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godot/core/math/geometry.cpp
lawnjelly d24c715678 Float literals - fix math classes to allow 32 bit calculations 
Converts float literals from double format (e.g. 0.0) to float format (e.g. 0.0f) where appropriate for 32 bit calculations, and cast to (real_t) or (float) as appropriate.

This ensures that appropriate calculations will be done at 32 bits when real_t is compiled as float, rather than promoted to 64 bits.
2022-02-24 16:46:02 +00:00

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/*************************************************************************/
/* geometry.cpp */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* 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. */
/*************************************************************************/
#include "geometry.h"
#include "core/local_vector.h"
#include "core/print_string.h"
#include "thirdparty/misc/clipper.hpp"
#include "thirdparty/misc/triangulator.h"
#define STB_RECT_PACK_IMPLEMENTATION
#include "thirdparty/stb_rect_pack/stb_rect_pack.h"
#define SCALE_FACTOR 100000.0 // Based on CMP_EPSILON.
// This implementation is very inefficient, commenting unless bugs happen. See the other one.
/*
bool Geometry::is_point_in_polygon(const Vector2 &p_point, const Vector<Vector2> &p_polygon) {
Vector<int> indices = Geometry::triangulate_polygon(p_polygon);
for (int j = 0; j + 3 <= indices.size(); j += 3) {
int i1 = indices[j], i2 = indices[j + 1], i3 = indices[j + 2];
if (Geometry::is_point_in_triangle(p_point, p_polygon[i1], p_polygon[i2], p_polygon[i3]))
return true;
}
return false;
}
*/
void Geometry::OccluderMeshData::clear() {
faces.clear();
vertices.clear();
}
void Geometry::MeshData::clear() {
faces.clear();
edges.clear();
vertices.clear();
}
void Geometry::MeshData::optimize_vertices() {
Map<int, int> vtx_remap;
for (int i = 0; i < faces.size(); i++) {
for (int j = 0; j < faces[i].indices.size(); j++) {
int idx = faces[i].indices[j];
if (!vtx_remap.has(idx)) {
int ni = vtx_remap.size();
vtx_remap[idx] = ni;
}
faces.write[i].indices.write[j] = vtx_remap[idx];
}
}
for (int i = 0; i < edges.size(); i++) {
int a = edges[i].a;
int b = edges[i].b;
if (!vtx_remap.has(a)) {
int ni = vtx_remap.size();
vtx_remap[a] = ni;
}
if (!vtx_remap.has(b)) {
int ni = vtx_remap.size();
vtx_remap[b] = ni;
}
edges.write[i].a = vtx_remap[a];
edges.write[i].b = vtx_remap[b];
}
Vector<Vector3> new_vertices;
new_vertices.resize(vtx_remap.size());
for (int i = 0; i < vertices.size(); i++) {
if (vtx_remap.has(i)) {
new_vertices.write[vtx_remap[i]] = vertices[i];
}
}
vertices = new_vertices;
}
struct _FaceClassify {
struct _Link {
int face;
int edge;
void clear() {
face = -1;
edge = -1;
}
_Link() {
face = -1;
edge = -1;
}
};
bool valid;
int group;
_Link links[3];
Face3 face;
_FaceClassify() {
group = -1;
valid = false;
};
};
static bool _connect_faces(_FaceClassify *p_faces, int len, int p_group) {
// Connect faces, error will occur if an edge is shared between more than 2 faces.
// Clear connections.
bool error = false;
for (int i = 0; i < len; i++) {
for (int j = 0; j < 3; j++) {
p_faces[i].links[j].clear();
}
}
for (int i = 0; i < len; i++) {
if (p_faces[i].group != p_group) {
continue;
}
for (int j = i + 1; j < len; j++) {
if (p_faces[j].group != p_group) {
continue;
}
for (int k = 0; k < 3; k++) {
Vector3 vi1 = p_faces[i].face.vertex[k];
Vector3 vi2 = p_faces[i].face.vertex[(k + 1) % 3];
for (int l = 0; l < 3; l++) {
Vector3 vj2 = p_faces[j].face.vertex[l];
Vector3 vj1 = p_faces[j].face.vertex[(l + 1) % 3];
if (vi1.distance_to(vj1) < 0.00001f &&
vi2.distance_to(vj2) < 0.00001f) {
if (p_faces[i].links[k].face != -1) {
ERR_PRINT("already linked\n");
error = true;
break;
}
if (p_faces[j].links[l].face != -1) {
ERR_PRINT("already linked\n");
error = true;
break;
}
p_faces[i].links[k].face = j;
p_faces[i].links[k].edge = l;
p_faces[j].links[l].face = i;
p_faces[j].links[l].edge = k;
}
}
if (error) {
break;
}
}
if (error) {
break;
}
}
if (error) {
break;
}
}
for (int i = 0; i < len; i++) {
p_faces[i].valid = true;
for (int j = 0; j < 3; j++) {
if (p_faces[i].links[j].face == -1) {
p_faces[i].valid = false;
}
}
}
return error;
}
static bool _group_face(_FaceClassify *p_faces, int len, int p_index, int p_group) {
if (p_faces[p_index].group >= 0) {
return false;
}
p_faces[p_index].group = p_group;
for (int i = 0; i < 3; i++) {
ERR_FAIL_INDEX_V(p_faces[p_index].links[i].face, len, true);
_group_face(p_faces, len, p_faces[p_index].links[i].face, p_group);
}
return true;
}
PoolVector<PoolVector<Face3>> Geometry::separate_objects(PoolVector<Face3> p_array) {
PoolVector<PoolVector<Face3>> objects;
int len = p_array.size();
PoolVector<Face3>::Read r = p_array.read();
const Face3 *arrayptr = r.ptr();
PoolVector<_FaceClassify> fc;
fc.resize(len);
PoolVector<_FaceClassify>::Write fcw = fc.write();
_FaceClassify *_fcptr = fcw.ptr();
for (int i = 0; i < len; i++) {
_fcptr[i].face = arrayptr[i];
}
bool error = _connect_faces(_fcptr, len, -1);
ERR_FAIL_COND_V_MSG(error, PoolVector<PoolVector<Face3>>(), "Invalid geometry.");
// Group connected faces in separate objects.
