Q.halfedge_);
const size_t numEdge = edges.size();
Vec<Box> QedgeBB(numEdge);
const auto& vertPos = Q.vertPos_;
auto policy = autoPolicy(numEdge, 1e5);
for_each_n(
policy, countAt(0), numEdge, [&QedgeBB, &edges, &vertPos](const int e) {
QedgeBB[e] = Box(vertPos[edges[e].first], vertPos[edges[e].second]);
});
SparseIndices q1p2(0);
if (inverted)
q1p2 = collider_.Collisions<false, true>(QedgeBB.cview());
else
q1p2 = collider_.Collisions<false, false>(QedgeBB.cview());
if (inverted)
for_each(policy, countAt(0_uz), countAt(q1p2.size()),
ReindexEdge<true>({edges, q1p2}));
else
for_each(policy, countAt(0_uz), countAt(q1p2.size()),
ReindexEdge<false>({edges, q1p2}));
return q1p2;
}
/**
* Returns a sparse array of the input vertices that project inside the XY
* bounding boxes of the faces of this manifold.
*/
SparseIndices Manifold::Impl::VertexCollisionsZ(VecView<const vec3> vertsIn,
bool inverted) const {
ZoneScoped;
if (inverted)
return collider_.Collisions<false, true>(vertsIn);
else
return collider_.Collisions<false, false>(vertsIn);
}
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <map>
#include "./collider.h"
#include "./shared.h"
#include "./sparse.h"
#include "./vec.h"
#include "manifold/manifold.h"
#include "manifold/polygon.h"
namespace manifold {
/** @ingroup Private */
struct Manifold::Impl {
struct Relation {
int originalID = -1;
mat3x4 transform = la::identity;
bool backSide = false;
};
struct MeshRelationD {
/// The originalID of this Manifold if it is an original; -1 otherwise.
int originalID = -1;
int numProp = 0;
Vec<double> properties;
std::map<int, Relation> meshIDtransform;
Vec<TriRef> triRef;
Vec<ivec3> triProperties;
};
struct BaryIndices {
int tri, start4, end4;
};
Box bBox_;
double epsilon_ = -1;
double tolerance_ = -1;
Error status_ = Error::NoError;
Vec<vec3> vertPos_;
Vec<Halfedge> halfedge_;
Vec<vec3> vertNormal_;
Vec<vec3> faceNormal_;
Vec<vec4> halfedgeTangent_;
MeshRelationD meshRelation_;
Collider collider_;
static std::atomic<uint32_t> meshIDCounter_;
static uint32_t ReserveIDs(uint32_t);
Impl() {}
enum class Shape { Tetrahedron, Cube, Octahedron };
Impl(Shape, const mat3x4 = la::identity);
template <typename Precision, typename I>
Impl(const MeshGLP<Precision, I>& meshGL) {
const uint32_t numVert = meshGL.NumVert();
const uint32_t numTri = meshGL.NumTri();
if (meshGL.numProp < 3) {
MarkFailure(Error::MissingPositionProperties);
return;
}
if (meshGL.mergeFromVert.size() != meshGL.mergeToVert.size()) {
MarkFailure(Error::MergeVectorsDifferentLengths);
return;
}
if (!meshGL.runTransform.empty() &&
12 * meshGL.runOriginalID.size() != meshGL.runTransform.size()) {
MarkFailure(Error::TransformWrongLength);
return;
}
if (!meshGL.runOriginalID.empty() && !meshGL.runIndex.empty() &&
meshGL.runOriginalID.size() + 1 != meshGL.runIndex.size() &&
meshGL.runOriginalID.size() != meshGL.runIndex.size()) {
MarkFailure(Error::RunIndexWrongLength);
return;
}
if (!meshGL.faceID.empty() && meshGL.faceID.size() != meshGL.NumTri()) {
MarkFailure(Error::FaceIDWrongLength);
return;
}
std::vector<int> prop2vert(numVert);
std::iota(prop2vert.begin(), prop2vert.end(), 0);
for (size_t i = 0; i < meshGL.mergeFromVert.size(); ++i) {
const uint32_t from = meshGL.mergeFromVert[i];
const uint32_t to = meshGL.mergeToVert[i];
if (from >= numVert || to >= numVert) {
MarkFailure(Error::MergeIndexOutOfBounds);
return;
}
prop2vert[from] = to;
}
const auto numProp = meshGL.numProp - 3;
meshRelation_.numProp = numProp;
meshRelation_.properties.resize(meshGL.NumVert() * numProp);
tolerance_ = meshGL.tolerance;
// This will have unreferenced duplicate positions that will be removed by
// Impl::RemoveUnreferencedVerts().
vertPos_.resize(meshGL.NumVert());
for (size_t i = 0; i < meshGL.NumVert(); ++i) {
for (const int j : {0, 1, 2})
vertPos_[i][j] = meshGL.vertProperties[meshGL.numProp * i + j];
for (size_t j = 0; j < numProp; ++j)
meshRelation_.properties[i * numProp + j] =
meshGL.vertProperties[meshGL.numProp * i + 3 + j];
}
halfedgeTangent_.resize(meshGL.halfedgeTangent.size() / 4);
for (size_t i = 0; i < halfedgeTangent_.size(); ++i) {
for (const int j : {0, 1, 2, 3})
halfedgeTangent_[i][j] = meshGL.halfedgeTangent[4 * i + j];
}
Vec<TriRef> triRef;
if (!meshGL.runOriginalID.empty()) {
auto runIndex = meshGL.runIndex;
const auto runEnd = meshGL.triVerts.size();
if (runIndex.empty()) {
runIndex = {0, static_cast<I>(runEnd)};
} else if (runIndex.size() == meshGL.runOriginalID.size()) {
runIndex.push_back(runEnd);
}
triRef.resize(meshGL.NumTri());
const auto startID = Impl::ReserveIDs(meshGL.runOriginalID.size());
for (size_t i = 0; i < meshGL.runOriginalID.size(); ++i) {
const int meshID = startID + i;
const int originalID = meshGL.runOriginalID[i];
for (size_t tri = runIndex[i] / 3; tri < runIndex[i + 1] / 3; ++tri) {
TriRef& ref = triRef[tri];
ref.meshID = meshID;
ref.originalID = originalID;
ref.tri = meshGL.faceID.empty() ? tri : meshGL.faceID[tri];
ref.faceID = tri;
}
if (meshGL.runTransform.empty()) {
meshRelation_.meshIDtransform[meshID] = {originalID};
} else {
const Precision* m = meshGL.runTransform.data() + 12 * i;
meshRelation_.meshIDtransform[meshID] = {originalID,
{{m[0], m[1], m[2]},
{m[3], m[4], m[5]},
{m[6], m[7], m[8]},
{m[9], m[10], m[11]}}};
}
}
}
Vec<ivec3> triVerts;
triVerts.reserve(numTri);
for (size_t i = 0; i < numTri; ++i) {
ivec3 tri;
for (const size_t j : {0, 1, 2}) {
uint32_t vert = (uint32_t)meshGL.triVerts[3 * i + j];
if (vert >= numVert) {
MarkFailure(Error::VertexOutOfBounds);
return;
}
tri[j] = prop2vert[vert];
}
if (tri[0] != tri[1] && tri[1] != tri[2] && tri[2] != tri[0]) {
triVerts.push_back(tri);
if (triRef.size() > 0) {
meshRelation_.triRef.push_back(triRef[i]);
}
if (numProp > 0) {
meshRelation_.triProperties.push_back(
ivec3(static_cast<uint32_t>(meshGL.triVerts[3 * i]),
static_cast<uint32_t>(meshGL.triVerts[3 * i + 1]),
static_cast<uint32_t>(meshGL.triVerts[3 * i + 2])));
}
}
}
CreateHalfedges(triVerts);
if (!IsManifold()) {
MarkFailure(Error::NotManifold);
return;
}
CalculateBBox();
if (!IsFinite()) {
MarkFailure(Error::NonFiniteVertex);
return;
}
SetEpsilon(-1, std::is_same<Precision, float>::value);
SplitPinchedVerts();
CalculateNormals();
if (meshGL.runOriginalID.empty()) {
InitializeOriginal();
}
CreateFaces();
SimplifyTopology();
Finish();
// A Manifold created from an input mesh is never an original - the input is
// the original.
meshRelation_.originalID = -1;
}
inline void ForVert(int halfedge, std::function<void(int halfedge)> func) {
int current = halfedge;
do {
current = NextHalfedge(halfedge_[current].pairedHalfedge);
func(current);
} while (current != halfedge);
}
template <typename T>
void ForVert(
int halfedge, std::function<T(int halfedge)> transform,
std::function<void(int halfedge, const T& here, T& next)> binaryOp) {
T here = transform(halfedge);
int current = halfedge;
do {
const int nextHalfedge = NextHalfedge(halfedge_[current].pairedHalfedge);
T next = transform(nextHalfedge);
binaryOp(current, here, next);
here = next;
current = nextHalfedge;
} while (current != halfedge);
}
void CreateFaces();
void RemoveUnreferencedVerts();
void InitializeOriginal(bool keepFaceID = false);
void CreateHalfedges(const Vec<ivec3>& triVerts);
void CalculateNormals();
void IncrementMeshIDs();
void Update();
void MarkFailure(Error status);
void Warp(std::function<void(vec3&)> warpFunc);
void WarpBatch(std::function<void(VecView<vec3>)> warpFunc);
Impl Transform(const mat3x4& transform) const;
SparseIndices EdgeCollisions(const Impl& B, bool inverted = false) const;
SparseIndices VertexCollisionsZ(VecView<const vec3> vertsIn,
bool inverted = false) const;
bool IsEmpty() const { return NumTri() == 0; }
size_t NumVert() const { return vertPos_.size(); }
size_t NumEdge() const { return halfedge_.size() / 2; }
size_t NumTri() const { return halfedge_.size() / 3; }
size_t NumProp() const { return meshRelation_.numProp; }
size_t NumPropVert() const {
return NumProp() == 0 ? NumVert()
: meshRelation_.properties.size() / NumProp();
}
// properties.cu
enum class Property { Volume, SurfaceArea };
double GetProperty(Property prop) const;
void CalculateCurvature(int gaussianIdx, int meanIdx);
void CalculateBBox();
bool IsFinite() const;
bool IsIndexInBounds(VecView<const ivec3> triVerts) const;
void SetEpsilon(double minEpsilon = -1, bool useSingle = false);
bool IsManifold() const;
bool Is2Manifold() const;
bool MatchesTriNormals() const;
int NumDegenerateTris() const;
double MinGap(const Impl& other, double searchLength) const;
// sort.cu
void Finish();
void SortVerts();
void ReindexVerts(const Vec<int>& vertNew2Old, size_t numOldVert);
void CompactProps();
void GetFaceBoxMorton(Vec<Box>& faceBox, Vec<uint32_t>& faceMorton) const;
void SortFaces(Vec<Box>& faceBox, Vec<uint32_t>& faceMorton);
void GatherFaces(const Vec<int>& faceNew2Old);
void GatherFaces(const Impl& old, const Vec<int>& faceNew2Old);
// face_op.cu
void Face2Tri(const Vec<int>& faceEdge, const Vec<TriRef>& halfedgeRef);
PolygonsIdx Face2Polygons(VecView<Halfedge>::IterC start,
VecView<Halfedge>::IterC end,
mat2x3 projection) const;
Polygons Slice(double height) const;
Polygons Project() const;
// edge_op.cu
void CleanupTopology();
void SimplifyTopology();
void DedupeEdge(int edge);
void CollapseEdge(int edge, std::vector<int>& edges);
void RecursiveEdgeSwap(int edge, int& tag, std::vector<int>& visited,
std::vector<int>& edgeSwapStack,
std::vector<int>& edges);
void RemoveIfFolded(int edge);
void PairUp(int edge0, int edge1);
void UpdateVert(int vert, int startEdge, int endEdge);
void FormLoop(int current, int end);
void CollapseTri(const ivec3& triEdge);
void SplitPinchedVerts();
// subdivision.cpp
int GetNeighbor(int tri) const;
ivec4 GetHalfedges(int tri) const;
BaryIndices GetIndices(int halfedge) const;
void FillRetainedVerts(Vec<Barycentric>& vertBary) const;
Vec<Barycentric> Subdivide(std::function<int(vec3, vec4, vec4)>,
bool = false);
// smoothing.cpp
bool IsInsideQuad(int halfedge) const;
bool IsMarkedInsideQuad(int halfedge) const;
vec3 GetNormal(int halfedge, int normalIdx) const;
vec4 TangentFromNormal(const vec3& normal, int halfedge) const;
std::vector<Smoothness> UpdateSharpenedEdges(
const std::vector<Smoothness>&) const;
Vec<bool> FlatFaces() const;
Vec<int> VertFlatFace(const Vec<bool>&) const;
Vec<int> VertHalfedge() const;
std::vector<Smoothness> SharpenEdges(double minSharpAngle,
double minSmoothness) const;
void SharpenTangent(int halfedge, double smoothness);
void SetNormals(int normalIdx, double minSharpAngle);
void LinearizeFlatTangents();
void DistributeTangents(const Vec<bool>& fixedHalfedges);
void CreateTangents(int normalIdx);
void CreateTangents(std::vector<Smoothness>);
void Refine(std::function<int(vec3, vec4, vec4)>, bool = false);
// quickhull.cpp
void Hull(VecView<vec3> vertPos);
};
} // namespace manifold

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// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./shared.h"
namespace {
using namespace manifold;
inline int FlipHalfedge(int halfedge) {
const int tri = halfedge / 3;
const int vert = 2 - (halfedge - 3 * tri);
return 3 * tri + vert;
}
struct TransformNormals {
mat3 transform;
vec3 operator()(vec3 normal) const {
normal = la::normalize(transform * normal);
if (std::isnan(normal.x)) normal = vec3(0.0);
return normal;
}
};
struct TransformTangents {
VecView<vec4> tangent;
const int edgeOffset;
const mat3 transform;
const bool invert;
VecView<const vec4> oldTangents;
VecView<const Halfedge> halfedge;
void operator()(const int edgeOut) {
const int edgeIn =
invert ? halfedge[FlipHalfedge(edgeOut)].pairedHalfedge : edgeOut;
tangent[edgeOut + edgeOffset] =
vec4(transform * vec3(oldTangents[edgeIn]), oldTangents[edgeIn].w);
}
};
struct FlipTris {
VecView<Halfedge> halfedge;
void operator()(const int tri) {
std::swap(halfedge[3 * tri], halfedge[3 * tri + 2]);
for (const int i : {0, 1, 2}) {
std::swap(halfedge[3 * tri + i].startVert, halfedge[3 * tri + i].endVert);
halfedge[3 * tri + i].pairedHalfedge =
FlipHalfedge(halfedge[3 * tri + i].pairedHalfedge);
}
}
};
} // namespace

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <limits>
#include "./impl.h"
#include "./parallel.h"
#include "./tri_dist.h"
namespace {
using namespace manifold;
struct CurvatureAngles {
VecView<double> meanCurvature;
VecView<double> gaussianCurvature;
VecView<double> area;
VecView<double> degree;
VecView<const Halfedge> halfedge;
VecView<const vec3> vertPos;
VecView<const vec3> triNormal;
void operator()(size_t tri) {
vec3 edge[3];
vec3 edgeLength(0.0);
for (int i : {0, 1, 2}) {
const int startVert = halfedge[3 * tri + i].startVert;
const int endVert = halfedge[3 * tri + i].endVert;
edge[i] = vertPos[endVert] - vertPos[startVert];
edgeLength[i] = la::length(edge[i]);
edge[i] /= edgeLength[i];
const int neighborTri = halfedge[3 * tri + i].pairedHalfedge / 3;
const double dihedral =
0.25 * edgeLength[i] *
std::asin(la::dot(la::cross(triNormal[tri], triNormal[neighborTri]),
edge[i]));
AtomicAdd(meanCurvature[startVert], dihedral);
AtomicAdd(meanCurvature[endVert], dihedral);
AtomicAdd(degree[startVert], 1.0);
}
vec3 phi;
phi[0] = std::acos(-la::dot(edge[2], edge[0]));
phi[1] = std::acos(-la::dot(edge[0], edge[1]));
phi[2] = kPi - phi[0] - phi[1];
const double area3 = edgeLength[0] * edgeLength[1] *
la::length(la::cross(edge[0], edge[1])) / 6;
for (int i : {0, 1, 2}) {
const int vert = halfedge[3 * tri + i].startVert;
AtomicAdd(gaussianCurvature[vert], -phi[i]);
AtomicAdd(area[vert], area3);
}
}
};
struct UpdateProperties {
VecView<ivec3> triProp;
VecView<double> properties;
VecView<uint8_t> counters;
VecView<const double> oldProperties;
VecView<const Halfedge> halfedge;
VecView<const double> meanCurvature;
VecView<const double> gaussianCurvature;
const int oldNumProp;
const int numProp;
const int gaussianIdx;
const int meanIdx;
void operator()(const size_t tri) {
for (const int i : {0, 1, 2}) {
const int vert = halfedge[3 * tri + i].startVert;
if (oldNumProp == 0) {
triProp[tri][i] = vert;
}
const int propVert = triProp[tri][i];
auto old = std::atomic_exchange(
reinterpret_cast<std::atomic<uint8_t>*>(&counters[propVert]),
static_cast<uint8_t>(1));
if (old == 1) continue;
for (int p = 0; p < oldNumProp; ++p) {
properties[numProp * propVert + p] =
oldProperties[oldNumProp * propVert + p];
}
if (gaussianIdx >= 0) {
properties[numProp * propVert + gaussianIdx] = gaussianCurvature[vert];
}
if (meanIdx >= 0) {
properties[numProp * propVert + meanIdx] = meanCurvature[vert];
}
}
}
};
struct CheckHalfedges {
VecView<const Halfedge> halfedges;
bool operator()(size_t edge) const {
const Halfedge halfedge = halfedges[edge];
if (halfedge.startVert == -1 || halfedge.endVert == -1) return true;
if (halfedge.pairedHalfedge == -1) return false;
const Halfedge paired = halfedges[halfedge.pairedHalfedge];
bool good = true;
good &= paired.pairedHalfedge == static_cast<int>(edge);
good &= halfedge.startVert != halfedge.endVert;
good &= halfedge.startVert == paired.endVert;
good &= halfedge.endVert == paired.startVert;
return good;
}
};
struct CheckCCW {
VecView<const Halfedge> halfedges;
VecView<const vec3> vertPos;
VecView<const vec3> triNormal;
const double tol;
bool operator()(size_t face) const {
if (halfedges[3 * face].pairedHalfedge < 0) return true;
const mat2x3 projection = GetAxisAlignedProjection(triNormal[face]);
vec2 v[3];
for (int i : {0, 1, 2})
v[i] = projection * vertPos[halfedges[3 * face + i].startVert];
int ccw = CCW(v[0], v[1], v[2], std::abs(tol));
bool check = tol > 0 ? ccw >= 0 : ccw == 0;
#ifdef MANIFOLD_DEBUG
if (tol > 0 && !check) {
vec2 v1 = v[1] - v[0];
vec2 v2 = v[2] - v[0];
double area = v1.x * v2.y - v1.y * v2.x;
double base2 = std::max(la::dot(v1, v1), la::dot(v2, v2));
double base = std::sqrt(base2);
vec3 V0 = vertPos[halfedges[3 * face].startVert];
vec3 V1 = vertPos[halfedges[3 * face + 1].startVert];
vec3 V2 = vertPos[halfedges[3 * face + 2].startVert];
vec3 norm = la::cross(V1 - V0, V2 - V0);
printf(
"Tri %ld does not match normal, approx height = %g, base = %g\n"
"tol = %g, area2 = %g, base2*tol2 = %g\n"
"normal = %g, %g, %g\n"
"norm = %g, %g, %g\nverts: %d, %d, %d\n",
face, area / base, base, tol, area * area, base2 * tol * tol,
triNormal[face].x, triNormal[face].y, triNormal[face].z, norm.x,
norm.y, norm.z, halfedges[3 * face].startVert,
halfedges[3 * face + 1].startVert, halfedges[3 * face + 2].startVert);
}
#endif
return check;
}
};
} // namespace
namespace manifold {
/**
* Returns true if this manifold is in fact an oriented even manifold and all of
* the data structures are consistent.
*/
bool Manifold::Impl::IsManifold() const {
if (halfedge_.size() == 0) return true;
return all_of(countAt(0_uz), countAt(halfedge_.size()),
CheckHalfedges({halfedge_}));
}
/**
* Returns true if this manifold is in fact an oriented 2-manifold and all of
* the data structures are consistent.
*/
bool Manifold::Impl::Is2Manifold() const {
if (halfedge_.size() == 0) return true;
if (!IsManifold()) return false;
Vec<Halfedge> halfedge(halfedge_);
stable_sort(halfedge.begin(), halfedge.end());
return all_of(
countAt(0_uz), countAt(2 * NumEdge() - 1), [&halfedge](size_t edge) {
const Halfedge h = halfedge[edge];
if (h.startVert == -1 && h.endVert == -1 && h.pairedHalfedge == -1)
return true;
return h.startVert != halfedge[edge + 1].startVert ||
h.endVert != halfedge[edge + 1].endVert;
});
}
/**
* Returns true if all triangles are CCW relative to their triNormals_.
*/
bool Manifold::Impl::MatchesTriNormals() const {
if (halfedge_.size() == 0 || faceNormal_.size() != NumTri()) return true;
return all_of(countAt(0_uz), countAt(NumTri()),
CheckCCW({halfedge_, vertPos_, faceNormal_, 2 * epsilon_}));
}
/**
* Returns the number of triangles that are colinear within epsilon_.
