Integrate SIMD API from oreh/server-trunk-oreh

1 files changed, 594 insertions, 590 deletions

diff --git a/indra/llmath/llquaternion.h b/indra/llmath/llquaternion.h
index 0769f29f23..bbd4326483 100644
--- a/indra/llmath/llquaternion.h
+++ b/indra/llmath/llquaternion.h
@@ -1,590 +1,594 @@
-/** 
- * @file llquaternion.h
- * @brief LLQuaternion class header file.
- *
- * $LicenseInfo:firstyear=2000&license=viewergpl$
- * 
- * Copyright (c) 2000-2009, Linden Research, Inc.
- * 
- * Second Life Viewer Source Code
- * The source code in this file ("Source Code") is provided by Linden Lab
- * to you under the terms of the GNU General Public License, version 2.0
- * ("GPL"), unless you have obtained a separate licensing agreement
- * ("Other License"), formally executed by you and Linden Lab.  Terms of
- * the GPL can be found in doc/GPL-license.txt in this distribution, or
- * online at http://secondlifegrid.net/programs/open_source/licensing/gplv2
- * 
- * There are special exceptions to the terms and conditions of the GPL as
- * it is applied to this Source Code. View the full text of the exception
- * in the file doc/FLOSS-exception.txt in this software distribution, or
- * online at
- * http://secondlifegrid.net/programs/open_source/licensing/flossexception
- * 
- * By copying, modifying or distributing this software, you acknowledge
- * that you have read and understood your obligations described above,
- * and agree to abide by those obligations.
- * 
- * ALL LINDEN LAB SOURCE CODE IS PROVIDED "AS IS." LINDEN LAB MAKES NO
- * WARRANTIES, EXPRESS, IMPLIED OR OTHERWISE, REGARDING ITS ACCURACY,
- * COMPLETENESS OR PERFORMANCE.
- * $/LicenseInfo$
- */
-
-#ifndef LLQUATERNION_H
-#define LLQUATERNION_H
-
-#include "llmath.h"
-
-class LLVector4;
-class LLVector3;
-class LLVector3d;
-class LLMatrix4;
-class LLMatrix3;
-
-//	NOTA BENE: Quaternion code is written assuming Unit Quaternions!!!!
-//			   Moreover, it is written assuming that all vectors and matricies
-//			   passed as arguments are normalized and unitary respectively.
-//			   VERY VERY VERY VERY BAD THINGS will happen if these assumptions fail.
-
-static const U32 LENGTHOFQUAT = 4;
-
-class LLQuaternion
-{
-public:
-	F32 mQ[LENGTHOFQUAT];
-
-	static const LLQuaternion DEFAULT;
-
-	LLQuaternion();									// Initializes Quaternion to (0,0,0,1)
-	explicit LLQuaternion(const LLMatrix4 &mat);				// Initializes Quaternion from Matrix4
-	explicit LLQuaternion(const LLMatrix3 &mat);				// Initializes Quaternion from Matrix3
-	LLQuaternion(F32 x, F32 y, F32 z, F32 w);		// Initializes Quaternion to normalize(x, y, z, w)
-	LLQuaternion(F32 angle, const LLVector4 &vec);	// Initializes Quaternion to axis_angle2quat(angle, vec)
-	LLQuaternion(F32 angle, const LLVector3 &vec);	// Initializes Quaternion to axis_angle2quat(angle, vec)
-	LLQuaternion(const F32 *q);						// Initializes Quaternion to normalize(x, y, z, w)
-	LLQuaternion(const LLVector3 &x_axis,
-				 const LLVector3 &y_axis,
-				 const LLVector3 &z_axis);			// Initializes Quaternion from Matrix3 = [x_axis ; y_axis ; z_axis]
-
-	BOOL isIdentity() const;
-	BOOL isNotIdentity() const;
-	BOOL isFinite() const;									// checks to see if all values of LLQuaternion are finite
-	void quantize16(F32 lower, F32 upper);					// changes the vector to reflect quatization
-	void quantize8(F32 lower, F32 upper);							// changes the vector to reflect quatization
-	void loadIdentity();											// Loads the quaternion that represents the identity rotation
-
-	const LLQuaternion&	set(F32 x, F32 y, F32 z, F32 w);		// Sets Quaternion to normalize(x, y, z, w)
-	const LLQuaternion&	set(const LLQuaternion &quat);			// Copies Quaternion
-	const LLQuaternion&	set(const F32 *q);						// Sets Quaternion to normalize(quat[VX], quat[VY], quat[VZ], quat[VW])
-	const LLQuaternion&	set(const LLMatrix3 &mat);				// Sets Quaternion to mat2quat(mat)
-	const LLQuaternion&	set(const LLMatrix4 &mat);				// Sets Quaternion to mat2quat(mat)
-
-	const LLQuaternion&	setAngleAxis(F32 angle, F32 x, F32 y, F32 z);	// Sets Quaternion to axis_angle2quat(angle, x, y, z)
-	const LLQuaternion&	setAngleAxis(F32 angle, const LLVector3 &vec);	// Sets Quaternion to axis_angle2quat(angle, vec)
-	const LLQuaternion&	setAngleAxis(F32 angle, const LLVector4 &vec);	// Sets Quaternion to axis_angle2quat(angle, vec)
-	const LLQuaternion&	setEulerAngles(F32 roll, F32 pitch, F32 yaw);	// Sets Quaternion to euler2quat(pitch, yaw, roll)
-
-	const LLQuaternion&	setQuatInit(F32 x, F32 y, F32 z, F32 w);	// deprecated
-	const LLQuaternion&	setQuat(const LLQuaternion &quat);			// deprecated
