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99acec63f1
This updates our local copy to commit 5ec8339b6fc491e3f09a34a4516e82787f053fcc. We need a recent master commit for some new features that we use in Godot (see #25543 and #28909). To avoid warnings generated by Bullet headers included in our own module, we include those headers with -isystem on GCC and Clang. Fixes #29503.
908 lines
28 KiB
C++
908 lines
28 KiB
C++
/*
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Copyright (c) 2003-2013 Gino van den Bergen / Erwin Coumans http://bulletphysics.org
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This software is provided 'as-is', without any express or implied warranty.
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In no event will the authors be held liable for any damages arising from the use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it freely,
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subject to the following restrictions:
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1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
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2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
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3. This notice may not be removed or altered from any source distribution.
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*/
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#ifndef B3_SIMD__QUATERNION_H_
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#define B3_SIMD__QUATERNION_H_
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#include "b3Vector3.h"
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#include "b3QuadWord.h"
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#ifdef B3_USE_SSE
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const __m128 B3_ATTRIBUTE_ALIGNED16(b3vOnes) = {1.0f, 1.0f, 1.0f, 1.0f};
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#endif
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#if defined(B3_USE_SSE) || defined(B3_USE_NEON)
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const b3SimdFloat4 B3_ATTRIBUTE_ALIGNED16(b3vQInv) = {-0.0f, -0.0f, -0.0f, +0.0f};
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const b3SimdFloat4 B3_ATTRIBUTE_ALIGNED16(b3vPPPM) = {+0.0f, +0.0f, +0.0f, -0.0f};
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#endif
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/**@brief The b3Quaternion implements quaternion to perform linear algebra rotations in combination with b3Matrix3x3, b3Vector3 and b3Transform. */
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class b3Quaternion : public b3QuadWord
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{
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public:
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/**@brief No initialization constructor */
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b3Quaternion() {}
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#if (defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)) || defined(B3_USE_NEON)
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// Set Vector
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B3_FORCE_INLINE b3Quaternion(const b3SimdFloat4 vec)
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{
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mVec128 = vec;
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}
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// Copy constructor
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B3_FORCE_INLINE b3Quaternion(const b3Quaternion& rhs)
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{
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mVec128 = rhs.mVec128;
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}
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// Assignment Operator
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B3_FORCE_INLINE b3Quaternion&
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operator=(const b3Quaternion& v)
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{
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mVec128 = v.mVec128;
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return *this;
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}
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#endif
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// template <typename b3Scalar>
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// explicit Quaternion(const b3Scalar *v) : Tuple4<b3Scalar>(v) {}
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/**@brief Constructor from scalars */
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b3Quaternion(const b3Scalar& _x, const b3Scalar& _y, const b3Scalar& _z, const b3Scalar& _w)
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: b3QuadWord(_x, _y, _z, _w)
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{
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//b3Assert(!((_x==1.f) && (_y==0.f) && (_z==0.f) && (_w==0.f)));
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}
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/**@brief Axis angle Constructor
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* @param axis The axis which the rotation is around
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* @param angle The magnitude of the rotation around the angle (Radians) */
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b3Quaternion(const b3Vector3& _axis, const b3Scalar& _angle)
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{
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setRotation(_axis, _angle);
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}