int group = 0;
for (int i = 0; i < len; i++) {
if (!_fcptr[i].valid) {
continue;
}
if (_group_face(_fcptr, len, i, group)) {
group++;
}
}
// Group connected faces in separate objects.
for (int i = 0; i < len; i++) {
_fcptr[i].face = arrayptr[i];
}
if (group >= 0) {
objects.resize(group);
PoolVector<PoolVector<Face3>>::Write obw = objects.write();
PoolVector<Face3> *group_faces = obw.ptr();
for (int i = 0; i < len; i++) {
if (!_fcptr[i].valid) {
continue;
}
if (_fcptr[i].group >= 0 && _fcptr[i].group < group) {
group_faces[_fcptr[i].group].push_back(_fcptr[i].face);
}
}
}
return objects;
}
/*** GEOMETRY WRAPPER ***/
enum _CellFlags {
_CELL_SOLID = 1,
_CELL_EXTERIOR = 2,
_CELL_STEP_MASK = 0x1C,
_CELL_STEP_NONE = 0 << 2,
_CELL_STEP_Y_POS = 1 << 2,
_CELL_STEP_Y_NEG = 2 << 2,
_CELL_STEP_X_POS = 3 << 2,
_CELL_STEP_X_NEG = 4 << 2,
_CELL_STEP_Z_POS = 5 << 2,
_CELL_STEP_Z_NEG = 6 << 2,
_CELL_STEP_DONE = 7 << 2,
_CELL_PREV_MASK = 0xE0,
_CELL_PREV_NONE = 0 << 5,
_CELL_PREV_Y_POS = 1 << 5,
_CELL_PREV_Y_NEG = 2 << 5,
_CELL_PREV_X_POS = 3 << 5,
_CELL_PREV_X_NEG = 4 << 5,
_CELL_PREV_Z_POS = 5 << 5,
_CELL_PREV_Z_NEG = 6 << 5,
_CELL_PREV_FIRST = 7 << 5,
};
static inline void _plot_face(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z, const Vector3 &voxelsize, const Face3 &p_face) {
AABB aabb(Vector3(x, y, z), Vector3(len_x, len_y, len_z));
aabb.position = aabb.position * voxelsize;
aabb.size = aabb.size * voxelsize;
if (!p_face.intersects_aabb(aabb)) {
return;
}
if (len_x == 1 && len_y == 1 && len_z == 1) {
p_cell_status[x][y][z] = _CELL_SOLID;
return;
}
int div_x = len_x > 1 ? 2 : 1;
int div_y = len_y > 1 ? 2 : 1;
int div_z = len_z > 1 ? 2 : 1;
#define _SPLIT(m_i, m_div, m_v, m_len_v, m_new_v, m_new_len_v) \
if (m_div == 1) { \
m_new_v = m_v; \
m_new_len_v = 1; \
} else if (m_i == 0) { \
m_new_v = m_v; \
m_new_len_v = m_len_v / 2; \
} else { \
m_new_v = m_v + m_len_v / 2; \
m_new_len_v = m_len_v - m_len_v / 2; \
}
int new_x;
int new_len_x;
int new_y;
int new_len_y;
int new_z;
int new_len_z;
for (int i = 0; i < div_x; i++) {
_SPLIT(i, div_x, x, len_x, new_x, new_len_x);
for (int j = 0; j < div_y; j++) {
_SPLIT(j, div_y, y, len_y, new_y, new_len_y);
for (int k = 0; k < div_z; k++) {
_SPLIT(k, div_z, z, len_z, new_z, new_len_z);
_plot_face(p_cell_status, new_x, new_y, new_z, new_len_x, new_len_y, new_len_z, voxelsize, p_face);
}
}
}
}
static inline void _mark_outside(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z) {
if (p_cell_status[x][y][z] & 3) {
return; // Nothing to do, already used and/or visited.
