1021 lines
31 KiB
C++
1021 lines
31 KiB
C++
/*
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Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans https://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 BT_SIMD__QUATERNION_H_
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#define BT_SIMD__QUATERNION_H_
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#include "btVector3.h"
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#include "btQuadWord.h"
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#ifdef BT_USE_DOUBLE_PRECISION
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#define btQuaternionData btQuaternionDoubleData
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#define btQuaternionDataName "btQuaternionDoubleData"
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#else
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#define btQuaternionData btQuaternionFloatData
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#define btQuaternionDataName "btQuaternionFloatData"
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#endif //BT_USE_DOUBLE_PRECISION
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#ifdef BT_USE_SSE
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//const __m128 ATTRIBUTE_ALIGNED16(vOnes) = {1.0f, 1.0f, 1.0f, 1.0f};
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#define vOnes (_mm_set_ps(1.0f, 1.0f, 1.0f, 1.0f))
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#endif
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#if defined(BT_USE_SSE)
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#define vQInv (_mm_set_ps(+0.0f, -0.0f, -0.0f, -0.0f))
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#define vPPPM (_mm_set_ps(-0.0f, +0.0f, +0.0f, +0.0f))
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#elif defined(BT_USE_NEON)
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const btSimdFloat4 ATTRIBUTE_ALIGNED16(vQInv) = {-0.0f, -0.0f, -0.0f, +0.0f};
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const btSimdFloat4 ATTRIBUTE_ALIGNED16(vPPPM) = {+0.0f, +0.0f, +0.0f, -0.0f};
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#endif
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/**@brief The btQuaternion implements quaternion to perform linear algebra rotations in combination with btMatrix3x3, btVector3 and btTransform. */
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class btQuaternion : public btQuadWord
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{
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public:
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/**@brief No initialization constructor */
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btQuaternion() {}
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#if (defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)) || defined(BT_USE_NEON)
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// Set Vector
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SIMD_FORCE_INLINE btQuaternion(const btSimdFloat4 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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SIMD_FORCE_INLINE btQuaternion(const btQuaternion& 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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SIMD_FORCE_INLINE btQuaternion&
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operator=(const btQuaternion& 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 btScalar>
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// explicit Quaternion(const btScalar *v) : Tuple4<btScalar>(v) {}
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/**@brief Constructor from scalars */
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btQuaternion(const btScalar& _x, const btScalar& _y, const btScalar& _z, const btScalar& _w)
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: btQuadWord(_x, _y, _z, _w)
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{
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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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btQuaternion(const btVector3& _axis, const btScalar& _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 BT_EULER_DEFAULT_ZYX defined then Z
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* @param pitch Angle around X unless BT_EULER_DEFAULT_ZYX defined then Y
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* @param roll Angle around Z unless BT_EULER_DEFAULT_ZYX defined then X */
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btQuaternion(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
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{
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#ifndef BT_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 btVector3& axis, const btScalar& _angle)
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{
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btScalar d = axis.length();
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btAssert(d != btScalar(0.0));
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btScalar s = btSin(_angle * btScalar(0.5)) / d;
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setValue(axis.x() * s, axis.y() * s, axis.z() * s,
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btCos(_angle * btScalar(0.5)));
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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 btScalar& yaw, const btScalar& pitch, const btScalar& roll)
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{
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btScalar halfYaw = btScalar(yaw) * btScalar(0.5);
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btScalar halfPitch = btScalar(pitch) * btScalar(0.5);
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btScalar halfRoll = btScalar(roll) * btScalar(0.5);
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btScalar cosYaw = btCos(halfYaw);
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btScalar sinYaw = btSin(halfYaw);
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btScalar cosPitch = btCos(halfPitch);
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btScalar sinPitch = btSin(halfPitch);
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btScalar cosRoll = btCos(halfRoll);
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btScalar sinRoll = btSin(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 btScalar& yawZ, const btScalar& pitchY, const btScalar& rollX)
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{
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btScalar halfYaw = btScalar(yawZ) * btScalar(0.5);
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btScalar halfPitch = btScalar(pitchY) * btScalar(0.5);
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btScalar halfRoll = btScalar(rollX) * btScalar(0.5);
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btScalar cosYaw = btCos(halfYaw);
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btScalar sinYaw = btSin(halfYaw);
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btScalar cosPitch = btCos(halfPitch);
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btScalar sinPitch = btSin(halfPitch);
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btScalar cosRoll = btCos(halfRoll);
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btScalar sinRoll = btSin(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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}
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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(btScalar& yawZ, btScalar& pitchY, btScalar& rollX) const
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{
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btScalar squ;
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btScalar sqx;
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btScalar sqy;
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btScalar sqz;
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btScalar 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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sarg = btScalar(-2.) * (m_floats[0] * m_floats[2] - m_floats[3] * m_floats[1]);
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// If the pitch angle is PI/2 or -PI/2, we can only compute
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// the sum roll + yaw. However, any combination that gives
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// the right sum will produce the correct orientation, so we
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// set rollX = 0 and compute yawZ.