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/**@brief Constructor from Euler angles
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* @param yaw Angle around Y unless B3_EULER_DEFAULT_ZYX defined then Z
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* @param pitch Angle around X unless B3_EULER_DEFAULT_ZYX defined then Y
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* @param roll Angle around Z unless B3_EULER_DEFAULT_ZYX defined then X */
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b3Quaternion(const b3Scalar& yaw, const b3Scalar& pitch, const b3Scalar& roll)
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{
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#ifndef B3_EULER_DEFAULT_ZYX
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setEuler(yaw, pitch, roll);
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#else
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setEulerZYX(yaw, pitch, roll);
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#endif
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}
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/**@brief Set the rotation using axis angle notation
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* @param axis The axis around which to rotate
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* @param angle The magnitude of the rotation in Radians */
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void setRotation(const b3Vector3& axis1, const b3Scalar& _angle)
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{
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b3Vector3 axis = axis1;
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axis.safeNormalize();
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b3Scalar d = axis.length();
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b3Assert(d != b3Scalar(0.0));
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if (d < B3_EPSILON)
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{
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setValue(0, 0, 0, 1);
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}
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else
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{
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b3Scalar s = b3Sin(_angle * b3Scalar(0.5)) / d;
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setValue(axis.getX() * s, axis.getY() * s, axis.getZ() * s,
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b3Cos(_angle * b3Scalar(0.5)));
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}
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}
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/**@brief Set the quaternion using Euler angles
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* @param yaw Angle around Y
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* @param pitch Angle around X
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* @param roll Angle around Z */
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void setEuler(const b3Scalar& yaw, const b3Scalar& pitch, const b3Scalar& roll)
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{
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b3Scalar halfYaw = b3Scalar(yaw) * b3Scalar(0.5);
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b3Scalar halfPitch = b3Scalar(pitch) * b3Scalar(0.5);
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b3Scalar halfRoll = b3Scalar(roll) * b3Scalar(0.5);
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b3Scalar cosYaw = b3Cos(halfYaw);
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b3Scalar sinYaw = b3Sin(halfYaw);
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b3Scalar cosPitch = b3Cos(halfPitch);
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b3Scalar sinPitch = b3Sin(halfPitch);
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b3Scalar cosRoll = b3Cos(halfRoll);
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b3Scalar sinRoll = b3Sin(halfRoll);
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setValue(cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw,
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cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw,
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sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw,
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cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw);
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}
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/**@brief Set the quaternion using euler angles
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* @param yaw Angle around Z
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* @param pitch Angle around Y
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* @param roll Angle around X */
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void setEulerZYX(const b3Scalar& yawZ, const b3Scalar& pitchY, const b3Scalar& rollX)
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{
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b3Scalar halfYaw = b3Scalar(yawZ) * b3Scalar(0.5);
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b3Scalar halfPitch = b3Scalar(pitchY) * b3Scalar(0.5);
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b3Scalar halfRoll = b3Scalar(rollX) * b3Scalar(0.5);
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b3Scalar cosYaw = b3Cos(halfYaw);
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b3Scalar sinYaw = b3Sin(halfYaw);
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b3Scalar cosPitch = b3Cos(halfPitch);
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b3Scalar sinPitch = b3Sin(halfPitch);