}
p_cell_status[x][y][z] = _CELL_PREV_FIRST;
while (true) {
uint8_t &c = p_cell_status[x][y][z];
if ((c & _CELL_STEP_MASK) == _CELL_STEP_NONE) {
// Haven't been in here, mark as outside.
p_cell_status[x][y][z] |= _CELL_EXTERIOR;
}
if ((c & _CELL_STEP_MASK) != _CELL_STEP_DONE) {
// If not done, increase step.
c += 1 << 2;
}
if ((c & _CELL_STEP_MASK) == _CELL_STEP_DONE) {
// Go back.
switch (c & _CELL_PREV_MASK) {
case _CELL_PREV_FIRST: {
return;
} break;
case _CELL_PREV_Y_POS: {
y++;
ERR_FAIL_COND(y >= len_y);
} break;
case _CELL_PREV_Y_NEG: {
y--;
ERR_FAIL_COND(y < 0);
} break;
case _CELL_PREV_X_POS: {
x++;
ERR_FAIL_COND(x >= len_x);
} break;
case _CELL_PREV_X_NEG: {
x--;
ERR_FAIL_COND(x < 0);
} break;
case _CELL_PREV_Z_POS: {
z++;
ERR_FAIL_COND(z >= len_z);
} break;
case _CELL_PREV_Z_NEG: {
z--;
ERR_FAIL_COND(z < 0);
} break;
default: {
ERR_FAIL();
}
}
continue;
}
int next_x = x, next_y = y, next_z = z;
uint8_t prev = 0;
switch (c & _CELL_STEP_MASK) {
case _CELL_STEP_Y_POS: {
next_y++;
prev = _CELL_PREV_Y_NEG;
} break;
case _CELL_STEP_Y_NEG: {
next_y--;
prev = _CELL_PREV_Y_POS;
} break;
case _CELL_STEP_X_POS: {
next_x++;
prev = _CELL_PREV_X_NEG;
} break;
case _CELL_STEP_X_NEG: {
next_x--;
prev = _CELL_PREV_X_POS;
} break;
case _CELL_STEP_Z_POS: {
next_z++;
prev = _CELL_PREV_Z_NEG;
} break;
case _CELL_STEP_Z_NEG: {
next_z--;
prev = _CELL_PREV_Z_POS;
} break;
default:
ERR_FAIL();
}
if (next_x < 0 || next_x >= len_x) {
continue;
}
if (next_y < 0 || next_y >= len_y) {
continue;
}
if (next_z < 0 || next_z >= len_z) {
continue;
}
if (p_cell_status[next_x][next_y][next_z] & 3) {
continue;
}
x = next_x;
y = next_y;
z = next_z;
p_cell_status[x][y][z] |= prev;
}
}
static inline void _build_faces(uint8_t ***p_cell_status, int x, int y, int z, int len_x, int len_y, int len_z, PoolVector<Face3> &p_faces) {
ERR_FAIL_INDEX(x, len_x);
ERR_FAIL_INDEX(y, len_y);
ERR_FAIL_INDEX(z, len_z);
if (p_cell_status[x][y][z] & _CELL_EXTERIOR) {
return;
}
#define vert(m_idx) Vector3(((m_idx)&4) >> 2, ((m_idx)&2) >> 1, (m_idx)&1)
static const uint8_t indices[6][4] = {
{ 7, 6, 4, 5 },
{ 7, 3, 2, 6 },
{ 7, 5, 1, 3 },
{ 0, 2, 3, 1 },
{ 0, 1, 5, 4 },
{ 0, 4, 6, 2 },
};
for (int i = 0; i < 6; i++) {
Vector3 face_points[4];
int disp_x = x + ((i % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
int disp_y = y + (((i - 1) % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
int disp_z = z + (((i - 2) % 3) == 0 ? ((i < 3) ? 1 : -1) : 0);
bool plot = false;
if (disp_x < 0 || disp_x >= len_x) {
plot = true;
}
if (disp_y < 0 || disp_y >= len_y) {
plot = true;
}
if (disp_z < 0 || disp_z >= len_z) {
plot = true;
}
if (!plot && (p_cell_status[disp_x][disp_y][disp_z] & _CELL_EXTERIOR)) {
plot = true;
}
if (!plot) {
continue;
}
for (int j = 0; j < 4; j++) {
face_points[j] = vert(indices[i][j]) + Vector3(x, y, z);
}
p_faces.push_back(
Face3(
face_points[0],
face_points[1],
face_points[2]));
p_faces.push_back(
Face3(
face_points[2],
face_points[3],
face_points[0]));
}
}
PoolVector<Face3> Geometry::wrap_geometry(PoolVector<Face3> p_array, real_t *p_error) {
#define _MIN_SIZE 1.0f
#define _MAX_LENGTH 20
int face_count = p_array.size();
PoolVector<Face3>::Read facesr = p_array.read();
const Face3 *faces = facesr.ptr();
AABB global_aabb;
for (int i = 0; i < face_count; i++) {
if (i == 0) {
global_aabb = faces[i].get_aabb();
} else {
global_aabb.merge_with(faces[i].get_aabb());
}
}
global_aabb.grow_by(0.01f); // Avoid numerical error.