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if (sarg <= -btScalar(0.99999))
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{
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pitchY = btScalar(-0.5) * SIMD_PI;
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rollX = 0;
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yawZ = btScalar(2) * btAtan2(m_floats[0], -m_floats[1]);
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}
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else if (sarg >= btScalar(0.99999))
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{
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pitchY = btScalar(0.5) * SIMD_PI;
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rollX = 0;
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yawZ = btScalar(2) * btAtan2(-m_floats[0], m_floats[1]);
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}
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else
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{
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pitchY = btAsin(sarg);
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rollX = btAtan2(2 * (m_floats[1] * m_floats[2] + m_floats[3] * m_floats[0]), squ - sqx - sqy + sqz);
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yawZ = btAtan2(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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}
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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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SIMD_FORCE_INLINE btQuaternion& operator+=(const btQuaternion& q)
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{
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#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
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mVec128 = _mm_add_ps(mVec128, q.mVec128);
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#elif defined(BT_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.x();
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m_floats[1] += q.y();
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m_floats[2] += q.z();
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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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btQuaternion& operator-=(const btQuaternion& q)
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{
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#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
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mVec128 = _mm_sub_ps(mVec128, q.mVec128);
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#elif defined(BT_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.x();
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m_floats[1] -= q.y();
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m_floats[2] -= q.z();
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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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btQuaternion& operator*=(const btScalar& s)
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{
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#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
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__m128 vs = _mm_load_ss(&s); // (S 0 0 0)
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vs = bt_pshufd_ps(vs, 0); // (S S S S)
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mVec128 = _mm_mul_ps(mVec128, vs);
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#elif defined(BT_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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btQuaternion& operator*=(const btQuaternion& q)
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{
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#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
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__m128 vQ2 = q.get128();
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__m128 A1 = bt_pshufd_ps(mVec128, BT_SHUFFLE(0, 1, 2, 0));
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__m128 B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0));
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A1 = A1 * B1;
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__m128 A2 = bt_pshufd_ps(mVec128, BT_SHUFFLE(1, 2, 0, 1));
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__m128 B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));
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A2 = A2 * B2;
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B1 = bt_pshufd_ps(mVec128, BT_SHUFFLE(2, 0, 1, 2));