-	const LLQuaternion&	setQuat(const F32 *q);						// deprecated
-	const LLQuaternion&	setQuat(const LLMatrix3 &mat);				// deprecated
-	const LLQuaternion&	setQuat(const LLMatrix4 &mat);				// deprecated
-	const LLQuaternion&	setQuat(F32 angle, F32 x, F32 y, F32 z);	// deprecated
-	const LLQuaternion&	setQuat(F32 angle, const LLVector3 &vec);	// deprecated
-	const LLQuaternion&	setQuat(F32 angle, const LLVector4 &vec);	// deprecated
-	const LLQuaternion&	setQuat(F32 roll, F32 pitch, F32 yaw);		// deprecated
-
-	LLMatrix4	getMatrix4(void) const;							// Returns the Matrix4 equivalent of Quaternion
-	LLMatrix3	getMatrix3(void) const;							// Returns the Matrix3 equivalent of Quaternion
-	void		getAngleAxis(F32* angle, F32* x, F32* y, F32* z) const;	// returns rotation in radians about axis x,y,z
-	void		getAngleAxis(F32* angle, LLVector3 &vec) const;
-	void		getEulerAngles(F32 *roll, F32* pitch, F32 *yaw) const;
-
-	F32	normalize();	// Normalizes Quaternion and returns magnitude
-	F32	normQuat();		// deprecated
-
-	const LLQuaternion&	conjugate(void);	// Conjugates Quaternion and returns result
-	const LLQuaternion&	conjQuat(void);		// deprecated
-
-	// Other useful methods
-	const LLQuaternion&	transpose();		// transpose (same as conjugate)
-	const LLQuaternion&	transQuat();		// deprecated
-
-	void			shortestArc(const LLVector3 &a, const LLVector3 &b);	// shortest rotation from a to b
-	const LLQuaternion& constrain(F32 radians);						// constrains rotation to a cone angle specified in radians
-
-	// Standard operators
-	friend std::ostream& operator<<(std::ostream &s, const LLQuaternion &a);					// Prints a
-	friend LLQuaternion operator+(const LLQuaternion &a, const LLQuaternion &b);	// Addition
-	friend LLQuaternion operator-(const LLQuaternion &a, const LLQuaternion &b);	// Subtraction
-	friend LLQuaternion operator-(const LLQuaternion &a);							// Negation
-	friend LLQuaternion operator*(F32 a, const LLQuaternion &q);					// Scale
-	friend LLQuaternion operator*(const LLQuaternion &q, F32 b);					// Scale
-	friend LLQuaternion operator*(const LLQuaternion &a, const LLQuaternion &b);	// Returns a * b
-	friend LLQuaternion operator~(const LLQuaternion &a);							// Returns a* (Conjugate of a)
-	bool operator==(const LLQuaternion &b) const;			// Returns a == b
-	bool operator!=(const LLQuaternion &b) const;			// Returns a != b
-
-	friend const LLQuaternion& operator*=(LLQuaternion &a, const LLQuaternion &b);	// Returns a * b
-
-	friend LLVector4 operator*(const LLVector4 &a, const LLQuaternion &rot);		// Rotates a by rot
-	friend LLVector3 operator*(const LLVector3 &a, const LLQuaternion &rot);		// Rotates a by rot
-	friend LLVector3d operator*(const LLVector3d &a, const LLQuaternion &rot);		// Rotates a by rot
-
-	// Non-standard operators
-	friend F32 dot(const LLQuaternion &a, const LLQuaternion &b);
-	friend LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q);		// linear interpolation (t = 0 to 1) from p to q
-	friend LLQuaternion lerp(F32 t, const LLQuaternion &q);								// linear interpolation (t = 0 to 1) from identity to q
-	friend LLQuaternion slerp(F32 t, const LLQuaternion &p, const LLQuaternion &q); 	// spherical linear interpolation from p to q
-	friend LLQuaternion slerp(F32 t, const LLQuaternion &q);							// spherical linear interpolation from identity to q
-	friend LLQuaternion nlerp(F32 t, const LLQuaternion &p, const LLQuaternion &q); 	// normalized linear interpolation from p to q
-	friend LLQuaternion nlerp(F32 t, const LLQuaternion &q); 							// normalized linear interpolation from p to q
-
-	LLVector3	packToVector3() const;						// Saves space by using the fact that our quaternions are normalized
-	void		unpackFromVector3(const LLVector3& vec);	// Saves space by using the fact that our quaternions are normalized
-
-	enum Order {
-		XYZ = 0,
-		YZX = 1,
-		ZXY = 2,
-		XZY = 3,
-		YXZ = 4,
-		ZYX = 5
-	};
-	// Creates a quaternions from maya's rotation representation,
-	// which is 3 rotations (in DEGREES) in the specified order
-	friend LLQuaternion mayaQ(F32 x, F32 y, F32 z, Order order);
-
-	// Conversions between Order and strings like "xyz" or "ZYX"
-	friend const char *OrderToString( const Order order );
-	friend Order StringToOrder( const char *str );
-
-	static BOOL parseQuat(const std::string& buf, LLQuaternion* value);
-
-	// For debugging, only
-	//static U32 mMultCount;
-};
-
-// checker
-inline BOOL	LLQuaternion::isFinite() const
-{
-	return (llfinite(mQ[VX]) && llfinite(mQ[VY]) && llfinite(mQ[VZ]) && llfinite(mQ[VS]));
-}
-
-inline BOOL LLQuaternion::isIdentity() const
-{
-	return 
-		( mQ[VX] == 0.f ) &&
-		( mQ[VY] == 0.f ) &&