// Determine amount of cells in grid axis.
int div_x, div_y, div_z;
if (global_aabb.size.x / _MIN_SIZE < _MAX_LENGTH) {
div_x = (int)(global_aabb.size.x / _MIN_SIZE) + 1;
} else {
div_x = _MAX_LENGTH;
}
if (global_aabb.size.y / _MIN_SIZE < _MAX_LENGTH) {
div_y = (int)(global_aabb.size.y / _MIN_SIZE) + 1;
} else {
div_y = _MAX_LENGTH;
}
if (global_aabb.size.z / _MIN_SIZE < _MAX_LENGTH) {
div_z = (int)(global_aabb.size.z / _MIN_SIZE) + 1;
} else {
div_z = _MAX_LENGTH;
}
Vector3 voxelsize = global_aabb.size;
voxelsize.x /= div_x;
voxelsize.y /= div_y;
voxelsize.z /= div_z;
// Create and initialize cells to zero.
uint8_t ***cell_status = memnew_arr(uint8_t **, div_x);
for (int i = 0; i < div_x; i++) {
cell_status[i] = memnew_arr(uint8_t *, div_y);
for (int j = 0; j < div_y; j++) {
cell_status[i][j] = memnew_arr(uint8_t, div_z);
for (int k = 0; k < div_z; k++) {
cell_status[i][j][k] = 0;
}
}
}
// Plot faces into cells.
for (int i = 0; i < face_count; i++) {
Face3 f = faces[i];
for (int j = 0; j < 3; j++) {
f.vertex[j] -= global_aabb.position;
}
_plot_face(cell_status, 0, 0, 0, div_x, div_y, div_z, voxelsize, f);
}
// Determine which cells connect to the outside by traversing the outside and recursively flood-fill marking.
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
_mark_outside(cell_status, i, j, 0, div_x, div_y, div_z);
_mark_outside(cell_status, i, j, div_z - 1, div_x, div_y, div_z);
}
}
for (int i = 0; i < div_z; i++) {
for (int j = 0; j < div_y; j++) {
_mark_outside(cell_status, 0, j, i, div_x, div_y, div_z);
_mark_outside(cell_status, div_x - 1, j, i, div_x, div_y, div_z);
}
}
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_z; j++) {
_mark_outside(cell_status, i, 0, j, div_x, div_y, div_z);
_mark_outside(cell_status, i, div_y - 1, j, div_x, div_y, div_z);
}
}
// Build faces for the inside-outside cell divisors.
PoolVector<Face3> wrapped_faces;
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
for (int k = 0; k < div_z; k++) {
_build_faces(cell_status, i, j, k, div_x, div_y, div_z, wrapped_faces);
}
}
}
// Transform face vertices to global coords.
int wrapped_faces_count = wrapped_faces.size();
PoolVector<Face3>::Write wrapped_facesw = wrapped_faces.write();
Face3 *wrapped_faces_ptr = wrapped_facesw.ptr();
for (int i = 0; i < wrapped_faces_count; i++) {
for (int j = 0; j < 3; j++) {
Vector3 &v = wrapped_faces_ptr[i].vertex[j];
v = v * voxelsize;
v += global_aabb.position;
}
}
// clean up grid
for (int i = 0; i < div_x; i++) {
for (int j = 0; j < div_y; j++) {
memdelete_arr(cell_status[i][j]);
}
memdelete_arr(cell_status[i]);
}
memdelete_arr(cell_status);
if (p_error) {
*p_error = voxelsize.length();
}
return wrapped_faces;
}
Vector<Vector<Vector2>> Geometry::decompose_polygon_in_convex(Vector<Point2> polygon) {
Vector<Vector<Vector2>> decomp;
List<TriangulatorPoly> in_poly, out_poly;
TriangulatorPoly inp;
inp.Init(polygon.size());
for (int i = 0; i < polygon.size(); i++) {
inp.GetPoint(i) = polygon[i];
}
inp.SetOrientation(TRIANGULATOR_CCW);
in_poly.push_back(inp);
TriangulatorPartition tpart;
if (tpart.ConvexPartition_HM(&in_poly, &out_poly) == 0) { // Failed.
ERR_PRINT("Convex decomposing failed!");
return decomp;
}
decomp.resize(out_poly.size());
int idx = 0;
for (List<TriangulatorPoly>::Element *I = out_poly.front(); I; I = I->next()) {
TriangulatorPoly &tp = I->get();
decomp.write[idx].resize(tp.GetNumPoints());
for (int64_t i = 0; i < tp.GetNumPoints(); i++) {
decomp.write[idx].write[i] = tp.GetPoint(i);
}
idx++;
}
return decomp;
}
Geometry::MeshData Geometry::build_convex_mesh(const PoolVector<Plane> &p_planes) {
MeshData mesh;
#define SUBPLANE_SIZE 1024.0
real_t subplane_size = 1024.0; // Should compute this from the actual plane.
for (int i = 0; i < p_planes.size(); i++) {
Plane p = p_planes[i];
Vector3 ref = Vector3(0.0, 1.0, 0.0);
if (ABS(p.normal.dot(ref)) > 0.95f) {
ref = Vector3(0.0, 0.0, 1.0); // Change axis.
}
Vector3 right = p.normal.cross(ref).normalized();
Vector3 up = p.normal.cross(right).normalized();
Vector<Vector3> vertices;
Vector3 center = p.get_any_point();
// make a quad clockwise
vertices.push_back(center - up * subplane_size + right * subplane_size);
vertices.push_back(center - up * subplane_size - right * subplane_size);
vertices.push_back(center + up * subplane_size - right * subplane_size);
vertices.push_back(center + up * subplane_size + right * subplane_size);
for (int j = 0; j < p_planes.size(); j++) {
if (j == i) {
continue;
}
Vector<Vector3> new_vertices;
Plane clip = p_planes[j];
if (clip.normal.dot(p.normal) > 0.95f) {
continue;
}
if (vertices.size() < 3) {
break;
}
for (int k = 0; k < vertices.size(); k++) {
int k_n = (k + 1) % vertices.size();
Vector3 edge0_A = vertices[k];
Vector3 edge1_A = vertices[k_n];
real_t dist0 = clip.distance_to(edge0_A);
real_t dist1 = clip.distance_to(edge1_A);
if (dist0 <= 0) { // Behind plane.
new_vertices.push_back(vertices[k]);
}
// Check for different sides and non coplanar.
if ((dist0 * dist1) < 0) {
// Calculate intersection.