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B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));
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B1 = B1 * B2; // A3 *= B3
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mVec128 = bt_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, vPPPM); // change sign of the last element
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mVec128 = mVec128 + A1; // AB03 + AB12
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#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
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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.x() + m_floats[0] * q.m_floats[3] + m_floats[1] * q.z() - m_floats[2] * q.y(),
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m_floats[3] * q.y() + m_floats[1] * q.m_floats[3] + m_floats[2] * q.x() - m_floats[0] * q.z(),
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m_floats[3] * q.z() + m_floats[2] * q.m_floats[3] + m_floats[0] * q.y() - m_floats[1] * q.x(),
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m_floats[3] * q.m_floats[3] - m_floats[0] * q.x() - m_floats[1] * q.y() - m_floats[2] * q.z());
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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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btScalar dot(const btQuaternion& q) const
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{
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#if defined BT_USE_SIMD_VECTOR3 && defined(BT_USE_SSE_IN_API) && defined(BT_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(BT_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.x() +
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m_floats[1] * q.y() +
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m_floats[2] * q.z() +
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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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btScalar 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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btScalar length() const
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{
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return btSqrt(length2());
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}
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btQuaternion& safeNormalize()
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{
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btScalar l2 = length2();
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if (l2 > SIMD_EPSILON)
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{
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normalize();
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}
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return *this;
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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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btQuaternion& normalize()
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{
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#if defined(BT_USE_SSE_IN_API) && defined(BT_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(vOnes, vd);
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vd = bt_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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SIMD_FORCE_INLINE btQuaternion
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operator*(const btScalar& s) const
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
__m128 vs = _mm_load_ss(&s); // (S 0 0 0)
|
|
vs = bt_pshufd_ps(vs, 0x00); // (S S S S)
|
|
|
|
return btQuaternion(_mm_mul_ps(mVec128, vs));
|
|
#elif defined(BT_USE_NEON)
|
|
return btQuaternion(vmulq_n_f32(mVec128, s));
|
|
#else
|
|
return btQuaternion(x() * s, y() * s, z() * s, m_floats[3] * s);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return an inversely scaled versionof this quaternion
|
|
* @param s The inverse scale factor */
|
|
btQuaternion operator/(const btScalar& s) const
|
|
{
|
|
btAssert(s != btScalar(0.0));
|
|
return *this * (btScalar(1.0) / s);
|
|
}
|
|
|
|
/**@brief Inversely scale this quaternion
|
|
* @param s The scale factor */
|
|
btQuaternion& operator/=(const btScalar& s)
|
|
{
|
|
btAssert(s != btScalar(0.0));
|
|
return *this *= btScalar(1.0) / s;
|
|
}
|
|
|
|
/**@brief Return a normalized version of this quaternion */
|
|
btQuaternion normalized() const
|
|
{
|
|
return *this / length();
|
|
}
|
|
/**@brief Return the ***half*** angle between this quaternion and the other
|
|
* @param q The other quaternion */
|
|
btScalar angle(const btQuaternion& q) const
|
|
{
|
|