*/
int Manifold::Impl::NumDegenerateTris() const {
if (halfedge_.size() == 0 || faceNormal_.size() != NumTri()) return true;
return count_if(
countAt(0_uz), countAt(NumTri()),
CheckCCW({halfedge_, vertPos_, faceNormal_, -1 * epsilon_ / 2}));
}
double Manifold::Impl::GetProperty(Property prop) const {
ZoneScoped;
if (IsEmpty()) return 0;
auto Volume = [this](size_t tri) {
const vec3 v = vertPos_[halfedge_[3 * tri].startVert];
vec3 crossP = la::cross(vertPos_[halfedge_[3 * tri + 1].startVert] - v,
vertPos_[halfedge_[3 * tri + 2].startVert] - v);
return la::dot(crossP, v) / 6.0;
};
auto Area = [this](size_t tri) {
const vec3 v = vertPos_[halfedge_[3 * tri].startVert];
return la::length(
la::cross(vertPos_[halfedge_[3 * tri + 1].startVert] - v,
vertPos_[halfedge_[3 * tri + 2].startVert] - v)) /
2.0;
};
// Kahan summation
double value = 0;
double valueCompensation = 0;
for (size_t i = 0; i < NumTri(); ++i) {
const double value1 = prop == Property::SurfaceArea ? Area(i) : Volume(i);
const double t = value + value1;
valueCompensation += (value - t) + value1;
value = t;
}
value += valueCompensation;
return value;
}
void Manifold::Impl::CalculateCurvature(int gaussianIdx, int meanIdx) {
ZoneScoped;
if (IsEmpty()) return;
if (gaussianIdx < 0 && meanIdx < 0) return;
Vec<double> vertMeanCurvature(NumVert(), 0);
Vec<double> vertGaussianCurvature(NumVert(), kTwoPi);
Vec<double> vertArea(NumVert(), 0);
Vec<double> degree(NumVert(), 0);
auto policy = autoPolicy(NumTri(), 1e4);
for_each(policy, countAt(0_uz), countAt(NumTri()),
CurvatureAngles({vertMeanCurvature, vertGaussianCurvature, vertArea,
degree, halfedge_, vertPos_, faceNormal_}));
for_each_n(policy, countAt(0), NumVert(),
[&vertMeanCurvature, &vertGaussianCurvature, &vertArea,
&degree](const int vert) {
const double factor = degree[vert] / (6 * vertArea[vert]);
vertMeanCurvature[vert] *= factor;
vertGaussianCurvature[vert] *= factor;
});
const int oldNumProp = NumProp();
const int numProp = std::max(oldNumProp, std::max(gaussianIdx, meanIdx) + 1);
const Vec<double> oldProperties = meshRelation_.properties;
meshRelation_.properties = Vec<double>(numProp * NumPropVert(), 0);
meshRelation_.numProp = numProp;
if (meshRelation_.triProperties.size() == 0) {
meshRelation_.triProperties.resize(NumTri());
}
const Vec<uint8_t> counters(NumPropVert(), 0);
for_each_n(
policy, countAt(0_uz), NumTri(),
UpdateProperties({meshRelation_.triProperties, meshRelation_.properties,
counters, oldProperties, halfedge_, vertMeanCurvature,
vertGaussianCurvature, oldNumProp, numProp, gaussianIdx,
meanIdx}));
}
/**
* Calculates the bounding box of the entire manifold, which is stored
* internally to short-cut Boolean operations. Ignores NaNs.
*/
void Manifold::Impl::CalculateBBox() {
bBox_.min =
reduce(vertPos_.begin(), vertPos_.end(),
vec3(std::numeric_limits<double>::infinity()), [](auto a, auto b) {
if (std::isnan(a.x)) return b;
if (std::isnan(b.x)) return a;
return la::min(a, b);
});
bBox_.max = reduce(vertPos_.begin(), vertPos_.end(),
vec3(-std::numeric_limits<double>::infinity()),
[](auto a, auto b) {
if (std::isnan(a.x)) return b;
if (std::isnan(b.x)) return a;
return la::max(a, b);
});
}
/**
* Determines if all verts are finite. Checking just the bounding box dimensions
* is insufficient as it ignores NaNs.
*/
bool Manifold::Impl::IsFinite() const {
return transform_reduce(
vertPos_.begin(), vertPos_.end(), true,
[](bool a, bool b) { return a && b; },
[](auto v) { return la::all(la::isfinite(v)); });
}
/**
* Checks that the input triVerts array has all indices inside bounds of the
* vertPos_ array.
*/
bool Manifold::Impl::IsIndexInBounds(VecView<const ivec3> triVerts) const {
ivec2 minmax = transform_reduce(
triVerts.begin(), triVerts.end(),
ivec2(std::numeric_limits<int>::max(), std::numeric_limits<int>::min()),
[](auto a, auto b) {
a[0] = std::min(a[0], b[0]);
a[1] = std::max(a[1], b[1]);
return a;
},
[](auto tri) {
return ivec2(std::min(tri[0], std::min(tri[1], tri[2])),
std::max(tri[0], std::max(tri[1], tri[2])));
});
return minmax[0] >= 0 && minmax[1] < static_cast<int>(NumVert());
}
/*
* Returns the minimum gap between two manifolds. Returns a double between
* 0 and searchLength.
*/
double Manifold::Impl::MinGap(const Manifold::Impl& other,
double searchLength) const {
ZoneScoped;
Vec<Box> faceBoxOther;
Vec<uint32_t> faceMortonOther;
other.GetFaceBoxMorton(faceBoxOther, faceMortonOther);
transform(faceBoxOther.begin(), faceBoxOther.end(), faceBoxOther.begin(),
[searchLength](const Box& box) {
return Box(box.min - vec3(searchLength),
box.max + vec3(searchLength));
});
SparseIndices collisions = collider_.Collisions(faceBoxOther.cview());
double minDistanceSquared = transform_reduce(
countAt(0_uz), countAt(collisions.size()), searchLength * searchLength,
[](double a, double b) { return std::min(a, b); },
[&collisions, this, &other](int i) {
const int tri = collisions.Get(i, 1);
const int triOther = collisions.Get(i, 0);
std::array<vec3, 3> p;
std::array<vec3, 3> q;
for (const int j : {0, 1, 2}) {
p[j] = vertPos_[halfedge_[3 * tri + j].startVert];
q[j] = other.vertPos_[other.halfedge_[3 * triOther + j].startVert];
}
return DistanceTriangleTriangleSquared(p, q);
});
return sqrt(minDistanceSquared);
};
} // namespace manifold

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thirdparty/manifold/src/quickhull.cpp vendored Normal file
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@ -0,0 +1,860 @@
// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Derived from the public domain work of Antti Kuukka at
// https://github.com/akuukka/quickhull
#include "quickhull.h"
#include <algorithm>
#include <limits>
#include "./impl.h"
namespace manifold {
double defaultEps() { return 0.0000001; }
inline double getSquaredDistanceBetweenPointAndRay(const vec3& p,
const Ray& r) {
const vec3 s = p - r.S;
double t = la::dot(s, r.V);
return la::dot(s, s) - t * t * r.VInvLengthSquared;
}
inline double getSquaredDistance(const vec3& p1, const vec3& p2) {
return la::dot(p1 - p2, p1 - p2);
}
// Note that the unit of distance returned is relative to plane's normal's
// length (divide by N.getNormalized() if needed to get the "real" distance).
inline double getSignedDistanceToPlane(const vec3& v, const Plane& p) {
return la::dot(p.N, v) + p.D;
}
inline vec3 getTriangleNormal(const vec3& a, const vec3& b, const vec3& c) {
// We want to get (a-c).crossProduct(b-c) without constructing temp vectors
double x = a.x - c.x;
double y = a.y - c.y;
double z = a.z - c.z;
double rhsx = b.x - c.x;
double rhsy = b.y - c.y;
double rhsz = b.z - c.z;
double px = y * rhsz - z * rhsy;
double py = z * rhsx - x * rhsz;
double pz = x * rhsy - y * rhsx;
return la::normalize(vec3(px, py, pz));
}
size_t MeshBuilder::addFace() {
if (disabledFaces.size()) {
size_t index = disabledFaces.back();
auto& f = faces[index];
DEBUG_ASSERT(f.isDisabled(), logicErr, "f should be disabled");
DEBUG_ASSERT(!f.pointsOnPositiveSide, logicErr,
"f should not be on the positive side");
f.mostDistantPointDist = 0;
disabledFaces.pop_back();
return index;
}
faces.emplace_back();
return faces.size() - 1;
}
size_t MeshBuilder::addHalfedge() {
if (disabledHalfedges.size()) {
const size_t index = disabledHalfedges.back();
disabledHalfedges.pop_back();
return index;
}
halfedges.push_back({});
halfedgeToFace.push_back(0);
halfedgeNext.push_back(0);
return halfedges.size() - 1;
}
void MeshBuilder::setup(int a, int b, int c, int d) {
faces.clear();
halfedges.clear();
halfedgeToFace.clear();
halfedgeNext.clear();
disabledFaces.clear();
disabledHalfedges.clear();
faces.reserve(4);
halfedges.reserve(12);
// Create halfedges
// AB
halfedges.push_back({0, b, 6});
halfedgeToFace.push_back(0);
halfedgeNext.push_back(1);
// BC
halfedges.push_back({0, c, 9});
halfedgeToFace.push_back(0);
halfedgeNext.push_back(2);
// CA
halfedges.push_back({0, a, 3});
halfedgeToFace.push_back(0);
halfedgeNext.push_back(0);
// AC
halfedges.push_back({0, c, 2});
halfedgeToFace.push_back(1);
halfedgeNext.push_back(4);
// CD
halfedges.push_back({0, d, 11});
halfedgeToFace.push_back(1);
halfedgeNext.push_back(5);
// DA
halfedges.push_back({0, a, 7});
halfedgeToFace.push_back(1);
halfedgeNext.push_back(3);
// BA
halfedges.push_back({0, a, 0});
halfedgeToFace.push_back(2);
halfedgeNext.push_back(7);
// AD
halfedges.push_back({0, d, 5});
halfedgeToFace.push_back(2);
halfedgeNext.push_back(8);
// DB
halfedges.push_back({0, b, 10});
halfedgeToFace.push_back(2);
halfedgeNext.push_back(6);
// CB
halfedges.push_back({0, b, 1});
halfedgeToFace.push_back(3);
halfedgeNext.push_back(10);
// BD
halfedges.push_back({0, d, 8});
halfedgeToFace.push_back(3);
halfedgeNext.push_back(11);
// DC
halfedges.push_back({0, c, 4});
halfedgeToFace.push_back(3);
halfedgeNext.push_back(9);
// Create faces
faces.emplace_back(0);
faces.emplace_back(3);
faces.emplace_back(6);
faces.emplace_back(9);
}
std::array<int, 3> MeshBuilder::getVertexIndicesOfFace(const Face& f) const {
std::array<int, 3> v;
size_t index = f.he;
auto* he = &halfedges[index];
v[0] = he->endVert;
index = halfedgeNext[index];
he = &halfedges[index];
v[1] = he->endVert;
index = halfedgeNext[index];
he = &halfedges[index];
v[2] = he->endVert;
return v;
}
HalfEdgeMesh::HalfEdgeMesh(const MeshBuilder& builderObject,
const VecView<vec3>& vertexData) {
std::unordered_map<size_t, size_t> faceMapping;
std::unordered_map<size_t, size_t> halfEdgeMapping;
std::unordered_map<size_t, size_t> vertexMapping;
size_t i = 0;
for (const auto& face : builderObject.faces) {
if (!face.isDisabled()) {
halfEdgeIndexFaces.emplace_back(static_cast<size_t>(face.he));
faceMapping[i] = halfEdgeIndexFaces.size() - 1;
const auto heIndices = builderObject.getHalfEdgeIndicesOfFace(face);
for (const auto heIndex : heIndices) {
const auto vertexIndex = builderObject.halfedges[heIndex].endVert;
if (vertexMapping.count(vertexIndex) == 0) {
vertices.push_back(vertexData[vertexIndex]);
vertexMapping[vertexIndex] = vertices.size() - 1;
}
}
}
i++;
}
i = 0;
for (const auto& halfEdge : builderObject.halfedges) {
if (halfEdge.pairedHalfedge != -1) {
halfedges.push_back({halfEdge.endVert, halfEdge.pairedHalfedge,
builderObject.halfedgeToFace[i]});
halfedgeToFace.push_back(builderObject.halfedgeToFace[i]);
halfedgeNext.push_back(builderObject.halfedgeNext[i]);
halfEdgeMapping[i] = halfedges.size() - 1;
}
i++;
}
for (auto& halfEdgeIndexFace : halfEdgeIndexFaces) {
DEBUG_ASSERT(halfEdgeMapping.count(halfEdgeIndexFace) == 1, logicErr,
"invalid halfedge mapping");
halfEdgeIndexFace = halfEdgeMapping[halfEdgeIndexFace];
}
for (size_t i = 0; i < halfedges.size(); i++) {
auto& he = halfedges[i];
halfedgeToFace[i] = faceMapping[halfedgeToFace[i]];
he.pairedHalfedge = halfEdgeMapping[he.pairedHalfedge];
halfedgeNext[i] = halfEdgeMapping[halfedgeNext[i]];
he.endVert = vertexMapping[he.endVert];
}
}
/*
* Implementation of the algorithm
*/
std::pair<Vec<Halfedge>, Vec<vec3>> QuickHull::buildMesh(double epsilon) {
if (originalVertexData.size() == 0) {
return {Vec<Halfedge>(), Vec<vec3>()};
}
// Very first: find extreme values and use them to compute the scale of the
// point cloud.
extremeValues = getExtremeValues();
scale = getScale(extremeValues);
// Epsilon we use depends on the scale
m_epsilon = epsilon * scale;
epsilonSquared = m_epsilon * m_epsilon;
// The planar case happens when all the points appear to lie on a two
// dimensional subspace of R^3.
planar = false;
createConvexHalfedgeMesh();
if (planar) {
const int extraPointIndex = planarPointCloudTemp.size() - 1;
for (auto& he : mesh.halfedges) {
if (he.endVert == extraPointIndex) {
he.endVert = 0;
}
}
planarPointCloudTemp.clear();
}
// reorder halfedges
Vec<Halfedge> halfedges(mesh.halfedges.size());
Vec<int> halfedgeToFace(mesh.halfedges.size());
Vec<int> counts(mesh.halfedges.size(), 0);
Vec<int> mapping(mesh.halfedges.size());
Vec<int> faceMap(mesh.faces.size());
// Some faces are disabled and should not go into the halfedge vector, we can
// update the face indices of the halfedges at the end using index/3
int j = 0;
for_each(
autoPolicy(mesh.halfedges.size()), countAt(0_uz),
countAt(mesh.halfedges.size()), [&](size_t i) {
if (mesh.halfedges[i].pairedHalfedge < 0) return;
if (mesh.faces[mesh.halfedgeToFace[i]].isDisabled()) return;
if (AtomicAdd(counts[mesh.halfedgeToFace[i]], 1) > 0) return;
int currIndex = AtomicAdd(j, 3);
mapping[i] = currIndex;
halfedges[currIndex + 0] = mesh.halfedges[i];
halfedgeToFace[currIndex + 0] = mesh.halfedgeToFace[i];
size_t k = mesh.halfedgeNext[i];
mapping[k] = currIndex + 1;
halfedges[currIndex + 1] = mesh.halfedges[k];
halfedgeToFace[currIndex + 1] = mesh.halfedgeToFace[k];
k = mesh.halfedgeNext[k];
mapping[k] = currIndex + 2;
halfedges[currIndex + 2] = mesh.halfedges[k];
halfedgeToFace[currIndex + 2] = mesh.halfedgeToFace[k];
halfedges[currIndex + 0].startVert = halfedges[currIndex + 2].endVert;
halfedges[currIndex + 1].startVert = halfedges[currIndex + 0].endVert;
halfedges[currIndex + 2].startVert = halfedges[currIndex + 1].endVert;
});
halfedges.resize(j);
halfedgeToFace.resize(j);
// fix pairedHalfedge id
for_each(
autoPolicy(halfedges.size()), halfedges.begin(), halfedges.end(),
[&](Halfedge& he) { he.pairedHalfedge = mapping[he.pairedHalfedge]; });
counts.resize(originalVertexData.size() + 1);
fill(counts.begin(), counts.end(), 0);
// remove unused vertices
for_each(autoPolicy(halfedges.size() / 3), countAt(0_uz),
countAt(halfedges.size() / 3), [&](size_t i) {
AtomicAdd(counts[halfedges[3 * i].startVert], 1);
AtomicAdd(counts[halfedges[3 * i + 1].startVert], 1);
AtomicAdd(counts[halfedges[3 * i + 2].startVert], 1);
});
auto saturate = [](int c) { return c > 0 ? 1 : 0; };
exclusive_scan(TransformIterator(counts.begin(), saturate),
TransformIterator(counts.end(), saturate), counts.begin(), 0);
Vec<vec3> vertices(counts.back());
for_each(autoPolicy(originalVertexData.size()), countAt(0_uz),
countAt(originalVertexData.size()), [&](size_t i) {
if (counts[i + 1] - counts[i] > 0) {
vertices[counts[i]] = originalVertexData[i];
}
});
for_each(autoPolicy(halfedges.size()), halfedges.begin(), halfedges.end(),
[&](Halfedge& he) {
he.startVert = counts[he.startVert];
he.endVert = counts[he.endVert];
});
return {std::move(halfedges), std::move(vertices)};
}
void QuickHull::createConvexHalfedgeMesh() {
visibleFaces.clear();
horizonEdgesData.clear();
possiblyVisibleFaces.clear();
// Compute base tetrahedron
setupInitialTetrahedron();
DEBUG_ASSERT(mesh.faces.size() == 4, logicErr, "not a tetrahedron");
// Init face stack with those faces that have points assigned to them
faceList.clear();
for (size_t i = 0; i < 4; i++) {
auto& f = mesh.faces[i];
if (f.pointsOnPositiveSide && f.pointsOnPositiveSide->size() > 0) {
faceList.push_back(i);
f.inFaceStack = 1;
}
}
// Process faces until the face list is empty.
size_t iter = 0;
while (!faceList.empty()) {
iter++;
if (iter == std::numeric_limits<size_t>::max()) {
// Visible face traversal marks visited faces with iteration counter (to
// mark that the face has been visited on this iteration) and the max
// value represents unvisited faces. At this point we have to reset
// iteration counter. This shouldn't be an issue on 64 bit machines.
iter = 0;
}
const auto topFaceIndex = faceList.front();
faceList.pop_front();
auto& tf = mesh.faces[topFaceIndex];
tf.inFaceStack = 0;
DEBUG_ASSERT(
!tf.pointsOnPositiveSide || tf.pointsOnPositiveSide->size() > 0,
logicErr, "there should be points on the positive side");
if (!tf.pointsOnPositiveSide || tf.isDisabled()) {
continue;
}
// Pick the most distant point to this triangle plane as the point to which
// we extrude
const vec3& activePoint = originalVertexData[tf.mostDistantPoint];
const size_t activePointIndex = tf.mostDistantPoint;
// Find out the faces that have our active point on their positive side
// (these are the "visible faces"). The face on top of the stack of course
// is one of them. At the same time, we create a list of horizon edges.
horizonEdgesData.clear();
possiblyVisibleFaces.clear();
visibleFaces.clear();
possiblyVisibleFaces.push_back({topFaceIndex, -1});
while (possiblyVisibleFaces.size()) {
const auto faceData = possiblyVisibleFaces.back();
possiblyVisibleFaces.pop_back();
auto& pvf = mesh.faces[faceData.faceIndex];
DEBUG_ASSERT(!pvf.isDisabled(), logicErr, "pvf should not be disabled");
if (pvf.visibilityCheckedOnIteration == iter) {
if (pvf.isVisibleFaceOnCurrentIteration) {
continue;
}
} else {
const Plane& P = pvf.P;
pvf.visibilityCheckedOnIteration = iter;
const double d = la::dot(P.N, activePoint) + P.D;
if (d > 0) {
pvf.isVisibleFaceOnCurrentIteration = 1;
pvf.horizonEdgesOnCurrentIteration = 0;
visibleFaces.push_back(faceData.faceIndex);
for (auto heIndex : mesh.getHalfEdgeIndicesOfFace(pvf)) {
if (mesh.halfedges[heIndex].pairedHalfedge !=
faceData.enteredFromHalfedge) {
possiblyVisibleFaces.push_back(
{mesh.halfedgeToFace[mesh.halfedges[heIndex].pairedHalfedge],
heIndex});
}
}
continue;
}
DEBUG_ASSERT(faceData.faceIndex != topFaceIndex, logicErr,
"face index invalid");
}
// The face is not visible. Therefore, the halfedge we came from is part
// of the horizon edge.
pvf.isVisibleFaceOnCurrentIteration = 0;
horizonEdgesData.push_back(faceData.enteredFromHalfedge);
// Store which half edge is the horizon edge. The other half edges of the
// face will not be part of the final mesh so their data slots can by
// recycled.
const auto halfEdgesMesh = mesh.getHalfEdgeIndicesOfFace(
mesh.faces[mesh.halfedgeToFace[faceData.enteredFromHalfedge]]);
const std::int8_t ind =
(halfEdgesMesh[0] == faceData.enteredFromHalfedge)
? 0
: (halfEdgesMesh[1] == faceData.enteredFromHalfedge ? 1 : 2);
mesh.faces[mesh.halfedgeToFace[faceData.enteredFromHalfedge]]
.horizonEdgesOnCurrentIteration |= (1 << ind);
}
const size_t horizonEdgeCount = horizonEdgesData.size();
// Order horizon edges so that they form a loop. This may fail due to
// numerical instability in which case we give up trying to solve horizon
// edge for this point and accept a minor degeneration in the convex hull.
if (!reorderHorizonEdges(horizonEdgesData)) {
failedHorizonEdges++;
int change_flag = 0;
for (size_t index = 0; index < tf.pointsOnPositiveSide->size(); index++) {
if ((*tf.pointsOnPositiveSide)[index] == activePointIndex) {
change_flag = 1;
} else if (change_flag == 1) {
change_flag = 2;
(*tf.pointsOnPositiveSide)[index - 1] =
(*tf.pointsOnPositiveSide)[index];
}
}
if (change_flag == 1)
tf.pointsOnPositiveSide->resize(tf.pointsOnPositiveSide->size() - 1);
if (tf.pointsOnPositiveSide->size() == 0) {
reclaimToIndexVectorPool(tf.pointsOnPositiveSide);
}
continue;
}
// Except for the horizon edges, all half edges of the visible faces can be
// marked as disabled. Their data slots will be reused. The faces will be
// disabled as well, but we need to remember the points that were on the
// positive side of them - therefore we save pointers to them.
newFaceIndices.clear();
newHalfedgeIndices.clear();
disabledFacePointVectors.clear();
size_t disableCounter = 0;
for (auto faceIndex : visibleFaces) {
auto& disabledFace = mesh.faces[faceIndex];
auto halfEdgesMesh = mesh.getHalfEdgeIndicesOfFace(disabledFace);
for (size_t j = 0; j < 3; j++) {
if ((disabledFace.horizonEdgesOnCurrentIteration & (1 << j)) == 0) {
if (disableCounter < horizonEdgeCount * 2) {
// Use on this iteration
newHalfedgeIndices.push_back(halfEdgesMesh[j]);
disableCounter++;
} else {
// Mark for reusal on later iteration step
mesh.disableHalfedge(halfEdgesMesh[j]);
}
}
}
// Disable the face, but retain pointer to the points that were on the
// positive side of it. We need to assign those points to the new faces we
// create shortly.
auto t = mesh.disableFace(faceIndex);
if (t) {
// Because we should not assign point vectors to faces unless needed...