Vector3 rel = edge1_A - edge0_A;
real_t den = clip.normal.dot(rel);
if (Math::is_zero_approx(den)) {
continue; // Point too short.
}
real_t dist = -(clip.normal.dot(edge0_A) - clip.d) / den;
Vector3 inters = edge0_A + rel * dist;
new_vertices.push_back(inters);
}
}
vertices = new_vertices;
}
if (vertices.size() < 3) {
continue;
}
// Result is a clockwise face.
MeshData::Face face;
// Add face indices.
for (int j = 0; j < vertices.size(); j++) {
int idx = -1;
for (int k = 0; k < mesh.vertices.size(); k++) {
if (mesh.vertices[k].distance_to(vertices[j]) < 0.001f) {
idx = k;
break;
}
}
if (idx == -1) {
idx = mesh.vertices.size();
mesh.vertices.push_back(vertices[j]);
}
face.indices.push_back(idx);
}
face.plane = p;
mesh.faces.push_back(face);
// Add edge.
for (int j = 0; j < face.indices.size(); j++) {
int a = face.indices[j];
int b = face.indices[(j + 1) % face.indices.size()];
bool found = false;
for (int k = 0; k < mesh.edges.size(); k++) {
if (mesh.edges[k].a == a && mesh.edges[k].b == b) {
found = true;
break;
}
if (mesh.edges[k].b == a && mesh.edges[k].a == b) {
found = true;
break;
}
}
if (found) {
continue;
}
MeshData::Edge edge;
edge.a = a;
edge.b = b;
mesh.edges.push_back(edge);
}
}
return mesh;
}
PoolVector<Plane> Geometry::build_box_planes(const Vector3 &p_extents) {
PoolVector<Plane> planes;
planes.push_back(Plane(Vector3(1, 0, 0), p_extents.x));
planes.push_back(Plane(Vector3(-1, 0, 0), p_extents.x));
planes.push_back(Plane(Vector3(0, 1, 0), p_extents.y));
planes.push_back(Plane(Vector3(0, -1, 0), p_extents.y));
planes.push_back(Plane(Vector3(0, 0, 1), p_extents.z));
planes.push_back(Plane(Vector3(0, 0, -1), p_extents.z));
return planes;
}
PoolVector<Plane> Geometry::build_cylinder_planes(real_t p_radius, real_t p_height, int p_sides, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, PoolVector<Plane>());
PoolVector<Plane> planes;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_sides);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_sides);
planes.push_back(Plane(normal, p_radius));
}
Vector3 axis;
axis[p_axis] = 1.0;
planes.push_back(Plane(axis, p_height * 0.5f));
planes.push_back(Plane(-axis, p_height * 0.5f));
return planes;
}
PoolVector<Plane> Geometry::build_sphere_planes(real_t p_radius, int p_lats, int p_lons, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, PoolVector<Plane>());
PoolVector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1;
axis_neg[(p_axis + 2) % 3] = 1;
axis_neg[p_axis] = -1;
for (int i = 0; i < p_lons; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_lons);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_lons);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
// FIXME: This is stupid.
Vector3 angle = normal.linear_interpolate(axis, j / (real_t)p_lats).normalized();
Vector3 pos = angle * p_radius;
planes.push_back(Plane(pos, angle));
planes.push_back(Plane(pos * axis_neg, angle * axis_neg));
}
}
return planes;
}
PoolVector<Plane> Geometry::build_capsule_planes(real_t p_radius, real_t p_height, int p_sides, int p_lats, Vector3::Axis p_axis) {
ERR_FAIL_INDEX_V(p_axis, 3, PoolVector<Plane>());
PoolVector<Plane> planes;
Vector3 axis;
axis[p_axis] = 1;
Vector3 axis_neg;
axis_neg[(p_axis + 1) % 3] = 1;
axis_neg[(p_axis + 2) % 3] = 1;
axis_neg[p_axis] = -1;
for (int i = 0; i < p_sides; i++) {
Vector3 normal;
normal[(p_axis + 1) % 3] = Math::cos(i * (real_t)(2.0 * Math_PI) / p_sides);
normal[(p_axis + 2) % 3] = Math::sin(i * (real_t)(2.0 * Math_PI) / p_sides);
planes.push_back(Plane(normal, p_radius));
for (int j = 1; j <= p_lats; j++) {
Vector3 angle = normal.linear_interpolate(axis, j / (real_t)p_lats).normalized();
Vector3 pos = axis * p_height * 0.5f + angle * p_radius;
planes.push_back(Plane(pos, angle));
planes.push_back(Plane(pos * axis_neg, angle * axis_neg));
}
}
return planes;
}
struct _AtlasWorkRect {
Size2i s;
Point2i p;
int idx;
_FORCE_INLINE_ bool operator<(const _AtlasWorkRect &p_r) const { return s.width > p_r.s.width; }
};
struct _AtlasWorkRectResult {
Vector<_AtlasWorkRect> result;
int max_w;
int max_h;
};
void Geometry::make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size) {
// Super simple, almost brute force scanline stacking fitter.
