Revision control
++ // Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
++ // Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
++ // SPDX-FileCopyrightText: Copyright (c) 2008-2026 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
++ // SPDX-License-Identifier: Apache-2.0
++
++ #ifndef PX_QUAT_H
++ #define PX_QUAT_H
++
++ #include "foundation/PxVec3.h"
++ #if !PX_DOXYGEN
++ namespace physx
++ {
++ #endif
++
++ template<class Type> class PxMat33T;
++
++ /**
++ \brief This is a quaternion class. For more information on quaternion mathematics
++ consult a mathematics source on complex numbers.
++ */
++
++ template<class Type>
++ class PxQuatT
++ {
++ public:
++
++ /**
++ \brief Default constructor, does not do any initialization.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT()
++ {
++ }
++
++ //! identity constructor
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(PxIDENTITY) : x(Type(0.0)), y(Type(0.0)), z(Type(0.0)), w(Type(1.0))
++ {
++ }
++
++ /**
++ \brief Constructor from a scalar: sets the real part w to the scalar value, and the imaginary parts (x,y,z) to zero
++ */
++ explicit PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(Type r) : x(Type(0.0)), y(Type(0.0)), z(Type(0.0)), w(r)
++ {
++ }
++
++ /**
++ \brief Constructor. Take note of the order of the elements!
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(Type nx, Type ny, Type nz, Type nw) : x(nx), y(ny), z(nz), w(nw)
++ {
++ }
++
++ /**
++ \brief Creates from angle-axis representation.
++
++ Axis must be normalized!
++
++ Angle is in radians!
++
++ <b>Unit:</b> Radians
++ */
++ PX_CUDA_CALLABLE PX_INLINE PxQuatT(Type angleRadians, const PxVec3T<Type>& unitAxis)
++ {
++ PX_ASSERT(PxAbs(Type(1.0) - unitAxis.magnitude()) < Type(1e-3));
++ const Type a = angleRadians * Type(0.5);
++
++ Type s;
++ PxSinCos(a, s, w);
++ x = unitAxis.x * s;
++ y = unitAxis.y * s;
++ z = unitAxis.z * s;
++ }
++
++ /**
++ \brief Copy ctor.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(const PxQuatT& v) : x(v.x), y(v.y), z(v.z), w(v.w)
++ {
++ }
++
++ /**
++ \brief Creates from orientation matrix.
++
++ \param[in] m Rotation matrix to extract quaternion from.
++ */
++ PX_CUDA_CALLABLE PX_INLINE explicit PxQuatT(const PxMat33T<Type>& m); /* defined in PxMat33.h */
++
++ /**
++ \brief returns true if quat is identity
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE bool isIdentity() const
++ {
++ return x==Type(0.0) && y==Type(0.0) && z==Type(0.0) && w==Type(1.0);
++ }
++
++ /**
++ \brief returns true if all elements are finite (not NAN or INF, etc.)
++ */
++ PX_CUDA_CALLABLE bool isFinite() const
++ {
++ return PxIsFinite(x) && PxIsFinite(y) && PxIsFinite(z) && PxIsFinite(w);
++ }
++
++ /**
++ \brief returns true if finite and magnitude is close to unit
++ */
++ PX_CUDA_CALLABLE bool isUnit() const
++ {
++ const Type unitTolerance = Type(1e-3);
++ return isFinite() && PxAbs(magnitude() - Type(1.0)) < unitTolerance;
++ }
++
++ /**
++ \brief returns true if finite and magnitude is reasonably close to unit to allow for some accumulation of error vs
++ isValid
++ */
++ PX_CUDA_CALLABLE bool isSane() const
++ {
++ const Type unitTolerance = Type(1e-2);
++ return isFinite() && PxAbs(magnitude() - Type(1.0)) < unitTolerance;
++ }
++
++ /**
++ \brief returns true if the two quaternions are exactly equal
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE bool operator==(const PxQuatT& q) const
++ {
++ return x == q.x && y == q.y && z == q.z && w == q.w;
++ }
++
++ /**
++ \brief converts this quaternion to angle-axis representation
++ */
++ PX_CUDA_CALLABLE PX_INLINE void toRadiansAndUnitAxis(Type& angle, PxVec3T<Type>& axis) const
++ {
++ const Type quatEpsilon = Type(1.0e-8);
++ const Type s2 = x * x + y * y + z * z;
++ if(s2 < quatEpsilon * quatEpsilon) // can't extract a sensible axis
++ {
++ angle = Type(0.0);
++ axis = PxVec3T<Type>(Type(1.0), Type(0.0), Type(0.0));
++ }
++ else
++ {
++ const Type s = PxRecipSqrt(s2);
++ axis = PxVec3T<Type>(x, y, z) * s;
++ angle = PxAbs(w) < quatEpsilon ? Type(PxPi) : PxAtan2(s2 * s, w) * Type(2.0);
++ }
++ }
++
++ /**
++ \brief Gets the angle between this quat and the identity quaternion.