DEBUG_ASSERT(t->size(), logicErr, "t should not be empty");
disabledFacePointVectors.push_back(std::move(t));
}
}
if (disableCounter < horizonEdgeCount * 2) {
const size_t newHalfEdgesNeeded = horizonEdgeCount * 2 - disableCounter;
for (size_t i = 0; i < newHalfEdgesNeeded; i++) {
newHalfedgeIndices.push_back(mesh.addHalfedge());
}
}
// Create new faces using the edgeloop
for (size_t i = 0; i < horizonEdgeCount; i++) {
const size_t AB = horizonEdgesData[i];
auto horizonEdgeVertexIndices =
mesh.getVertexIndicesOfHalfEdge(mesh.halfedges[AB]);
size_t A, B, C;
A = horizonEdgeVertexIndices[0];
B = horizonEdgeVertexIndices[1];
C = activePointIndex;
const size_t newFaceIndex = mesh.addFace();
newFaceIndices.push_back(newFaceIndex);
const size_t CA = newHalfedgeIndices[2 * i + 0];
const size_t BC = newHalfedgeIndices[2 * i + 1];
mesh.halfedgeNext[AB] = BC;
mesh.halfedgeNext[BC] = CA;
mesh.halfedgeNext[CA] = AB;
mesh.halfedgeToFace[BC] = newFaceIndex;
mesh.halfedgeToFace[CA] = newFaceIndex;
mesh.halfedgeToFace[AB] = newFaceIndex;
mesh.halfedges[CA].endVert = A;
mesh.halfedges[BC].endVert = C;
auto& newFace = mesh.faces[newFaceIndex];
const vec3 planeNormal = getTriangleNormal(
originalVertexData[A], originalVertexData[B], activePoint);
newFace.P = Plane(planeNormal, activePoint);
newFace.he = AB;
mesh.halfedges[CA].pairedHalfedge =
newHalfedgeIndices[i > 0 ? i * 2 - 1 : 2 * horizonEdgeCount - 1];
mesh.halfedges[BC].pairedHalfedge =
newHalfedgeIndices[((i + 1) * 2) % (horizonEdgeCount * 2)];
}
// Assign points that were on the positive side of the disabled faces to the
// new faces.
for (auto& disabledPoints : disabledFacePointVectors) {
DEBUG_ASSERT(disabledPoints != nullptr, logicErr,
"disabledPoints should not be null");
for (const auto& point : *(disabledPoints)) {
if (point == activePointIndex) {
continue;
}
for (size_t j = 0; j < horizonEdgeCount; j++) {
if (addPointToFace(mesh.faces[newFaceIndices[j]], point)) {
break;
}
}
}
// The points are no longer needed: we can move them to the vector pool
// for reuse.
reclaimToIndexVectorPool(disabledPoints);
}
// Increase face stack size if needed
for (const auto newFaceIndex : newFaceIndices) {
auto& newFace = mesh.faces[newFaceIndex];
if (newFace.pointsOnPositiveSide) {
DEBUG_ASSERT(newFace.pointsOnPositiveSide->size() > 0, logicErr,
"there should be points on the positive side");
if (!newFace.inFaceStack) {
faceList.push_back(newFaceIndex);
newFace.inFaceStack = 1;
}
}
}
}
// Cleanup
indexVectorPool.clear();
}
/*
* Private helper functions
*/
std::array<size_t, 6> QuickHull::getExtremeValues() {
std::array<size_t, 6> outIndices{0, 0, 0, 0, 0, 0};
double extremeVals[6] = {originalVertexData[0].x, originalVertexData[0].x,
originalVertexData[0].y, originalVertexData[0].y,
originalVertexData[0].z, originalVertexData[0].z};
const size_t vCount = originalVertexData.size();
for (size_t i = 1; i < vCount; i++) {
const vec3& pos = originalVertexData[i];
if (pos.x > extremeVals[0]) {
extremeVals[0] = pos.x;
outIndices[0] = i;
} else if (pos.x < extremeVals[1]) {
extremeVals[1] = pos.x;
outIndices[1] = i;
}
if (pos.y > extremeVals[2]) {
extremeVals[2] = pos.y;
outIndices[2] = i;
} else if (pos.y < extremeVals[3]) {
extremeVals[3] = pos.y;
outIndices[3] = i;
}
if (pos.z > extremeVals[4]) {
extremeVals[4] = pos.z;
outIndices[4] = i;
} else if (pos.z < extremeVals[5]) {
extremeVals[5] = pos.z;
outIndices[5] = i;
}
}
return outIndices;
}
bool QuickHull::reorderHorizonEdges(VecView<size_t>& horizonEdges) {
const size_t horizonEdgeCount = horizonEdges.size();
for (size_t i = 0; i + 1 < horizonEdgeCount; i++) {
const size_t endVertexCheck = mesh.halfedges[horizonEdges[i]].endVert;
bool foundNext = false;
for (size_t j = i + 1; j < horizonEdgeCount; j++) {
const size_t beginVertex =
mesh.halfedges[mesh.halfedges[horizonEdges[j]].pairedHalfedge]
.endVert;
if (beginVertex == endVertexCheck) {
std::swap(horizonEdges[i + 1], horizonEdges[j]);
foundNext = true;
break;
}
}
if (!foundNext) {
return false;
}
}
DEBUG_ASSERT(
mesh.halfedges[horizonEdges[horizonEdges.size() - 1]].endVert ==
mesh.halfedges[mesh.halfedges[horizonEdges[0]].pairedHalfedge]
.endVert,
logicErr, "invalid halfedge");
return true;
}
double QuickHull::getScale(const std::array<size_t, 6>& extremeValuesInput) {
double s = 0;
for (size_t i = 0; i < 6; i++) {
const double* v =
(const double*)(&originalVertexData[extremeValuesInput[i]]);
v += i / 2;
auto a = std::abs(*v);
if (a > s) {
s = a;
}
}
return s;
}
void QuickHull::setupInitialTetrahedron() {
const size_t vertexCount = originalVertexData.size();
// If we have at most 4 points, just return a degenerate tetrahedron:
if (vertexCount <= 4) {
size_t v[4] = {0, std::min((size_t)1, vertexCount - 1),
std::min((size_t)2, vertexCount - 1),
std::min((size_t)3, vertexCount - 1)};
const vec3 N =
getTriangleNormal(originalVertexData[v[0]], originalVertexData[v[1]],
originalVertexData[v[2]]);
const Plane trianglePlane(N, originalVertexData[v[0]]);
if (trianglePlane.isPointOnPositiveSide(originalVertexData[v[3]])) {
std::swap(v[0], v[1]);
}
return mesh.setup(v[0], v[1], v[2], v[3]);
}
// Find two most distant extreme points.
double maxD = epsilonSquared;
std::pair<size_t, size_t> selectedPoints;
for (size_t i = 0; i < 6; i++) {
for (size_t j = i + 1; j < 6; j++) {
// I found a function for squaredDistance but i can't seem to include it
// like this for some reason
const double d = getSquaredDistance(originalVertexData[extremeValues[i]],
originalVertexData[extremeValues[j]]);
if (d > maxD) {
maxD = d;
selectedPoints = {extremeValues[i], extremeValues[j]};
}
}
}
if (maxD == epsilonSquared) {
// A degenerate case: the point cloud seems to consists of a single point
return mesh.setup(0, std::min((size_t)1, vertexCount - 1),
std::min((size_t)2, vertexCount - 1),
std::min((size_t)3, vertexCount - 1));
}
DEBUG_ASSERT(selectedPoints.first != selectedPoints.second, logicErr,
"degenerate selectedPoints");
// Find the most distant point to the line between the two chosen extreme
// points.
const Ray r(originalVertexData[selectedPoints.first],
(originalVertexData[selectedPoints.second] -
originalVertexData[selectedPoints.first]));
maxD = epsilonSquared;
size_t maxI = std::numeric_limits<size_t>::max();
const size_t vCount = originalVertexData.size();
for (size_t i = 0; i < vCount; i++) {
const double distToRay =
getSquaredDistanceBetweenPointAndRay(originalVertexData[i], r);
if (distToRay > maxD) {
maxD = distToRay;
maxI = i;
}
}
if (maxD == epsilonSquared) {
// It appears that the point cloud belongs to a 1 dimensional subspace of
// R^3: convex hull has no volume => return a thin triangle Pick any point
// other than selectedPoints.first and selectedPoints.second as the third
// point of the triangle
auto it =
std::find_if(originalVertexData.begin(), originalVertexData.end(),
[&](const vec3& ve) {
return ve != originalVertexData[selectedPoints.first] &&
ve != originalVertexData[selectedPoints.second];
});
const size_t thirdPoint =
(it == originalVertexData.end())
? selectedPoints.first
: std::distance(originalVertexData.begin(), it);
it =
std::find_if(originalVertexData.begin(), originalVertexData.end(),
[&](const vec3& ve) {
return ve != originalVertexData[selectedPoints.first] &&
ve != originalVertexData[selectedPoints.second] &&
ve != originalVertexData[thirdPoint];
});
const size_t fourthPoint =
(it == originalVertexData.end())
? selectedPoints.first
: std::distance(originalVertexData.begin(), it);
return mesh.setup(selectedPoints.first, selectedPoints.second, thirdPoint,
fourthPoint);
}
// These three points form the base triangle for our tetrahedron.
DEBUG_ASSERT(selectedPoints.first != maxI && selectedPoints.second != maxI,
logicErr, "degenerate selectedPoints");
std::array<size_t, 3> baseTriangle{selectedPoints.first,
selectedPoints.second, maxI};
const vec3 baseTriangleVertices[] = {originalVertexData[baseTriangle[0]],
originalVertexData[baseTriangle[1]],
originalVertexData[baseTriangle[2]]};
// Next step is to find the 4th vertex of the tetrahedron. We naturally choose
// the point farthest away from the triangle plane.
maxD = m_epsilon;
maxI = 0;
const vec3 N =
getTriangleNormal(baseTriangleVertices[0], baseTriangleVertices[1],
baseTriangleVertices[2]);
Plane trianglePlane(N, baseTriangleVertices[0]);
for (size_t i = 0; i < vCount; i++) {
const double d = std::abs(
getSignedDistanceToPlane(originalVertexData[i], trianglePlane));
if (d > maxD) {
maxD = d;
maxI = i;
}
}
if (maxD == m_epsilon) {
// All the points seem to lie on a 2D subspace of R^3. How to handle this?
// Well, let's add one extra point to the point cloud so that the convex
// hull will have volume.
planar = true;
const vec3 N1 =
getTriangleNormal(baseTriangleVertices[1], baseTriangleVertices[2],
baseTriangleVertices[0]);
planarPointCloudTemp = Vec<vec3>(originalVertexData);
const vec3 extraPoint = N1 + originalVertexData[0];
planarPointCloudTemp.push_back(extraPoint);
maxI = planarPointCloudTemp.size() - 1;
originalVertexData = planarPointCloudTemp;
}
// Enforce CCW orientation (if user prefers clockwise orientation, swap two
// vertices in each triangle when final mesh is created)
const Plane triPlane(N, baseTriangleVertices[0]);
if (triPlane.isPointOnPositiveSide(originalVertexData[maxI])) {
std::swap(baseTriangle[0], baseTriangle[1]);
}
// Create a tetrahedron half edge mesh and compute planes defined by each
// triangle
mesh.setup(baseTriangle[0], baseTriangle[1], baseTriangle[2], maxI);
for (auto& f : mesh.faces) {
auto v = mesh.getVertexIndicesOfFace(f);
const vec3 N1 =
getTriangleNormal(originalVertexData[v[0]], originalVertexData[v[1]],
originalVertexData[v[2]]);
const Plane plane(N1, originalVertexData[v[0]]);
f.P = plane;
}
// Finally we assign a face for each vertex outside the tetrahedron (vertices
// inside the tetrahedron have no role anymore)
for (size_t i = 0; i < vCount; i++) {
for (auto& face : mesh.faces) {
if (addPointToFace(face, i)) {
break;
}
}
}
}
std::unique_ptr<Vec<size_t>> QuickHull::getIndexVectorFromPool() {
auto r = indexVectorPool.get();
r->resize(0);
return r;
}
void QuickHull::reclaimToIndexVectorPool(std::unique_ptr<Vec<size_t>>& ptr) {
const size_t oldSize = ptr->size();
if ((oldSize + 1) * 128 < ptr->capacity()) {
// Reduce memory usage! Huge vectors are needed at the beginning of
// iteration when faces have many points on their positive side. Later on,
// smaller vectors will suffice.
ptr.reset(nullptr);
return;
}
indexVectorPool.reclaim(ptr);
}
bool QuickHull::addPointToFace(typename MeshBuilder::Face& f,
size_t pointIndex) {
const double D =
getSignedDistanceToPlane(originalVertexData[pointIndex], f.P);
if (D > 0 && D * D > epsilonSquared * f.P.sqrNLength) {
if (!f.pointsOnPositiveSide) {
f.pointsOnPositiveSide = getIndexVectorFromPool();
}
f.pointsOnPositiveSide->push_back(pointIndex);
if (D > f.mostDistantPointDist) {
f.mostDistantPointDist = D;
f.mostDistantPoint = pointIndex;
}
return true;
}
return false;
}
// Wrapper to call the QuickHull algorithm with the given vertex data to build
// the Impl
void Manifold::Impl::Hull(VecView<vec3> vertPos) {
size_t numVert = vertPos.size();
if (numVert < 4) {
status_ = Error::InvalidConstruction;
return;
}
QuickHull qh(vertPos);
std::tie(halfedge_, vertPos_) = qh.buildMesh();
CalculateBBox();
SetEpsilon();
CalculateNormals();
InitializeOriginal();
Finish();
CreateFaces();
}
} // namespace manifold

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// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Derived from the public domain work of Antti Kuukka at
// https://github.com/akuukka/quickhull
/*
* INPUT: a list of points in 3D space (for example, vertices of a 3D mesh)
*
* OUTPUT: a ConvexHull object which provides vertex and index buffers of the
*generated convex hull as a triangle mesh.
*
*
*
* The implementation is thread-safe if each thread is using its own QuickHull
*object.
*
*
* SUMMARY OF THE ALGORITHM:
* - Create initial simplex (tetrahedron) using extreme points. We have
*four faces now and they form a convex mesh M.
* - For each point, assign them to the first face for which they are on
*the positive side of (so each point is assigned to at most one face). Points
*inside the initial tetrahedron are left behind now and no longer affect the
*calculations.
* - Add all faces that have points assigned to them to Face Stack.
* - Iterate until Face Stack is empty:
* - Pop topmost face F from the stack
* - From the points assigned to F, pick the point P that is
*farthest away from the plane defined by F.
* - Find all faces of M that have P on their positive side. Let us
*call these the "visible faces".
* - Because of the way M is constructed, these faces are
*connected. Solve their horizon edge loop.
* - "Extrude to P": Create new faces by connecting
*P with the points belonging to the horizon edge. Add the new faces to M and
*remove the visible faces from M.
* - Each point that was assigned to visible faces is now assigned
*to at most one of the newly created faces.
* - Those new faces that have points assigned to them are added to
*the top of Face Stack.
* - M is now the convex hull.
*
* */
#pragma once
#include <array>
#include <deque>
#include <vector>
#include "./shared.h"
#include "./vec.h"
namespace manifold {
class Pool {
std::vector<std::unique_ptr<Vec<size_t>>> data;
public:
void clear() { data.clear(); }
void reclaim(std::unique_ptr<Vec<size_t>>& ptr) {
data.push_back(std::move(ptr));
}
std::unique_ptr<Vec<size_t>> get() {
if (data.size() == 0) {
return std::make_unique<Vec<size_t>>();
}
auto it = data.end() - 1;
std::unique_ptr<Vec<size_t>> r = std::move(*it);
data.erase(it);
return r;
}
};
class Plane {
public:
vec3 N;
// Signed distance (if normal is of length 1) to the plane from origin
double D;
// Normal length squared
double sqrNLength;
bool isPointOnPositiveSide(const vec3& Q) const {
double d = la::dot(N, Q) + D;
if (d >= 0) return true;
return false;
}
Plane() = default;
// Construct a plane using normal N and any point P on the plane
Plane(const vec3& N, const vec3& P)
: N(N), D(la::dot(-N, P)), sqrNLength(la::dot(N, N)) {}
};
struct Ray {
const vec3 S;
const vec3 V;
const double VInvLengthSquared;
Ray(const vec3& S, const vec3& V)
: S(S), V(V), VInvLengthSquared(1 / (la::dot(V, V))) {}
};
class MeshBuilder {
public:
struct Face {
int he;
Plane P{};
double mostDistantPointDist = 0.0;
size_t mostDistantPoint = 0;
size_t visibilityCheckedOnIteration = 0;
std::uint8_t isVisibleFaceOnCurrentIteration : 1;
std::uint8_t inFaceStack : 1;
// Bit for each half edge assigned to this face, each being 0 or 1 depending
// on whether the edge belongs to horizon edge
std::uint8_t horizonEdgesOnCurrentIteration : 3;
std::unique_ptr<Vec<size_t>> pointsOnPositiveSide;
Face(size_t he)
: he(he),
isVisibleFaceOnCurrentIteration(0),
inFaceStack(0),
horizonEdgesOnCurrentIteration(0) {}
Face()
: he(-1),
isVisibleFaceOnCurrentIteration(0),
inFaceStack(0),
horizonEdgesOnCurrentIteration(0) {}
void disable() { he = -1; }
bool isDisabled() const { return he == -1; }
};
// Mesh data
std::vector<Face> faces;
Vec<Halfedge> halfedges;
Vec<int> halfedgeToFace;
Vec<int> halfedgeNext;
// When the mesh is modified and faces and half edges are removed from it, we
// do not actually remove them from the container vectors. Insted, they are
// marked as disabled which means that the indices can be reused when we need
// to add new faces and half edges to the mesh. We store the free indices in
// the following vectors.
Vec<size_t> disabledFaces, disabledHalfedges;
size_t addFace();
size_t addHalfedge();
// Mark a face as disabled and return a pointer to the points that were on the
// positive of it.
std::unique_ptr<Vec<size_t>> disableFace(size_t faceIndex) {
auto& f = faces[faceIndex];
f.disable();
disabledFaces.push_back(faceIndex);
return std::move(f.pointsOnPositiveSide);
}
void disableHalfedge(size_t heIndex) {
auto& he = halfedges[heIndex];
he.pairedHalfedge = -1;
disabledHalfedges.push_back(heIndex);
}
MeshBuilder() = default;
// Create a mesh with initial tetrahedron ABCD. Dot product of AB with the
// normal of triangle ABC should be negative.
void setup(int a, int b, int c, int d);
std::array<int, 3> getVertexIndicesOfFace(const Face& f) const;
std::array<int, 2> getVertexIndicesOfHalfEdge(const Halfedge& he) const {
return {halfedges[he.pairedHalfedge].endVert, he.endVert};
}
std::array<int, 3> getHalfEdgeIndicesOfFace(const Face& f) const {
return {f.he, halfedgeNext[f.he], halfedgeNext[halfedgeNext[f.he]]};
}
};
class HalfEdgeMesh {
public:
Vec<vec3> vertices;
// Index of one of the half edges of the faces
std::vector<size_t> halfEdgeIndexFaces;
Vec<Halfedge> halfedges;
Vec<int> halfedgeToFace;
Vec<int> halfedgeNext;
HalfEdgeMesh(const MeshBuilder& builderObject,
const VecView<vec3>& vertexData);
};
double defaultEps();
class QuickHull {
struct FaceData {
int faceIndex;
// If the face turns out not to be visible, this half edge will be marked as
// horizon edge
int enteredFromHalfedge;
};
double m_epsilon, epsilonSquared, scale;
bool planar;
Vec<vec3> planarPointCloudTemp;
VecView<vec3> originalVertexData;
MeshBuilder mesh;
std::array<size_t, 6> extremeValues;
size_t failedHorizonEdges = 0;
// Temporary variables used during iteration process
Vec<size_t> newFaceIndices;
Vec<size_t> newHalfedgeIndices;
Vec<size_t> visibleFaces;
Vec<size_t> horizonEdgesData;
Vec<FaceData> possiblyVisibleFaces;
std::vector<std::unique_ptr<Vec<size_t>>> disabledFacePointVectors;
std::deque<int> faceList;
// Create a half edge mesh representing the base tetrahedron from which the
// QuickHull iteration proceeds. extremeValues must be properly set up when
// this is called.
void setupInitialTetrahedron();
// Given a list of half edges, try to rearrange them so that they form a loop.
// Return true on success.
bool reorderHorizonEdges(VecView<size_t>& horizonEdges);
// Find indices of extreme values (max x, min x, max y, min y, max z, min z)
// for the given point cloud
std::array<size_t, 6> getExtremeValues();
// Compute scale of the vertex data.
double getScale(const std::array<size_t, 6>& extremeValuesInput);
// Each face contains a unique pointer to a vector of indices. However, many -
// often most - faces do not have any points on the positive side of them
// especially at the the end of the iteration. When a face is removed from the
// mesh, its associated point vector, if such exists, is moved to the index
// vector pool, and when we need to add new faces with points on the positive
// side to the mesh, we reuse these vectors. This reduces the amount of
// std::vectors we have to deal with, and impact on performance is remarkable.
Pool indexVectorPool;
inline std::unique_ptr<Vec<size_t>> getIndexVectorFromPool();
inline void reclaimToIndexVectorPool(std::unique_ptr<Vec<size_t>>& ptr);
// Associates a point with a face if the point resides on the positive side of
// the plane. Returns true if the points was on the positive side.
inline bool addPointToFace(typename MeshBuilder::Face& f, size_t pointIndex);
// This will create HalfedgeMesh from which we create the ConvexHull object
// that buildMesh function returns
void createConvexHalfedgeMesh();
public:
// This function assumes that the pointCloudVec data resides in memory in the
// following format: x_0,y_0,z_0,x_1,y_1,z_1,...