// It's pretty basic for now, but it tries to make sure that the aspect ratio of the
// resulting atlas is somehow square. This is necessary because video cards have limits.
// On texture size (usually 2048 or 4096), so the more square a texture, the more chances.
// It will work in every hardware.
// For example, it will prioritize a 1024x1024 atlas (works everywhere) instead of a
// 256x8192 atlas (won't work anywhere).
ERR_FAIL_COND(p_rects.size() == 0);
for (int i = 0; i < p_rects.size(); i++) {
ERR_FAIL_COND(p_rects[i].width <= 0);
ERR_FAIL_COND(p_rects[i].height <= 0);
}
Vector<_AtlasWorkRect> wrects;
wrects.resize(p_rects.size());
for (int i = 0; i < p_rects.size(); i++) {
wrects.write[i].s = p_rects[i];
wrects.write[i].idx = i;
}
wrects.sort();
int widest = wrects[0].s.width;
Vector<_AtlasWorkRectResult> results;
for (int i = 0; i <= 12; i++) {
int w = 1 << i;
int max_h = 0;
int max_w = 0;
if (w < widest) {
continue;
}
Vector<int> hmax;
hmax.resize(w);
for (int j = 0; j < w; j++) {
hmax.write[j] = 0;
}
// Place them.
int ofs = 0;
int limit_h = 0;
for (int j = 0; j < wrects.size(); j++) {
if (ofs + wrects[j].s.width > w) {
ofs = 0;
}
int from_y = 0;
for (int k = 0; k < wrects[j].s.width; k++) {
if (hmax[ofs + k] > from_y) {
from_y = hmax[ofs + k];
}
}
wrects.write[j].p.x = ofs;
wrects.write[j].p.y = from_y;
int end_h = from_y + wrects[j].s.height;
int end_w = ofs + wrects[j].s.width;
if (ofs == 0) {
limit_h = end_h;
}
for (int k = 0; k < wrects[j].s.width; k++) {
hmax.write[ofs + k] = end_h;
}
if (end_h > max_h) {
max_h = end_h;
}
if (end_w > max_w) {
max_w = end_w;
}
if (ofs == 0 || end_h > limit_h) { // While h limit not reached, keep stacking.
ofs += wrects[j].s.width;
}
}
_AtlasWorkRectResult result;
result.result = wrects;
result.max_h = max_h;
result.max_w = max_w;
results.push_back(result);
}
// Find the result with the best aspect ratio.
int best = -1;
real_t best_aspect = 1e20;
for (int i = 0; i < results.size(); i++) {
real_t h = next_power_of_2(results[i].max_h);
real_t w = next_power_of_2(results[i].max_w);
real_t aspect = h > w ? h / w : w / h;
if (aspect < best_aspect) {
best = i;
best_aspect = aspect;
}
}
r_result.resize(p_rects.size());
for (int i = 0; i < p_rects.size(); i++) {
r_result.write[results[best].result[i].idx] = results[best].result[i].p;
}
r_size = Size2(results[best].max_w, results[best].max_h);
}
Vector<Vector<Point2>> Geometry::_polypaths_do_operation(PolyBooleanOperation p_op, const Vector<Point2> &p_polypath_a, const Vector<Point2> &p_polypath_b, bool is_a_open) {
using namespace ClipperLib;
ClipType op = ctUnion;
switch (p_op) {
case OPERATION_UNION:
op = ctUnion;
break;
case OPERATION_DIFFERENCE:
op = ctDifference;
break;
case OPERATION_INTERSECTION:
op = ctIntersection;
break;
case OPERATION_XOR:
op = ctXor;
break;
}
Path path_a, path_b;
// Need to scale points (Clipper's requirement for robust computation).
for (int i = 0; i != p_polypath_a.size(); ++i) {
path_a << IntPoint(p_polypath_a[i].x * (real_t)SCALE_FACTOR, p_polypath_a[i].y * (real_t)SCALE_FACTOR);
}
for (int i = 0; i != p_polypath_b.size(); ++i) {
path_b << IntPoint(p_polypath_b[i].x * (real_t)SCALE_FACTOR, p_polypath_b[i].y * (real_t)SCALE_FACTOR);
}
Clipper clp;
clp.AddPath(path_a, ptSubject, !is_a_open); // Forward compatible with Clipper 10.0.0.
clp.AddPath(path_b, ptClip, true); // Polylines cannot be set as clip.
Paths paths;
if (is_a_open) {
PolyTree tree; // Needed to populate polylines.
clp.Execute(op, tree);
OpenPathsFromPolyTree(tree, paths);
} else {
clp.Execute(op, paths); // Works on closed polygons only.
}
// Have to scale points down now.