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b3Scalar cosRoll = b3Cos(halfRoll);
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b3Scalar sinRoll = b3Sin(halfRoll);
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setValue(sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw, //x
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cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw, //y
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cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw, //z
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cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw); //formerly yzx
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normalize();
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}
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/**@brief Get the euler angles from this quaternion
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* @param yaw Angle around Z
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* @param pitch Angle around Y
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* @param roll Angle around X */
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void getEulerZYX(b3Scalar& yawZ, b3Scalar& pitchY, b3Scalar& rollX) const
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{
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b3Scalar squ;
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b3Scalar sqx;
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b3Scalar sqy;
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b3Scalar sqz;
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b3Scalar sarg;
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sqx = m_floats[0] * m_floats[0];
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sqy = m_floats[1] * m_floats[1];
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sqz = m_floats[2] * m_floats[2];
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squ = m_floats[3] * m_floats[3];
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rollX = b3Atan2(2 * (m_floats[1] * m_floats[2] + m_floats[3] * m_floats[0]), squ - sqx - sqy + sqz);
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sarg = b3Scalar(-2.) * (m_floats[0] * m_floats[2] - m_floats[3] * m_floats[1]);
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pitchY = sarg <= b3Scalar(-1.0) ? b3Scalar(-0.5) * B3_PI : (sarg >= b3Scalar(1.0) ? b3Scalar(0.5) * B3_PI : b3Asin(sarg));
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yawZ = b3Atan2(2 * (m_floats[0] * m_floats[1] + m_floats[3] * m_floats[2]), squ + sqx - sqy - sqz);
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}
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/**@brief Add two quaternions
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* @param q The quaternion to add to this one */
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B3_FORCE_INLINE b3Quaternion& operator+=(const b3Quaternion& q)
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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mVec128 = _mm_add_ps(mVec128, q.mVec128);
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#elif defined(B3_USE_NEON)
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mVec128 = vaddq_f32(mVec128, q.mVec128);
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#else
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m_floats[0] += q.getX();
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m_floats[1] += q.getY();
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m_floats[2] += q.getZ();
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m_floats[3] += q.m_floats[3];
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#endif
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return *this;
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}
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/**@brief Subtract out a quaternion
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* @param q The quaternion to subtract from this one */
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b3Quaternion& operator-=(const b3Quaternion& q)
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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mVec128 = _mm_sub_ps(mVec128, q.mVec128);
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#elif defined(B3_USE_NEON)
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mVec128 = vsubq_f32(mVec128, q.mVec128);
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#else
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m_floats[0] -= q.getX();
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m_floats[1] -= q.getY();
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m_floats[2] -= q.getZ();
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m_floats[3] -= q.m_floats[3];
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#endif
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return *this;
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}
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/**@brief Scale this quaternion
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* @param s The scalar to scale by */
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b3Quaternion& operator*=(const b3Scalar& s)
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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__m128 vs = _mm_load_ss(&s); // (S 0 0 0)
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vs = b3_pshufd_ps(vs, 0); // (S S S S)
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mVec128 = _mm_mul_ps(mVec128, vs);
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#elif defined(B3_USE_NEON)