QuickHull(VecView<vec3> pointCloudVec)
: originalVertexData(VecView(pointCloudVec)) {}
// Computes convex hull for a given point cloud. Params: eps: minimum distance
// to a plane to consider a point being on positive side of it (for a point
// cloud with scale 1) Returns: Convex hull of the point cloud as halfEdge
// vector and vertex vector
std::pair<Vec<Halfedge>, Vec<vec3>> buildMesh(double eps = defaultEps());
};
} // namespace manifold

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// Copyright 2023 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./hashtable.h"
#include "./impl.h"
#include "./parallel.h"
#include "./utils.h"
#include "./vec.h"
#include "manifold/manifold.h"
namespace {
using namespace manifold;
constexpr int kCrossing = -2;
constexpr int kNone = -1;
constexpr ivec4 kVoxelOffset(1, 1, 1, 0);
// Maximum fraction of spacing that a vert can move.
constexpr double kS = 0.25;
// Corresponding approximate distance ratio bound.
constexpr double kD = 1 / kS - 1;
// Maximum number of opposed verts (of 7) to allow collapse.
constexpr int kMaxOpposed = 3;
ivec3 TetTri0(int i) {
constexpr ivec3 tetTri0[16] = {{-1, -1, -1}, //
{0, 3, 4}, //
{0, 1, 5}, //
{1, 5, 3}, //
{1, 4, 2}, //
{1, 0, 3}, //
{2, 5, 0}, //
{5, 3, 2}, //
{2, 3, 5}, //
{0, 5, 2}, //
{3, 0, 1}, //
{2, 4, 1}, //
{3, 5, 1}, //
{5, 1, 0}, //
{4, 3, 0}, //
{-1, -1, -1}};
return tetTri0[i];
}
ivec3 TetTri1(int i) {
constexpr ivec3 tetTri1[16] = {{-1, -1, -1}, //
{-1, -1, -1}, //
{-1, -1, -1}, //
{3, 4, 1}, //
{-1, -1, -1}, //
{3, 2, 1}, //
{0, 4, 2}, //
{-1, -1, -1}, //
{-1, -1, -1}, //
{2, 4, 0}, //
{1, 2, 3}, //
{-1, -1, -1}, //
{1, 4, 3}, //
{-1, -1, -1}, //
{-1, -1, -1}, //
{-1, -1, -1}};
return tetTri1[i];
}
ivec4 Neighbor(ivec4 base, int i) {
constexpr ivec4 neighbors[14] = {{0, 0, 0, 1}, //
{1, 0, 0, 0}, //
{0, 1, 0, 0}, //
{0, 0, 1, 0}, //
{-1, 0, 0, 1}, //
{0, -1, 0, 1}, //
{0, 0, -1, 1}, //
{-1, -1, -1, 1}, //
{-1, 0, 0, 0}, //
{0, -1, 0, 0}, //
{0, 0, -1, 0}, //
{0, -1, -1, 1}, //
{-1, 0, -1, 1}, //
{-1, -1, 0, 1}};
ivec4 neighborIndex = base + neighbors[i];
if (neighborIndex.w == 2) {
neighborIndex += 1;
neighborIndex.w = 0;
}
return neighborIndex;
}
Uint64 EncodeIndex(ivec4 gridPos, ivec3 gridPow) {
return static_cast<Uint64>(gridPos.w) | static_cast<Uint64>(gridPos.z) << 1 |
static_cast<Uint64>(gridPos.y) << (1 + gridPow.z) |
static_cast<Uint64>(gridPos.x) << (1 + gridPow.z + gridPow.y);
}
ivec4 DecodeIndex(Uint64 idx, ivec3 gridPow) {
ivec4 gridPos;
gridPos.w = idx & 1;
idx = idx >> 1;
gridPos.z = idx & ((1 << gridPow.z) - 1);
idx = idx >> gridPow.z;
gridPos.y = idx & ((1 << gridPow.y) - 1);
idx = idx >> gridPow.y;
gridPos.x = idx & ((1 << gridPow.x) - 1);
return gridPos;
}
vec3 Position(ivec4 gridIndex, vec3 origin, vec3 spacing) {
return origin + spacing * (vec3(gridIndex) + (gridIndex.w == 1 ? 0.0 : -0.5));
}
vec3 Bound(vec3 pos, vec3 origin, vec3 spacing, ivec3 gridSize) {
return min(max(pos, origin), origin + spacing * (vec3(gridSize) - 1));
}
double BoundedSDF(ivec4 gridIndex, vec3 origin, vec3 spacing, ivec3 gridSize,
double level, std::function<double(vec3)> sdf) {
const ivec3 xyz(gridIndex);
const int lowerBoundDist = minelem(xyz);
const int upperBoundDist = minelem(gridSize - xyz);
const int boundDist = std::min(lowerBoundDist, upperBoundDist - gridIndex.w);
if (boundDist < 0) {
return 0.0;
}
const double d = sdf(Position(gridIndex, origin, spacing)) - level;
return boundDist == 0 ? std::min(d, 0.0) : d;
}
// Simplified ITP root finding algorithm - same worst-case performance as
// bisection, better average performance.
inline vec3 FindSurface(vec3 pos0, double d0, vec3 pos1, double d1, double tol,
double level, std::function<double(vec3)> sdf) {
if (d0 == 0) {
return pos0;
} else if (d1 == 0) {
return pos1;
}
// Sole tuning parameter, k: (0, 1) - smaller value gets better median
// performance, but also hits the worst case more often.
const double k = 0.1;
const double check = 2 * tol / la::length(pos0 - pos1);
double frac = 1;
double biFrac = 1;
while (frac > check) {
const double t = la::lerp(d0 / (d0 - d1), 0.5, k);
const double r = biFrac / frac - 0.5;
const double x = la::abs(t - 0.5) < r ? t : 0.5 - r * (t < 0.5 ? 1 : -1);
const vec3 mid = la::lerp(pos0, pos1, x);
const double d = sdf(mid) - level;
if ((d > 0) == (d0 > 0)) {
d0 = d;
pos0 = mid;
frac *= 1 - x;
} else {
d1 = d;
pos1 = mid;
frac *= x;
}
biFrac /= 2;
}
return la::lerp(pos0, pos1, d0 / (d0 - d1));
}
/**
* Each GridVert is connected to 14 others, and in charge of 7 of these edges
* (see Neighbor() above). Each edge that changes sign contributes one vert,
* unless the GridVert is close enough to the surface, in which case it
* contributes only a single movedVert and all crossing edgeVerts refer to that.
*/
struct GridVert {
double distance = NAN;
int movedVert = kNone;
int edgeVerts[7] = {kNone, kNone, kNone, kNone, kNone, kNone, kNone};
inline bool HasMoved() const { return movedVert >= 0; }
inline bool SameSide(double dist) const {
return (dist > 0) == (distance > 0);
}
inline int Inside() const { return distance > 0 ? 1 : -1; }
inline int NeighborInside(int i) const {
return Inside() * (edgeVerts[i] == kNone ? 1 : -1);
}
};
struct NearSurface {
VecView<vec3> vertPos;
VecView<int> vertIndex;
HashTableD<GridVert> gridVerts;
VecView<const double> voxels;
const std::function<double(vec3)> sdf;
const vec3 origin;
const ivec3 gridSize;
const ivec3 gridPow;
const vec3 spacing;
const double level;
const double tol;
inline void operator()(Uint64 index) {
ZoneScoped;
if (gridVerts.Full()) return;
const ivec4 gridIndex = DecodeIndex(index, gridPow);
if (la::any(la::greater(ivec3(gridIndex), gridSize))) return;
GridVert gridVert;
gridVert.distance = voxels[EncodeIndex(gridIndex + kVoxelOffset, gridPow)];
bool keep = false;
double vMax = 0;
int closestNeighbor = -1;
int opposedVerts = 0;
for (int i = 0; i < 7; ++i) {
const double val =
voxels[EncodeIndex(Neighbor(gridIndex, i) + kVoxelOffset, gridPow)];
const double valOp = voxels[EncodeIndex(
Neighbor(gridIndex, i + 7) + kVoxelOffset, gridPow)];
if (!gridVert.SameSide(val)) {
gridVert.edgeVerts[i] = kCrossing;
keep = true;
if (!gridVert.SameSide(valOp)) {
++opposedVerts;
}
// Approximate bound on vert movement.
if (la::abs(val) > kD * la::abs(gridVert.distance) &&
la::abs(val) > la::abs(vMax)) {
vMax = val;
closestNeighbor = i;
}
} else if (!gridVert.SameSide(valOp) &&
la::abs(valOp) > kD * la::abs(gridVert.distance) &&
la::abs(valOp) > la::abs(vMax)) {
vMax = valOp;
closestNeighbor = i + 7;
}
}
// This is where we collapse all the crossing edge verts into this GridVert,
// speeding up the algorithm and avoiding poor quality triangles. Without
// this step the result is guaranteed 2-manifold, but with this step it can
// become an even-manifold with kissing verts. These must be removed in a
// post-process: CleanupTopology().
if (closestNeighbor >= 0 && opposedVerts <= kMaxOpposed) {
const vec3 gridPos = Position(gridIndex, origin, spacing);
const ivec4 neighborIndex = Neighbor(gridIndex, closestNeighbor);
const vec3 pos = FindSurface(gridPos, gridVert.distance,
Position(neighborIndex, origin, spacing),
vMax, tol, level, sdf);
// Bound the delta of each vert to ensure the tetrahedron cannot invert.
if (la::all(la::less(la::abs(pos - gridPos), kS * spacing))) {
const int idx = AtomicAdd(vertIndex[0], 1);
vertPos[idx] = Bound(pos, origin, spacing, gridSize);
gridVert.movedVert = idx;
for (int j = 0; j < 7; ++j) {
if (gridVert.edgeVerts[j] == kCrossing) gridVert.edgeVerts[j] = idx;
}
keep = true;
}
} else {
for (int j = 0; j < 7; ++j) gridVert.edgeVerts[j] = kNone;
}
if (keep) gridVerts.Insert(index, gridVert);
}
};
struct ComputeVerts {
VecView<vec3> vertPos;
VecView<int> vertIndex;
HashTableD<GridVert> gridVerts;
VecView<const double> voxels;
const std::function<double(vec3)> sdf;
const vec3 origin;
const ivec3 gridSize;
const ivec3 gridPow;
const vec3 spacing;
const double level;
const double tol;
void operator()(int idx) {
ZoneScoped;
Uint64 baseKey = gridVerts.KeyAt(idx);
if (baseKey == kOpen) return;
GridVert& gridVert = gridVerts.At(idx);
if (gridVert.HasMoved()) return;
const ivec4 gridIndex = DecodeIndex(baseKey, gridPow);
const vec3 position = Position(gridIndex, origin, spacing);
// These seven edges are uniquely owned by this gridVert; any of them
// which intersect the surface create a vert.
for (int i = 0; i < 7; ++i) {
const ivec4 neighborIndex = Neighbor(gridIndex, i);
const GridVert& neighbor = gridVerts[EncodeIndex(neighborIndex, gridPow)];
const double val =
std::isfinite(neighbor.distance)
? neighbor.distance
: voxels[EncodeIndex(neighborIndex + kVoxelOffset, gridPow)];
if (gridVert.SameSide(val)) continue;
if (neighbor.HasMoved()) {
gridVert.edgeVerts[i] = neighbor.movedVert;
continue;
}
const int idx = AtomicAdd(vertIndex[0], 1);
const vec3 pos = FindSurface(position, gridVert.distance,
Position(neighborIndex, origin, spacing),
val, tol, level, sdf);
vertPos[idx] = Bound(pos, origin, spacing, gridSize);
gridVert.edgeVerts[i] = idx;
}
}
};
struct BuildTris {
VecView<ivec3> triVerts;
VecView<int> triIndex;
const HashTableD<GridVert> gridVerts;
const ivec3 gridPow;
void CreateTri(const ivec3& tri, const int edges[6]) {
if (tri[0] < 0) return;
const ivec3 verts(edges[tri[0]], edges[tri[1]], edges[tri[2]]);
if (verts[0] == verts[1] || verts[1] == verts[2] || verts[2] == verts[0])
return;
int idx = AtomicAdd(triIndex[0], 1);
triVerts[idx] = verts;
}
void CreateTris(const ivec4& tet, const int edges[6]) {
const int i = (tet[0] > 0 ? 1 : 0) + (tet[1] > 0 ? 2 : 0) +
(tet[2] > 0 ? 4 : 0) + (tet[3] > 0 ? 8 : 0);
CreateTri(TetTri0(i), edges);
CreateTri(TetTri1(i), edges);
}
void operator()(int idx) {
ZoneScoped;
Uint64 baseKey = gridVerts.KeyAt(idx);
if (baseKey == kOpen) return;
const GridVert& base = gridVerts.At(idx);
const ivec4 baseIndex = DecodeIndex(baseKey, gridPow);
ivec4 leadIndex = baseIndex;
if (leadIndex.w == 0)
leadIndex.w = 1;
else {
leadIndex += 1;
leadIndex.w = 0;
}
// This GridVert is in charge of the 6 tetrahedra surrounding its edge in
// the (1,1,1) direction (edge 0).
ivec4 tet(base.NeighborInside(0), base.Inside(), -2, -2);
ivec4 thisIndex = baseIndex;
thisIndex.x += 1;
GridVert thisVert = gridVerts[EncodeIndex(thisIndex, gridPow)];
tet[2] = base.NeighborInside(1);
for (const int i : {0, 1, 2}) {
thisIndex = leadIndex;
--thisIndex[Prev3(i)];
// Indices take unsigned input, so check for negatives, given the
// decrement. If negative, the vert is outside and only connected to other
// outside verts - no edgeVerts.
GridVert nextVert = thisIndex[Prev3(i)] < 0
? GridVert()
: gridVerts[EncodeIndex(thisIndex, gridPow)];
tet[3] = base.NeighborInside(Prev3(i) + 4);
const int edges1[6] = {base.edgeVerts[0],
base.edgeVerts[i + 1],
nextVert.edgeVerts[Next3(i) + 4],
nextVert.edgeVerts[Prev3(i) + 1],
thisVert.edgeVerts[i + 4],
base.edgeVerts[Prev3(i) + 4]};
thisVert = nextVert;
CreateTris(tet, edges1);
thisIndex = baseIndex;
++thisIndex[Next3(i)];
nextVert = gridVerts[EncodeIndex(thisIndex, gridPow)];
tet[2] = tet[3];
tet[3] = base.NeighborInside(Next3(i) + 1);
const int edges2[6] = {base.edgeVerts[0],
edges1[5],
thisVert.edgeVerts[i + 4],
nextVert.edgeVerts[Next3(i) + 4],
edges1[3],
base.edgeVerts[Next3(i) + 1]};
thisVert = nextVert;
CreateTris(tet, edges2);
tet[2] = tet[3];
}
}
};
} // namespace
namespace manifold {
/**
* Constructs a level-set manifold from the input Signed-Distance Function
* (SDF). This uses a form of Marching Tetrahedra (akin to Marching
* Cubes, but better for manifoldness). Instead of using a cubic grid, it uses a
* body-centered cubic grid (two shifted cubic grids). These grid points are
* snapped to the surface where possible to keep short edges from forming.
*
* @param sdf The signed-distance functor, containing this function signature:
* `double operator()(vec3 point)`, which returns the
* signed distance of a given point in R^3. Positive values are inside,
* negative outside. There is no requirement that the function be a true
* distance, or even continuous.
* @param bounds An axis-aligned box that defines the extent of the grid.
* @param edgeLength Approximate maximum edge length of the triangles in the
* final result. This affects grid spacing, and hence has a strong effect on
* performance.
* @param level Extract the surface at this value of your sdf; defaults to
* zero. You can inset your mesh by using a positive value, or outset it with a
* negative value.
* @param tolerance Ensure each vertex is within this distance of the true
* surface. Defaults to -1, which will return the interpolated
* crossing-point based on the two nearest grid points. Small positive values
* will require more sdf evaluations per output vertex.
* @param canParallel Parallel policies violate will crash language runtimes
* with runtime locks that expect to not be called back by unregistered threads.
* This allows bindings use LevelSet despite being compiled with MANIFOLD_PAR
* active.
*/
Manifold Manifold::LevelSet(std::function<double(vec3)> sdf, Box bounds,
double edgeLength, double level, double tolerance,
bool canParallel) {
if (tolerance <= 0) {
tolerance = std::numeric_limits<double>::infinity();
}
auto pImpl_ = std::make_shared<Impl>();
auto& vertPos = pImpl_->vertPos_;
const vec3 dim = bounds.Size();
const ivec3 gridSize(dim / edgeLength + 1.0);
const vec3 spacing = dim / (vec3(gridSize - 1));
const ivec3 gridPow(la::log2(gridSize + 2) + 1);
const Uint64 maxIndex = EncodeIndex(ivec4(gridSize + 2, 1), gridPow);
// Parallel policies violate will crash language runtimes with runtime locks
// that expect to not be called back by unregistered threads. This allows
// bindings use LevelSet despite being compiled with MANIFOLD_PAR
// active.
const auto pol = canParallel ? autoPolicy(maxIndex) : ExecutionPolicy::Seq;
const vec3 origin = bounds.min;
Vec<double> voxels(maxIndex);
for_each_n(
pol, countAt(0_uz), maxIndex,
[&voxels, sdf, level, origin, spacing, gridSize, gridPow](Uint64 idx) {
voxels[idx] = BoundedSDF(DecodeIndex(idx, gridPow) - kVoxelOffset,
origin, spacing, gridSize, level, sdf);
});
size_t tableSize = std::min(
2 * maxIndex, static_cast<Uint64>(10 * la::pow(maxIndex, 0.667)));
HashTable<GridVert> gridVerts(tableSize);
vertPos.resize(gridVerts.Size() * 7);
while (1) {
Vec<int> index(1, 0);
for_each_n(pol, countAt(0_uz), EncodeIndex(ivec4(gridSize, 1), gridPow),
NearSurface({vertPos, index, gridVerts.D(), voxels, sdf, origin,
gridSize, gridPow, spacing, level, tolerance}));
if (gridVerts.Full()) { // Resize HashTable
const vec3 lastVert = vertPos[index[0] - 1];
const Uint64 lastIndex =
EncodeIndex(ivec4(ivec3((lastVert - origin) / spacing), 1), gridPow);
const double ratio = static_cast<double>(maxIndex) / lastIndex;
if (ratio > 1000) // do not trust the ratio if it is too large
tableSize *= 2;
else
tableSize *= ratio;
gridVerts = HashTable<GridVert>(tableSize);
vertPos = Vec<vec3>(gridVerts.Size() * 7);
} else { // Success
for_each_n(
pol, countAt(0), gridVerts.Size(),
ComputeVerts({vertPos, index, gridVerts.D(), voxels, sdf, origin,
gridSize, gridPow, spacing, level, tolerance}));
vertPos.resize(index[0]);
break;
}
}
Vec<ivec3> triVerts(gridVerts.Entries() * 12); // worst case
Vec<int> index(1, 0);
for_each_n(pol, countAt(0), gridVerts.Size(),
BuildTris({triVerts, index, gridVerts.D(), gridPow}));
triVerts.resize(index[0]);
pImpl_->CreateHalfedges(triVerts);
pImpl_->CleanupTopology();
pImpl_->Finish();
pImpl_->InitializeOriginal();
return Manifold(pImpl_);
}
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./parallel.h"
#include "./sparse.h"
#include "./utils.h"
#include "./vec.h"
namespace manifold {
inline vec3 SafeNormalize(vec3 v) {
v = la::normalize(v);
return std::isfinite(v.x) ? v : vec3(0.0);
}
inline double MaxEpsilon(double minEpsilon, const Box& bBox) {
double epsilon = std::max(minEpsilon, kPrecision * bBox.Scale());
return std::isfinite(epsilon) ? epsilon : -1;
}
inline int NextHalfedge(int current) {
++current;
if (current % 3 == 0) current -= 3;
return current;
}
inline mat3 NormalTransform(const mat3x4& transform) {
return la::inverse(la::transpose(mat3(transform)));
}
/**
* By using the closest axis-aligned projection to the normal instead of a
* projection along the normal, we avoid introducing any rounding error.
*/
inline mat2x3 GetAxisAlignedProjection(vec3 normal) {
vec3 absNormal = la::abs(normal);
double xyzMax;
mat3x2 projection;
if (absNormal.z > absNormal.x && absNormal.z > absNormal.y) {
projection = mat3x2({1.0, 0.0, 0.0}, //
{0.0, 1.0, 0.0});
xyzMax = normal.z;
} else if (absNormal.y > absNormal.x) {
projection = mat3x2({0.0, 0.0, 1.0}, //
{1.0, 0.0, 0.0});
xyzMax = normal.y;
} else {
projection = mat3x2({0.0, 1.0, 0.0}, //
{0.0, 0.0, 1.0});
xyzMax = normal.x;
}
if (xyzMax < 0) projection[0] *= -1.0;
return la::transpose(projection);
}
inline vec3 GetBarycentric(const vec3& v, const mat3& triPos,
double tolerance) {
const mat3 edges(triPos[2] - triPos[1], triPos[0] - triPos[2],
triPos[1] - triPos[0]);
const vec3 d2(la::dot(edges[0], edges[0]), la::dot(edges[1], edges[1]),
la::dot(edges[2], edges[2]));
const int longSide = d2[0] > d2[1] && d2[0] > d2[2] ? 0
: d2[1] > d2[2] ? 1
: 2;
const vec3 crossP = la::cross(edges[0], edges[1]);
const double area2 = la::dot(crossP, crossP);
const double tol2 = tolerance * tolerance;
vec3 uvw(0.0);
for (const int i : {0, 1, 2}) {
const vec3 dv = v - triPos[i];
if (la::dot(dv, dv) < tol2) {
// Return exactly equal if within tolerance of vert.
uvw[i] = 1;
return uvw;
}
}
if (d2[longSide] < tol2) { // point
return vec3(1, 0, 0);
} else if (area2 > d2[longSide] * tol2) { // triangle
for (const int i : {0, 1, 2}) {
const int j = Next3(i);
const vec3 crossPv = la::cross(edges[i], v - triPos[j]);
const double area2v = la::dot(crossPv, crossPv);
// Return exactly equal if within tolerance of edge.
uvw[i] = area2v < d2[i] * tol2 ? 0 : la::dot(crossPv, crossP);
}
uvw /= (uvw[0] + uvw[1] + uvw[2]);
return uvw;
} else { // line
const int nextV = Next3(longSide);
const double alpha =
la::dot(v - triPos[nextV], edges[longSide]) / d2[longSide];
uvw[longSide] = 0;
uvw[nextV] = 1 - alpha;
const int lastV = Next3(nextV);
uvw[lastV] = alpha;
return uvw;
}
}
/**
* The fundamental component of the halfedge data structure used for storing and
* operating on the Manifold.
*/
struct Halfedge {
int startVert, endVert;
int pairedHalfedge;
bool IsForward() const { return startVert < endVert; }
bool operator<(const Halfedge& other) const {
return startVert == other.startVert ? endVert < other.endVert
: startVert < other.startVert;
}
};
struct Barycentric {
int tri;
vec4 uvw;
};
struct TriRef {
/// The unique ID of the mesh instance of this triangle. If .meshID and .tri
/// match for two triangles, then they are coplanar and came from the same
/// face.
int meshID;
/// The OriginalID of the mesh this triangle came from. This ID is ideal for
/// reapplying properties like UV coordinates to the output mesh.
int originalID;
/// Probably the triangle index of the original triangle this was part of:
/// Mesh.triVerts[tri], but it's an input, so just pass it along unchanged.
int tri;
/// Triangles with the same face ID are coplanar.
int faceID;
bool SameFace(const TriRef& other) const {
return meshID == other.meshID && faceID == other.faceID;
}
};
/**
* This is a temporary edge structure which only stores edges forward and
* references the halfedge it was created from.