-		( mQ[VZ] == 0.f ) &&
-		( mQ[VS] == 1.f );
-}
-
-inline BOOL LLQuaternion::isNotIdentity() const
-{
-	return 
-		( mQ[VX] != 0.f ) ||
-		( mQ[VY] != 0.f ) ||
-		( mQ[VZ] != 0.f ) ||
-		( mQ[VS] != 1.f );
-}
-
-
-
-inline LLQuaternion::LLQuaternion(void)
-{
-	mQ[VX] = 0.f;
-	mQ[VY] = 0.f;
-	mQ[VZ] = 0.f;
-	mQ[VS] = 1.f;
-}
-
-inline LLQuaternion::LLQuaternion(F32 x, F32 y, F32 z, F32 w)
-{
-	mQ[VX] = x;
-	mQ[VY] = y;
-	mQ[VZ] = z;
-	mQ[VS] = w;
-
-	//RN: don't normalize this case as its used mainly for temporaries during calculations
-	//normalize();
-	/*
-	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);
-	mag -= 1.f;
-	mag = fabs(mag);
-	llassert(mag < 10.f*FP_MAG_THRESHOLD);
-	*/
-}
-
-inline LLQuaternion::LLQuaternion(const F32 *q)
-{
-	mQ[VX] = q[VX];
-	mQ[VY] = q[VY];
-	mQ[VZ] = q[VZ];
-	mQ[VS] = q[VW];
-
-	normalize();
-	/*
-	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);
-	mag -= 1.f;
-	mag = fabs(mag);
-	llassert(mag < FP_MAG_THRESHOLD);
-	*/
-}
-
-
-inline void LLQuaternion::loadIdentity()
-{
-	mQ[VX] = 0.0f;
-	mQ[VY] = 0.0f;
-	mQ[VZ] = 0.0f;
-	mQ[VW] = 1.0f;
-}
-
-
-inline const LLQuaternion&	LLQuaternion::set(F32 x, F32 y, F32 z, F32 w)
-{
-	mQ[VX] = x;
-	mQ[VY] = y;
-	mQ[VZ] = z;
-	mQ[VS] = w;
-	normalize();
-	return (*this);
-}
-
-inline const LLQuaternion&	LLQuaternion::set(const LLQuaternion &quat)
-{
-	mQ[VX] = quat.mQ[VX];
-	mQ[VY] = quat.mQ[VY];
-	mQ[VZ] = quat.mQ[VZ];
-	mQ[VW] = quat.mQ[VW];
-	normalize();
-	return (*this);
-}
-
-inline const LLQuaternion&	LLQuaternion::set(const F32 *q)
-{
-	mQ[VX] = q[VX];
-	mQ[VY] = q[VY];
-	mQ[VZ] = q[VZ];
-	mQ[VS] = q[VW];
-	normalize();
-	return (*this);
-}
-
-
-// deprecated
-inline const LLQuaternion&	LLQuaternion::setQuatInit(F32 x, F32 y, F32 z, F32 w)
-{
-	mQ[VX] = x;
-	mQ[VY] = y;
-	mQ[VZ] = z;
-	mQ[VS] = w;
-	normalize();
-	return (*this);
-}
-
-// deprecated
-inline const LLQuaternion&	LLQuaternion::setQuat(const LLQuaternion &quat)
-{
-	mQ[VX] = quat.mQ[VX];
-	mQ[VY] = quat.mQ[VY];
-	mQ[VZ] = quat.mQ[VZ];
-	mQ[VW] = quat.mQ[VW];
-	normalize();
-	return (*this);
-}
-
-// deprecated
-inline const LLQuaternion&	LLQuaternion::setQuat(const F32 *q)
-{
-	mQ[VX] = q[VX];
-	mQ[VY] = q[VY];
-	mQ[VZ] = q[VZ];
-	mQ[VS] = q[VW];
-	normalize();
-	return (*this);
-}
-
-// There may be a cheaper way that avoids the sqrt.
-// Does sin_a = VX*VX + VY*VY + VZ*VZ?
-// Copied from Matrix and Quaternion FAQ 1.12
-inline void LLQuaternion::getAngleAxis(F32* angle, F32* x, F32* y, F32* z) const
-{
-	F32 cos_a = mQ[VW];
-	if (cos_a > 1.0f) cos_a = 1.0f;
-	if (cos_a < -1.0f) cos_a = -1.0f;
-
-    F32 sin_a = (F32) sqrt( 1.0f - cos_a * cos_a );
-
-    if ( fabs( sin_a ) < 0.0005f )
-		sin_a = 1.0f;
-	else
-		sin_a = 1.f/sin_a;
-
-    F32 temp_angle = 2.0f * (F32) acos( cos_a );
-	if (temp_angle > F_PI)
-	{
-		// The (angle,axis) pair should never have angles outside [PI, -PI]
-		// since we want the _shortest_ (angle,axis) solution.
-		// Since acos is defined for [0, PI], and we multiply by 2.0, we
-		// can push the angle outside the acceptible range.
-		// When this happens we set the angle to the other portion of a 
-		// full 2PI rotation, and negate the axis, which reverses the 
-		// direction of the rotation (by the right-hand rule).
-		*angle = 2.f * F_PI - temp_angle;
-    	*x = - mQ[VX] * sin_a;
-    	*y = - mQ[VY] * sin_a;
-    	*z = - mQ[VZ] * sin_a;
-	}
-	else
-	{
-		*angle = temp_angle;
-    	*x = mQ[VX] * sin_a;
-    	*y = mQ[VY] * sin_a;
-    	*z = mQ[VZ] * sin_a;
-	}
-}
-
-inline const LLQuaternion& LLQuaternion::conjugate()
-{
-	mQ[VX] *= -1.f;
-	mQ[VY] *= -1.f;
-	mQ[VZ] *= -1.f;
-	return (*this);
-}
-
-inline const LLQuaternion& LLQuaternion::conjQuat()
-{
-	mQ[VX] *= -1.f;
-	mQ[VY] *= -1.f;
-	mQ[VZ] *= -1.f;
-	return (*this);
-}
-
-// Transpose
-inline const LLQuaternion& LLQuaternion::transpose()
-{
-	mQ[VX] *= -1.f;
-	mQ[VY] *= -1.f;
-	mQ[VZ] *= -1.f;
-	return (*this);
-}
-
-// deprecated
-inline const LLQuaternion& LLQuaternion::transQuat()
-{
-	mQ[VX] *= -1.f;
-	mQ[VY] *= -1.f;
-	mQ[VZ] *= -1.f;
-	return (*this);
-}
-
-
-inline LLQuaternion 	operator+(const LLQuaternion &a, const LLQuaternion &b)
-{
-	return LLQuaternion( 
-		a.mQ[VX] + b.mQ[VX],
-		a.mQ[VY] + b.mQ[VY],
-		a.mQ[VZ] + b.mQ[VZ],
-		a.mQ[VW] + b.mQ[VW] );
-}
-
-
-inline LLQuaternion 	operator-(const LLQuaternion &a, const LLQuaternion &b)
-{
-	return LLQuaternion( 
-		a.mQ[VX] - b.mQ[VX],
-		a.mQ[VY] - b.mQ[VY],
-		a.mQ[VZ] - b.mQ[VZ],
-		a.mQ[VW] - b.mQ[VW] );
-}
-
-
-inline LLQuaternion 	operator-(const LLQuaternion &a)
-{
-	return LLQuaternion(
-		-a.mQ[VX],
-		-a.mQ[VY],
-		-a.mQ[VZ],
-		-a.mQ[VW] );
-}
-
-