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mVec128 = vmulq_n_f32(mVec128, s);
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#else
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m_floats[0] *= s;
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m_floats[1] *= s;
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m_floats[2] *= s;
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m_floats[3] *= s;
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#endif
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return *this;
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}
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/**@brief Multiply this quaternion by q on the right
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* @param q The other quaternion
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* Equivilant to this = this * q */
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b3Quaternion& operator*=(const b3Quaternion& q)
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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__m128 vQ2 = q.get128();
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__m128 A1 = b3_pshufd_ps(mVec128, B3_SHUFFLE(0, 1, 2, 0));
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__m128 B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0));
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A1 = A1 * B1;
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__m128 A2 = b3_pshufd_ps(mVec128, B3_SHUFFLE(1, 2, 0, 1));
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__m128 B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
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A2 = A2 * B2;
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B1 = b3_pshufd_ps(mVec128, B3_SHUFFLE(2, 0, 1, 2));
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B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
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B1 = B1 * B2; // A3 *= B3
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mVec128 = b3_splat_ps(mVec128, 3); // A0
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mVec128 = mVec128 * vQ2; // A0 * B0
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A1 = A1 + A2; // AB12
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mVec128 = mVec128 - B1; // AB03 = AB0 - AB3
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A1 = _mm_xor_ps(A1, b3vPPPM); // change sign of the last element
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mVec128 = mVec128 + A1; // AB03 + AB12
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#elif defined(B3_USE_NEON)
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float32x4_t vQ1 = mVec128;
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float32x4_t vQ2 = q.get128();
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float32x4_t A0, A1, B1, A2, B2, A3, B3;
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float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
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{
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float32x2x2_t tmp;
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tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1)); // {z x}, {w y}
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vQ1zx = tmp.val[0];
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tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2)); // {z x}, {w y}
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vQ2zx = tmp.val[0];
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}
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vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
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vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
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vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
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vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
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A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx); // X Y z x
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B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx); // W W W X
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A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
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B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
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A3 = vcombine_f32(vQ1zx, vQ1yz); // Z X Y Z
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B3 = vcombine_f32(vQ2yz, vQ2xz); // Y Z x z
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A1 = vmulq_f32(A1, B1);
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A2 = vmulq_f32(A2, B2);
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A3 = vmulq_f32(A3, B3); // A3 *= B3
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A0 = vmulq_lane_f32(vQ2, vget_high_f32(vQ1), 1); // A0 * B0
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A1 = vaddq_f32(A1, A2); // AB12 = AB1 + AB2
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A0 = vsubq_f32(A0, A3); // AB03 = AB0 - AB3
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// change the sign of the last element
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A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
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A0 = vaddq_f32(A0, A1); // AB03 + AB12
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mVec128 = A0;
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#else
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setValue(
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m_floats[3] * q.getX() + m_floats[0] * q.m_floats[3] + m_floats[1] * q.getZ() - m_floats[2] * q.getY(),
