407 lines
11 KiB
C
407 lines
11 KiB
C
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions
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// are met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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// * Neither the name of NVIDIA CORPORATION nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY
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// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Copyright (c) 2008-2023 NVIDIA Corporation. All rights reserved.
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// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
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// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
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#ifndef PX_QUAT_H
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#define PX_QUAT_H
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/** \addtogroup foundation
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@{
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*/
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#include "foundation/PxVec3.h"
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#if !PX_DOXYGEN
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namespace physx
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{
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#endif
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/**
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\brief This is a quaternion class. For more information on quaternion mathematics
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consult a mathematics source on complex numbers.
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*/
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template<class Type>
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class PxQuatT
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{
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public:
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/**
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\brief Default constructor, does not do any initialization.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT()
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{
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}
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//! identity constructor
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(PxIDENTITY) : x(Type(0.0)), y(Type(0.0)), z(Type(0.0)), w(Type(1.0))
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{
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}
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/**
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\brief Constructor from a scalar: sets the real part w to the scalar value, and the imaginary parts (x,y,z) to zero
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*/
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explicit PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(Type r) : x(Type(0.0)), y(Type(0.0)), z(Type(0.0)), w(r)
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{
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}
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/**
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\brief Constructor. Take note of the order of the elements!
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(Type nx, Type ny, Type nz, Type nw) : x(nx), y(ny), z(nz), w(nw)
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{
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}
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/**
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\brief Creates from angle-axis representation.
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Axis must be normalized!
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Angle is in radians!
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<b>Unit:</b> Radians
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*/
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PX_CUDA_CALLABLE PX_INLINE PxQuatT(Type angleRadians, const PxVec3T<Type>& unitAxis)
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{
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PX_ASSERT(PxAbs(Type(1.0) - unitAxis.magnitude()) < Type(1e-3));
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const Type a = angleRadians * Type(0.5);
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Type s;
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PxSinCos(a, s, w);
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x = unitAxis.x * s;
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y = unitAxis.y * s;
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z = unitAxis.z * s;
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}
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/**
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\brief Copy ctor.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT(const PxQuatT& v) : x(v.x), y(v.y), z(v.z), w(v.w)
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{
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}
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/**
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\brief Creates from orientation matrix.
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\param[in] m Rotation matrix to extract quaternion from.
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*/
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PX_CUDA_CALLABLE PX_INLINE explicit PxQuatT(const PxMat33T<Type>& m); /* defined in PxMat33.h */
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/**
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\brief returns true if quat is identity
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE bool isIdentity() const
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{
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return x==Type(0.0) && y==Type(0.0) && z==Type(0.0) && w==Type(1.0);
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}
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/**
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\brief returns true if all elements are finite (not NAN or INF, etc.)
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*/
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PX_CUDA_CALLABLE bool isFinite() const
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{
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return PxIsFinite(x) && PxIsFinite(y) && PxIsFinite(z) && PxIsFinite(w);
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}
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/**
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\brief returns true if finite and magnitude is close to unit
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*/
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PX_CUDA_CALLABLE bool isUnit() const
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{
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const Type unitTolerance = Type(1e-3);
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return isFinite() && PxAbs(magnitude() - Type(1.0)) < unitTolerance;
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}
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/**
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\brief returns true if finite and magnitude is reasonably close to unit to allow for some accumulation of error vs
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isValid
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*/
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PX_CUDA_CALLABLE bool isSane() const
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{
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const Type unitTolerance = Type(1e-2);
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return isFinite() && PxAbs(magnitude() - Type(1.0)) < unitTolerance;
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}
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/**
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\brief returns true if the two quaternions are exactly equal
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE bool operator==(const PxQuatT& q) const
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{
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return x == q.x && y == q.y && z == q.z && w == q.w;
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}
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/**
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\brief converts this quaternion to angle-axis representation
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*/
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PX_CUDA_CALLABLE PX_INLINE void toRadiansAndUnitAxis(Type& angle, PxVec3T<Type>& axis) const
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{
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const Type quatEpsilon = Type(1.0e-8);
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const Type s2 = x * x + y * y + z * z;
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if(s2 < quatEpsilon * quatEpsilon) // can't extract a sensible axis
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{
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angle = Type(0.0);
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axis = PxVec3T<Type>(Type(1.0), Type(0.0), Type(0.0));
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}
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else
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{
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const Type s = PxRecipSqrt(s2);
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axis = PxVec3T<Type>(x, y, z) * s;
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angle = PxAbs(w) < quatEpsilon ? Type(PxPi) : PxAtan2(s2 * s, w) * Type(2.0);
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}
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}
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/**
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\brief Gets the angle between this quat and the identity quaternion.
