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+// This code contains NVIDIA Confidential Information and is disclosed to you
+// under a form of NVIDIA software license agreement provided separately to you.
+//
+// Notice
+// NVIDIA Corporation and its licensors retain all intellectual property and
+// proprietary rights in and to this software and related documentation and
+// any modifications thereto. Any use, reproduction, disclosure, or
+// distribution of this software and related documentation without an express
+// license agreement from NVIDIA Corporation is strictly prohibited.
+//
+// ALL NVIDIA DESIGN SPECIFICATIONS, CODE ARE PROVIDED "AS IS.". NVIDIA MAKES
+// NO WARRANTIES, EXPRESSED, IMPLIED, STATUTORY, OR OTHERWISE WITH RESPECT TO
+// THE MATERIALS, AND EXPRESSLY DISCLAIMS ALL IMPLIED WARRANTIES OF NONINFRINGEMENT,
+// MERCHANTABILITY, AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// Information and code furnished is believed to be accurate and reliable.
+// However, NVIDIA Corporation assumes no responsibility for the consequences of use of such
+// information or for any infringement of patents or other rights of third parties that may
+// result from its use. No license is granted by implication or otherwise under any patent
+// or patent rights of NVIDIA Corporation. Details are subject to change without notice.
+// This code supersedes and replaces all information previously supplied.
+// NVIDIA Corporation products are not authorized for use as critical
+// components in life support devices or systems without express written approval of
+// NVIDIA Corporation.
+//
+// Copyright (c) 2008-2016 NVIDIA Corporation. All rights reserved.
+// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
+// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
+
+#ifndef PXFOUNDATION_PXQUAT_H
+#define PXFOUNDATION_PXQUAT_H
+
+/** \addtogroup foundation
+@{
+*/
+
+#include "foundation/PxVec3.h"
+#if !PX_DOXYGEN
+namespace physx
+{
+#endif
+
+/**
+\brief This is a quaternion class. For more information on quaternion mathematics
+consult a mathematics source on complex numbers.
+
+*/
+
+class PxQuat
+{
+  public:
+	/**
+	\brief Default constructor, does not do any initialization.
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat()
+	{
+	}
+
+	//! identity constructor
+	PX_CUDA_CALLABLE PX_INLINE PxQuat(PxIDENTITY r) : x(0.0f), y(0.0f), z(0.0f), w(1.0f)
+	{
+		PX_UNUSED(r);
+	}
+
+	/**
+	\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 PxQuat(float r) : x(0.0f), y(0.0f), z(0.0f), w(r)
+	{
+	}
+
+	/**
+	\brief Constructor.  Take note of the order of the elements!
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat(float nx, float ny, float nz, float 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 PxQuat(float angleRadians, const PxVec3& unitAxis)
+	{
+		PX_ASSERT(PxAbs(1.0f - unitAxis.magnitude()) < 1e-3f);
+		const float a = angleRadians * 0.5f;
+		const float s = PxSin(a);
+		w = PxCos(a);
+		x = unitAxis.x * s;
+		y = unitAxis.y * s;
+		z = unitAxis.z * s;
+	}
+
+	/**
+	\brief Copy ctor.
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat(const PxQuat& 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 PxQuat(const PxMat33& m); /* defined in PxMat33.h */
+
+	/**
+	\brief returns true if quat is identity
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE bool isIdentity() const
+	{
+		return x==0.0f && y==0.0f && z==0.0f && w==1.0f;
+	}
+
+	/**
+	\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 float unitTolerance = 1e-4f;
+		return isFinite() && PxAbs(magnitude() - 1) < 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 float unitTolerance = 1e-2f;
+		return isFinite() && PxAbs(magnitude() - 1) < unitTolerance;
+	}
+
+	/**
+	\brief returns true if the two quaternions are exactly equal
+	*/
+	PX_CUDA_CALLABLE PX_INLINE bool operator==(const PxQuat& 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(float& angle, PxVec3& axis) const
+	{
+		const float quatEpsilon = 1.0e-8f;
+		const float s2 = x * x + y * y + z * z;
+		if(s2 < quatEpsilon * quatEpsilon) // can't extract a sensible axis
+		{
+			angle = 0.0f;
+			axis = PxVec3(1.0f, 0.0f, 0.0f);
+		}
+		else
+		{
+			const float s = PxRecipSqrt(s2);
+			axis = PxVec3(x, y, z) * s;
+			angle = PxAbs(w) < quatEpsilon ? PxPi : PxAtan2(s2 * s, w) * 2.0f;
+		}
+	}
+
+	/**
+	\brief Gets the angle between this quat and the identity quaternion.
+
+	<b>Unit:</b> Radians
+	*/
+	PX_CUDA_CALLABLE PX_INLINE float getAngle() const
+	{
+		return PxAcos(w) * 2.0f;
+	}
+
+	/**
+	\brief Gets the angle between this quat and the argument
+
+	<b>Unit:</b> Radians
+	*/
+	PX_CUDA_CALLABLE PX_INLINE float getAngle(const PxQuat& q) const
+	{
+		return PxAcos(dot(q)) * 2.0f;
+	}
+
+	/**
+	\brief This is the squared 4D vector length, should be 1 for unit quaternions.