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m_floats[3] * q.getY() + m_floats[1] * q.m_floats[3] + m_floats[2] * q.getX() - m_floats[0] * q.getZ(),
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m_floats[3] * q.getZ() + m_floats[2] * q.m_floats[3] + m_floats[0] * q.getY() - m_floats[1] * q.getX(),
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m_floats[3] * q.m_floats[3] - m_floats[0] * q.getX() - m_floats[1] * q.getY() - m_floats[2] * q.getZ());
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#endif
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return *this;
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}
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/**@brief Return the dot product between this quaternion and another
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* @param q The other quaternion */
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b3Scalar dot(const b3Quaternion& q) const
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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__m128 vd;
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vd = _mm_mul_ps(mVec128, q.mVec128);
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__m128 t = _mm_movehl_ps(vd, vd);
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vd = _mm_add_ps(vd, t);
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t = _mm_shuffle_ps(vd, vd, 0x55);
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vd = _mm_add_ss(vd, t);
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return _mm_cvtss_f32(vd);
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#elif defined(B3_USE_NEON)
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float32x4_t vd = vmulq_f32(mVec128, q.mVec128);
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float32x2_t x = vpadd_f32(vget_low_f32(vd), vget_high_f32(vd));
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x = vpadd_f32(x, x);
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return vget_lane_f32(x, 0);
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#else
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return m_floats[0] * q.getX() +
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m_floats[1] * q.getY() +
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m_floats[2] * q.getZ() +
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m_floats[3] * q.m_floats[3];
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#endif
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}
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/**@brief Return the length squared of the quaternion */
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b3Scalar length2() const
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{
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return dot(*this);
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}
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/**@brief Return the length of the quaternion */
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b3Scalar length() const
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{
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return b3Sqrt(length2());
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}
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/**@brief Normalize the quaternion
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* Such that x^2 + y^2 + z^2 +w^2 = 1 */
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b3Quaternion& normalize()
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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__m128 vd;
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vd = _mm_mul_ps(mVec128, mVec128);
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__m128 t = _mm_movehl_ps(vd, vd);
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vd = _mm_add_ps(vd, t);
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t = _mm_shuffle_ps(vd, vd, 0x55);
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vd = _mm_add_ss(vd, t);
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vd = _mm_sqrt_ss(vd);
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vd = _mm_div_ss(b3vOnes, vd);
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vd = b3_pshufd_ps(vd, 0); // splat
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mVec128 = _mm_mul_ps(mVec128, vd);
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return *this;
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#else
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return *this /= length();
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#endif
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}
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/**@brief Return a scaled version of this quaternion
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* @param s The scale factor */
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B3_FORCE_INLINE b3Quaternion
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operator*(const b3Scalar& s) const
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{
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#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
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__m128 vs = _mm_load_ss(&s); // (S 0 0 0)
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vs = b3_pshufd_ps(vs, 0x00); // (S S S S)
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return b3Quaternion(_mm_mul_ps(mVec128, vs));
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#elif defined(B3_USE_NEON)
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return b3Quaternion(vmulq_n_f32(mVec128, s));