-inline LLQuaternion 	operator*(F32 a, const LLQuaternion &q)
-{
-	return LLQuaternion(
-		a * q.mQ[VX],
-		a * q.mQ[VY],
-		a * q.mQ[VZ],
-		a * q.mQ[VW] );
-}
-
-
-inline LLQuaternion 	operator*(const LLQuaternion &q, F32 a)
-{
-	return LLQuaternion(
-		a * q.mQ[VX],
-		a * q.mQ[VY],
-		a * q.mQ[VZ],
-		a * q.mQ[VW] );
-}
-
-inline LLQuaternion	operator~(const LLQuaternion &a)
-{
-	LLQuaternion q(a);
-	q.conjQuat();
-	return q;
-}
-
-inline bool	LLQuaternion::operator==(const LLQuaternion &b) const
-{
-	return (  (mQ[VX] == b.mQ[VX])
-			&&(mQ[VY] == b.mQ[VY])
-			&&(mQ[VZ] == b.mQ[VZ])
-			&&(mQ[VS] == b.mQ[VS]));
-}
-
-inline bool	LLQuaternion::operator!=(const LLQuaternion &b) const
-{
-	return (  (mQ[VX] != b.mQ[VX])
-			||(mQ[VY] != b.mQ[VY])
-			||(mQ[VZ] != b.mQ[VZ])
-			||(mQ[VS] != b.mQ[VS]));
-}
-
-inline const LLQuaternion&	operator*=(LLQuaternion &a, const LLQuaternion &b)
-{
-#if 1
-	LLQuaternion q(
-		b.mQ[3] * a.mQ[0] + b.mQ[0] * a.mQ[3] + b.mQ[1] * a.mQ[2] - b.mQ[2] * a.mQ[1],
-		b.mQ[3] * a.mQ[1] + b.mQ[1] * a.mQ[3] + b.mQ[2] * a.mQ[0] - b.mQ[0] * a.mQ[2],
-		b.mQ[3] * a.mQ[2] + b.mQ[2] * a.mQ[3] + b.mQ[0] * a.mQ[1] - b.mQ[1] * a.mQ[0],
-		b.mQ[3] * a.mQ[3] - b.mQ[0] * a.mQ[0] - b.mQ[1] * a.mQ[1] - b.mQ[2] * a.mQ[2]
-	);
-	a = q;
-#else
-	a = a * b;
-#endif
-	return a;
-}
-
-const F32 ONE_PART_IN_A_MILLION = 0.000001f;
-
-inline F32	LLQuaternion::normalize()
-{
-	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);
-
-	if (mag > FP_MAG_THRESHOLD)
-	{
-		// Floating point error can prevent some quaternions from achieving
-		// exact unity length.  When trying to renormalize such quaternions we
-		// can oscillate between multiple quantized states.  To prevent such
-		// drifts we only renomalize if the length is far enough from unity.
-		if (fabs(1.f - mag) > ONE_PART_IN_A_MILLION)
-		{
-			F32 oomag = 1.f/mag;
-			mQ[VX] *= oomag;
-			mQ[VY] *= oomag;
-			mQ[VZ] *= oomag;
-			mQ[VS] *= oomag;
-		}
-	}
-	else
-	{
-		// we were given a very bad quaternion so we set it to identity
-		mQ[VX] = 0.f;
-		mQ[VY] = 0.f;
-		mQ[VZ] = 0.f;
-		mQ[VS] = 1.f;
-	}
-
-	return mag;
-}
-
-// deprecated
-inline F32	LLQuaternion::normQuat()
-{
-	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);
-
-	if (mag > FP_MAG_THRESHOLD)
-	{
-		if (fabs(1.f - mag) > ONE_PART_IN_A_MILLION)
-		{
-			// only renormalize if length not close enough to 1.0 already
-			F32 oomag = 1.f/mag;
-			mQ[VX] *= oomag;
-			mQ[VY] *= oomag;
-			mQ[VZ] *= oomag;
-			mQ[VS] *= oomag;
-		}
-	}
-	else
-	{
-		mQ[VX] = 0.f;
-		mQ[VY] = 0.f;
-		mQ[VZ] = 0.f;
-		mQ[VS] = 1.f;
-	}
-
-	return mag;
-}
-
-LLQuaternion::Order StringToOrder( const char *str );
-
-// Some notes about Quaternions
-
-// What is a Quaternion?
-// ---------------------
-// A quaternion is a point in 4-dimensional complex space.
-// Q = { Qx, Qy, Qz, Qw }
-// 
-//
-// Why Quaternions?
-// ----------------
-// The set of quaternions that make up the the 4-D unit sphere 
-// can be mapped to the set of all rotations in 3-D space.  Sometimes
-// it is easier to describe/manipulate rotations in quaternion space
-// than rotation-matrix space.
-//
-//
-// How Quaternions?
-// ----------------
-// In order to take advantage of quaternions we need to know how to
-// go from rotation-matricies to quaternions and back.  We also have
-// to agree what variety of rotations we're generating.
-// 
-// Consider the equation...   v' = v * R 
-//
-// There are two ways to think about rotations of vectors.
-// 1) v' is the same vector in a different reference frame
-// 2) v' is a new vector in the same reference frame
-//
-// bookmark -- which way are we using?
-// 
-// 
-// Quaternion from Angle-Axis:
-// ---------------------------
-// Suppose we wanted to represent a rotation of some angle (theta) 
-// about some axis ({Ax, Ay, Az})...
-//
-// axis of rotation = {Ax, Ay, Az} 
-// angle_of_rotation = theta
-//
-// s = sin(0.5 * theta)
-// c = cos(0.5 * theta)
-// Q = { s * Ax, s * Ay, s * Az, c }
-//
-//
-// 3x3 Matrix from Quaternion
-// --------------------------
-//
-//     |                                                                    |
-//     | 1 - 2 * (y^2 + z^2)   2 * (x * y + z * w)     2 * (y * w - x * z)  |
-//     |                                                                    |
-// M = | 2 * (x * y - z * w)   1 - 2 * (x^2 + z^2)     2 * (y * z + x * w)  |
-//     |                                                                    |
-//     | 2 * (x * z + y * w)   2 * (y * z - x * w)     1 - 2 * (x^2 + y^2)  |
-//     |                                                                    |
-
-#endif
+/** 