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<b>Unit:</b> Radians
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type getAngle() const
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{
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return PxAcos(w) * Type(2.0);
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}
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/**
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\brief Gets the angle between this quat and the argument
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<b>Unit:</b> Radians
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type getAngle(const PxQuatT& q) const
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{
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return PxAcos(dot(q)) * Type(2.0);
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}
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/**
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\brief This is the squared 4D vector length, should be 1 for unit quaternions.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type magnitudeSquared() const
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{
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return x * x + y * y + z * z + w * w;
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}
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/**
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\brief returns the scalar product of this and other.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type dot(const PxQuatT& v) const
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{
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return x * v.x + y * v.y + z * v.z + w * v.w;
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT getNormalized() const
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{
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const Type s = Type(1.0) / magnitude();
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return PxQuatT(x * s, y * s, z * s, w * s);
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type magnitude() const
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{
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return PxSqrt(magnitudeSquared());
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}
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// modifiers:
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/**
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\brief maps to the closest unit quaternion.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE Type normalize() // convert this PxQuatT to a unit quaternion
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{
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const Type mag = magnitude();
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if(mag != Type(0.0))
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{
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const Type imag = Type(1.0) / mag;
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x *= imag;
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y *= imag;
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z *= imag;
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w *= imag;
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}
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return mag;
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}
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/*
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\brief returns the conjugate.
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\note for unit quaternions, this is the inverse.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT getConjugate() const
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{
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return PxQuatT(-x, -y, -z, w);
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}
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/*
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\brief returns imaginary part.
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getImaginaryPart() const
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{
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return PxVec3T<Type>(x, y, z);
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}
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/** brief computes rotation of x-axis */
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector0() const
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{
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const Type x2 = x * Type(2.0);
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const Type w2 = w * Type(2.0);
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return PxVec3T<Type>((w * w2) - Type(1.0) + x * x2, (z * w2) + y * x2, (-y * w2) + z * x2);
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}
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/** brief computes rotation of y-axis */
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector1() const
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{
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const Type y2 = y * Type(2.0);
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const Type w2 = w * Type(2.0);
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return PxVec3T<Type>((-z * w2) + x * y2, (w * w2) - Type(1.0) + y * y2, (x * w2) + z * y2);
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}
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/** brief computes rotation of z-axis */
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3T<Type> getBasisVector2() const
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{
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const Type z2 = z * Type(2.0);
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const Type w2 = w * Type(2.0);
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return PxVec3T<Type>((y * w2) + x * z2, (-x * w2) + y * z2, (w * w2) - Type(1.0) + z * z2);
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}
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/**
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rotates passed vec by this (assumed unitary)
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3T<Type> rotate(const PxVec3T<Type>& v) const
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{
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const Type vx = Type(2.0) * v.x;
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const Type vy = Type(2.0) * v.y;
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const Type vz = Type(2.0) * v.z;
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const Type w2 = w * w - 0.5f;
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const Type dot2 = (x * vx + y * vy + z * vz);
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return PxVec3T<Type>((vx * w2 + (y * vz - z * vy) * w + x * dot2), (vy * w2 + (z * vx - x * vz) * w + y * dot2),
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(vz * w2 + (x * vy - y * vx) * w + z * dot2));
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}
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/**
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inverse rotates passed vec by this (assumed unitary)
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3T<Type> rotateInv(const PxVec3T<Type>& v) const
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{
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const Type vx = Type(2.0) * v.x;
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const Type vy = Type(2.0) * v.y;
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const Type vz = Type(2.0) * v.z;
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const Type w2 = w * w - 0.5f;
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const Type dot2 = (x * vx + y * vy + z * vz);
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return PxVec3T<Type>((vx * w2 - (y * vz - z * vy) * w + x * dot2), (vy * w2 - (z * vx - x * vz) * w + y * dot2),
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(vz * w2 - (x * vy - y * vx) * w + z * dot2));
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}
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/**
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\brief Assignment operator
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*/
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator=(const PxQuatT& p)
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{
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x = p.x;
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y = p.y;
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z = p.z;
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w = p.w;
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return *this;
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator*=(const PxQuatT& q)
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{
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const Type tx = w * q.x + q.w * x + y * q.z - q.y * z;
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const Type ty = w * q.y + q.w * y + z * q.x - q.z * x;
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const Type tz = w * q.z + q.w * z + x * q.y - q.x * y;
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w = w * q.w - q.x * x - y * q.y - q.z * z;
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x = tx;
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y = ty;
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z = tz;
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return *this;
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator+=(const PxQuatT& q)
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{
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x += q.x;
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y += q.y;
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z += q.z;
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w += q.w;
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return *this;
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator-=(const PxQuatT& q)
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{
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x -= q.x;
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y -= q.y;
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z -= q.z;
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w -= q.w;
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return *this;
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}
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT& operator*=(const Type s)
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{
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x *= s;
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y *= s;
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z *= s;
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w *= s;
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return *this;
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}
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/** quaternion multiplication */
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator*(const PxQuatT& q) const
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{
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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,
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w * q.z + q.w * z + x * q.y - q.x * y, w * q.w - x * q.x - y * q.y - z * q.z);
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}
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|
|
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|
|
/** quaternion addition */
|
||
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PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuatT operator+(const PxQuatT& q) const
|
||
|
|
{
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||
|
|
return PxQuatT(x + q.x, y + q.y, z + q.z, w + q.w);
|
||
|
|
}
|
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|
|
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|
|
/** 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
|
||
|
|
|