*/
struct TmpEdge {
int first, second, halfedgeIdx;
TmpEdge() {}
TmpEdge(int start, int end, int idx) {
first = std::min(start, end);
second = std::max(start, end);
halfedgeIdx = idx;
}
bool operator<(const TmpEdge& other) const {
return first == other.first ? second < other.second : first < other.first;
}
};
Vec<TmpEdge> inline CreateTmpEdges(const Vec<Halfedge>& halfedge) {
Vec<TmpEdge> edges(halfedge.size());
for_each_n(autoPolicy(edges.size()), countAt(0), edges.size(),
[&edges, &halfedge](const int idx) {
const Halfedge& half = halfedge[idx];
edges[idx] = TmpEdge(half.startVert, half.endVert,
half.IsForward() ? idx : -1);
});
size_t numEdge =
remove_if(edges.begin(), edges.end(),
[](const TmpEdge& edge) { return edge.halfedgeIdx < 0; }) -
edges.begin();
DEBUG_ASSERT(numEdge == halfedge.size() / 2, topologyErr, "Not oriented!");
edges.resize(numEdge);
return edges;
}
template <const bool inverted>
struct ReindexEdge {
VecView<const TmpEdge> edges;
SparseIndices& indices;
void operator()(size_t i) {
int& edge = indices.Get(i, inverted);
edge = edges[edge].halfedgeIdx;
}
};
#ifdef MANIFOLD_DEBUG
inline std::ostream& operator<<(std::ostream& stream, const Halfedge& edge) {
return stream << "startVert = " << edge.startVert
<< ", endVert = " << edge.endVert
<< ", pairedHalfedge = " << edge.pairedHalfedge;
}
inline std::ostream& operator<<(std::ostream& stream, const Barycentric& bary) {
return stream << "tri = " << bary.tri << ", uvw = " << bary.uvw;
}
inline std::ostream& operator<<(std::ostream& stream, const TriRef& ref) {
return stream << "meshID: " << ref.meshID
<< ", originalID: " << ref.originalID << ", tri: " << ref.tri
<< ", faceID: " << ref.faceID;
}
#endif
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <atomic>
#include <set>
#include "./impl.h"
#include "./parallel.h"
namespace {
using namespace manifold;
constexpr uint32_t kNoCode = 0xFFFFFFFFu;
uint32_t MortonCode(vec3 position, Box bBox) {
// Unreferenced vertices are marked NaN, and this will sort them to the end
// (the Morton code only uses the first 30 of 32 bits).
if (std::isnan(position.x)) return kNoCode;
return Collider::MortonCode(position, bBox);
}
struct Reindex {
VecView<const int> indexInv;
void operator()(Halfedge& edge) {
if (edge.startVert < 0) return;
edge.startVert = indexInv[edge.startVert];
edge.endVert = indexInv[edge.endVert];
}
};
struct MarkProp {
VecView<int> keep;
void operator()(ivec3 triProp) {
for (const int i : {0, 1, 2}) {
reinterpret_cast<std::atomic<int>*>(&keep[triProp[i]])
->store(1, std::memory_order_relaxed);
}
}
};
struct ReindexProps {
VecView<const int> old2new;
void operator()(ivec3& triProp) {
for (const int i : {0, 1, 2}) {
triProp[i] = old2new[triProp[i]];
}
}
};
struct ReindexFace {
VecView<Halfedge> halfedge;
VecView<vec4> halfedgeTangent;
VecView<const Halfedge> oldHalfedge;
VecView<const vec4> oldHalfedgeTangent;
VecView<const int> faceNew2Old;
VecView<const int> faceOld2New;
void operator()(int newFace) {
const int oldFace = faceNew2Old[newFace];
for (const int i : {0, 1, 2}) {
const int oldEdge = 3 * oldFace + i;
Halfedge edge = oldHalfedge[oldEdge];
const int pairedFace = edge.pairedHalfedge / 3;
const int offset = edge.pairedHalfedge - 3 * pairedFace;
edge.pairedHalfedge = 3 * faceOld2New[pairedFace] + offset;
const int newEdge = 3 * newFace + i;
halfedge[newEdge] = edge;
if (!oldHalfedgeTangent.empty()) {
halfedgeTangent[newEdge] = oldHalfedgeTangent[oldEdge];
}
}
}
};
template <typename Precision, typename I>
bool MergeMeshGLP(MeshGLP<Precision, I>& mesh) {
ZoneScoped;
std::multiset<std::pair<int, int>> openEdges;
std::vector<int> merge(mesh.NumVert());
std::iota(merge.begin(), merge.end(), 0);
for (size_t i = 0; i < mesh.mergeFromVert.size(); ++i) {
merge[mesh.mergeFromVert[i]] = mesh.mergeToVert[i];
}
const auto numVert = mesh.NumVert();
const auto numTri = mesh.NumTri();
const int next[3] = {1, 2, 0};
for (size_t tri = 0; tri < numTri; ++tri) {
for (int i : {0, 1, 2}) {
auto edge = std::make_pair(merge[mesh.triVerts[3 * tri + next[i]]],
merge[mesh.triVerts[3 * tri + i]]);
auto it = openEdges.find(edge);
if (it == openEdges.end()) {
std::swap(edge.first, edge.second);
openEdges.insert(edge);
} else {
openEdges.erase(it);
}
}
}
if (openEdges.empty()) {
return false;
}
const auto numOpenVert = openEdges.size();
Vec<int> openVerts(numOpenVert);
int i = 0;
for (const auto& edge : openEdges) {
const int vert = edge.first;
openVerts[i++] = vert;
}
Vec<Precision> vertPropD(mesh.vertProperties);
Box bBox;
for (const int i : {0, 1, 2}) {
auto iPos =
StridedRange(vertPropD.begin() + i, vertPropD.end(), mesh.numProp);
auto minMax = manifold::transform_reduce(
iPos.begin(), iPos.end(),
std::make_pair(std::numeric_limits<double>::infinity(),
-std::numeric_limits<double>::infinity()),
[](auto a, auto b) {
return std::make_pair(std::min(a.first, b.first),
std::max(a.second, b.second));
},
[](double f) { return std::make_pair(f, f); });
bBox.min[i] = minMax.first;
bBox.max[i] = minMax.second;
}
const double tolerance = std::max(static_cast<double>(mesh.tolerance),
(std::is_same<Precision, float>::value
? std::numeric_limits<float>::epsilon()
: kPrecision) *
bBox.Scale());
auto policy = autoPolicy(numOpenVert, 1e5);
Vec<Box> vertBox(numOpenVert);
Vec<uint32_t> vertMorton(numOpenVert);
for_each_n(policy, countAt(0), numOpenVert,
[&vertMorton, &vertBox, &openVerts, &bBox, &mesh,
tolerance](const int i) {
int vert = openVerts[i];
const vec3 center(mesh.vertProperties[mesh.numProp * vert],
mesh.vertProperties[mesh.numProp * vert + 1],
mesh.vertProperties[mesh.numProp * vert + 2]);
vertBox[i].min = center - tolerance / 2.0;
vertBox[i].max = center + tolerance / 2.0;
vertMorton[i] = MortonCode(center, bBox);
});
Vec<int> vertNew2Old(numOpenVert);
sequence(vertNew2Old.begin(), vertNew2Old.end());
stable_sort(vertNew2Old.begin(), vertNew2Old.end(),
[&vertMorton](const int& a, const int& b) {
return vertMorton[a] < vertMorton[b];
});
Permute(vertMorton, vertNew2Old);
Permute(vertBox, vertNew2Old);
Permute(openVerts, vertNew2Old);
Collider collider(vertBox, vertMorton);
SparseIndices toMerge = collider.Collisions<true>(vertBox.cview());
UnionFind<> uf(numVert);
for (size_t i = 0; i < mesh.mergeFromVert.size(); ++i) {
uf.unionXY(static_cast<int>(mesh.mergeFromVert[i]),
static_cast<int>(mesh.mergeToVert[i]));
}
for (size_t i = 0; i < toMerge.size(); ++i) {
uf.unionXY(openVerts[toMerge.Get(i, false)],
openVerts[toMerge.Get(i, true)]);
}
mesh.mergeToVert.clear();
mesh.mergeFromVert.clear();
for (size_t v = 0; v < numVert; ++v) {
const size_t mergeTo = uf.find(v);
if (mergeTo != v) {
mesh.mergeFromVert.push_back(v);
mesh.mergeToVert.push_back(mergeTo);
}
}
return true;
}
} // namespace
namespace manifold {
/**
* Once halfedge_ has been filled in, this function can be called to create the
* rest of the internal data structures. This function also removes the verts
* and halfedges flagged for removal (NaN verts and -1 halfedges).
*/
void Manifold::Impl::Finish() {
if (halfedge_.size() == 0) return;
CalculateBBox();
SetEpsilon(epsilon_);
if (!bBox_.IsFinite()) {
// Decimated out of existence - early out.
MarkFailure(Error::NoError);
return;
}
SortVerts();
Vec<Box> faceBox;
Vec<uint32_t> faceMorton;
GetFaceBoxMorton(faceBox, faceMorton);
SortFaces(faceBox, faceMorton);
if (halfedge_.size() == 0) return;
CompactProps();
DEBUG_ASSERT(halfedge_.size() % 6 == 0, topologyErr,
"Not an even number of faces after sorting faces!");
#ifdef MANIFOLD_DEBUG
auto MaxOrMinus = [](int a, int b) {
return std::min(a, b) < 0 ? -1 : std::max(a, b);
};
int face = 0;
Halfedge extrema = {0, 0, 0};
for (size_t i = 0; i < halfedge_.size(); i++) {
Halfedge e = halfedge_[i];
if (!e.IsForward()) std::swap(e.startVert, e.endVert);
extrema.startVert = std::min(extrema.startVert, e.startVert);
extrema.endVert = std::min(extrema.endVert, e.endVert);
extrema.pairedHalfedge =
MaxOrMinus(extrema.pairedHalfedge, e.pairedHalfedge);
face = MaxOrMinus(face, i / 3);
}
DEBUG_ASSERT(extrema.startVert >= 0, topologyErr,
"Vertex index is negative!");
DEBUG_ASSERT(extrema.endVert < static_cast<int>(NumVert()), topologyErr,
"Vertex index exceeds number of verts!");
DEBUG_ASSERT(extrema.pairedHalfedge >= 0, topologyErr,
"Halfedge index is negative!");
DEBUG_ASSERT(extrema.pairedHalfedge < 2 * static_cast<int>(NumEdge()),
topologyErr, "Halfedge index exceeds number of halfedges!");
DEBUG_ASSERT(face >= 0, topologyErr, "Face index is negative!");
DEBUG_ASSERT(face < static_cast<int>(NumTri()), topologyErr,
"Face index exceeds number of faces!");
#endif
DEBUG_ASSERT(meshRelation_.triRef.size() == NumTri() ||
meshRelation_.triRef.size() == 0,
logicErr, "Mesh Relation doesn't fit!");
DEBUG_ASSERT(faceNormal_.size() == NumTri() || faceNormal_.size() == 0,
logicErr,
"faceNormal size = " + std::to_string(faceNormal_.size()) +
", NumTri = " + std::to_string(NumTri()));
CalculateNormals();
collider_ = Collider(faceBox, faceMorton);
DEBUG_ASSERT(Is2Manifold(), logicErr, "mesh is not 2-manifold!");
}
/**
* Sorts the vertices according to their Morton code.
*/
void Manifold::Impl::SortVerts() {
ZoneScoped;
const auto numVert = NumVert();
Vec<uint32_t> vertMorton(numVert);
auto policy = autoPolicy(numVert, 1e5);
for_each_n(policy, countAt(0), numVert, [this, &vertMorton](const int vert) {
vertMorton[vert] = MortonCode(vertPos_[vert], bBox_);
});
Vec<int> vertNew2Old(numVert);
sequence(vertNew2Old.begin(), vertNew2Old.end());
stable_sort(vertNew2Old.begin(), vertNew2Old.end(),
[&vertMorton](const int& a, const int& b) {
return vertMorton[a] < vertMorton[b];
});
ReindexVerts(vertNew2Old, numVert);
// Verts were flagged for removal with NaNs and assigned kNoCode to sort
// them to the end, which allows them to be removed.
const auto newNumVert = std::find_if(vertNew2Old.begin(), vertNew2Old.end(),
[&vertMorton](const int vert) {
return vertMorton[vert] == kNoCode;
}) -
vertNew2Old.begin();
vertNew2Old.resize(newNumVert);
Permute(vertPos_, vertNew2Old);
if (vertNormal_.size() == numVert) {
Permute(vertNormal_, vertNew2Old);
}
}
/**
* Updates the halfedges to point to new vert indices based on a mapping,
* vertNew2Old. This may be a subset, so the total number of original verts is
* also given.
*/
void Manifold::Impl::ReindexVerts(const Vec<int>& vertNew2Old,
size_t oldNumVert) {
ZoneScoped;
Vec<int> vertOld2New(oldNumVert);
scatter(countAt(0), countAt(static_cast<int>(NumVert())), vertNew2Old.begin(),
vertOld2New.begin());
for_each(autoPolicy(oldNumVert, 1e5), halfedge_.begin(), halfedge_.end(),
Reindex({vertOld2New}));
}
/**
* Removes unreferenced property verts and reindexes triProperties.
*/
void Manifold::Impl::CompactProps() {
ZoneScoped;
if (meshRelation_.numProp == 0) return;
const auto numVerts = meshRelation_.properties.size() / meshRelation_.numProp;
Vec<int> keep(numVerts, 0);
auto policy = autoPolicy(numVerts, 1e5);
for_each(policy, meshRelation_.triProperties.cbegin(),
meshRelation_.triProperties.cend(), MarkProp({keep}));
Vec<int> propOld2New(numVerts + 1, 0);
inclusive_scan(keep.begin(), keep.end(), propOld2New.begin() + 1);
Vec<double> oldProp = meshRelation_.properties;
const int numVertsNew = propOld2New[numVerts];
const int numProp = meshRelation_.numProp;
auto& properties = meshRelation_.properties;
properties.resize(numProp * numVertsNew);
for_each_n(
policy, countAt(0), numVerts,
[&properties, &oldProp, &propOld2New, &keep, &numProp](const int oldIdx) {
if (keep[oldIdx] == 0) return;
for (int p = 0; p < numProp; ++p) {
properties[propOld2New[oldIdx] * numProp + p] =
oldProp[oldIdx * numProp + p];
}
});
for_each_n(policy, meshRelation_.triProperties.begin(), NumTri(),
ReindexProps({propOld2New}));
}
/**
* Fills the faceBox and faceMorton input with the bounding boxes and Morton
* codes of the faces, respectively. The Morton code is based on the center of
* the bounding box.
*/
void Manifold::Impl::GetFaceBoxMorton(Vec<Box>& faceBox,
Vec<uint32_t>& faceMorton) const {
ZoneScoped;
faceBox.resize(NumTri());
faceMorton.resize(NumTri());
for_each_n(autoPolicy(NumTri(), 1e5), countAt(0), NumTri(),
[this, &faceBox, &faceMorton](const int face) {
// Removed tris are marked by all halfedges having pairedHalfedge
// = -1, and this will sort them to the end (the Morton code only
// uses the first 30 of 32 bits).
if (halfedge_[3 * face].pairedHalfedge < 0) {
faceMorton[face] = kNoCode;
return;
}
vec3 center(0.0);
for (const int i : {0, 1, 2}) {
const vec3 pos = vertPos_[halfedge_[3 * face + i].startVert];
center += pos;
faceBox[face].Union(pos);
}
center /= 3;
faceMorton[face] = MortonCode(center, bBox_);
});
}
/**
* Sorts the faces of this manifold according to their input Morton code. The
* bounding box and Morton code arrays are also sorted accordingly.
*/
void Manifold::Impl::SortFaces(Vec<Box>& faceBox, Vec<uint32_t>& faceMorton) {
ZoneScoped;
Vec<int> faceNew2Old(NumTri());
sequence(faceNew2Old.begin(), faceNew2Old.end());
stable_sort(faceNew2Old.begin(), faceNew2Old.end(),
[&faceMorton](const int& a, const int& b) {
return faceMorton[a] < faceMorton[b];
});
// Tris were flagged for removal with pairedHalfedge = -1 and assigned kNoCode
// to sort them to the end, which allows them to be removed.
const int newNumTri = std::find_if(faceNew2Old.begin(), faceNew2Old.end(),
[&faceMorton](const int face) {
return faceMorton[face] == kNoCode;
}) -
faceNew2Old.begin();
faceNew2Old.resize(newNumTri);
Permute(faceMorton, faceNew2Old);
Permute(faceBox, faceNew2Old);
GatherFaces(faceNew2Old);
}
/**
* Creates the halfedge_ vector for this manifold by copying a set of faces from
* another manifold, given by oldHalfedge. Input faceNew2Old defines the old
* faces to gather into this.
*/
void Manifold::Impl::GatherFaces(const Vec<int>& faceNew2Old) {
ZoneScoped;
const auto numTri = faceNew2Old.size();
if (meshRelation_.triRef.size() == NumTri())
Permute(meshRelation_.triRef, faceNew2Old);
if (meshRelation_.triProperties.size() == NumTri())
Permute(meshRelation_.triProperties, faceNew2Old);
if (faceNormal_.size() == NumTri()) Permute(faceNormal_, faceNew2Old);
Vec<Halfedge> oldHalfedge(std::move(halfedge_));
Vec<vec4> oldHalfedgeTangent(std::move(halfedgeTangent_));
Vec<int> faceOld2New(oldHalfedge.size() / 3);
auto policy = autoPolicy(numTri, 1e5);
scatter(countAt(0_uz), countAt(numTri), faceNew2Old.begin(),
faceOld2New.begin());
halfedge_.resize(3 * numTri);
if (oldHalfedgeTangent.size() != 0) halfedgeTangent_.resize(3 * numTri);
for_each_n(policy, countAt(0), numTri,
ReindexFace({halfedge_, halfedgeTangent_, oldHalfedge,
oldHalfedgeTangent, faceNew2Old, faceOld2New}));
}
void Manifold::Impl::GatherFaces(const Impl& old, const Vec<int>& faceNew2Old) {
ZoneScoped;
const auto numTri = faceNew2Old.size();
meshRelation_.triRef.resize(numTri);
gather(faceNew2Old.begin(), faceNew2Old.end(),
old.meshRelation_.triRef.begin(), meshRelation_.triRef.begin());
for (const auto& pair : old.meshRelation_.meshIDtransform) {
meshRelation_.meshIDtransform[pair.first] = pair.second;
}
if (old.meshRelation_.triProperties.size() > 0) {
meshRelation_.triProperties.resize(numTri);
gather(faceNew2Old.begin(), faceNew2Old.end(),
old.meshRelation_.triProperties.begin(),
meshRelation_.triProperties.begin());
meshRelation_.numProp = old.meshRelation_.numProp;
meshRelation_.properties = old.meshRelation_.properties;
}
if (old.faceNormal_.size() == old.NumTri()) {
faceNormal_.resize(numTri);
gather(faceNew2Old.begin(), faceNew2Old.end(), old.faceNormal_.begin(),
faceNormal_.begin());
}
Vec<int> faceOld2New(old.NumTri());
scatter(countAt(0_uz), countAt(numTri), faceNew2Old.begin(),
faceOld2New.begin());
halfedge_.resize(3 * numTri);
if (old.halfedgeTangent_.size() != 0) halfedgeTangent_.resize(3 * numTri);
for_each_n(autoPolicy(numTri, 1e5), countAt(0), numTri,
ReindexFace({halfedge_, halfedgeTangent_, old.halfedge_,
old.halfedgeTangent_, faceNew2Old, faceOld2New}));
}
/**
* Updates the mergeFromVert and mergeToVert vectors in order to create a
* manifold solid. If the MeshGL is already manifold, no change will occur and
* the function will return false. Otherwise, this will merge verts along open
* edges within tolerance (the maximum of the MeshGL tolerance and the
* baseline bounding-box tolerance), keeping any from the existing merge
* vectors, and return true.
*
* There is no guarantee the result will be manifold - this is a best-effort
* helper function designed primarily to aid in the case where a manifold
* multi-material MeshGL was produced, but its merge vectors were lost due to
* a round-trip through a file format. Constructing a Manifold from the result
* will report an error status if it is not manifold.