+ * @file llquaternion.h

+ * @brief LLQuaternion class header file.

+ *

+ * $LicenseInfo:firstyear=2000&license=viewergpl$

+ * 

+ * Copyright (c) 2000-2009, Linden Research, Inc.

+ * 

+ * Second Life Viewer Source Code

+ * The source code in this file ("Source Code") is provided by Linden Lab

+ * to you under the terms of the GNU General Public License, version 2.0

+ * ("GPL"), unless you have obtained a separate licensing agreement

+ * ("Other License"), formally executed by you and Linden Lab.  Terms of

+ * the GPL can be found in doc/GPL-license.txt in this distribution, or

+ * online at http://secondlifegrid.net/programs/open_source/licensing/gplv2

+ * 

+ * There are special exceptions to the terms and conditions of the GPL as

+ * it is applied to this Source Code. View the full text of the exception

+ * in the file doc/FLOSS-exception.txt in this software distribution, or

+ * online at

+ * http://secondlifegrid.net/programs/open_source/licensing/flossexception

+ * 

+ * By copying, modifying or distributing this software, you acknowledge

+ * that you have read and understood your obligations described above,

+ * and agree to abide by those obligations.

+ * 

+ * ALL LINDEN LAB SOURCE CODE IS PROVIDED "AS IS." LINDEN LAB MAKES NO

+ * WARRANTIES, EXPRESS, IMPLIED OR OTHERWISE, REGARDING ITS ACCURACY,

+ * COMPLETENESS OR PERFORMANCE.

+ * $/LicenseInfo$

+ */

+

+#ifndef LLQUATERNION_H

+#define LLQUATERNION_H

+

+#include <iostream>

+

+#ifndef LLMATH_H //enforce specific include order to avoid tangling inline dependencies

+#error "Please include llmath.h first."

+#endif

+

+class LLVector4;

+class LLVector3;

+class LLVector3d;

+class LLMatrix4;

+class LLMatrix3;

+

+//	NOTA BENE: Quaternion code is written assuming Unit Quaternions!!!!

+//			   Moreover, it is written assuming that all vectors and matricies

+//			   passed as arguments are normalized and unitary respectively.

+//			   VERY VERY VERY VERY BAD THINGS will happen if these assumptions fail.

+

+static const U32 LENGTHOFQUAT = 4;

+

+class LLQuaternion

+{

+public:

+	F32 mQ[LENGTHOFQUAT];

+

+	static const LLQuaternion DEFAULT;

+

+	LLQuaternion();									// Initializes Quaternion to (0,0,0,1)

+	explicit LLQuaternion(const LLMatrix4 &mat);				// Initializes Quaternion from Matrix4

+	explicit LLQuaternion(const LLMatrix3 &mat);				// Initializes Quaternion from Matrix3

+	LLQuaternion(F32 x, F32 y, F32 z, F32 w);		// Initializes Quaternion to normalize(x, y, z, w)

+	LLQuaternion(F32 angle, const LLVector4 &vec);	// Initializes Quaternion to axis_angle2quat(angle, vec)

+	LLQuaternion(F32 angle, const LLVector3 &vec);	// Initializes Quaternion to axis_angle2quat(angle, vec)

+	LLQuaternion(const F32 *q);						// Initializes Quaternion to normalize(x, y, z, w)

+	LLQuaternion(const LLVector3 &x_axis,

+				 const LLVector3 &y_axis,

+				 const LLVector3 &z_axis);			// Initializes Quaternion from Matrix3 = [x_axis ; y_axis ; z_axis]

+

+	BOOL isIdentity() const;

+	BOOL isNotIdentity() const;

+	BOOL isFinite() const;									// checks to see if all values of LLQuaternion are finite

+	void quantize16(F32 lower, F32 upper);					// changes the vector to reflect quatization

+	void quantize8(F32 lower, F32 upper);							// changes the vector to reflect quatization

+	void loadIdentity();											// Loads the quaternion that represents the identity rotation

+

+	const LLQuaternion&	set(F32 x, F32 y, F32 z, F32 w);		// Sets Quaternion to normalize(x, y, z, w)

+	const LLQuaternion&	set(const LLQuaternion &quat);			// Copies Quaternion

+	const LLQuaternion&	set(const F32 *q);						// Sets Quaternion to normalize(quat[VX], quat[VY], quat[VZ], quat[VW])

+	const LLQuaternion&	set(const LLMatrix3 &mat);				// Sets Quaternion to mat2quat(mat)

+	const LLQuaternion&	set(const LLMatrix4 &mat);				// Sets Quaternion to mat2quat(mat)

+

+	const LLQuaternion&	setAngleAxis(F32 angle, F32 x, F32 y, F32 z);	// Sets Quaternion to axis_angle2quat(angle, x, y, z)

+	const LLQuaternion&	setAngleAxis(F32 angle, const LLVector3 &vec);	// Sets Quaternion to axis_angle2quat(angle, vec)

+	const LLQuaternion&	setAngleAxis(F32 angle, const LLVector4 &vec);	// Sets Quaternion to axis_angle2quat(angle, vec)

+	const LLQuaternion&	setEulerAngles(F32 roll, F32 pitch, F32 yaw);	// Sets Quaternion to euler2quat(pitch, yaw, roll)

+

+	const LLQuaternion&	setQuatInit(F32 x, F32 y, F32 z, F32 w);	// deprecated

+	const LLQuaternion&	setQuat(const LLQuaternion &quat);			// deprecated

+	const LLQuaternion&	setQuat(const F32 *q);						// deprecated

+	const LLQuaternion&	setQuat(const LLMatrix3 &mat);				// deprecated

+	const LLQuaternion&	setQuat(const LLMatrix4 &mat);				// deprecated

+	const LLQuaternion&	setQuat(F32 angle, F32 x, F32 y, F32 z);	// deprecated

+	const LLQuaternion&	setQuat(F32 angle, const LLVector3 &vec);	// deprecated

+	const LLQuaternion&	setQuat(F32 angle, const LLVector4 &vec);	// deprecated

+	const LLQuaternion&	setQuat(F32 roll, F32 pitch, F32 yaw);		// deprecated

+

+	LLMatrix4	getMatrix4(void) const;							// Returns the Matrix4 equivalent of Quaternion