btScalar s = btSqrt(length2() * q.length2());
|
|
btAssert(s != btScalar(0.0));
|
|
return btAcos(dot(q) / s);
|
|
}
|
|
|
|
/**@brief Return the angle between this quaternion and the other along the shortest path
|
|
* @param q The other quaternion */
|
|
btScalar angleShortestPath(const btQuaternion& q) const
|
|
{
|
|
btScalar s = btSqrt(length2() * q.length2());
|
|
btAssert(s != btScalar(0.0));
|
|
if (dot(q) < 0) // Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
|
|
return btAcos(dot(-q) / s) * btScalar(2.0);
|
|
else
|
|
return btAcos(dot(q) / s) * btScalar(2.0);
|
|
}
|
|
|
|
/**@brief Return the angle [0, 2Pi] of rotation represented by this quaternion */
|
|
btScalar getAngle() const
|
|
{
|
|
btScalar s = btScalar(2.) * btAcos(m_floats[3]);
|
|
return s;
|
|
}
|
|
|
|
/**@brief Return the angle [0, Pi] of rotation represented by this quaternion along the shortest path */
|
|
btScalar getAngleShortestPath() const
|
|
{
|
|
btScalar s;
|
|
if (m_floats[3] >= 0)
|
|
s = btScalar(2.) * btAcos(m_floats[3]);
|
|
else
|
|
s = btScalar(2.) * btAcos(-m_floats[3]);
|
|
return s;
|
|
}
|
|
|
|
/**@brief Return the axis of the rotation represented by this quaternion */
|
|
btVector3 getAxis() const
|
|
{
|
|
btScalar s_squared = 1.f - m_floats[3] * m_floats[3];
|
|
|
|
if (s_squared < btScalar(10.) * SIMD_EPSILON) //Check for divide by zero
|
|
return btVector3(1.0, 0.0, 0.0); // Arbitrary
|
|
btScalar s = 1.f / btSqrt(s_squared);
|
|
return btVector3(m_floats[0] * s, m_floats[1] * s, m_floats[2] * s);
|
|
}
|
|
|
|
/**@brief Return the inverse of this quaternion */
|
|
btQuaternion inverse() const
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
return btQuaternion(_mm_xor_ps(mVec128, vQInv));
|
|
#elif defined(BT_USE_NEON)
|
|
return btQuaternion((btSimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)vQInv));
|
|
#else
|
|
return btQuaternion(-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 */
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
operator+(const btQuaternion& q2) const
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
return btQuaternion(_mm_add_ps(mVec128, q2.mVec128));
|
|
#elif defined(BT_USE_NEON)
|
|
return btQuaternion(vaddq_f32(mVec128, q2.mVec128));
|
|
#else
|
|
const btQuaternion& q1 = *this;
|
|
return btQuaternion(q1.x() + q2.x(), q1.y() + q2.y(), q1.z() + q2.z(), q1.m_floats[3] + q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return the difference between this quaternion and the other
|
|
* @param q2 The other quaternion */
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
operator-(const btQuaternion& q2) const
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
return btQuaternion(_mm_sub_ps(mVec128, q2.mVec128));
|
|
#elif defined(BT_USE_NEON)
|
|
return btQuaternion(vsubq_f32(mVec128, q2.mVec128));
|
|
#else
|
|
const btQuaternion& q1 = *this;
|
|
return btQuaternion(q1.x() - q2.x(), q1.y() - q2.y(), q1.z() - q2.z(), q1.m_floats[3] - q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
|
|
/**@brief Return the negative of this quaternion
|
|
* This simply negates each element */
|
|
SIMD_FORCE_INLINE btQuaternion operator-() const
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
return btQuaternion(_mm_xor_ps(mVec128, btvMzeroMask));
|
|
#elif defined(BT_USE_NEON)
|
|
return btQuaternion((btSimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)btvMzeroMask));
|
|
#else
|
|
const btQuaternion& q2 = *this;
|
|
return btQuaternion(-q2.x(), -q2.y(), -q2.z(), -q2.m_floats[3]);
|
|
#endif
|
|
}
|
|
/**@todo document this and it's use */
|
|
SIMD_FORCE_INLINE btQuaternion farthest(const btQuaternion& qd) const
|
|
{
|
|
btQuaternion 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 */
|
|
SIMD_FORCE_INLINE btQuaternion nearest(const btQuaternion& qd) const
|
|
{
|
|
btQuaternion 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. */
|
|
btQuaternion slerp(const btQuaternion& q, const btScalar& t) const
|
|
{
|
|
const btScalar magnitude = btSqrt(length2() * q.length2());
|
|
btAssert(magnitude > btScalar(0));
|
|
|
|
const btScalar product = dot(q) / magnitude;
|
|
const btScalar absproduct = btFabs(product);
|
|
|
|
if (absproduct < btScalar(1.0 - SIMD_EPSILON))
|
|
{
|
|
// Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
|
|
const btScalar theta = btAcos(absproduct);
|
|
const btScalar d = btSin(theta);
|
|
btAssert(d > btScalar(0));
|
|
|
|
const btScalar sign = (product < 0) ? btScalar(-1) : btScalar(1);
|
|
const btScalar s0 = btSin((btScalar(1.0) - t) * theta) / d;
|
|
const btScalar s1 = btSin(sign * t * theta) / d;
|
|
|
|
return btQuaternion(
|
|
(m_floats[0] * s0 + q.x() * s1),
|
|
(m_floats[1] * s0 + q.y() * s1),
|
|
(m_floats[2] * s0 + q.z() * s1),
|
|