*/
template <>
bool MeshGL::Merge() {
return MergeMeshGLP(*this);
}
template <>
bool MeshGL64::Merge() {
return MergeMeshGLP(*this);
}
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include "./parallel.h"
#include "./utils.h"
#include "./vec.h"
#include "manifold/common.h"
#include "manifold/optional_assert.h"
namespace {
template <typename T>
inline bool FirstFinite(T v) {
return std::isfinite(v[0]);
}
template <>
inline bool FirstFinite<double>(double v) {
return std::isfinite(v);
}
} // namespace
namespace manifold {
/** @ingroup Private */
class SparseIndices {
// sparse indices where {p1: q1, p2: q2, ...} are laid out as
// p1 q1 p2 q2 or q1 p1 q2 p2, depending on endianness
// such that the indices are sorted by (p << 32) | q
public:
#if defined(__BYTE_ORDER) && __BYTE_ORDER == __BIG_ENDIAN || \
defined(__BIG_ENDIAN__) || defined(__ARMEB__) || defined(__THUMBEB__) || \
defined(__AARCH64EB__) || defined(_MIBSEB) || defined(__MIBSEB) || \
defined(__MIBSEB__)
static constexpr size_t pOffset = 0;
#elif defined(__BYTE_ORDER) && __BYTE_ORDER == __LITTLE_ENDIAN || \
defined(__LITTLE_ENDIAN__) || defined(__ARMEL__) || \
defined(__THUMBEL__) || defined(__AARCH64EL__) || defined(_MIPSEL) || \
defined(__MIPSEL) || defined(__MIPSEL__) || defined(__EMSCRIPTEN__) || \
defined(_WIN32)
static constexpr size_t pOffset = 1;
#else
#error "unknown architecture"
#endif
static constexpr int64_t EncodePQ(int p, int q) {
return (int64_t(p) << 32) | q;
}
SparseIndices() = default;
SparseIndices(size_t size) { data_ = Vec<char>(size * sizeof(int64_t)); }
void Clear() { data_.clear(false); }
void FromIndices(const std::vector<SparseIndices>& indices) {
std::vector<size_t> sizes;
size_t total_size = 0;
for (const auto& ind : indices) {
sizes.push_back(total_size);
total_size += ind.data_.size();
}
data_ = Vec<char>(total_size);
for_each_n(ExecutionPolicy::Par, countAt(0), indices.size(), [&](size_t i) {
std::copy(indices[i].data_.begin(), indices[i].data_.end(),
data_.begin() + sizes[i]);
});
}
size_t size() const { return data_.size() / sizeof(int64_t); }
Vec<int> Copy(bool use_q) const {
Vec<int> out(size());
size_t offset = pOffset;
if (use_q) offset = 1 - offset;
const int* p = ptr();
for_each(autoPolicy(out.size()), countAt(0_uz), countAt(out.size()),
[&](size_t i) { out[i] = p[i * 2 + offset]; });
return out;
}
void Sort() {
VecView<int64_t> view = AsVec64();
stable_sort(view.begin(), view.end());
}
void Resize(size_t size) { data_.resize(size * sizeof(int64_t), -1); }
inline int& Get(size_t i, bool use_q) {
if (use_q)
return ptr()[2 * i + 1 - pOffset];
else
return ptr()[2 * i + pOffset];
}
inline int Get(size_t i, bool use_q) const {
if (use_q)
return ptr()[2 * i + 1 - pOffset];
else
return ptr()[2 * i + pOffset];
}
inline int64_t GetPQ(size_t i) const {
VecView<const int64_t> view = AsVec64();
return view[i];
}
inline void Set(size_t i, int p, int q) {
VecView<int64_t> view = AsVec64();
view[i] = EncodePQ(p, q);
}
inline void SetPQ(size_t i, int64_t pq) {
VecView<int64_t> view = AsVec64();
view[i] = pq;
}
VecView<int64_t> AsVec64() {
return VecView<int64_t>(reinterpret_cast<int64_t*>(data_.data()),
data_.size() / sizeof(int64_t));
}
VecView<const int64_t> AsVec64() const {
return VecView<const int64_t>(
reinterpret_cast<const int64_t*>(data_.data()),
data_.size() / sizeof(int64_t));
}
VecView<int32_t> AsVec32() {
return VecView<int32_t>(reinterpret_cast<int32_t*>(data_.data()),
data_.size() / sizeof(int32_t));
}
VecView<const int32_t> AsVec32() const {
return VecView<const int32_t>(
reinterpret_cast<const int32_t*>(data_.data()),
data_.size() / sizeof(int32_t));
}
inline void Add(int p, int q, bool seq = false) {
data_.extend(sizeof(int64_t), seq);
Set(size() - 1, p, q);
}
void Unique() {
Sort();
VecView<int64_t> view = AsVec64();
size_t newSize = unique(view.begin(), view.end()) - view.begin();
Resize(newSize);
}
size_t RemoveZeros(Vec<int>& S) {
DEBUG_ASSERT(S.size() == size(), userErr,
"Different number of values than indicies!");
Vec<size_t> new2Old(S.size());
sequence(new2Old.begin(), new2Old.end());
size_t size = copy_if(countAt(0_uz), countAt(S.size()), new2Old.begin(),
[&S](const size_t i) { return S[i] != 0; }) -
new2Old.begin();
new2Old.resize(size);
Permute(S, new2Old);
Vec<char> tmp(std::move(data_));
Resize(size);
gather(new2Old.begin(), new2Old.end(),
reinterpret_cast<int64_t*>(tmp.data()),
reinterpret_cast<int64_t*>(data_.data()));
return size;
}
template <typename T>
size_t KeepFinite(Vec<T>& v, Vec<int>& x) {
DEBUG_ASSERT(x.size() == size(), userErr,
"Different number of values than indicies!");
Vec<int> new2Old(v.size());
size_t size = copy_if(countAt(0_uz), countAt(v.size()), new2Old.begin(),
[&v](size_t i) { return FirstFinite(v[i]); }) -
new2Old.begin();
new2Old.resize(size);
Permute(v, new2Old);
Permute(x, new2Old);
Vec<char> tmp(std::move(data_));
Resize(size);
gather(new2Old.begin(), new2Old.end(),
reinterpret_cast<int64_t*>(tmp.data()),
reinterpret_cast<int64_t*>(data_.data()));
return size;
}
#ifdef MANIFOLD_DEBUG
void Dump() const {
std::cout << "SparseIndices = " << std::endl;
const int* p = ptr();
for (size_t i = 0; i < size(); ++i) {
std::cout << i << ", p = " << Get(i, false) << ", q = " << Get(i, true)
<< std::endl;
}
std::cout << std::endl;
}
#endif
private:
Vec<char> data_;
inline int* ptr() { return reinterpret_cast<int32_t*>(data_.data()); }
inline const int* ptr() const {
return reinterpret_cast<const int32_t*>(data_.data());
}
};
} // namespace manifold

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// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "./impl.h"
#include "./parallel.h"
template <>
struct std::hash<manifold::ivec4> {
size_t operator()(const manifold::ivec4& p) const {
return std::hash<int>()(p.x) ^ std::hash<int>()(p.y) ^
std::hash<int>()(p.z) ^ std::hash<int>()(p.w);
}
};
namespace {
using namespace manifold;
class Partition {
public:
// The cached partitions don't have idx - it's added to the copy returned
// from GetPartition that contains the mapping of the input divisions into the
// sorted divisions that are uniquely cached.
ivec4 idx;
ivec4 sortedDivisions;
Vec<vec4> vertBary;
Vec<ivec3> triVert;
int InteriorOffset() const {
return sortedDivisions[0] + sortedDivisions[1] + sortedDivisions[2] +
sortedDivisions[3];
}
int NumInterior() const { return vertBary.size() - InteriorOffset(); }
static Partition GetPartition(ivec4 divisions) {
if (divisions[0] == 0) return Partition(); // skip wrong side of quad
ivec4 sortedDiv = divisions;
ivec4 triIdx = {0, 1, 2, 3};
if (divisions[3] == 0) { // triangle
if (sortedDiv[2] > sortedDiv[1]) {
std::swap(sortedDiv[2], sortedDiv[1]);
std::swap(triIdx[2], triIdx[1]);
}
if (sortedDiv[1] > sortedDiv[0]) {
std::swap(sortedDiv[1], sortedDiv[0]);
std::swap(triIdx[1], triIdx[0]);
if (sortedDiv[2] > sortedDiv[1]) {
std::swap(sortedDiv[2], sortedDiv[1]);
std::swap(triIdx[2], triIdx[1]);
}
}
} else { // quad
int minIdx = 0;
int min = divisions[minIdx];
int next = divisions[1];
for (const int i : {1, 2, 3}) {
const int n = divisions[(i + 1) % 4];
if (divisions[i] < min || (divisions[i] == min && n < next)) {
minIdx = i;
min = divisions[i];
next = n;
}
}
// Backwards (mirrored) quads get a separate cache key for now for
// simplicity, so there is no reversal necessary for quads when
// re-indexing.
ivec4 tmp = sortedDiv;
for (const int i : {0, 1, 2, 3}) {
triIdx[i] = (i + minIdx) % 4;
sortedDiv[i] = tmp[triIdx[i]];
}
}
Partition partition = GetCachedPartition(sortedDiv);
partition.idx = triIdx;
return partition;
}
Vec<ivec3> Reindex(ivec4 triVerts, ivec4 edgeOffsets, bvec4 edgeFwd,
int interiorOffset) const {
Vec<int> newVerts;
newVerts.reserve(vertBary.size());
ivec4 triIdx = idx;
ivec4 outTri = {0, 1, 2, 3};
if (triVerts[3] < 0 && idx[1] != Next3(idx[0])) {
triIdx = {idx[2], idx[0], idx[1], idx[3]};
edgeFwd = !edgeFwd;
std::swap(outTri[0], outTri[1]);
}
for (const int i : {0, 1, 2, 3}) {
if (triVerts[triIdx[i]] >= 0) newVerts.push_back(triVerts[triIdx[i]]);
}
for (const int i : {0, 1, 2, 3}) {
const int n = sortedDivisions[i] - 1;
int offset = edgeOffsets[idx[i]] + (edgeFwd[idx[i]] ? 0 : n - 1);
for (int j = 0; j < n; ++j) {
newVerts.push_back(offset);
offset += edgeFwd[idx[i]] ? 1 : -1;
}
}
const int offset = interiorOffset - newVerts.size();
size_t old = newVerts.size();
newVerts.resize(vertBary.size());
std::iota(newVerts.begin() + old, newVerts.end(), old + offset);
const int numTri = triVert.size();
Vec<ivec3> newTriVert(numTri);
for_each_n(autoPolicy(numTri), countAt(0), numTri,
[&newTriVert, &outTri, &newVerts, this](const int tri) {
for (const int j : {0, 1, 2}) {
newTriVert[tri][outTri[j]] = newVerts[triVert[tri][j]];
}
});
return newTriVert;
}
private:
static inline auto cacheLock = std::mutex();
static inline auto cache =
std::unordered_map<ivec4, std::unique_ptr<Partition>>();
// This triangulation is purely topological - it depends only on the number of
// divisions of the three sides of the triangle. This allows them to be cached
// and reused for similar triangles. The shape of the final surface is defined
// by the tangents and the barycentric coordinates of the new verts. For
// triangles, the input must be sorted: n[0] >= n[1] >= n[2] > 0.
static Partition GetCachedPartition(ivec4 n) {
{
auto lockGuard = std::lock_guard<std::mutex>(cacheLock);
auto cached = cache.find(n);
if (cached != cache.end()) {
return *cached->second;
}
}
Partition partition;
partition.sortedDivisions = n;
if (n[3] > 0) { // quad
partition.vertBary.push_back({1, 0, 0, 0});
partition.vertBary.push_back({0, 1, 0, 0});
partition.vertBary.push_back({0, 0, 1, 0});
partition.vertBary.push_back({0, 0, 0, 1});
ivec4 edgeOffsets;
edgeOffsets[0] = 4;
for (const int i : {0, 1, 2, 3}) {
if (i > 0) {
edgeOffsets[i] = edgeOffsets[i - 1] + n[i - 1] - 1;
}
const vec4 nextBary = partition.vertBary[(i + 1) % 4];
for (int j = 1; j < n[i]; ++j) {
partition.vertBary.push_back(
la::lerp(partition.vertBary[i], nextBary, (double)j / n[i]));
}
}
PartitionQuad(partition.triVert, partition.vertBary, {0, 1, 2, 3},
edgeOffsets, n - 1, {true, true, true, true});
} else { // tri
partition.vertBary.push_back({1, 0, 0, 0});
partition.vertBary.push_back({0, 1, 0, 0});
partition.vertBary.push_back({0, 0, 1, 0});
for (const int i : {0, 1, 2}) {
const vec4 nextBary = partition.vertBary[(i + 1) % 3];
for (int j = 1; j < n[i]; ++j) {
partition.vertBary.push_back(
la::lerp(partition.vertBary[i], nextBary, (double)j / n[i]));
}
}
const ivec3 edgeOffsets = {3, 3 + n[0] - 1, 3 + n[0] - 1 + n[1] - 1};
const double f = n[2] * n[2] + n[0] * n[0];
if (n[1] == 1) {
if (n[0] == 1) {
partition.triVert.push_back({0, 1, 2});
} else {
PartitionFan(partition.triVert, {0, 1, 2}, n[0] - 1, edgeOffsets[0]);
}
} else if (n[1] * n[1] > f - std::sqrt(2.0) * n[0] * n[2]) { // acute-ish
partition.triVert.push_back({edgeOffsets[1] - 1, 1, edgeOffsets[1]});
PartitionQuad(partition.triVert, partition.vertBary,
{edgeOffsets[1] - 1, edgeOffsets[1], 2, 0},
{-1, edgeOffsets[1] + 1, edgeOffsets[2], edgeOffsets[0]},
{0, n[1] - 2, n[2] - 1, n[0] - 2},
{true, true, true, true});
} else { // obtuse -> spit into two acute
// portion of n[0] under n[2]
const int ns =
std::min(n[0] - 2, (int)std::round((f - n[1] * n[1]) / (2 * n[0])));
// height from n[0]: nh <= n[2]
const int nh =
std::max(1., std::round(std::sqrt(n[2] * n[2] - ns * ns)));
const int hOffset = partition.vertBary.size();
const vec4 middleBary = partition.vertBary[edgeOffsets[0] + ns - 1];
for (int j = 1; j < nh; ++j) {
partition.vertBary.push_back(
la::lerp(partition.vertBary[2], middleBary, (double)j / nh));
}
partition.triVert.push_back({edgeOffsets[1] - 1, 1, edgeOffsets[1]});
PartitionQuad(
partition.triVert, partition.vertBary,
{edgeOffsets[1] - 1, edgeOffsets[1], 2, edgeOffsets[0] + ns - 1},
{-1, edgeOffsets[1] + 1, hOffset, edgeOffsets[0] + ns},
{0, n[1] - 2, nh - 1, n[0] - ns - 2}, {true, true, true, true});
if (n[2] == 1) {
PartitionFan(partition.triVert, {0, edgeOffsets[0] + ns - 1, 2},
ns - 1, edgeOffsets[0]);
} else {
if (ns == 1) {
partition.triVert.push_back({hOffset, 2, edgeOffsets[2]});
PartitionQuad(partition.triVert, partition.vertBary,
{hOffset, edgeOffsets[2], 0, edgeOffsets[0]},
{-1, edgeOffsets[2] + 1, -1, hOffset + nh - 2},
{0, n[2] - 2, ns - 1, nh - 2},
{true, true, true, false});
} else {
partition.triVert.push_back({hOffset - 1, 0, edgeOffsets[0]});
PartitionQuad(
partition.triVert, partition.vertBary,
{hOffset - 1, edgeOffsets[0], edgeOffsets[0] + ns - 1, 2},
{-1, edgeOffsets[0] + 1, hOffset + nh - 2, edgeOffsets[2]},
{0, ns - 2, nh - 1, n[2] - 2}, {true, true, false, true});
}
}
}
}
auto lockGuard = std::lock_guard<std::mutex>(cacheLock);
cache.insert({n, std::make_unique<Partition>(partition)});
return partition;
}
// Side 0 has added edges while sides 1 and 2 do not. Fan spreads from vert 2.
static void PartitionFan(Vec<ivec3>& triVert, ivec3 cornerVerts, int added,
int edgeOffset) {
int last = cornerVerts[0];
for (int i = 0; i < added; ++i) {
const int next = edgeOffset + i;
triVert.push_back({last, next, cornerVerts[2]});
last = next;
}
triVert.push_back({last, cornerVerts[1], cornerVerts[2]});
}
// Partitions are parallel to the first edge unless two consecutive edgeAdded
// are zero, in which case a terminal triangulation is performed.
static void PartitionQuad(Vec<ivec3>& triVert, Vec<vec4>& vertBary,
ivec4 cornerVerts, ivec4 edgeOffsets,
ivec4 edgeAdded, bvec4 edgeFwd) {
auto GetEdgeVert = [&](int edge, int idx) {
return edgeOffsets[edge] + (edgeFwd[edge] ? 1 : -1) * idx;
};
DEBUG_ASSERT(la::all(la::gequal(edgeAdded, ivec4(0))), logicErr,
"negative divisions!");
int corner = -1;
int last = 3;
int maxEdge = -1;
for (const int i : {0, 1, 2, 3}) {
if (corner == -1 && edgeAdded[i] == 0 && edgeAdded[last] == 0) {
corner = i;
}
if (edgeAdded[i] > 0) {
maxEdge = maxEdge == -1 ? i : -2;
}
last = i;
}
if (corner >= 0) { // terminate
if (maxEdge >= 0) {
ivec4 edge = (ivec4(0, 1, 2, 3) + maxEdge) % 4;
const int middle = edgeAdded[maxEdge] / 2;
triVert.push_back({cornerVerts[edge[2]], cornerVerts[edge[3]],
GetEdgeVert(maxEdge, middle)});
int last = cornerVerts[edge[0]];
for (int i = 0; i <= middle; ++i) {
const int next = GetEdgeVert(maxEdge, i);
triVert.push_back({cornerVerts[edge[3]], last, next});
last = next;
}
last = cornerVerts[edge[1]];
for (int i = edgeAdded[maxEdge] - 1; i >= middle; --i) {
const int next = GetEdgeVert(maxEdge, i);
triVert.push_back({cornerVerts[edge[2]], next, last});
last = next;
}
} else {
int sideVert = cornerVerts[0]; // initial value is unused
for (const int j : {1, 2}) {
const int side = (corner + j) % 4;
if (j == 2 && edgeAdded[side] > 0) {
triVert.push_back(
{cornerVerts[side], GetEdgeVert(side, 0), sideVert});
} else {
sideVert = cornerVerts[side];
}
for (int i = 0; i < edgeAdded[side]; ++i) {
const int nextVert = GetEdgeVert(side, i);
triVert.push_back({cornerVerts[corner], sideVert, nextVert});
sideVert = nextVert;
}
if (j == 2 || edgeAdded[side] == 0) {
triVert.push_back({cornerVerts[corner], sideVert,
cornerVerts[(corner + j + 1) % 4]});
}
}
}
return;
}
// recursively partition
const int partitions = 1 + std::min(edgeAdded[1], edgeAdded[3]);
ivec4 newCornerVerts = {cornerVerts[1], -1, -1, cornerVerts[0]};
ivec4 newEdgeOffsets = {edgeOffsets[1], -1,
GetEdgeVert(3, edgeAdded[3] + 1), edgeOffsets[0]};
ivec4 newEdgeAdded = {0, -1, 0, edgeAdded[0]};
bvec4 newEdgeFwd = {edgeFwd[1], true, edgeFwd[3], edgeFwd[0]};
for (int i = 1; i < partitions; ++i) {
const int cornerOffset1 = (edgeAdded[1] * i) / partitions;
const int cornerOffset3 =
edgeAdded[3] - 1 - (edgeAdded[3] * i) / partitions;
const int nextOffset1 = GetEdgeVert(1, cornerOffset1 + 1);
const int nextOffset3 = GetEdgeVert(3, cornerOffset3 + 1);
const int added = std::round(la::lerp(
(double)edgeAdded[0], (double)edgeAdded[2], (double)i / partitions));
newCornerVerts[1] = GetEdgeVert(1, cornerOffset1);
newCornerVerts[2] = GetEdgeVert(3, cornerOffset3);
newEdgeAdded[0] = std::abs(nextOffset1 - newEdgeOffsets[0]) - 1;
newEdgeAdded[1] = added;
newEdgeAdded[2] = std::abs(nextOffset3 - newEdgeOffsets[2]) - 1;
newEdgeOffsets[1] = vertBary.size();
newEdgeOffsets[2] = nextOffset3;
for (int j = 0; j < added; ++j) {
vertBary.push_back(la::lerp(vertBary[newCornerVerts[1]],
vertBary[newCornerVerts[2]],
(j + 1.0) / (added + 1.0)));
}
PartitionQuad(triVert, vertBary, newCornerVerts, newEdgeOffsets,
newEdgeAdded, newEdgeFwd);
newCornerVerts[0] = newCornerVerts[1];
newCornerVerts[3] = newCornerVerts[2];
newEdgeAdded[3] = newEdgeAdded[1];
newEdgeOffsets[0] = nextOffset1;
newEdgeOffsets[3] = newEdgeOffsets[1] + newEdgeAdded[1] - 1;
newEdgeFwd[3] = false;
}
newCornerVerts[1] = cornerVerts[2];
newCornerVerts[2] = cornerVerts[3];
newEdgeOffsets[1] = edgeOffsets[2];
newEdgeAdded[0] =
edgeAdded[1] - std::abs(newEdgeOffsets[0] - edgeOffsets[1]);
newEdgeAdded[1] = edgeAdded[2];
newEdgeAdded[2] = std::abs(newEdgeOffsets[2] - edgeOffsets[3]) - 1;
newEdgeOffsets[2] = edgeOffsets[3];
newEdgeFwd[1] = edgeFwd[2];
PartitionQuad(triVert, vertBary, newCornerVerts, newEdgeOffsets,
newEdgeAdded, newEdgeFwd);
}
};
} // namespace
namespace manifold {
/**
* Returns the tri side index (0-2) connected to the other side of this quad if
* this tri is part of a quad, or -1 otherwise.
*/
int Manifold::Impl::GetNeighbor(int tri) const {
int neighbor = -1;
for (const int i : {0, 1, 2}) {
if (IsMarkedInsideQuad(3 * tri + i)) {
neighbor = neighbor == -1 ? i : -2;
}
}
return neighbor;
}
/**
* For the given triangle index, returns either the three halfedge indices of
* that triangle and halfedges[3] = -1, or if the triangle is part of a quad, it
* returns those four indices. If the triangle is part of a quad and is not the
* lower of the two triangle indices, it returns all -1s.
*/
ivec4 Manifold::Impl::GetHalfedges(int tri) const {
ivec4 halfedges(-1);
for (const int i : {0, 1, 2}) {
halfedges[i] = 3 * tri + i;
}
const int neighbor = GetNeighbor(tri);
if (neighbor >= 0) { // quad
const int pair = halfedge_[3 * tri + neighbor].pairedHalfedge;
if (pair / 3 < tri) {
return ivec4(-1); // only process lower tri index
}
// The order here matters to keep small quads split the way they started, or
// else it can create a 4-manifold edge.
halfedges[2] = NextHalfedge(halfedges[neighbor]);
halfedges[3] = NextHalfedge(halfedges[2]);
halfedges[0] = NextHalfedge(pair);
halfedges[1] = NextHalfedge(halfedges[0]);
}
return halfedges;
}
/**
* Returns the BaryIndices, which gives the tri and indices (0-3), such that
* GetHalfedges(val.tri)[val.start4] points back to this halfedge, and val.end4
* will point to the next one. This function handles this for both triangles and
* quads. Returns {-1, -1, -1} if the edge is the interior of a quad.
*/
Manifold::Impl::BaryIndices Manifold::Impl::GetIndices(int halfedge) const {
int tri = halfedge / 3;
int idx = halfedge % 3;
const int neighbor = GetNeighbor(tri);
if (idx == neighbor) {
return {-1, -1, -1};
}
if (neighbor < 0) { // tri
return {tri, idx, Next3(idx)};
} else { // quad
const int pair = halfedge_[3 * tri + neighbor].pairedHalfedge;
if (pair / 3 < tri) {
tri = pair / 3;
idx = Next3(neighbor) == idx ? 0 : 1;
} else {
idx = Next3(neighbor) == idx ? 2 : 3;
}
return {tri, idx, (idx + 1) % 4};
}
}
/**
* Retained verts are part of several triangles, and it doesn't matter which one
* the vertBary refers to. Here, whichever is last will win and it's done on the
* CPU for simplicity for now. Using AtomicCAS on .tri should work for a GPU
* version if desired.
*/
void Manifold::Impl::FillRetainedVerts(Vec<Barycentric>& vertBary) const {
const int numTri = halfedge_.size() / 3;
for (int tri = 0; tri < numTri; ++tri) {
for (const int i : {0, 1, 2}) {
const BaryIndices indices = GetIndices(3 * tri + i);
if (indices.start4 < 0) continue; // skip quad interiors
vec4 uvw(0.0);
uvw[indices.start4] = 1;
vertBary[halfedge_[3 * tri + i].startVert] = {indices.tri, uvw};
}
}
}
/**
* Split each edge into n pieces as defined by calling the edgeDivisions
* function, and sub-triangulate each triangle accordingly. This function
* doesn't run Finish(), as that is expensive and it'll need to be run after
* the new vertices have moved, which is a likely scenario after refinement
* (smoothing).