++
++ <b>Unit:</b> Radians
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type getAngle() const
++ {
++ return PxAcos(w) * Type(2.0);
++ }
++
++ /**
++ \brief Gets the angle between this quat and the argument
++
++ <b>Unit:</b> Radians
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type getAngle(const PxQuatT& q) const
++ {
++ return PxAcos(dot(q)) * Type(2.0);
++ }
++
++ /**
++ \brief This is the squared 4D vector length, should be 1 for unit quaternions.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type magnitudeSquared() const
++ {
++ return x * x + y * y + z * z + w * w;
++ }
++
++ /**
++ \brief returns the scalar product of this and other.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type dot(const PxQuatT& v) const
++ {
++ return x * v.x + y * v.y + z * v.z + w * v.w;
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT getNormalized() const
++ {
++ const Type s = Type(1.0) / magnitude();
++ return PxQuatT(x * s, y * s, z * s, w * s);
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type magnitude() const
++ {
++ return PxSqrt(magnitudeSquared());
++ }
++
++ // modifiers:
++ /**
++ \brief maps to the closest unit quaternion.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE Type normalize() // convert this PxQuatT to a unit quaternion
++ {
++ const Type mag = magnitude();
++ if(mag != Type(0.0))
++ {
++ const Type imag = Type(1.0) / mag;
++
++ x *= imag;
++ y *= imag;
++ z *= imag;
++ w *= imag;
++ }
++ return mag;
++ }
++
++ /*
++ \brief returns the conjugate.
++
++ \note for unit quaternions, this is the inverse.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT getConjugate() const
++ {
++ return PxQuatT(-x, -y, -z, w);
++ }
++
++ /*
++ \brief returns imaginary part.
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getImaginaryPart() const
++ {
++ return PxVec3T<Type>(x, y, z);
++ }
++
++ /** brief computes rotation of x-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector0() const
++ {
++ const Type x2 = x * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((w * w2) - Type(1.0) + x * x2, (z * w2) + y * x2, (-y * w2) + z * x2);
++ }
++
++ /** brief computes rotation of y-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector1() const
++ {
++ const Type y2 = y * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((-z * w2) + x * y2, (w * w2) - Type(1.0) + y * y2, (x * w2) + z * y2);
++ }
++
++ /** brief computes rotation of z-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector2() const
++ {
++ const Type z2 = z * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((y * w2) + x * z2, (-x * w2) + y * z2, (w * w2) - Type(1.0) + z * z2);
++ }
++
++ /**
++ rotates passed vec by this (assumed unitary)
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> rotate(const PxVec3T<Type>& v) const
++ {
++ const Type vx = Type(2.0) * v.x;
++ const Type vy = Type(2.0) * v.y;
++ const Type vz = Type(2.0) * v.z;
++ const Type w2 = w * w - Type(0.5);
++ const Type dot2 = (x * vx + y * vy + z * vz);
++ return PxVec3T<Type>((vx * w2 + (y * vz - z * vy) * w + x * dot2), (vy * w2 + (z * vx - x * vz) * w + y * dot2),
++ (vz * w2 + (x * vy - y * vx) * w + z * dot2));
++ }
++
++ /** \brief computes inverse rotation of x-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getInvBasisVector0() const
++ {