|
|
#else
|
|
return b3Quaternion(getX() * s, getY() * s, getZ() * s, m_floats[3] * s);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return an inversely scaled versionof this quaternion
|
|
* @param s The inverse scale factor */
|
|
b3Quaternion operator/(const b3Scalar& s) const
|
|
{
|
|
b3Assert(s != b3Scalar(0.0));
|
|
return *this * (b3Scalar(1.0) / s);
|
|
}
|
|
|
|
/**@brief Inversely scale this quaternion
|
|
* @param s The scale factor */
|
|
b3Quaternion& operator/=(const b3Scalar& s)
|
|
{
|
|
b3Assert(s != b3Scalar(0.0));
|
|
return *this *= b3Scalar(1.0) / s;
|
|
}
|
|
|
|
/**@brief Return a normalized version of this quaternion */
|
|
b3Quaternion normalized() const
|
|
{
|
|
return *this / length();
|
|
}
|
|
/**@brief Return the angle between this quaternion and the other
|
|
* @param q The other quaternion */
|
|
b3Scalar angle(const b3Quaternion& q) const
|
|
{
|
|
b3Scalar s = b3Sqrt(length2() * q.length2());
|
|
b3Assert(s != b3Scalar(0.0));
|
|
return b3Acos(dot(q) / s);
|
|
}
|
|
/**@brief Return the angle of rotation represented by this quaternion */
|
|
b3Scalar getAngle() const
|
|
{
|
|
b3Scalar s = b3Scalar(2.) * b3Acos(m_floats[3]);
|
|
return s;
|
|
}
|
|
|
|
/**@brief Return the axis of the rotation represented by this quaternion */
|
|
b3Vector3 getAxis() const
|
|
{
|
|
b3Scalar s_squared = 1.f - m_floats[3] * m_floats[3];
|
|
|
|
if (s_squared < b3Scalar(10.) * B3_EPSILON) //Check for divide by zero
|
|
return b3MakeVector3(1.0, 0.0, 0.0); // Arbitrary
|
|
b3Scalar s = 1.f / b3Sqrt(s_squared);
|
|
return b3MakeVector3(m_floats[0] * s, m_floats[1] * s, m_floats[2] * s);
|
|
}
|
|
|
|
/**@brief Return the inverse of this quaternion */
|
|
b3Quaternion inverse() const
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
return b3Quaternion(_mm_xor_ps(mVec128, b3vQInv));
|
|
#elif defined(B3_USE_NEON)
|
|
return b3Quaternion((b3SimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)b3vQInv));
|
|
#else
|
|
return b3Quaternion(-m_floats[0], -m_floats[1], -m_floats[2], m_floats[3]);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return the sum of this quaternion and the other
|
|
* @param q2 The other quaternion */
|
|
B3_FORCE_INLINE b3Quaternion
|
|
operator+(const b3Quaternion& q2) const
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
return b3Quaternion(_mm_add_ps(mVec128, q2.mVec128));
|
|
#elif defined(B3_USE_NEON)
|
|
return b3Quaternion(vaddq_f32(mVec128, q2.mVec128));
|
|
#else
|
|
const b3Quaternion& q1 = *this;
|
|
return b3Quaternion(q1.getX() + q2.getX(), q1.getY() + q2.getY(), q1.getZ() + q2.getZ(), q1.m_floats[3] + q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return the difference between this quaternion and the other
|
|
* @param q2 The other quaternion */
|
|
B3_FORCE_INLINE b3Quaternion
|
|
operator-(const b3Quaternion& q2) const
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
return b3Quaternion(_mm_sub_ps(mVec128, q2.mVec128));
|
|
#elif defined(B3_USE_NEON)
|
|
return b3Quaternion(vsubq_f32(mVec128, q2.mVec128));
|
|
#else
|
|
const b3Quaternion& q1 = *this;
|
|
return b3Quaternion(q1.getX() - q2.getX(), q1.getY() - q2.getY(), q1.getZ() - q2.getZ(), q1.m_floats[3] - q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return the negative of this quaternion
|
|
* This simply negates each element */
|
|
B3_FORCE_INLINE b3Quaternion operator-() const
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
return b3Quaternion(_mm_xor_ps(mVec128, b3vMzeroMask));
|
|
#elif defined(B3_USE_NEON)
|
|
return b3Quaternion((b3SimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)b3vMzeroMask));
|
|
#else
|
|
const b3Quaternion& q2 = *this;
|
|
return b3Quaternion(-q2.getX(), -q2.getY(), -q2.getZ(), -q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
/**@todo document this and it's use */
|
|
B3_FORCE_INLINE b3Quaternion farthest(const b3Quaternion& qd) const
|
|
{
|
|
b3Quaternion diff, sum;
|
|
diff = *this - qd;
|
|
sum = *this + qd;
|
|
if (diff.dot(diff) > sum.dot(sum))
|
|
return qd;
|
|
return (-qd);
|
|
}
|
|
|
|
/**@todo document this and it's use */
|
|
B3_FORCE_INLINE b3Quaternion nearest(const b3Quaternion& qd) const
|
|
{
|
|
b3Quaternion diff, sum;
|
|
diff = *this - qd;
|
|
sum = *this + qd;
|
|
if (diff.dot(diff) < sum.dot(sum))
|
|
return qd;
|
|
return (-qd);
|
|
}
|
|
|
|
/**@brief Return the quaternion which is the result of Spherical Linear Interpolation between this and the other quaternion
|
|
* @param q The other quaternion to interpolate with
|
|
* @param t The ratio between this and q to interpolate. If t = 0 the result is this, if t=1 the result is q.
|
|
* Slerp interpolates assuming constant velocity. */
|
|
b3Quaternion slerp(const b3Quaternion& q, const b3Scalar& t) const
|
|
{
|
|
b3Scalar magnitude = b3Sqrt(length2() * q.length2());
|
|
b3Assert(magnitude > b3Scalar(0));
|
|
|
|
b3Scalar product = dot(q) / magnitude;
|
|
if (b3Fabs(product) < b3Scalar(1))
|
|
{
|
|
// Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
|
|
const b3Scalar sign = (product < 0) ? b3Scalar(-1) : b3Scalar(1);
|
|
|
|
const b3Scalar theta = b3Acos(sign * product);
|
|
const b3Scalar s1 = b3Sin(sign * t * theta);
|
|
const b3Scalar d = b3Scalar(1.0) / b3Sin(theta);
|
|
const b3Scalar s0 = b3Sin((b3Scalar(1.0) - t) * theta);
|
|
|
|
return b3Quaternion(
|
|
(m_floats[0] * s0 + q.getX() * s1) * d,
|
|
(m_floats[1] * s0 + q.getY() * s1) * d,
|
|
(m_floats[2] * s0 + q.getZ() * s1) * d,
|
|
(m_floats[3] * s0 + q.m_floats[3] * s1) * d);
|
|
}
|
|
else
|
|
{
|
|
return *this;
|
|
}
|
|
}
|
|
|
|
static const b3Quaternion& getIdentity()
|
|
{
|
|
static const b3Quaternion identityQuat(b3Scalar(0.), b3Scalar(0.), b3Scalar(0.), b3Scalar(1.));
|
|
return identityQuat;