+	LLMatrix3	getMatrix3(void) const;							// Returns the Matrix3 equivalent of Quaternion

+	void		getAngleAxis(F32* angle, F32* x, F32* y, F32* z) const;	// returns rotation in radians about axis x,y,z

+	void		getAngleAxis(F32* angle, LLVector3 &vec) const;

+	void		getEulerAngles(F32 *roll, F32* pitch, F32 *yaw) const;

+

+	F32	normalize();	// Normalizes Quaternion and returns magnitude

+	F32	normQuat();		// deprecated

+

+	const LLQuaternion&	conjugate(void);	// Conjugates Quaternion and returns result

+	const LLQuaternion&	conjQuat(void);		// deprecated

+

+	// Other useful methods

+	const LLQuaternion&	transpose();		// transpose (same as conjugate)

+	const LLQuaternion&	transQuat();		// deprecated

+

+	void			shortestArc(const LLVector3 &a, const LLVector3 &b);	// shortest rotation from a to b

+	const LLQuaternion& constrain(F32 radians);						// constrains rotation to a cone angle specified in radians

+

+	// Standard operators

+	friend std::ostream& operator<<(std::ostream &s, const LLQuaternion &a);					// Prints a

+	friend LLQuaternion operator+(const LLQuaternion &a, const LLQuaternion &b);	// Addition

+	friend LLQuaternion operator-(const LLQuaternion &a, const LLQuaternion &b);	// Subtraction

+	friend LLQuaternion operator-(const LLQuaternion &a);							// Negation

+	friend LLQuaternion operator*(F32 a, const LLQuaternion &q);					// Scale

+	friend LLQuaternion operator*(const LLQuaternion &q, F32 b);					// Scale

+	friend LLQuaternion operator*(const LLQuaternion &a, const LLQuaternion &b);	// Returns a * b

+	friend LLQuaternion operator~(const LLQuaternion &a);							// Returns a* (Conjugate of a)

+	bool operator==(const LLQuaternion &b) const;			// Returns a == b

+	bool operator!=(const LLQuaternion &b) const;			// Returns a != b

+

+	friend const LLQuaternion& operator*=(LLQuaternion &a, const LLQuaternion &b);	// Returns a * b

+

+	friend LLVector4 operator*(const LLVector4 &a, const LLQuaternion &rot);		// Rotates a by rot

+	friend LLVector3 operator*(const LLVector3 &a, const LLQuaternion &rot);		// Rotates a by rot

+	friend LLVector3d operator*(const LLVector3d &a, const LLQuaternion &rot);		// Rotates a by rot

+

+	// Non-standard operators

+	friend F32 dot(const LLQuaternion &a, const LLQuaternion &b);

+	friend LLQuaternion lerp(F32 t, const LLQuaternion &p, const LLQuaternion &q);		// linear interpolation (t = 0 to 1) from p to q

+	friend LLQuaternion lerp(F32 t, const LLQuaternion &q);								// linear interpolation (t = 0 to 1) from identity to q

+	friend LLQuaternion slerp(F32 t, const LLQuaternion &p, const LLQuaternion &q); 	// spherical linear interpolation from p to q

+	friend LLQuaternion slerp(F32 t, const LLQuaternion &q);							// spherical linear interpolation from identity to q

+	friend LLQuaternion nlerp(F32 t, const LLQuaternion &p, const LLQuaternion &q); 	// normalized linear interpolation from p to q

+	friend LLQuaternion nlerp(F32 t, const LLQuaternion &q); 							// normalized linear interpolation from p to q

+

+	LLVector3	packToVector3() const;						// Saves space by using the fact that our quaternions are normalized

+	void		unpackFromVector3(const LLVector3& vec);	// Saves space by using the fact that our quaternions are normalized

+

+	enum Order {

+		XYZ = 0,

+		YZX = 1,

+		ZXY = 2,

+		XZY = 3,

+		YXZ = 4,

+		ZYX = 5

+	};

+	// Creates a quaternions from maya's rotation representation,

+	// which is 3 rotations (in DEGREES) in the specified order

+	friend LLQuaternion mayaQ(F32 x, F32 y, F32 z, Order order);

+

+	// Conversions between Order and strings like "xyz" or "ZYX"

+	friend const char *OrderToString( const Order order );

+	friend Order StringToOrder( const char *str );

+

+	static BOOL parseQuat(const std::string& buf, LLQuaternion* value);

+

+	// For debugging, only

+	//static U32 mMultCount;

+};

+

+// checker

+inline BOOL	LLQuaternion::isFinite() const

+{

+	return (llfinite(mQ[VX]) && llfinite(mQ[VY]) && llfinite(mQ[VZ]) && llfinite(mQ[VS]));

+}

+

+inline BOOL LLQuaternion::isIdentity() const

+{

+	return 

+		( mQ[VX] == 0.f ) &&

+		( mQ[VY] == 0.f ) &&

+		( mQ[VZ] == 0.f ) &&

+		( mQ[VS] == 1.f );

+}

+

+inline BOOL LLQuaternion::isNotIdentity() const

+{

+	return 

+		( mQ[VX] != 0.f ) ||

+		( mQ[VY] != 0.f ) ||

+		( mQ[VZ] != 0.f ) ||

+		( mQ[VS] != 1.f );

+}

+

+

+

+inline LLQuaternion::LLQuaternion(void)

+{

+	mQ[VX] = 0.f;

+	mQ[VY] = 0.f;

+	mQ[VZ] = 0.f;

+	mQ[VS] = 1.f;

+}

+

+inline LLQuaternion::LLQuaternion(F32 x, F32 y, F32 z, F32 w)

+{

+	mQ[VX] = x;

+	mQ[VY] = y;

+	mQ[VZ] = z;

+	mQ[VS] = w;