++ const Type x2 = x * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((w * w2) - Type(1.0) + x * x2, (-z * w2) + y * x2, (y * w2) + z * x2);
++ }
++
++ /** \brief computes the inverse rotation of the y-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getInvBasisVector1() const
++ {
++ const Type y2 = y * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((z * w2) + x * y2, (w * w2) - Type(1.0) + y * y2, (-x * w2) + z * y2);
++ }
++
++ /** \brief computes the inverse rotation of the z-axis */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getInvBasisVector2() const
++ {
++ const Type z2 = z * Type(2.0);
++ const Type w2 = w * Type(2.0);
++ return PxVec3T<Type>((-y * w2) + x * z2, (x * w2) + y * z2, (w * w2) - Type(1.0) + z * z2);
++ }
++
++ /**
++ inverse rotates passed vec by this (assumed unitary)
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> rotateInv(const PxVec3T<Type>& v) const
++ {
++ const Type vx = Type(2.0) * v.x;
++ const Type vy = Type(2.0) * v.y;
++ const Type vz = Type(2.0) * v.z;
++ const Type w2 = w * w - Type(0.5);
++ const Type dot2 = (x * vx + y * vy + z * vz);
++ return PxVec3T<Type>((vx * w2 - (y * vz - z * vy) * w + x * dot2), (vy * w2 - (z * vx - x * vz) * w + y * dot2),
++ (vz * w2 - (x * vy - y * vx) * w + z * dot2));
++ }
++
++ /**
++ \brief Assignment operator
++ */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator=(const PxQuatT& p)
++ {
++ x = p.x;
++ y = p.y;
++ z = p.z;
++ w = p.w;
++ return *this;
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator*=(const PxQuatT& q)
++ {
++ const Type tx = w * q.x + q.w * x + y * q.z - q.y * z;
++ const Type ty = w * q.y + q.w * y + z * q.x - q.z * x;
++ const Type tz = w * q.z + q.w * z + x * q.y - q.x * y;
++
++ w = w * q.w - q.x * x - y * q.y - q.z * z;
++ x = tx;
++ y = ty;
++ z = tz;
++ return *this;
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator+=(const PxQuatT& q)
++ {
++ x += q.x;
++ y += q.y;
++ z += q.z;
++ w += q.w;
++ return *this;
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator-=(const PxQuatT& q)
++ {
++ x -= q.x;
++ y -= q.y;
++ z -= q.z;
++ w -= q.w;
++ return *this;
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator*=(const Type s)
++ {
++ x *= s;
++ y *= s;
++ z *= s;
++ w *= s;
++ return *this;
++ }
++
++ /** quaternion multiplication */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator*(const PxQuatT& q) const
++ {
++ return PxQuatT(w * q.x + q.w * x + y * q.z - q.y * z, w * q.y + q.w * y + z * q.x - q.z * x,
++ w * q.z + q.w * z + x * q.y - q.x * y, w * q.w - x * q.x - y * q.y - z * q.z);
++ }
++
++ /** quaternion addition */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator+(const PxQuatT& q) const
++ {
++ return PxQuatT(x + q.x, y + q.y, z + q.z, w + q.w);
++ }
++
++ /** quaternion subtraction */
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator-() const
++ {
++ return PxQuatT(-x, -y, -z, -w);
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator-(const PxQuatT& q) const
++ {
++ return PxQuatT(x - q.x, y - q.y, z - q.z, w - q.w);
++ }
++
++ PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator*(Type r) const
++ {
++ return PxQuatT(x * r, y * r, z * r, w * r);
++ }
++
++ /** the quaternion elements */
++ Type x, y, z, w;
++ };
++
++ typedef PxQuatT<float> PxQuat;
++ typedef PxQuatT<double> PxQuatd;
++
++ #if !PX_DOXYGEN
++ } // namespace physx
++ #endif
++
++ #endif
++