(m_floats[3] * s0 + q.w() * s1));
|
|
}
|
|
else
|
|
{
|
|
return *this;
|
|
}
|
|
}
|
|
|
|
static const btQuaternion& getIdentity()
|
|
{
|
|
static const btQuaternion identityQuat(btScalar(0.), btScalar(0.), btScalar(0.), btScalar(1.));
|
|
return identityQuat;
|
|
}
|
|
|
|
SIMD_FORCE_INLINE const btScalar& getW() const { return m_floats[3]; }
|
|
|
|
SIMD_FORCE_INLINE void serialize(struct btQuaternionData& dataOut) const;
|
|
|
|
SIMD_FORCE_INLINE void deSerialize(const struct btQuaternionFloatData& dataIn);
|
|
|
|
SIMD_FORCE_INLINE void deSerialize(const struct btQuaternionDoubleData& dataIn);
|
|
|
|
SIMD_FORCE_INLINE void serializeFloat(struct btQuaternionFloatData& dataOut) const;
|
|
|
|
SIMD_FORCE_INLINE void deSerializeFloat(const struct btQuaternionFloatData& dataIn);
|
|
|
|
SIMD_FORCE_INLINE void serializeDouble(struct btQuaternionDoubleData& dataOut) const;
|
|
|
|
SIMD_FORCE_INLINE void deSerializeDouble(const struct btQuaternionDoubleData& dataIn);
|
|
};
|
|
|
|
/**@brief Return the product of two quaternions */
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
operator*(const btQuaternion& q1, const btQuaternion& q2)
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
__m128 vQ1 = q1.get128();
|
|
__m128 vQ2 = q2.get128();
|
|
__m128 A0, A1, B1, A2, B2;
|
|
|
|
A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(0, 1, 2, 0)); // X Y z x // vtrn
|
|
B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0)); // W W W X // vdup vext
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1)); // Y Z X Y // vext
|
|
B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1)); // z x Y Y // vtrn vdup
|
|
|
|
A2 = A2 * B2;
|
|
|
|
B1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2)); // z x Y Z // vtrn vext
|
|
B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2)); // Y Z x z // vext vtrn
|
|
|
|
B1 = B1 * B2; // A3 *= B3
|
|
|
|
A0 = bt_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, vPPPM); // change sign of the last element
|
|
A0 = A0 + A1; // AB03 + AB12
|
|
|
|
return btQuaternion(A0);
|
|
|
|
#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
|
|
A0 = vaddq_f32(A0, A1); // AB03 + AB12
|
|
|
|
return btQuaternion(A0);
|
|
|
|
#else
|
|
return btQuaternion(
|
|
q1.w() * q2.x() + q1.x() * q2.w() + q1.y() * q2.z() - q1.z() * q2.y(),
|
|
q1.w() * q2.y() + q1.y() * q2.w() + q1.z() * q2.x() - q1.x() * q2.z(),
|
|
q1.w() * q2.z() + q1.z() * q2.w() + q1.x() * q2.y() - q1.y() * q2.x(),
|
|
q1.w() * q2.w() - q1.x() * q2.x() - q1.y() * q2.y() - q1.z() * q2.z());
|
|
#endif
|
|
}
|
|
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
operator*(const btQuaternion& q, const btVector3& w)
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
__m128 vQ1 = q.get128();
|
|
__m128 vQ2 = w.get128();
|
|
__m128 A1, B1, A2, B2, A3, B3;
|
|
|
|
A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(3, 3, 3, 0));
|
|
B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(0, 1, 2, 0));
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1));
|
|
B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));
|
|
|
|
A2 = A2 * B2;
|
|
|
|
A3 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2));
|
|
B3 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));
|
|
|
|
A3 = A3 * B3; // A3 *= B3
|
|
|
|
A1 = A1 + A2; // AB12
|
|
A1 = _mm_xor_ps(A1, vPPPM); // change sign of the last element
|
|
A1 = A1 - A3; // AB123 = AB12 - AB3
|
|
|
|
return btQuaternion(A1);
|
|
|
|
#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
|
|
|
|
A1 = vsubq_f32(A1, A3); // AB123 = AB12 - AB3
|
|
|
|
return btQuaternion(A1);
|
|
|
|
#else
|
|
return btQuaternion(
|
|
q.w() * w.x() + q.y() * w.z() - q.z() * w.y(),
|
|
q.w() * w.y() + q.z() * w.x() - q.x() * w.z(),
|
|
q.w() * w.z() + q.x() * w.y() - q.y() * w.x(),
|
|
-q.x() * w.x() - q.y() * w.y() - q.z() * w.z());
|
|
#endif
|
|
}
|
|
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
operator*(const btVector3& w, const btQuaternion& q)
|
|
{
|
|
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
__m128 vQ1 = w.get128();
|
|
__m128 vQ2 = q.get128();
|
|
__m128 A1, B1, A2, B2, A3, B3;
|
|
|
|
A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(0, 1, 2, 0)); // X Y z x
|
|
B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0)); // W W W X
|
|
|
|
A1 = A1 * B1;
|
|
|
|
A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1));
|
|
B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));
|
|
|
|
A2 = A2 * B2;
|
|
|
|
A3 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2));
|
|
B3 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));
|
|
|
|
A3 = A3 * B3; // A3 *= B3
|
|
|
|
A1 = A1 + A2; // AB12
|
|
A1 = _mm_xor_ps(A1, vPPPM); // change sign of the last element
|
|
A1 = A1 - A3; // AB123 = AB12 - AB3