Vector<Vector<Point2>> polypaths;
for (Paths::size_type i = 0; i < paths.size(); ++i) {
Vector<Vector2> polypath;
const Path &scaled_path = paths[i];
for (Paths::size_type j = 0; j < scaled_path.size(); ++j) {
polypath.push_back(Point2(
static_cast<real_t>(scaled_path[j].X) / (real_t)SCALE_FACTOR,
static_cast<real_t>(scaled_path[j].Y) / (real_t)SCALE_FACTOR));
}
polypaths.push_back(polypath);
}
return polypaths;
}
Vector<Vector<Point2>> Geometry::_polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
using namespace ClipperLib;
JoinType jt = jtSquare;
switch (p_join_type) {
case JOIN_SQUARE:
jt = jtSquare;
break;
case JOIN_ROUND:
jt = jtRound;
break;
case JOIN_MITER:
jt = jtMiter;
break;
}
EndType et = etClosedPolygon;
switch (p_end_type) {
case END_POLYGON:
et = etClosedPolygon;
break;
case END_JOINED:
et = etClosedLine;
break;
case END_BUTT:
et = etOpenButt;
break;
case END_SQUARE:
et = etOpenSquare;
break;
case END_ROUND:
et = etOpenRound;
break;
}
ClipperOffset co(2.0f, 0.25f * (real_t)SCALE_FACTOR); // Defaults from ClipperOffset.
Path path;
// Need to scale points (Clipper's requirement for robust computation).
for (int i = 0; i != p_polypath.size(); ++i) {
path << IntPoint(p_polypath[i].x * (real_t)SCALE_FACTOR, p_polypath[i].y * (real_t)SCALE_FACTOR);
}
co.AddPath(path, jt, et);
Paths paths;
co.Execute(paths, p_delta * (real_t)SCALE_FACTOR); // Inflate/deflate.
// Have to scale points down now.
Vector<Vector<Point2>> polypaths;
for (Paths::size_type i = 0; i < paths.size(); ++i) {
Vector<Vector2> polypath;
const Path &scaled_path = paths[i];
for (Paths::size_type j = 0; j < scaled_path.size(); ++j) {
polypath.push_back(Point2(
static_cast<real_t>(scaled_path[j].X) / (real_t)SCALE_FACTOR,
static_cast<real_t>(scaled_path[j].Y) / (real_t)SCALE_FACTOR));
}
polypaths.push_back(polypath);
}
return polypaths;
}
real_t Geometry::calculate_convex_hull_volume(const Geometry::MeshData &p_md) {
if (!p_md.vertices.size()) {
return 0;
}
// find center
Vector3 center;
for (int n = 0; n < p_md.vertices.size(); n++) {
center += p_md.vertices[n];
}
center /= p_md.vertices.size();
Face3 fa;
real_t volume = 0.0;
// volume of each cone is 1/3 * height * area of face
for (int f = 0; f < p_md.faces.size(); f++) {
const Geometry::MeshData::Face &face = p_md.faces[f];
real_t height = 0.0;
real_t face_area = 0.0;
for (int c = 0; c < face.indices.size() - 2; c++) {
fa.vertex[0] = p_md.vertices[face.indices[0]];
fa.vertex[1] = p_md.vertices[face.indices[c + 1]];
fa.vertex[2] = p_md.vertices[face.indices[c + 2]];
if (!c) {
// calculate height
Plane plane(fa.vertex[0], fa.vertex[1], fa.vertex[2]);
height = -plane.distance_to(center);
}
face_area += Math::sqrt(fa.get_twice_area_squared());
}
volume += face_area * height;
}
volume *= (real_t)((1.0 / 3.0) * 0.5);
return volume;
}
// note this function is slow, because it builds meshes etc. Not ideal to use in realtime.
// Planes must face OUTWARD from the center of the convex hull, by convention.
bool Geometry::convex_hull_intersects_convex_hull(const Plane *p_planes_a, int p_plane_count_a, const Plane *p_planes_b, int p_plane_count_b) {
if (!p_plane_count_a || !p_plane_count_b) {
return false;
}
// OR alternative approach, we can call compute_convex_mesh_points()
// with both sets of planes, to get an intersection. Not sure which method is
// faster... this may be faster with more complex hulls.
// the usual silliness to get from one vector format to another...
PoolVector<Plane> planes_a;
PoolVector<Plane> planes_b;
{
planes_a.resize(p_plane_count_a);
PoolVector<Plane>::Write w = planes_a.write();
memcpy(w.ptr(), p_planes_a, p_plane_count_a * sizeof(Plane));
}
{
planes_b.resize(p_plane_count_b);
PoolVector<Plane>::Write w = planes_b.write();
memcpy(w.ptr(), p_planes_b, p_plane_count_b * sizeof(Plane));
}
Geometry::MeshData md_A = build_convex_mesh(planes_a);
Geometry::MeshData md_B = build_convex_mesh(planes_b);
// hull can't be built
if (!md_A.vertices.size() || !md_B.vertices.size()) {
return false;
}
// first check the points against the planes
for (int p = 0; p < p_plane_count_a; p++) {
const Plane &plane = p_planes_a[p];
for (int n = 0; n < md_B.vertices.size(); n++) {
if (!plane.is_point_over(md_B.vertices[n])) {
return true;
}
}
}
for (int p = 0; p < p_plane_count_b; p++) {
const Plane &plane = p_planes_b[p];
for (int n = 0; n < md_A.vertices.size(); n++) {
if (!plane.is_point_over(md_A.vertices[n])) {
return true;
}
}
}
// now check edges
for (int n = 0; n < md_A.edges.size(); n++) {
const Vector3 &pt_a = md_A.vertices[md_A.edges[n].a];
const Vector3 &pt_b = md_A.vertices[md_A.edges[n].b];
if (segment_intersects_convex(pt_a, pt_b, p_planes_b, p_plane_count_b, nullptr, nullptr)) {
return true;
}
}
for (int n = 0; n < md_B.edges.size(); n++) {
const Vector3 &pt_a = md_B.vertices[md_B.edges[n].a];
const Vector3 &pt_b = md_B.vertices[md_B.edges[n].b];
if (segment_intersects_convex(pt_a, pt_b, p_planes_a, p_plane_count_a, nullptr, nullptr)) {
return true;
}
}
return false;
}
Vector<Vector3> Geometry::compute_convex_mesh_points(const Plane *p_planes, int p_plane_count, real_t p_epsilon) {
Vector<Vector3> points;
// Iterate through every unique combination of any three planes.