+

+	//RN: don't normalize this case as its used mainly for temporaries during calculations

+	//normalize();

+	/*

+	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);

+	mag -= 1.f;

+	mag = fabs(mag);

+	llassert(mag < 10.f*FP_MAG_THRESHOLD);

+	*/

+}

+

+inline LLQuaternion::LLQuaternion(const F32 *q)

+{

+	mQ[VX] = q[VX];

+	mQ[VY] = q[VY];

+	mQ[VZ] = q[VZ];

+	mQ[VS] = q[VW];

+

+	normalize();

+	/*

+	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);

+	mag -= 1.f;

+	mag = fabs(mag);

+	llassert(mag < FP_MAG_THRESHOLD);

+	*/

+}

+

+

+inline void LLQuaternion::loadIdentity()

+{

+	mQ[VX] = 0.0f;

+	mQ[VY] = 0.0f;

+	mQ[VZ] = 0.0f;

+	mQ[VW] = 1.0f;

+}

+

+

+inline const LLQuaternion&	LLQuaternion::set(F32 x, F32 y, F32 z, F32 w)

+{

+	mQ[VX] = x;

+	mQ[VY] = y;

+	mQ[VZ] = z;

+	mQ[VS] = w;

+	normalize();

+	return (*this);

+}

+

+inline const LLQuaternion&	LLQuaternion::set(const LLQuaternion &quat)

+{

+	mQ[VX] = quat.mQ[VX];

+	mQ[VY] = quat.mQ[VY];

+	mQ[VZ] = quat.mQ[VZ];

+	mQ[VW] = quat.mQ[VW];

+	normalize();

+	return (*this);

+}

+

+inline const LLQuaternion&	LLQuaternion::set(const F32 *q)

+{

+	mQ[VX] = q[VX];

+	mQ[VY] = q[VY];

+	mQ[VZ] = q[VZ];

+	mQ[VS] = q[VW];

+	normalize();

+	return (*this);

+}

+

+

+// deprecated

+inline const LLQuaternion&	LLQuaternion::setQuatInit(F32 x, F32 y, F32 z, F32 w)

+{

+	mQ[VX] = x;

+	mQ[VY] = y;

+	mQ[VZ] = z;

+	mQ[VS] = w;

+	normalize();

+	return (*this);

+}

+

+// deprecated

+inline const LLQuaternion&	LLQuaternion::setQuat(const LLQuaternion &quat)

+{

+	mQ[VX] = quat.mQ[VX];

+	mQ[VY] = quat.mQ[VY];

+	mQ[VZ] = quat.mQ[VZ];

+	mQ[VW] = quat.mQ[VW];

+	normalize();

+	return (*this);

+}

+

+// deprecated

+inline const LLQuaternion&	LLQuaternion::setQuat(const F32 *q)

+{

+	mQ[VX] = q[VX];

+	mQ[VY] = q[VY];

+	mQ[VZ] = q[VZ];

+	mQ[VS] = q[VW];

+	normalize();

+	return (*this);

+}

+

+// There may be a cheaper way that avoids the sqrt.

+// Does sin_a = VX*VX + VY*VY + VZ*VZ?

+// Copied from Matrix and Quaternion FAQ 1.12

+inline void LLQuaternion::getAngleAxis(F32* angle, F32* x, F32* y, F32* z) const

+{

+	F32 cos_a = mQ[VW];

+	if (cos_a > 1.0f) cos_a = 1.0f;

+	if (cos_a < -1.0f) cos_a = -1.0f;

+

+    F32 sin_a = (F32) sqrt( 1.0f - cos_a * cos_a );

+

+    if ( fabs( sin_a ) < 0.0005f )

+		sin_a = 1.0f;

+	else

+		sin_a = 1.f/sin_a;

+

+    F32 temp_angle = 2.0f * (F32) acos( cos_a );

+	if (temp_angle > F_PI)

+	{

+		// The (angle,axis) pair should never have angles outside [PI, -PI]

+		// since we want the _shortest_ (angle,axis) solution.

+		// Since acos is defined for [0, PI], and we multiply by 2.0, we

+		// can push the angle outside the acceptible range.

+		// When this happens we set the angle to the other portion of a 

+		// full 2PI rotation, and negate the axis, which reverses the 

+		// direction of the rotation (by the right-hand rule).

+		*angle = 2.f * F_PI - temp_angle;

+    	*x = - mQ[VX] * sin_a;

+    	*y = - mQ[VY] * sin_a;

+    	*z = - mQ[VZ] * sin_a;

+	}

+	else

+	{

+		*angle = temp_angle;

+    	*x = mQ[VX] * sin_a;

+    	*y = mQ[VY] * sin_a;

+    	*z = mQ[VZ] * sin_a;

+	}

+}

+

+inline const LLQuaternion& LLQuaternion::conjugate()

+{

+	mQ[VX] *= -1.f;

+	mQ[VY] *= -1.f;

+	mQ[VZ] *= -1.f;

+	return (*this);

+}

+

+inline const LLQuaternion& LLQuaternion::conjQuat()

+{

+	mQ[VX] *= -1.f;

+	mQ[VY] *= -1.f;

+	mQ[VZ] *= -1.f;

+	return (*this);

+}

+

+// Transpose

+inline const LLQuaternion& LLQuaternion::transpose()

+{

+	mQ[VX] *= -1.f;

+	mQ[VY] *= -1.f;

+	mQ[VZ] *= -1.f;

+	return (*this);

+}

+

+// deprecated

+inline const LLQuaternion& LLQuaternion::transQuat()

+{

+	mQ[VX] *= -1.f;

+	mQ[VY] *= -1.f;

+	mQ[VZ] *= -1.f;

+	return (*this);

+}

+

+

+inline LLQuaternion 	operator+(const LLQuaternion &a, const LLQuaternion &b)

+{

+	return LLQuaternion( 

+		a.mQ[VX] + b.mQ[VX],

+		a.mQ[VY] + b.mQ[VY],

+		a.mQ[VZ] + b.mQ[VZ],

+		a.mQ[VW] + b.mQ[VW] );

+}

+

+

+inline LLQuaternion 	operator-(const LLQuaternion &a, const LLQuaternion &b)