*/
Vec<Barycentric> Manifold::Impl::Subdivide(
std::function<int(vec3, vec4, vec4)> edgeDivisions, bool keepInterior) {
Vec<TmpEdge> edges = CreateTmpEdges(halfedge_);
const int numVert = NumVert();
const int numEdge = edges.size();
const int numTri = NumTri();
Vec<int> half2Edge(2 * numEdge);
auto policy = autoPolicy(numEdge, 1e4);
for_each_n(policy, countAt(0), numEdge,
[&half2Edge, &edges, this](const int edge) {
const int idx = edges[edge].halfedgeIdx;
half2Edge[idx] = edge;
half2Edge[halfedge_[idx].pairedHalfedge] = edge;
});
Vec<ivec4> faceHalfedges(numTri);
for_each_n(policy, countAt(0), numTri, [&faceHalfedges, this](const int tri) {
faceHalfedges[tri] = GetHalfedges(tri);
});
Vec<int> edgeAdded(numEdge);
for_each_n(policy, countAt(0), numEdge,
[&edgeAdded, &edges, edgeDivisions, this](const int i) {
const TmpEdge edge = edges[i];
const int hIdx = edge.halfedgeIdx;
if (IsMarkedInsideQuad(hIdx)) {
edgeAdded[i] = 0;
return;
}
const vec3 vec = vertPos_[edge.first] - vertPos_[edge.second];
const vec4 tangent0 = halfedgeTangent_.empty()
? vec4(0.0)
: halfedgeTangent_[hIdx];
const vec4 tangent1 =
halfedgeTangent_.empty()
? vec4(0.0)
: halfedgeTangent_[halfedge_[hIdx].pairedHalfedge];
edgeAdded[i] = edgeDivisions(vec, tangent0, tangent1);
});
if (keepInterior) {
// Triangles where the greatest number of divisions exceeds the sum of the
// other two sides will be triangulated as a strip, since if the sub-edges
// were all equal length it would be degenerate. This leads to poor results
// with RefineToTolerance, so we avoid this case by adding some extra
// divisions to the short sides so that the triangulation has some thickness
// and creates more interior facets.
Vec<int> tmp(numEdge);
for_each_n(
policy, countAt(0), numEdge,
[&tmp, &edgeAdded, &edges, &half2Edge, this](const int i) {
tmp[i] = edgeAdded[i];
const TmpEdge edge = edges[i];
int hIdx = edge.halfedgeIdx;
if (IsMarkedInsideQuad(hIdx)) return;
const int thisAdded = tmp[i];
auto Added = [&edgeAdded, &half2Edge, thisAdded, this](int hIdx) {
int longest = 0;
int total = 0;
for (int j : {0, 1, 2}) {
const int added = edgeAdded[half2Edge[hIdx]];
longest = la::max(longest, added);
total += added;
hIdx = NextHalfedge(hIdx);
if (IsMarkedInsideQuad(hIdx)) {
// No extra on quads
longest = 0;
total = 1;
break;
}
}
const int minExtra = longest * 0.2 + 1;
const int extra = 2 * longest + minExtra - total;
return extra > 0 ? (extra * (longest - thisAdded)) / longest : 0;
};
tmp[i] += la::max(Added(hIdx), Added(halfedge_[hIdx].pairedHalfedge));
});
edgeAdded.swap(tmp);
}
Vec<int> edgeOffset(numEdge);
exclusive_scan(edgeAdded.begin(), edgeAdded.end(), edgeOffset.begin(),
numVert);
Vec<Barycentric> vertBary(edgeOffset.back() + edgeAdded.back());
const int totalEdgeAdded = vertBary.size() - numVert;
FillRetainedVerts(vertBary);
for_each_n(policy, countAt(0), numEdge,
[&vertBary, &edges, &edgeAdded, &edgeOffset, this](const int i) {
const int n = edgeAdded[i];
const int offset = edgeOffset[i];
const BaryIndices indices = GetIndices(edges[i].halfedgeIdx);
if (indices.tri < 0) {
return; // inside quad
}
const double frac = 1.0 / (n + 1);
for (int i = 0; i < n; ++i) {
vec4 uvw(0.0);
uvw[indices.end4] = (i + 1) * frac;
uvw[indices.start4] = 1 - uvw[indices.end4];
vertBary[offset + i].uvw = uvw;
vertBary[offset + i].tri = indices.tri;
}
});
std::vector<Partition> subTris(numTri);
for_each_n(policy, countAt(0), numTri,
[this, &subTris, &half2Edge, &edgeAdded, &faceHalfedges](int tri) {
const ivec4 halfedges = faceHalfedges[tri];
ivec4 divisions(0);
for (const int i : {0, 1, 2, 3}) {
if (halfedges[i] >= 0) {
divisions[i] = edgeAdded[half2Edge[halfedges[i]]] + 1;
}
}
subTris[tri] = Partition::GetPartition(divisions);
});
Vec<int> triOffset(numTri);
auto numSubTris =
TransformIterator(subTris.begin(), [](const Partition& part) {
return static_cast<int>(part.triVert.size());
});
manifold::exclusive_scan(numSubTris, numSubTris + numTri, triOffset.begin(),
0);
Vec<int> interiorOffset(numTri);
auto numInterior =
TransformIterator(subTris.begin(), [](const Partition& part) {
return static_cast<int>(part.NumInterior());
});
manifold::exclusive_scan(numInterior, numInterior + numTri,
interiorOffset.begin(),
static_cast<int>(vertBary.size()));
Vec<ivec3> triVerts(triOffset.back() + subTris.back().triVert.size());
vertBary.resize(interiorOffset.back() + subTris.back().NumInterior());
Vec<TriRef> triRef(triVerts.size());
for_each_n(
policy, countAt(0), numTri,
[this, &triVerts, &triRef, &vertBary, &subTris, &edgeOffset, &half2Edge,
&triOffset, &interiorOffset, &faceHalfedges](int tri) {
const ivec4 halfedges = faceHalfedges[tri];
if (halfedges[0] < 0) return;
ivec4 tri3;
ivec4 edgeOffsets;
bvec4 edgeFwd(false);
for (const int i : {0, 1, 2, 3}) {
if (halfedges[i] < 0) {
tri3[i] = -1;
continue;
}
const Halfedge& halfedge = halfedge_[halfedges[i]];
tri3[i] = halfedge.startVert;
edgeOffsets[i] = edgeOffset[half2Edge[halfedges[i]]];
edgeFwd[i] = halfedge.IsForward();
}
Vec<ivec3> newTris = subTris[tri].Reindex(tri3, edgeOffsets, edgeFwd,
interiorOffset[tri]);
copy(newTris.begin(), newTris.end(), triVerts.begin() + triOffset[tri]);
auto start = triRef.begin() + triOffset[tri];
fill(start, start + newTris.size(), meshRelation_.triRef[tri]);
const ivec4 idx = subTris[tri].idx;
const ivec4 vIdx = halfedges[3] >= 0 || idx[1] == Next3(idx[0])
? idx
: ivec4(idx[2], idx[0], idx[1], idx[3]);
ivec4 rIdx;
for (const int i : {0, 1, 2, 3}) {
rIdx[vIdx[i]] = i;
}
const auto& subBary = subTris[tri].vertBary;
transform(subBary.begin() + subTris[tri].InteriorOffset(),
subBary.end(), vertBary.begin() + interiorOffset[tri],
[tri, rIdx](vec4 bary) {
return Barycentric({tri,
{bary[rIdx[0]], bary[rIdx[1]],
bary[rIdx[2]], bary[rIdx[3]]}});
});
});
meshRelation_.triRef = triRef;
Vec<vec3> newVertPos(vertBary.size());
for_each_n(policy, countAt(0), vertBary.size(),
[&newVertPos, &vertBary, &faceHalfedges, this](const int vert) {
const Barycentric bary = vertBary[vert];
const ivec4 halfedges = faceHalfedges[bary.tri];
if (halfedges[3] < 0) {
mat3 triPos;
for (const int i : {0, 1, 2}) {
triPos[i] = vertPos_[halfedge_[halfedges[i]].startVert];
}
newVertPos[vert] = triPos * vec3(bary.uvw);
} else {
mat3x4 quadPos;
for (const int i : {0, 1, 2, 3}) {
quadPos[i] = vertPos_[halfedge_[halfedges[i]].startVert];
}
newVertPos[vert] = quadPos * bary.uvw;
}
});
vertPos_ = newVertPos;
faceNormal_.resize(0);
if (meshRelation_.numProp > 0) {
const int numPropVert = NumPropVert();
const int addedVerts = NumVert() - numVert;
const int propOffset = numPropVert - numVert;
Vec<double> prop(meshRelation_.numProp *
(numPropVert + addedVerts + totalEdgeAdded));
// copy retained prop verts
copy(meshRelation_.properties.begin(), meshRelation_.properties.end(),
prop.begin());
// copy interior prop verts and forward edge prop verts
for_each_n(
policy, countAt(0), addedVerts,
[&prop, &vertBary, &faceHalfedges, numVert, numPropVert,
this](const int i) {
const int vert = numPropVert + i;
const Barycentric bary = vertBary[numVert + i];
const ivec4 halfedges = faceHalfedges[bary.tri];
auto& rel = meshRelation_;
for (int p = 0; p < rel.numProp; ++p) {
if (halfedges[3] < 0) {
vec3 triProp;
for (const int i : {0, 1, 2}) {
triProp[i] = rel.properties[rel.triProperties[bary.tri][i] *
rel.numProp +
p];
}
prop[vert * rel.numProp + p] = la::dot(triProp, vec3(bary.uvw));
} else {
vec4 quadProp;
for (const int i : {0, 1, 2, 3}) {
const int tri = halfedges[i] / 3;
const int j = halfedges[i] % 3;
quadProp[i] =
rel.properties[rel.triProperties[tri][j] * rel.numProp + p];
}
prop[vert * rel.numProp + p] = la::dot(quadProp, bary.uvw);
}
}
});
// copy backward edge prop verts
for_each_n(policy, countAt(0), numEdge,
[this, &prop, &edges, &edgeAdded, &edgeOffset, propOffset,
addedVerts](const int i) {
const int n = edgeAdded[i];
const int offset = edgeOffset[i] + propOffset + addedVerts;
auto& rel = meshRelation_;
const double frac = 1.0 / (n + 1);
const int halfedgeIdx =
halfedge_[edges[i].halfedgeIdx].pairedHalfedge;
const int v0 = halfedgeIdx % 3;
const int tri = halfedgeIdx / 3;
const int prop0 = rel.triProperties[tri][v0];
const int prop1 = rel.triProperties[tri][Next3(v0)];
for (int i = 0; i < n; ++i) {
for (int p = 0; p < rel.numProp; ++p) {
prop[(offset + i) * rel.numProp + p] =
la::lerp(rel.properties[prop0 * rel.numProp + p],
rel.properties[prop1 * rel.numProp + p],
(i + 1) * frac);
}
}
});
Vec<ivec3> triProp(triVerts.size());
for_each_n(policy, countAt(0), numTri,
[this, &triProp, &subTris, &edgeOffset, &half2Edge, &triOffset,
&interiorOffset, &faceHalfedges, propOffset,
addedVerts](const int tri) {
const ivec4 halfedges = faceHalfedges[tri];
if (halfedges[0] < 0) return;
auto& rel = meshRelation_;
ivec4 tri3;
ivec4 edgeOffsets;
bvec4 edgeFwd(true);
for (const int i : {0, 1, 2, 3}) {
if (halfedges[i] < 0) {
tri3[i] = -1;
continue;
}
const int thisTri = halfedges[i] / 3;
const int j = halfedges[i] % 3;
const Halfedge& halfedge = halfedge_[halfedges[i]];
tri3[i] = rel.triProperties[thisTri][j];
edgeOffsets[i] = edgeOffset[half2Edge[halfedges[i]]];
if (!halfedge.IsForward()) {
const int pairTri = halfedge.pairedHalfedge / 3;
const int k = halfedge.pairedHalfedge % 3;
if (rel.triProperties[pairTri][k] !=
rel.triProperties[thisTri][Next3(j)] ||
rel.triProperties[pairTri][Next3(k)] !=
rel.triProperties[thisTri][j]) {
edgeOffsets[i] += addedVerts;
} else {
edgeFwd[i] = false;
}
}
}
Vec<ivec3> newTris = subTris[tri].Reindex(
tri3, edgeOffsets + propOffset, edgeFwd,
interiorOffset[tri] + propOffset);
copy(newTris.begin(), newTris.end(),
triProp.begin() + triOffset[tri]);
});
meshRelation_.properties = prop;
meshRelation_.triProperties = triProp;
}
CreateHalfedges(triVerts);
return vertBary;
}
} // namespace manifold

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// MIT License
// Copyright (c) 2019 wi-re
// Copyright 2023 The Manifold Authors.
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
// Modified from https://github.com/wi-re/tbtSVD, removing CUDA dependence and
// approximate inverse square roots.
#include <cmath>
#include "manifold/common.h"
namespace {
using manifold::mat3;
using manifold::vec3;
using manifold::vec4;
// Constants used for calculation of Givens quaternions
inline constexpr double _gamma = 5.82842712474619; // sqrt(8)+3;
inline constexpr double _cStar = 0.9238795325112867; // cos(pi/8)
inline constexpr double _sStar = 0.3826834323650898; // sin(pi/8)
// Threshold value
inline constexpr double _SVD_EPSILON = 1e-6;
// Iteration counts for Jacobi Eigen Analysis, influences precision
inline constexpr int JACOBI_STEPS = 12;
// Helper function used to swap X with Y and Y with X if c == true
inline void CondSwap(bool c, double& X, double& Y) {
double Z = X;
X = c ? Y : X;
Y = c ? Z : Y;
}
// Helper function used to swap X with Y and Y with -X if c == true
inline void CondNegSwap(bool c, double& X, double& Y) {
double Z = -X;
X = c ? Y : X;
Y = c ? Z : Y;
}
// A simple symmetric 3x3 Matrix class (contains no storage for (0, 1) (0, 2)
// and (1, 2)
struct Symmetric3x3 {
double m_00 = 1.0;
double m_10 = 0.0, m_11 = 1.0;
double m_20 = 0.0, m_21 = 0.0, m_22 = 1.0;
Symmetric3x3(double a11 = 1.0, double a21 = 0.0, double a22 = 1.0,
double a31 = 0.0, double a32 = 0.0, double a33 = 1.0)
: m_00(a11), m_10(a21), m_11(a22), m_20(a31), m_21(a32), m_22(a33) {}
Symmetric3x3(mat3 o)
: m_00(o[0][0]),
m_10(o[0][1]),
m_11(o[1][1]),
m_20(o[0][2]),
m_21(o[1][2]),
m_22(o[2][2]) {}
};
// Helper struct to store 2 doubles to avoid OUT parameters on functions
struct Givens {
double ch = _cStar;
double sh = _sStar;
};
// Helper struct to store 2 Matrices to avoid OUT parameters on functions
struct QR {
mat3 Q, R;
};
// Calculates the squared norm of the vector.
inline double Dist2(vec3 v) { return la::dot(v, v); }
// For an explanation of the math see
// http://pages.cs.wisc.edu/~sifakis/papers/SVD_TR1690.pdf Computing the
// Singular Value Decomposition of 3 x 3 matrices with minimal branching and
// elementary floating point operations See Algorithm 2 in reference. Given a
// matrix A this function returns the Givens quaternion (x and w component, y
// and z are 0)
inline Givens ApproximateGivensQuaternion(Symmetric3x3& A) {
Givens g{2.0 * (A.m_00 - A.m_11), A.m_10};
bool b = _gamma * g.sh * g.sh < g.ch * g.ch;
double w = 1.0 / hypot(g.ch, g.sh);
if (!std::isfinite(w)) b = 0;
return Givens{b ? w * g.ch : _cStar, b ? w * g.sh : _sStar};
}
// Function used to apply a Givens rotation S. Calculates the weights and
// updates the quaternion to contain the cumulative rotation
inline void JacobiConjugation(const int32_t x, const int32_t y, const int32_t z,
Symmetric3x3& S, vec4& q) {
auto g = ApproximateGivensQuaternion(S);
double scale = 1.0 / fma(g.ch, g.ch, g.sh * g.sh);
double a = fma(g.ch, g.ch, -g.sh * g.sh) * scale;
double b = 2.0 * g.sh * g.ch * scale;
Symmetric3x3 _S = S;
// perform conjugation S = Q'*S*Q
S.m_00 =
fma(a, fma(a, _S.m_00, b * _S.m_10), b * (fma(a, _S.m_10, b * _S.m_11)));
S.m_10 = fma(a, fma(-b, _S.m_00, a * _S.m_10),
b * (fma(-b, _S.m_10, a * _S.m_11)));
S.m_11 = fma(-b, fma(-b, _S.m_00, a * _S.m_10),
a * (fma(-b, _S.m_10, a * _S.m_11)));
S.m_20 = fma(a, _S.m_20, b * _S.m_21);
S.m_21 = fma(-b, _S.m_20, a * _S.m_21);
S.m_22 = _S.m_22;
// update cumulative rotation qV
vec3 tmp = g.sh * vec3(q);
g.sh *= q[3];
// (x,y,z) corresponds to ((0,1,2),(1,2,0),(2,0,1)) for (p,q) =
// ((0,1),(1,2),(0,2))
q[z] = fma(q[z], g.ch, g.sh);
q[3] = fma(q[3], g.ch, -tmp[z]); // w
q[x] = fma(q[x], g.ch, tmp[y]);
q[y] = fma(q[y], g.ch, -tmp[x]);
// re-arrange matrix for next iteration
_S.m_00 = S.m_11;
_S.m_10 = S.m_21;
_S.m_11 = S.m_22;
_S.m_20 = S.m_10;
_S.m_21 = S.m_20;
_S.m_22 = S.m_00;
S.m_00 = _S.m_00;
S.m_10 = _S.m_10;
S.m_11 = _S.m_11;
S.m_20 = _S.m_20;
S.m_21 = _S.m_21;
S.m_22 = _S.m_22;
}
// Function used to contain the Givens permutations and the loop of the jacobi
// steps controlled by JACOBI_STEPS Returns the quaternion q containing the
// cumulative result used to reconstruct S
inline mat3 JacobiEigenAnalysis(Symmetric3x3 S) {
vec4 q(0, 0, 0, 1);
for (int32_t i = 0; i < JACOBI_STEPS; i++) {
JacobiConjugation(0, 1, 2, S, q);
JacobiConjugation(1, 2, 0, S, q);
JacobiConjugation(2, 0, 1, S, q);
}
return mat3({1.0 - 2.0 * (fma(q.y, q.y, q.z * q.z)), //
2.0 * fma(q.x, q.y, +q.w * q.z), //
2.0 * fma(q.x, q.z, -q.w * q.y)}, //
{2 * fma(q.x, q.y, -q.w * q.z), //
1 - 2 * fma(q.x, q.x, q.z * q.z), //
2 * fma(q.y, q.z, q.w * q.x)}, //
{2 * fma(q.x, q.z, q.w * q.y), //
2 * fma(q.y, q.z, -q.w * q.x), //
1 - 2 * fma(q.x, q.x, q.y * q.y)});
}
// Implementation of Algorithm 3
inline void SortSingularValues(mat3& B, mat3& V) {
double rho1 = Dist2(B[0]);
double rho2 = Dist2(B[1]);
double rho3 = Dist2(B[2]);
bool c;
c = rho1 < rho2;
CondNegSwap(c, B[0][0], B[1][0]);
CondNegSwap(c, V[0][0], V[1][0]);
CondNegSwap(c, B[0][1], B[1][1]);
CondNegSwap(c, V[0][1], V[1][1]);
CondNegSwap(c, B[0][2], B[1][2]);
CondNegSwap(c, V[0][2], V[1][2]);
CondSwap(c, rho1, rho2);
c = rho1 < rho3;
CondNegSwap(c, B[0][0], B[2][0]);
CondNegSwap(c, V[0][0], V[2][0]);
CondNegSwap(c, B[0][1], B[2][1]);
CondNegSwap(c, V[0][1], V[2][1]);
CondNegSwap(c, B[0][2], B[2][2]);
CondNegSwap(c, V[0][2], V[2][2]);
CondSwap(c, rho1, rho3);
c = rho2 < rho3;
CondNegSwap(c, B[1][0], B[2][0]);
CondNegSwap(c, V[1][0], V[2][0]);
CondNegSwap(c, B[1][1], B[2][1]);
CondNegSwap(c, V[1][1], V[2][1]);
CondNegSwap(c, B[1][2], B[2][2]);
CondNegSwap(c, V[1][2], V[2][2]);
}
// Implementation of Algorithm 4
inline Givens QRGivensQuaternion(double a1, double a2) {
// a1 = pivot point on diagonal
// a2 = lower triangular entry we want to annihilate
double epsilon = _SVD_EPSILON;
double rho = hypot(a1, a2);
Givens g{fabs(a1) + fmax(rho, epsilon), rho > epsilon ? a2 : 0};
bool b = a1 < 0.0;
CondSwap(b, g.sh, g.ch);
double w = 1.0 / hypot(g.ch, g.sh);
g.ch *= w;
g.sh *= w;
return g;
}
// Implements a QR decomposition of a Matrix, see Sec 4.2
inline QR QRDecomposition(mat3& B) {
mat3 Q, R;
// first Givens rotation (ch,0,0,sh)
auto g1 = QRGivensQuaternion(B[0][0], B[0][1]);
auto a = fma(-2.0, g1.sh * g1.sh, 1.0);
auto b = 2.0 * g1.ch * g1.sh;
// apply B = Q' * B
R[0][0] = fma(a, B[0][0], b * B[0][1]);
R[1][0] = fma(a, B[1][0], b * B[1][1]);
R[2][0] = fma(a, B[2][0], b * B[2][1]);
R[0][1] = fma(-b, B[0][0], a * B[0][1]);
R[1][1] = fma(-b, B[1][0], a * B[1][1]);
R[2][1] = fma(-b, B[2][0], a * B[2][1]);
R[0][2] = B[0][2];
R[1][2] = B[1][2];
R[2][2] = B[2][2];
// second Givens rotation (ch,0,-sh,0)
auto g2 = QRGivensQuaternion(R[0][0], R[0][2]);
a = fma(-2.0, g2.sh * g2.sh, 1.0);
b = 2.0 * g2.ch * g2.sh;
// apply B = Q' * B;
B[0][0] = fma(a, R[0][0], b * R[0][2]);
B[1][0] = fma(a, R[1][0], b * R[1][2]);
B[2][0] = fma(a, R[2][0], b * R[2][2]);
B[0][1] = R[0][1];
B[1][1] = R[1][1];
B[2][1] = R[2][1];
B[0][2] = fma(-b, R[0][0], a * R[0][2]);
B[1][2] = fma(-b, R[1][0], a * R[1][2]);
B[2][2] = fma(-b, R[2][0], a * R[2][2]);
// third Givens rotation (ch,sh,0,0)
auto g3 = QRGivensQuaternion(B[1][1], B[1][2]);
a = fma(-2.0, g3.sh * g3.sh, 1.0);
b = 2.0 * g3.ch * g3.sh;
// R is now set to desired value
R[0][0] = B[0][0];
R[1][0] = B[1][0];
R[2][0] = B[2][0];
R[0][1] = fma(a, B[0][1], b * B[0][2]);
R[1][1] = fma(a, B[1][1], b * B[1][2]);
R[2][1] = fma(a, B[2][1], b * B[2][2]);
R[0][2] = fma(-b, B[0][1], a * B[0][2]);
R[1][2] = fma(-b, B[1][1], a * B[1][2]);
R[2][2] = fma(-b, B[2][1], a * B[2][2]);
// construct the cumulative rotation Q=Q1 * Q2 * Q3
// the number of floating point operations for three quaternion
// multiplications is more or less comparable to the explicit form of the
// joined matrix. certainly more memory-efficient!
auto sh12 = 2.0 * fma(g1.sh, g1.sh, -0.5);
auto sh22 = 2.0 * fma(g2.sh, g2.sh, -0.5);
auto sh32 = 2.0 * fma(g3.sh, g3.sh, -0.5);
Q[0][0] = sh12 * sh22;
Q[1][0] = fma(4.0 * g2.ch * g3.ch, sh12 * g2.sh * g3.sh,
2.0 * g1.ch * g1.sh * sh32);
Q[2][0] = fma(4.0 * g1.ch * g3.ch, g1.sh * g3.sh,
-2.0 * g2.ch * sh12 * g2.sh * sh32);
Q[0][1] = -2.0 * g1.ch * g1.sh * sh22;
Q[1][1] =
fma(-8.0 * g1.ch * g2.ch * g3.ch, g1.sh * g2.sh * g3.sh, sh12 * sh32);
Q[2][1] = fma(
-2.0 * g3.ch, g3.sh,
4.0 * g1.sh * fma(g3.ch * g1.sh, g3.sh, g1.ch * g2.ch * g2.sh * sh32));
Q[0][2] = 2.0 * g2.ch * g2.sh;
Q[1][2] = -2.0 * g3.ch * sh22 * g3.sh;
Q[2][2] = sh22 * sh32;
return QR{Q, R};
}
} // namespace
namespace manifold {
/**
* The three matrices of a Singular Value Decomposition.