|
|
|
|
return btQuaternion(A1);
|
|
|
|
#elif defined(BT_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;
|
|
|
|
{
|
|
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
|
|
|
|
A1 = vaddq_f32(A1, A2); // AB12 = AB1 + AB2
|
|
|
|
// change the sign of the last element
|
|
A1 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
|
|
|
|
A1 = vsubq_f32(A1, A3); // AB123 = AB12 - AB3
|
|
|
|
return btQuaternion(A1);
|
|
|
|
#else
|
|
return btQuaternion(
|
|
+w.x() * q.w() + w.y() * q.z() - w.z() * q.y(),
|
|
+w.y() * q.w() + w.z() * q.x() - w.x() * q.z(),
|
|
+w.z() * q.w() + w.x() * q.y() - w.y() * q.x(),
|
|
-w.x() * q.x() - w.y() * q.y() - w.z() * q.z());
|
|
#endif
|
|
}
|
|
|
|
/**@brief Calculate the dot product between two quaternions */
|
|
SIMD_FORCE_INLINE btScalar
|
|
dot(const btQuaternion& q1, const btQuaternion& q2)
|
|
{
|
|
return q1.dot(q2);
|
|
}
|
|
|
|
/**@brief Return the length of a quaternion */
|
|
SIMD_FORCE_INLINE btScalar
|
|
length(const btQuaternion& q)
|
|
{
|
|
return q.length();
|
|
}
|
|
|
|
/**@brief Return the angle between two quaternions*/
|
|
SIMD_FORCE_INLINE btScalar
|
|
btAngle(const btQuaternion& q1, const btQuaternion& q2)
|
|
{
|
|
return q1.angle(q2);
|
|
}
|
|
|
|
/**@brief Return the inverse of a quaternion*/
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
inverse(const btQuaternion& 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. */
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
slerp(const btQuaternion& q1, const btQuaternion& q2, const btScalar& t)
|
|
{
|
|
return q1.slerp(q2, t);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE btVector3
|
|
quatRotate(const btQuaternion& rotation, const btVector3& v)
|
|
{
|
|
btQuaternion q = rotation * v;
|
|
q *= rotation.inverse();
|
|
#if defined BT_USE_SIMD_VECTOR3 && defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
|
|
return btVector3(_mm_and_ps(q.get128(), btvFFF0fMask));
|
|
#elif defined(BT_USE_NEON)
|
|
return btVector3((float32x4_t)vandq_s32((int32x4_t)q.get128(), btvFFF0Mask));
|
|
#else
|
|
return btVector3(q.getX(), q.getY(), q.getZ());
|
|
#endif
|
|
}
|
|
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
shortestArcQuat(const btVector3& v0, const btVector3& v1) // Game Programming Gems 2.10. make sure v0,v1 are normalized
|
|
{
|
|
btVector3 c = v0.cross(v1);
|
|
btScalar d = v0.dot(v1);
|
|
|
|
if (d < -1.0 + SIMD_EPSILON)
|
|
{
|
|
btVector3 n, unused;
|
|
btPlaneSpace1(v0, n, unused);
|
|
return btQuaternion(n.x(), n.y(), n.z(), 0.0f); // just pick any vector that is orthogonal to v0
|
|
}
|
|
|
|
btScalar s = btSqrt((1.0f + d) * 2.0f);
|
|
btScalar rs = 1.0f / s;
|
|
|
|
return btQuaternion(c.getX() * rs, c.getY() * rs, c.getZ() * rs, s * 0.5f);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE btQuaternion
|
|
shortestArcQuatNormalize2(btVector3& v0, btVector3& v1)
|
|
{
|
|
v0.normalize();
|
|
v1.normalize();
|
|
return shortestArcQuat(v0, v1);
|
|
}
|
|
|
|
struct btQuaternionFloatData
|
|
{
|
|
float m_floats[4];
|
|
};
|
|
|
|
struct btQuaternionDoubleData
|
|
{
|
|
double m_floats[4];
|
|
};
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::serializeFloat(struct btQuaternionFloatData& dataOut) const
|
|
{
|
|
///could also do a memcpy, check if it is worth it
|
|
for (int i = 0; i < 4; i++)
|
|
dataOut.m_floats[i] = float(m_floats[i]);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::deSerializeFloat(const struct btQuaternionFloatData& dataIn)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
m_floats[i] = btScalar(dataIn.m_floats[i]);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::serializeDouble(struct btQuaternionDoubleData& dataOut) const
|
|
{
|
|
///could also do a memcpy, check if it is worth it
|
|
for (int i = 0; i < 4; i++)
|
|
dataOut.m_floats[i] = double(m_floats[i]);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::deSerializeDouble(const struct btQuaternionDoubleData& dataIn)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
m_floats[i] = btScalar(dataIn.m_floats[i]);
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::serialize(struct btQuaternionData& dataOut) const
|
|
{
|
|
///could also do a memcpy, check if it is worth it
|
|
for (int i = 0; i < 4; i++)
|
|
dataOut.m_floats[i] = m_floats[i];
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::deSerialize(const struct btQuaternionFloatData& dataIn)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
m_floats[i] = (btScalar)dataIn.m_floats[i];
|
|
}
|
|
|
|
SIMD_FORCE_INLINE void btQuaternion::deSerialize(const struct btQuaternionDoubleData& dataIn)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
m_floats[i] = (btScalar)dataIn.m_floats[i];
|
|
}
|
|
|
|
#endif //BT_SIMD__QUATERNION_H_
|