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE float 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 float dot(const PxQuat& v) const
+	{
+		return x * v.x + y * v.y + z * v.z + w * v.w;
+	}
+
+	PX_CUDA_CALLABLE PX_INLINE PxQuat getNormalized() const
+	{
+		const float s = 1.0f / magnitude();
+		return PxQuat(x * s, y * s, z * s, w * s);
+	}
+
+	PX_CUDA_CALLABLE PX_INLINE float magnitude() const
+	{
+		return PxSqrt(magnitudeSquared());
+	}
+
+	// modifiers:
+	/**
+	\brief maps to the closest unit quaternion.
+	*/
+	PX_CUDA_CALLABLE PX_INLINE float normalize() // convert this PxQuat to a unit quaternion
+	{
+		const float mag = magnitude();
+		if(mag != 0.0f)
+		{
+			const float imag = 1.0f / 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_INLINE PxQuat getConjugate() const
+	{
+		return PxQuat(-x, -y, -z, w);
+	}
+
+	/*
+	\brief returns imaginary part.
+	*/
+	PX_CUDA_CALLABLE PX_INLINE PxVec3 getImaginaryPart() const
+	{
+		return PxVec3(x, y, z);
+	}
+
+	/** brief computes rotation of x-axis */
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3 getBasisVector0() const
+	{
+		const float x2 = x * 2.0f;
+		const float w2 = w * 2.0f;
+		return PxVec3((w * w2) - 1.0f + x * x2, (z * w2) + y * x2, (-y * w2) + z * x2);
+	}
+
+	/** brief computes rotation of y-axis */
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3 getBasisVector1() const
+	{
+		const float y2 = y * 2.0f;
+		const float w2 = w * 2.0f;
+		return PxVec3((-z * w2) + x * y2, (w * w2) - 1.0f + y * y2, (x * w2) + z * y2);
+	}
+
+	/** brief computes rotation of z-axis */
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3 getBasisVector2() const
+	{
+		const float z2 = z * 2.0f;
+		const float w2 = w * 2.0f;
+		return PxVec3((y * w2) + x * z2, (-x * w2) + y * z2, (w * w2) - 1.0f + z * z2);
+	}
+
+	/**
+	rotates passed vec by this (assumed unitary)
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3 rotate(const PxVec3& v) const
+	{
+		const float vx = 2.0f * v.x;
+		const float vy = 2.0f * v.y;
+		const float vz = 2.0f * v.z;
+		const float w2 = w * w - 0.5f;
+		const float dot2 = (x * vx + y * vy + z * vz);
+		return PxVec3((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));
+	}
+
+	/**
+	inverse rotates passed vec by this (assumed unitary)
+	*/
+	PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3 rotateInv(const PxVec3& v) const
+	{
+		const float vx = 2.0f * v.x;
+		const float vy = 2.0f * v.y;
+		const float vz = 2.0f * v.z;
+		const float w2 = w * w - 0.5f;
+		const float dot2 = (x * vx + y * vy + z * vz);
+		return PxVec3((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 PxQuat& operator=(const PxQuat& p)
+	{
+		x = p.x;
+		y = p.y;
+		z = p.z;
+		w = p.w;
+		return *this;
+	}
+
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat& operator*=(const PxQuat& q)
+	{
+		const float tx = w * q.x + q.w * x + y * q.z - q.y * z;
+		const float ty = w * q.y + q.w * y + z * q.x - q.z * x;
+		const float 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 PxQuat& operator+=(const PxQuat& q)
+	{
+		x += q.x;
+		y += q.y;
+		z += q.z;
+		w += q.w;
+		return *this;
+	}
+
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat& operator-=(const PxQuat& q)
+	{
+		x -= q.x;
+		y -= q.y;
+		z -= q.z;
+		w -= q.w;
+		return *this;
+	}
+
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat& operator*=(const float s)
+	{
+		x *= s;
+		y *= s;
+		z *= s;
+		w *= s;
+		return *this;
+	}
+
+	/** quaternion multiplication */
+	PX_CUDA_CALLABLE PX_INLINE PxQuat operator*(const PxQuat& q) const
+	{
+		return PxQuat(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 PxQuat operator+(const PxQuat& q) const
+	{
+		return PxQuat(x + q.x, y + q.y, z + q.z, w + q.w);
+	}
+
+	/** quaternion subtraction */
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat operator-() const
+	{
+		return PxQuat(-x, -y, -z, -w);
+	}
+
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat operator-(const PxQuat& q) const
+	{
+		return PxQuat(x - q.x, y - q.y, z - q.z, w - q.w);
+	}
+
+	PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat operator*(float r) const
+	{
+		return PxQuat(x * r, y * r, z * r, w * r);
+	}
+
+	/** the quaternion elements */
+	float x, y, z, w;
+};
+
+#if !PX_DOXYGEN
+} // namespace physx
+#endif
+
+/** @} */
+#endif // #ifndef PXFOUNDATION_PXQUAT_H