408 lines
9.9 KiB
C++
408 lines
9.9 KiB
C++
// 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) 2008-2013 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 PX_FOUNDATION_PX_QUAT_H
|
|
#define PX_FOUNDATION_PX_QUAT_H
|
|
|
|
/** \addtogroup foundation
|
|
@{
|
|
*/
|
|
|
|
#include "foundation/PxVec3.h"
|
|
#ifndef 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() { }
|
|
|
|
|
|
/**
|
|
\brief Constructor. Take note of the order of the elements!
|
|
*/
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE PxQuat(PxReal nx, PxReal ny, PxReal nz, PxReal 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(PxReal angleRadians, const PxVec3& unitAxis)
|
|
{
|
|
PX_ASSERT(PxAbs(1.0f-unitAxis.magnitude())<1e-3f);
|
|
const PxReal a = angleRadians * 0.5f;
|
|
const PxReal 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 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 PxReal unitTolerance = PxReal(1e-4);
|
|
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 PxReal unitTolerance = PxReal(1e-2);
|
|
return isFinite() && PxAbs(magnitude()-1)<unitTolerance;
|
|
}
|
|
|
|
/**
|
|
\brief converts this quaternion to angle-axis representation
|
|
*/
|
|
|
|
PX_CUDA_CALLABLE PX_INLINE void toRadiansAndUnitAxis(PxReal& angle, PxVec3& axis) const
|
|
{
|
|
const PxReal quatEpsilon = (PxReal(1.0e-8f));
|
|
const PxReal s2 = x*x+y*y+z*z;
|
|
if(s2<quatEpsilon*quatEpsilon) // can't extract a sensible axis
|
|
{
|
|
angle = 0;
|
|
axis = PxVec3(1,0,0);
|
|
}
|
|
else
|
|
{
|
|
const PxReal s = PxRecipSqrt(s2);
|
|
axis = PxVec3(x,y,z) * s;
|
|
angle = PxAbs(w)<quatEpsilon ? PxPi : PxAtan2(s2*s, w) * 2;
|
|
}
|
|
|
|
}
|
|
|
|
/**
|
|
\brief Gets the angle between this quat and the identity quaternion.
|
|
|
|
<b>Unit:</b> Radians
|
|
*/
|
|
PX_CUDA_CALLABLE PX_INLINE PxReal getAngle() const
|
|
{
|
|
return PxAcos(w) * PxReal(2);
|
|
}
|
|
|
|
|
|
/**
|
|
\brief Gets the angle between this quat and the argument
|
|
|
|
<b>Unit:</b> Radians
|
|
*/
|
|
PX_CUDA_CALLABLE PX_INLINE PxReal getAngle(const PxQuat& q) const
|
|
{
|
|
return PxAcos(dot(q)) * PxReal(2);
|
|
}
|
|
|
|
|
|
/**
|
|
\brief This is the squared 4D vector length, should be 1 for unit quaternions.
|
|
*/
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE PxReal 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 PxReal 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 PxReal 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 PxReal normalize() // convert this PxQuat to a unit quaternion
|
|
{
|
|
const PxReal mag = magnitude();
|
|
if (mag)
|
|
{
|
|
const PxReal imag = PxReal(1) / 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
|
|
{
|
|
// return rotate(PxVec3(1,0,0));
|
|
const PxF32 x2 = x*2.0f;
|
|
const PxF32 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
|
|
{
|
|
// return rotate(PxVec3(0,1,0));
|
|
const PxF32 y2 = y*2.0f;
|
|
const PxF32 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
|
|
{
|
|
// return rotate(PxVec3(0,0,1));
|
|
const PxF32 z2 = z*2.0f;
|
|
const PxF32 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
|
|
// PX_CUDA_CALLABLE PX_INLINE const PxVec3 rotate(const PxVec3& v) const
|
|
{
|
|
const PxF32 vx = 2.0f*v.x;
|
|
const PxF32 vy = 2.0f*v.y;
|
|
const PxF32 vz = 2.0f*v.z;
|
|
const PxF32 w2 = w*w-0.5f;
|
|
const PxF32 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)
|
|
);
|
|
/*
|
|
const PxVec3 qv(x,y,z);
|
|
return (v*(w*w-0.5f) + (qv.cross(v))*w + qv*(qv.dot(v)))*2;
|
|
*/
|
|
}
|
|
|
|
/**
|
|
inverse rotates passed vec by this (assumed unitary)
|
|
*/
|
|
PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3 rotateInv(const PxVec3& v) const
|
|
// PX_CUDA_CALLABLE PX_INLINE const PxVec3 rotateInv(const PxVec3& v) const
|
|
{
|
|
const PxF32 vx = 2.0f*v.x;
|
|
const PxF32 vy = 2.0f*v.y;
|
|
const PxF32 vz = 2.0f*v.z;
|
|
const PxF32 w2 = w*w-0.5f;
|
|
const PxF32 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)
|
|
);
|
|
// const PxVec3 qv(x,y,z);
|
|
// return (v*(w*w-0.5f) - (qv.cross(v))*w + qv*(qv.dot(v)))*2;
|
|
}
|
|
|
|
/**
|
|
\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 PxReal tx = w*q.x + q.w*x + y*q.z - q.y*z;
|
|
const PxReal ty = w*q.y + q.w*y + z*q.x - q.z*x;
|
|
const PxReal 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 PxReal 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*(PxReal r) const
|
|
{
|
|
return PxQuat(x*r,y*r,z*r,w*r);
|
|
}
|
|
|
|
static PX_CUDA_CALLABLE PX_INLINE PxQuat createIdentity() { return PxQuat(0,0,0,1); }
|
|
|
|
/** the quaternion elements */
|
|
PxReal x,y,z,w;
|
|
};
|
|
|
|
#ifndef PX_DOXYGEN
|
|
} // namespace physx
|
|
#endif
|
|
|
|
/** @} */
|
|
#endif // PX_FOUNDATION_PX_QUAT_H
|