*/
struct SVDSet {
mat3 U, S, V;
};
/**
* Returns the Singular Value Decomposition of A: A = U * S * la::transpose(V).
*
* @param A The matrix to decompose.
*/
inline SVDSet SVD(mat3 A) {
mat3 V = JacobiEigenAnalysis(la::transpose(A) * A);
auto B = A * V;
SortSingularValues(B, V);
QR qr = QRDecomposition(B);
return SVDSet{qr.Q, qr.R, V};
}
/**
* Returns the largest singular value of A.
*
* @param A The matrix to measure.
*/
inline double SpectralNorm(mat3 A) {
SVDSet usv = SVD(A);
return usv.S[0][0];
}
} // namespace manifold

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// Copyright 2024 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <array>
#include "manifold/common.h"
namespace manifold {
// From NVIDIA-Omniverse PhysX - BSD 3-Clause "New" or "Revised" License
// https://github.com/NVIDIA-Omniverse/PhysX/blob/main/LICENSE.md
// https://github.com/NVIDIA-Omniverse/PhysX/blob/main/physx/source/geomutils/src/sweep/GuSweepCapsuleCapsule.cpp
// With minor modifications
/**
* Returns the distance between two line segments.
*
* @param[out] x Closest point on line segment pa.
* @param[out] y Closest point on line segment qb.
* @param[in] p One endpoint of the first line segment.
* @param[in] a Other endpoint of the first line segment.
* @param[in] p One endpoint of the second line segment.
* @param[in] b Other endpoint of the second line segment.
*/
inline void EdgeEdgeDist(vec3& x, vec3& y, // closest points
const vec3& p,
const vec3& a, // seg 1 origin, vector
const vec3& q,
const vec3& b) // seg 2 origin, vector
{
const vec3 T = q - p;
const auto ADotA = la::dot(a, a);
const auto BDotB = la::dot(b, b);
const auto ADotB = la::dot(a, b);
const auto ADotT = la::dot(a, T);
const auto BDotT = la::dot(b, T);
// t parameterizes ray (p, a)
// u parameterizes ray (q, b)
// Compute t for the closest point on ray (p, a) to ray (q, b)
const auto Denom = ADotA * BDotB - ADotB * ADotB;
double t; // We will clamp result so t is on the segment (p, a)
t = Denom != 0.0
? la::clamp((ADotT * BDotB - BDotT * ADotB) / Denom, 0.0, 1.0)
: 0.0;
// find u for point on ray (q, b) closest to point at t
double u;
if (BDotB != 0.0) {
u = (t * ADotB - BDotT) / BDotB;
// if u is on segment (q, b), t and u correspond to closest points,
// otherwise, clamp u, recompute and clamp t
if (u < 0.0) {
u = 0.0;
t = ADotA != 0.0 ? la::clamp(ADotT / ADotA, 0.0, 1.0) : 0.0;
} else if (u > 1.0) {
u = 1.0;
t = ADotA != 0.0 ? la::clamp((ADotB + ADotT) / ADotA, 0.0, 1.0) : 0.0;
}
} else {
u = 0.0;
t = ADotA != 0.0 ? la::clamp(ADotT / ADotA, 0.0, 1.0) : 0.0;
}
x = p + a * t;
y = q + b * u;
}
// From NVIDIA-Omniverse PhysX - BSD 3-Clause "New" or "Revised" License
// https://github.com/NVIDIA-Omniverse/PhysX/blob/main/LICENSE.md
// https://github.com/NVIDIA-Omniverse/PhysX/blob/main/physx/source/geomutils/src/distance/GuDistanceTriangleTriangle.cpp
// With minor modifications
/**
* Returns the minimum squared distance between two triangles.
*
* @param p First triangle.
* @param q Second triangle.
*/
inline auto DistanceTriangleTriangleSquared(const std::array<vec3, 3>& p,
const std::array<vec3, 3>& q) {
std::array<vec3, 3> Sv;
Sv[0] = p[1] - p[0];
Sv[1] = p[2] - p[1];
Sv[2] = p[0] - p[2];
std::array<vec3, 3> Tv;
Tv[0] = q[1] - q[0];
Tv[1] = q[2] - q[1];
Tv[2] = q[0] - q[2];
bool shown_disjoint = false;
auto mindd = std::numeric_limits<double>::max();
for (uint32_t i = 0; i < 3; i++) {
for (uint32_t j = 0; j < 3; j++) {
vec3 cp;
vec3 cq;
EdgeEdgeDist(cp, cq, p[i], Sv[i], q[j], Tv[j]);
const vec3 V = cq - cp;
const auto dd = la::dot(V, V);
if (dd <= mindd) {
mindd = dd;
uint32_t id = i + 2;
if (id >= 3) id -= 3;
vec3 Z = p[id] - cp;
auto a = la::dot(Z, V);
id = j + 2;
if (id >= 3) id -= 3;
Z = q[id] - cq;
auto b = la::dot(Z, V);
if ((a <= 0.0) && (b >= 0.0)) {
return la::dot(V, V);
};
if (a <= 0.0)
a = 0.0;
else if (b > 0.0)
b = 0.0;
if ((mindd - a + b) > 0.0) shown_disjoint = true;
}
}
}
vec3 Sn = la::cross(Sv[0], Sv[1]);
auto Snl = la::dot(Sn, Sn);
if (Snl > 1e-15) {
const vec3 Tp(la::dot(p[0] - q[0], Sn), la::dot(p[0] - q[1], Sn),
la::dot(p[0] - q[2], Sn));
int index = -1;
if ((Tp[0] > 0.0) && (Tp[1] > 0.0) && (Tp[2] > 0.0)) {
index = Tp[0] < Tp[1] ? 0 : 1;
if (Tp[2] < Tp[index]) index = 2;
} else if ((Tp[0] < 0.0) && (Tp[1] < 0.0) && (Tp[2] < 0.0)) {
index = Tp[0] > Tp[1] ? 0 : 1;
if (Tp[2] > Tp[index]) index = 2;
}
if (index >= 0) {
shown_disjoint = true;
const vec3& qIndex = q[index];
vec3 V = qIndex - p[0];
vec3 Z = la::cross(Sn, Sv[0]);
if (la::dot(V, Z) > 0.0) {
V = qIndex - p[1];
Z = la::cross(Sn, Sv[1]);
if (la::dot(V, Z) > 0.0) {
V = qIndex - p[2];
Z = la::cross(Sn, Sv[2]);
if (la::dot(V, Z) > 0.0) {
vec3 cp = qIndex + Sn * Tp[index] / Snl;
vec3 cq = qIndex;
return la::dot(cp - cq, cp - cq);
}
}
}
}
}
vec3 Tn = la::cross(Tv[0], Tv[1]);
auto Tnl = la::dot(Tn, Tn);
if (Tnl > 1e-15) {
const vec3 Sp(la::dot(q[0] - p[0], Tn), la::dot(q[0] - p[1], Tn),
la::dot(q[0] - p[2], Tn));
int index = -1;
if ((Sp[0] > 0.0) && (Sp[1] > 0.0) && (Sp[2] > 0.0)) {
index = Sp[0] < Sp[1] ? 0 : 1;
if (Sp[2] < Sp[index]) index = 2;
} else if ((Sp[0] < 0.0) && (Sp[1] < 0.0) && (Sp[2] < 0.0)) {
index = Sp[0] > Sp[1] ? 0 : 1;
if (Sp[2] > Sp[index]) index = 2;
}
if (index >= 0) {
shown_disjoint = true;
const vec3& pIndex = p[index];
vec3 V = pIndex - q[0];
vec3 Z = la::cross(Tn, Tv[0]);
if (la::dot(V, Z) > 0.0) {
V = pIndex - q[1];
Z = la::cross(Tn, Tv[1]);
if (la::dot(V, Z) > 0.0) {
V = pIndex - q[2];
Z = la::cross(Tn, Tv[2]);
if (la::dot(V, Z) > 0.0) {
vec3 cp = pIndex;
vec3 cq = pIndex + Tn * Sp[index] / Tnl;
return la::dot(cp - cq, cp - cq);
}
}
}
}
}
return shown_disjoint ? mindd : 0.0;
};
} // namespace manifold

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// Copyright 2020 The Manifold Authors, Jared Hoberock and Nathan Bell of
// NVIDIA Research
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#include <atomic>
#include <memory>
#include <mutex>
#include <unordered_map>
#include "./vec.h"
#include "manifold/common.h"
#ifndef MANIFOLD_PAR
#error "MANIFOLD_PAR must be defined to either 1 (parallel) or -1 (series)"
#else
#if (MANIFOLD_PAR != 1) && (MANIFOLD_PAR != -1)
#define XSTR(x) STR(x)
#define STR(x) #x
#pragma message "Current value of MANIFOLD_PAR is: " XSTR(MANIFOLD_PAR)
#error "MANIFOLD_PAR must be defined to either 1 (parallel) or -1 (series)"
#endif
#endif
#include "./parallel.h"
#if __has_include(<tracy/Tracy.hpp>)
#include <tracy/Tracy.hpp>
#else
#define FrameMarkStart(x)
#define FrameMarkEnd(x)
// putting ZoneScoped in a function will instrument the function execution when
// TRACY_ENABLE is set, which allows the profiler to record more accurate
// timing.
#define ZoneScoped
#define ZoneScopedN(name)
#endif
namespace manifold {
/**
* Stand-in for C++23's operator""uz (P0330R8)[https://wg21.link/P0330R8].
*/
[[nodiscard]] constexpr std::size_t operator""_uz(
unsigned long long n) noexcept {
return n;
}
constexpr double kPrecision = 1e-12;
inline int Next3(int i) {
constexpr ivec3 next3(1, 2, 0);
return next3[i];
}
inline int Prev3(int i) {
constexpr ivec3 prev3(2, 0, 1);
return prev3[i];
}
template <typename T, typename T1>
void Permute(Vec<T>& inOut, const Vec<T1>& new2Old) {
Vec<T> tmp(std::move(inOut));
inOut.resize(new2Old.size());
gather(new2Old.begin(), new2Old.end(), tmp.begin(), inOut.begin());
}
template <typename T, typename T1>
void Permute(std::vector<T>& inOut, const Vec<T1>& new2Old) {
std::vector<T> tmp(std::move(inOut));
inOut.resize(new2Old.size());
gather(new2Old.begin(), new2Old.end(), tmp.begin(), inOut.begin());
}
template <typename T>
T AtomicAdd(T& target, T add) {
std::atomic<T>& tar = reinterpret_cast<std::atomic<T>&>(target);
T old_val = tar.load();
while (!tar.compare_exchange_weak(old_val, old_val + add,
std::memory_order_seq_cst)) {
}
return old_val;
}
template <>
inline int AtomicAdd(int& target, int add) {
std::atomic<int>& tar = reinterpret_cast<std::atomic<int>&>(target);
int old_val = tar.fetch_add(add, std::memory_order_seq_cst);
return old_val;
}
template <typename T>
class ConcurrentSharedPtr {
public:
ConcurrentSharedPtr(T value) : impl(std::make_shared<T>(value)) {}
ConcurrentSharedPtr(const ConcurrentSharedPtr<T>& other)
: impl(other.impl), mutex(other.mutex) {}
class SharedPtrGuard {
public:
SharedPtrGuard(std::recursive_mutex* mutex, T* content)
: mutex(mutex), content(content) {
mutex->lock();
}
~SharedPtrGuard() { mutex->unlock(); }
T& operator*() { return *content; }
T* operator->() { return content; }
private:
std::recursive_mutex* mutex;
T* content;
};
SharedPtrGuard GetGuard() { return SharedPtrGuard(mutex.get(), impl.get()); };
unsigned int UseCount() { return impl.use_count(); };
private:
std::shared_ptr<T> impl;
std::shared_ptr<std::recursive_mutex> mutex =
std::make_shared<std::recursive_mutex>();
};
template <typename I = int, typename R = unsigned char>
struct UnionFind {
Vec<I> parents;
// we do union by rank
// note that we shift rank by 1, rank 0 means it is not connected to anything
// else
Vec<R> ranks;
UnionFind(I numNodes) : parents(numNodes), ranks(numNodes, 0) {
sequence(parents.begin(), parents.end());
}
I find(I x) {
while (parents[x] != x) {
parents[x] = parents[parents[x]];
x = parents[x];
}
return x;
}
void unionXY(I x, I y) {
if (x == y) return;
if (ranks[x] == 0) ranks[x] = 1;
if (ranks[y] == 0) ranks[y] = 1;
x = find(x);
y = find(y);
if (x == y) return;
if (ranks[x] < ranks[y]) std::swap(x, y);
if (ranks[x] == ranks[y]) ranks[x]++;
parents[y] = x;
}
I connectedComponents(std::vector<I>& components) {
components.resize(parents.size());
I lonelyNodes = 0;
std::unordered_map<I, I> toLabel;
for (size_t i = 0; i < parents.size(); ++i) {
// we optimize for connected component of size 1
// no need to put them into the hashmap
if (ranks[i] == 0) {
components[i] = static_cast<I>(toLabel.size()) + lonelyNodes++;
continue;
}
parents[i] = find(i);
auto iter = toLabel.find(parents[i]);
if (iter == toLabel.end()) {
I s = static_cast<I>(toLabel.size()) + lonelyNodes;
toLabel.insert(std::make_pair(parents[i], s));
components[i] = s;
} else {
components[i] = iter->second;
}
}
return toLabel.size() + lonelyNodes;
}
};
template <typename T>
struct Identity {
T operator()(T v) const { return v; }
};
template <typename T>
struct Negate {
T operator()(T v) const { return -v; }
};
/**
* Determines if the three points are wound counter-clockwise, clockwise, or
* colinear within the specified tolerance.
*
* @param p0 First point
* @param p1 Second point
* @param p2 Third point
* @param tol Tolerance value for colinearity
* @return int, like Signum, this returns 1 for CCW, -1 for CW, and 0 if within
* tol of colinear.
*/
inline int CCW(vec2 p0, vec2 p1, vec2 p2, double tol) {
vec2 v1 = p1 - p0;
vec2 v2 = p2 - p0;
double area = fma(v1.x, v2.y, -v1.y * v2.x);
double base2 = la::max(la::dot(v1, v1), la::dot(v2, v2));
if (area * area * 4 <= base2 * tol * tol)
return 0;
else
return area > 0 ? 1 : -1;
}
inline mat4 Mat4(mat3x4 a) {
return mat4({a[0], 0}, {a[1], 0}, {a[2], 0}, {a[3], 1});
}
inline mat3 Mat3(mat2x3 a) { return mat3({a[0], 0}, {a[1], 0}, {a[2], 1}); }
} // namespace manifold

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// Copyright 2021 The Manifold Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#pragma once
#if TRACY_ENABLE && TRACY_MEMORY_USAGE
#include "tracy/Tracy.hpp"
#else
#define TracyAllocS(ptr, size, n) (void)0
#define TracyFreeS(ptr, n) (void)0
#endif
#include <vector>
#include "./parallel.h"
#include "manifold/vec_view.h"
namespace manifold {
template <typename T>
class Vec;
/*
* Specialized vector implementation with multithreaded fill and uninitialized
* memory optimizations.
* Note that the constructor and resize function will not perform initialization
* if the parameter val is not set. Also, this implementation is a toy
* implementation that did not consider things like non-trivial
* constructor/destructor, please keep T trivial.
*/
template <typename T>
class Vec : public VecView<T> {
public:
Vec() {}
// Note that the vector constructed with this constructor will contain
// uninitialized memory. Please specify `val` if you need to make sure that
// the data is initialized.
Vec(size_t size) {
reserve(size);
this->size_ = size;
}
Vec(size_t size, T val) { resize(size, val); }
Vec(const Vec<T> &vec) { *this = Vec(vec.view()); }
Vec(const VecView<const T> &vec) {
this->size_ = vec.size();
this->capacity_ = this->size_;
auto policy = autoPolicy(this->size_);
if (this->size_ != 0) {
this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
ASSERT(this->ptr_ != nullptr, std::bad_alloc());
TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
copy(policy, vec.begin(), vec.end(), this->ptr_);
}
}
Vec(const std::vector<T> &vec) {
this->size_ = vec.size();
this->capacity_ = this->size_;
auto policy = autoPolicy(this->size_);
if (this->size_ != 0) {
this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
ASSERT(this->ptr_ != nullptr, std::bad_alloc());
TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
copy(policy, vec.begin(), vec.end(), this->ptr_);
}
}
Vec(Vec<T> &&vec) {
this->ptr_ = vec.ptr_;
this->size_ = vec.size_;
capacity_ = vec.capacity_;
vec.ptr_ = nullptr;
vec.size_ = 0;
vec.capacity_ = 0;
}
operator VecView<T>() { return {this->ptr_, this->size_}; }
operator VecView<const T>() const { return {this->ptr_, this->size_}; }
~Vec() {
if (this->ptr_ != nullptr) {
TracyFreeS(this->ptr_, 3);
free(this->ptr_);
}
this->ptr_ = nullptr;
this->size_ = 0;
capacity_ = 0;
}
Vec<T> &operator=(const Vec<T> &other) {
if (&other == this) return *this;
if (this->ptr_ != nullptr) {
TracyFreeS(this->ptr_, 3);
free(this->ptr_);
}
this->size_ = other.size_;
capacity_ = other.size_;
if (this->size_ != 0) {
this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
ASSERT(this->ptr_ != nullptr, std::bad_alloc());
TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
manifold::copy(other.begin(), other.end(), this->ptr_);
}
return *this;
}
Vec<T> &operator=(Vec<T> &&other) {
if (&other == this) return *this;
if (this->ptr_ != nullptr) {
TracyFreeS(this->ptr_, 3);
free(this->ptr_);
}
this->size_ = other.size_;
capacity_ = other.capacity_;
this->ptr_ = other.ptr_;
other.ptr_ = nullptr;
other.size_ = 0;
other.capacity_ = 0;
return *this;
}
operator VecView<T>() const { return {this->ptr_, this->size_}; }
void swap(Vec<T> &other) {
std::swap(this->ptr_, other.ptr_);
std::swap(this->size_, other.size_);
std::swap(capacity_, other.capacity_);
}
inline void push_back(const T &val, bool seq = false) {
if (this->size_ >= capacity_) {
// avoid dangling pointer in case val is a reference of our array
T val_copy = val;
reserve(capacity_ == 0 ? 128 : capacity_ * 2, seq);
this->ptr_[this->size_++] = val_copy;
return;
}
this->ptr_[this->size_++] = val;
}
inline void extend(size_t n, bool seq = false) {
if (this->size_ + n >= capacity_)
reserve(capacity_ == 0 ? 128 : std::max(capacity_ * 2, this->size_ + n),
seq);
this->size_ += n;
}
void reserve(size_t n, bool seq = false) {
if (n > capacity_) {
T *newBuffer = reinterpret_cast<T *>(malloc(n * sizeof(T)));
ASSERT(newBuffer != nullptr, std::bad_alloc());
TracyAllocS(newBuffer, n * sizeof(T), 3);
if (this->size_ > 0)
manifold::copy(seq ? ExecutionPolicy::Seq : autoPolicy(this->size_),
this->ptr_, this->ptr_ + this->size_, newBuffer);
if (this->ptr_ != nullptr) {
TracyFreeS(this->ptr_, 3);
free(this->ptr_);
}
this->ptr_ = newBuffer;
capacity_ = n;
}
}
void resize(size_t newSize, T val = T()) {
bool shrink = this->size_ > 2 * newSize;
reserve(newSize);
if (this->size_ < newSize) {
fill(autoPolicy(newSize - this->size_), this->ptr_ + this->size_,
this->ptr_ + newSize, val);
}
this->size_ = newSize;
if (shrink) shrink_to_fit();
}
void pop_back() { resize(this->size_ - 1); }
void clear(bool shrink = true) {
this->size_ = 0;
if (shrink) shrink_to_fit();
}
void shrink_to_fit() {
T *newBuffer = nullptr;
if (this->size_ > 0) {
newBuffer = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
ASSERT(newBuffer != nullptr, std::bad_alloc());
TracyAllocS(newBuffer, this->size_ * sizeof(T), 3);
manifold::copy(this->ptr_, this->ptr_ + this->size_, newBuffer);
}
if (this->ptr_ != nullptr) {
TracyFreeS(this->ptr_, 3);
free(this->ptr_);
}
this->ptr_ = newBuffer;
capacity_ = this->size_;
}
size_t capacity() const { return capacity_; }
private:
size_t capacity_ = 0;
static_assert(std::is_trivially_destructible<T>::value);
};
} // namespace manifold