for (int i = p_plane_count - 1; i >= 0; i--) {
for (int j = i - 1; j >= 0; j--) {
for (int k = j - 1; k >= 0; k--) {
// Find the point where these planes all cross over (if they
// do at all).
Vector3 convex_shape_point;
if (p_planes[i].intersect_3(p_planes[j], p_planes[k], &convex_shape_point)) {
// See if any *other* plane excludes this point because it's
// on the wrong side.
bool excluded = false;
for (int n = 0; n < p_plane_count; n++) {
if (n != i && n != j && n != k) {
real_t dist = p_planes[n].distance_to(convex_shape_point);
if (dist > p_epsilon) {
excluded = true;
break;
}
}
}
// Only add the point if it passed all tests.
if (!excluded) {
points.push_back(convex_shape_point);
}
}
}
}
}
return points;
}
Vector<Geometry::PackRectsResult> Geometry::partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size) {
Vector<stbrp_node> nodes;
nodes.resize(p_atlas_size.width);
memset(nodes.ptrw(), 0, sizeof(stbrp_node) * nodes.size());
stbrp_context context;
stbrp_init_target(&context, p_atlas_size.width, p_atlas_size.height, nodes.ptrw(), p_atlas_size.width);
Vector<stbrp_rect> rects;
rects.resize(p_sizes.size());
for (int i = 0; i < p_sizes.size(); i++) {
rects.write[i].id = i;
rects.write[i].w = p_sizes[i].width;
rects.write[i].h = p_sizes[i].height;
rects.write[i].x = 0;
rects.write[i].y = 0;
rects.write[i].was_packed = 0;
}
stbrp_pack_rects(&context, rects.ptrw(), rects.size());
Vector<PackRectsResult> ret;
ret.resize(p_sizes.size());
for (int i = 0; i < p_sizes.size(); i++) {
ret.write[rects[i].id] = { rects[i].x, rects[i].y, static_cast<bool>(rects[i].was_packed) };
}
return ret;
}
// Expects polygon as a triangle fan
real_t Geometry::find_polygon_area(const Vector3 *p_verts, int p_num_verts) {
if (!p_verts || (p_num_verts < 3)) {
return 0.0;
}
Face3 f;
f.vertex[0] = p_verts[0];
f.vertex[1] = p_verts[1];
f.vertex[2] = p_verts[1];
real_t area = 0.0;
for (int n = 2; n < p_num_verts; n++) {
f.vertex[1] = f.vertex[2];
f.vertex[2] = p_verts[n];
area += Math::sqrt(f.get_twice_area_squared());
}
return area * 0.5f;
}
// adapted from:
// https://stackoverflow.com/questions/6989100/sort-points-in-clockwise-order
void Geometry::sort_polygon_winding(Vector<Vector2> &r_verts, bool p_clockwise) {
// sort winding order of a (primarily convex) polygon.
// It can handle some concave polygons, but not
// where a vertex 'goes back on' a previous vertex ..
// i.e. it will change the shape in some concave cases.
struct ElementComparator {
Vector2 center;
bool operator()(const Vector2 &a, const Vector2 &b) const {
if (a.x - center.x >= 0 && b.x - center.x < 0) {
return true;
}
if (a.x - center.x < 0 && b.x - center.x >= 0) {
return false;
}
if (a.x - center.x == 0 && b.x - center.x == 0) {
if (a.y - center.y >= 0 || b.y - center.y >= 0) {
return a.y > b.y;
}
return b.y > a.y;
}
// compute the cross product of vectors (center -> a) x (center -> b)
real_t det = (a.x - center.x) * (b.y - center.y) - (b.x - center.x) * (a.y - center.y);
if (det < 0) {
return true;
}
if (det > 0) {
return false;
}
// points a and b are on the same line from the center
// check which point is closer to the center
real_t d1 = (a.x - center.x) * (a.x - center.x) + (a.y - center.y) * (a.y - center.y);
real_t d2 = (b.x - center.x) * (b.x - center.x) + (b.y - center.y) * (b.y - center.y);
return d1 > d2;
}
};
int npoints = r_verts.size();
if (!npoints) {
return;
}
// first calculate center
Vector2 center;
for (int n = 0; n < npoints; n++) {
center += r_verts[n];
}
center /= npoints;
SortArray<Vector2, ElementComparator> sorter;
sorter.compare.center = center;
sorter.sort(r_verts.ptrw(), r_verts.size());
// if not clockwise, reverse order
if (!p_clockwise) {
r_verts.invert();
}
}
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