|
|
}
|
|
|
|
B3_FORCE_INLINE const b3Scalar& getW() const { return m_floats[3]; }
|
|
};
|
|
|
|
/**@brief Return the product of two quaternions */
|
|
B3_FORCE_INLINE b3Quaternion
|
|
operator*(const b3Quaternion& q1, const b3Quaternion& q2)
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
__m128 vQ1 = q1.get128();
|
|
__m128 vQ2 = q2.get128();
|
|
__m128 A0, A1, B1, A2, B2;
|
|
|
|
A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(0, 1, 2, 0)); // X Y z x // vtrn
|
|
B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0)); // W W W X // vdup vext
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1)); // Y Z X Y // vext
|
|
B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1)); // z x Y Y // vtrn vdup
|
|
|
|
A2 = A2 * B2;
|
|
|
|
B1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2)); // z x Y Z // vtrn vext
|
|
B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2)); // Y Z x z // vext vtrn
|
|
|
|
B1 = B1 * B2; // A3 *= B3
|
|
|
|
A0 = b3_splat_ps(vQ1, 3); // A0
|
|
A0 = A0 * vQ2; // A0 * B0
|
|
|
|
A1 = A1 + A2; // AB12
|
|
A0 = A0 - B1; // AB03 = AB0 - AB3
|
|
|
|
A1 = _mm_xor_ps(A1, b3vPPPM); // change sign of the last element
|
|
A0 = A0 + A1; // AB03 + AB12
|
|
|
|
return b3Quaternion(A0);
|
|
|
|
#elif defined(B3_USE_NEON)
|
|
|
|
float32x4_t vQ1 = q1.get128();
|
|
float32x4_t vQ2 = q2.get128();
|
|
float32x4_t A0, A1, B1, A2, B2, A3, B3;
|
|
float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
|
|
|
|
{
|
|
float32x2x2_t tmp;
|
|
tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1)); // {z x}, {w y}
|
|
vQ1zx = tmp.val[0];
|
|
|
|
tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2)); // {z x}, {w y}
|
|
vQ2zx = tmp.val[0];
|
|
}
|
|
vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
|
|
|
|
vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
|
|
|
|
vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
|
|
vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
|
|
|
|
A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx); // X Y z x
|
|
B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx); // W W W X
|
|
|
|
A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
|
|
B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
|
|
|
|
A3 = vcombine_f32(vQ1zx, vQ1yz); // Z X Y Z
|
|
B3 = vcombine_f32(vQ2yz, vQ2xz); // Y Z x z
|
|
|
|
A1 = vmulq_f32(A1, B1);
|
|
A2 = vmulq_f32(A2, B2);
|
|
A3 = vmulq_f32(A3, B3); // A3 *= B3
|
|
A0 = vmulq_lane_f32(vQ2, vget_high_f32(vQ1), 1); // A0 * B0
|
|
|
|
A1 = vaddq_f32(A1, A2); // AB12 = AB1 + AB2
|
|
A0 = vsubq_f32(A0, A3); // AB03 = AB0 - AB3
|
|
|
|
// change the sign of the last element
|
|
A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
|
|
A0 = vaddq_f32(A0, A1); // AB03 + AB12
|
|
|
|
return b3Quaternion(A0);
|
|
|
|
#else
|
|
return b3Quaternion(
|
|
q1.getW() * q2.getX() + q1.getX() * q2.getW() + q1.getY() * q2.getZ() - q1.getZ() * q2.getY(),
|
|
q1.getW() * q2.getY() + q1.getY() * q2.getW() + q1.getZ() * q2.getX() - q1.getX() * q2.getZ(),
|
|
q1.getW() * q2.getZ() + q1.getZ() * q2.getW() + q1.getX() * q2.getY() - q1.getY() * q2.getX(),
|
|
q1.getW() * q2.getW() - q1.getX() * q2.getX() - q1.getY() * q2.getY() - q1.getZ() * q2.getZ());
|
|
#endif
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
operator*(const b3Quaternion& q, const b3Vector3& w)
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
__m128 vQ1 = q.get128();
|
|
__m128 vQ2 = w.get128();
|
|
__m128 A1, B1, A2, B2, A3, B3;
|
|
|
|
A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(3, 3, 3, 0));
|
|
B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(0, 1, 2, 0));
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1));
|
|
B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
|
|
|
|
A2 = A2 * B2;
|
|
|
|
A3 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2));
|
|
B3 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
|
|
|
|
A3 = A3 * B3; // A3 *= B3
|
|
|
|
A1 = A1 + A2; // AB12
|
|
A1 = _mm_xor_ps(A1, b3vPPPM); // change sign of the last element
|
|
A1 = A1 - A3; // AB123 = AB12 - AB3
|
|
|
|
return b3Quaternion(A1);
|
|
|
|
#elif defined(B3_USE_NEON)
|
|
|
|
float32x4_t vQ1 = q.get128();
|
|
float32x4_t vQ2 = w.get128();
|
|
float32x4_t A1, B1, A2, B2, A3, B3;
|
|
float32x2_t vQ1wx, vQ2zx, vQ1yz, vQ2yz, vQ1zx, vQ2xz;
|
|
|
|
vQ1wx = vext_f32(vget_high_f32(vQ1), vget_low_f32(vQ1), 1);
|
|
{
|
|
float32x2x2_t tmp;
|
|
|
|
tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2)); // {z x}, {w y}
|
|
vQ2zx = tmp.val[0];
|
|
|
|
tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1)); // {z x}, {w y}
|
|
vQ1zx = tmp.val[0];
|
|
}
|
|
|
|
vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
|
|
|
|
vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
|
|
vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
|
|
|
|
A1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ1), 1), vQ1wx); // W W W X
|
|
B1 = vcombine_f32(vget_low_f32(vQ2), vQ2zx); // X Y z x
|
|
|
|
A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
|
|
B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
|
|
|
|
A3 = vcombine_f32(vQ1zx, vQ1yz); // Z X Y Z
|
|
B3 = vcombine_f32(vQ2yz, vQ2xz); // Y Z x z
|
|
|
|
A1 = vmulq_f32(A1, B1);
|
|
A2 = vmulq_f32(A2, B2);
|
|
A3 = vmulq_f32(A3, B3); // A3 *= B3
|
|
|
|
A1 = vaddq_f32(A1, A2); // AB12 = AB1 + AB2
|
|
|
|
// change the sign of the last element
|
|
A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
|
|
|
|
A1 = vsubq_f32(A1, A3); // AB123 = AB12 - AB3
|
|
|
|
return b3Quaternion(A1);
|
|
|
|
#else
|
|
return b3Quaternion(
|
|
q.getW() * w.getX() + q.getY() * w.getZ() - q.getZ() * w.getY(),
|
|
q.getW() * w.getY() + q.getZ() * w.getX() - q.getX() * w.getZ(),
|
|
q.getW() * w.getZ() + q.getX() * w.getY() - q.getY() * w.getX(),
|
|
-q.getX() * w.getX() - q.getY() * w.getY() - q.getZ() * w.getZ());
|
|
#endif
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
operator*(const b3Vector3& w, const b3Quaternion& q)
|
|
{
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
__m128 vQ1 = w.get128();
|
|
__m128 vQ2 = q.get128();
|
|
__m128 A1, B1, A2, B2, A3, B3;
|
|
|
|
A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(0, 1, 2, 0)); // X Y z x
|
|
B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0)); // W W W X
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1));
|
|
B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
|
|
|
|
A2 = A2 * B2;
|
|
|
|
A3 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2));
|
|
B3 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
|
|
|
|
A3 = A3 * B3; // A3 *= B3
|
|
|
|
A1 = A1 + A2; // AB12
|
|
A1 = _mm_xor_ps(A1, b3vPPPM); // change sign of the last element
|
|
A1 = A1 - A3; // AB123 = AB12 - AB3
|
|
|
|
return b3Quaternion(A1);
|
|
|
|
#elif defined(B3_USE_NEON)
|
|
|
|
float32x4_t vQ1 = w.get128();
|
|
float32x4_t vQ2 = q.get128();
|
|
float32x4_t A1, B1, A2, B2, A3, B3;
|
|
float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
|
|
|
|
{
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|
float32x2x2_t tmp;
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|
|
|
tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1)); // {z x}, {w y}
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|
vQ1zx = tmp.val[0];
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|
|
|
tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2)); // {z x}, {w y}
|
|
vQ2zx = tmp.val[0];
|
|
}
|
|
vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
|
|
|
|
vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
|
|
|
|
vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
|
|
vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
|
|
|
|
A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx); // X Y z x
|
|
B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx); // W W W X
|
|
|
|
A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
|
|
B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
|
|
|
|
A3 = vcombine_f32(vQ1zx, vQ1yz); // Z X Y Z
|
|
B3 = vcombine_f32(vQ2yz, vQ2xz); // Y Z x z
|
|
|
|
A1 = vmulq_f32(A1, B1);
|
|
A2 = vmulq_f32(A2, B2);
|
|
A3 = vmulq_f32(A3, B3); // A3 *= B3
|
|
|
|
A1 = vaddq_f32(A1, A2); // AB12 = AB1 + AB2
|
|
|
|
// change the sign of the last element
|
|
A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
|
|
|
|
A1 = vsubq_f32(A1, A3); // AB123 = AB12 - AB3
|
|
|
|
return b3Quaternion(A1);
|
|
|
|
#else
|
|
return b3Quaternion(
|
|
+w.getX() * q.getW() + w.getY() * q.getZ() - w.getZ() * q.getY(),
|
|
+w.getY() * q.getW() + w.getZ() * q.getX() - w.getX() * q.getZ(),
|
|
+w.getZ() * q.getW() + w.getX() * q.getY() - w.getY() * q.getX(),
|
|
-w.getX() * q.getX() - w.getY() * q.getY() - w.getZ() * q.getZ());
|
|
#endif
|
|
}
|
|
|
|
/**@brief Calculate the dot product between two quaternions */
|
|
B3_FORCE_INLINE b3Scalar
|
|
b3Dot(const b3Quaternion& q1, const b3Quaternion& q2)
|
|
{
|
|
return q1.dot(q2);
|
|
}
|
|
|
|
/**@brief Return the length of a quaternion */
|
|
B3_FORCE_INLINE b3Scalar
|
|
b3Length(const b3Quaternion& q)
|
|
{
|
|
return q.length();
|
|
}
|
|
|
|
/**@brief Return the angle between two quaternions*/
|
|
B3_FORCE_INLINE b3Scalar
|
|
b3Angle(const b3Quaternion& q1, const b3Quaternion& q2)
|
|
{
|
|
return q1.angle(q2);
|
|
}
|
|
|
|
/**@brief Return the inverse of a quaternion*/
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3Inverse(const b3Quaternion& q)
|
|
{
|
|
return q.inverse();
|
|
}
|
|
|
|
/**@brief Return the result of spherical linear interpolation betwen two quaternions
|
|
* @param q1 The first quaternion
|
|
* @param q2 The second quaternion
|
|
* @param t The ration between q1 and q2. t = 0 return q1, t=1 returns q2
|
|
* Slerp assumes constant velocity between positions. */
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3Slerp(const b3Quaternion& q1, const b3Quaternion& q2, const b3Scalar& t)
|
|
{
|
|
return q1.slerp(q2, t);
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3QuatMul(const b3Quaternion& rot0, const b3Quaternion& rot1)
|
|
{
|
|
return rot0 * rot1;
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3QuatNormalized(const b3Quaternion& orn)
|
|
{
|
|
return orn.normalized();
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Vector3
|
|
b3QuatRotate(const b3Quaternion& rotation, const b3Vector3& v)
|
|
{
|
|
b3Quaternion q = rotation * v;
|
|
q *= rotation.inverse();
|
|
#if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
|
|
return b3MakeVector3(_mm_and_ps(q.get128(), b3vFFF0fMask));
|
|
#elif defined(B3_USE_NEON)
|
|
return b3MakeVector3((float32x4_t)vandq_s32((int32x4_t)q.get128(), b3vFFF0Mask));
|
|
#else
|
|
return b3MakeVector3(q.getX(), q.getY(), q.getZ());
|
|
#endif
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3ShortestArcQuat(const b3Vector3& v0, const b3Vector3& v1) // Game Programming Gems 2.10. make sure v0,v1 are normalized
|
|
{
|
|
b3Vector3 c = v0.cross(v1);
|
|
b3Scalar d = v0.dot(v1);
|
|
|
|
if (d < -1.0 + B3_EPSILON)
|
|
{
|
|
b3Vector3 n, unused;
|
|
b3PlaneSpace1(v0, n, unused);
|
|
return b3Quaternion(n.getX(), n.getY(), n.getZ(), 0.0f); // just pick any vector that is orthogonal to v0
|
|
}
|
|
|
|
b3Scalar s = b3Sqrt((1.0f + d) * 2.0f);
|
|
b3Scalar rs = 1.0f / s;
|
|
|
|
return b3Quaternion(c.getX() * rs, c.getY() * rs, c.getZ() * rs, s * 0.5f);
|
|
}
|
|
|
|
B3_FORCE_INLINE b3Quaternion
|
|
b3ShortestArcQuatNormalize2(b3Vector3& v0, b3Vector3& v1)
|
|
{
|
|
v0.normalize();
|
|
v1.normalize();
|
|
return b3ShortestArcQuat(v0, v1);
|
|
}
|
|
|
|
#endif //B3_SIMD__QUATERNION_H_
|