+{

+	return LLQuaternion( 

+		a.mQ[VX] - b.mQ[VX],

+		a.mQ[VY] - b.mQ[VY],

+		a.mQ[VZ] - b.mQ[VZ],

+		a.mQ[VW] - b.mQ[VW] );

+}

+

+

+inline LLQuaternion 	operator-(const LLQuaternion &a)

+{

+	return LLQuaternion(

+		-a.mQ[VX],

+		-a.mQ[VY],

+		-a.mQ[VZ],

+		-a.mQ[VW] );

+}

+

+

+inline LLQuaternion 	operator*(F32 a, const LLQuaternion &q)

+{

+	return LLQuaternion(

+		a * q.mQ[VX],

+		a * q.mQ[VY],

+		a * q.mQ[VZ],

+		a * q.mQ[VW] );

+}

+

+

+inline LLQuaternion 	operator*(const LLQuaternion &q, F32 a)

+{

+	return LLQuaternion(

+		a * q.mQ[VX],

+		a * q.mQ[VY],

+		a * q.mQ[VZ],

+		a * q.mQ[VW] );

+}

+

+inline LLQuaternion	operator~(const LLQuaternion &a)

+{

+	LLQuaternion q(a);

+	q.conjQuat();

+	return q;

+}

+

+inline bool	LLQuaternion::operator==(const LLQuaternion &b) const

+{

+	return (  (mQ[VX] == b.mQ[VX])

+			&&(mQ[VY] == b.mQ[VY])

+			&&(mQ[VZ] == b.mQ[VZ])

+			&&(mQ[VS] == b.mQ[VS]));

+}

+

+inline bool	LLQuaternion::operator!=(const LLQuaternion &b) const

+{

+	return (  (mQ[VX] != b.mQ[VX])

+			||(mQ[VY] != b.mQ[VY])

+			||(mQ[VZ] != b.mQ[VZ])

+			||(mQ[VS] != b.mQ[VS]));

+}

+

+inline const LLQuaternion&	operator*=(LLQuaternion &a, const LLQuaternion &b)

+{

+#if 1

+	LLQuaternion q(

+		b.mQ[3] * a.mQ[0] + b.mQ[0] * a.mQ[3] + b.mQ[1] * a.mQ[2] - b.mQ[2] * a.mQ[1],

+		b.mQ[3] * a.mQ[1] + b.mQ[1] * a.mQ[3] + b.mQ[2] * a.mQ[0] - b.mQ[0] * a.mQ[2],

+		b.mQ[3] * a.mQ[2] + b.mQ[2] * a.mQ[3] + b.mQ[0] * a.mQ[1] - b.mQ[1] * a.mQ[0],

+		b.mQ[3] * a.mQ[3] - b.mQ[0] * a.mQ[0] - b.mQ[1] * a.mQ[1] - b.mQ[2] * a.mQ[2]

+	);

+	a = q;

+#else

+	a = a * b;

+#endif

+	return a;

+}

+

+const F32 ONE_PART_IN_A_MILLION = 0.000001f;

+

+inline F32	LLQuaternion::normalize()

+{

+	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);

+

+	if (mag > FP_MAG_THRESHOLD)

+	{

+		// Floating point error can prevent some quaternions from achieving

+		// exact unity length.  When trying to renormalize such quaternions we

+		// can oscillate between multiple quantized states.  To prevent such

+		// drifts we only renomalize if the length is far enough from unity.

+		if (fabs(1.f - mag) > ONE_PART_IN_A_MILLION)

+		{

+			F32 oomag = 1.f/mag;

+			mQ[VX] *= oomag;

+			mQ[VY] *= oomag;

+			mQ[VZ] *= oomag;

+			mQ[VS] *= oomag;

+		}

+	}

+	else

+	{

+		// we were given a very bad quaternion so we set it to identity

+		mQ[VX] = 0.f;

+		mQ[VY] = 0.f;

+		mQ[VZ] = 0.f;

+		mQ[VS] = 1.f;

+	}

+

+	return mag;

+}

+

+// deprecated

+inline F32	LLQuaternion::normQuat()

+{

+	F32 mag = sqrtf(mQ[VX]*mQ[VX] + mQ[VY]*mQ[VY] + mQ[VZ]*mQ[VZ] + mQ[VS]*mQ[VS]);

+

+	if (mag > FP_MAG_THRESHOLD)

+	{

+		if (fabs(1.f - mag) > ONE_PART_IN_A_MILLION)

+		{

+			// only renormalize if length not close enough to 1.0 already

+			F32 oomag = 1.f/mag;

+			mQ[VX] *= oomag;

+			mQ[VY] *= oomag;

+			mQ[VZ] *= oomag;

+			mQ[VS] *= oomag;

+		}

+	}

+	else

+	{

+		mQ[VX] = 0.f;

+		mQ[VY] = 0.f;

+		mQ[VZ] = 0.f;

+		mQ[VS] = 1.f;

+	}

+

+	return mag;

+}

+

+LLQuaternion::Order StringToOrder( const char *str );

+

+// Some notes about Quaternions

+

+// What is a Quaternion?

+// ---------------------

+// A quaternion is a point in 4-dimensional complex space.

+// Q = { Qx, Qy, Qz, Qw }

+// 

+//

+// Why Quaternions?

+// ----------------

+// The set of quaternions that make up the the 4-D unit sphere 

+// can be mapped to the set of all rotations in 3-D space.  Sometimes

+// it is easier to describe/manipulate rotations in quaternion space

+// than rotation-matrix space.

+//

+//

+// How Quaternions?

+// ----------------

+// In order to take advantage of quaternions we need to know how to

+// go from rotation-matricies to quaternions and back.  We also have

+// to agree what variety of rotations we're generating.

+// 

+// Consider the equation...   v' = v * R 

+//

+// There are two ways to think about rotations of vectors.

+// 1) v' is the same vector in a different reference frame

+// 2) v' is a new vector in the same reference frame

+//

+// bookmark -- which way are we using?

+// 

+// 

+// Quaternion from Angle-Axis:

+// ---------------------------

+// Suppose we wanted to represent a rotation of some angle (theta) 

+// about some axis ({Ax, Ay, Az})...

+//

+// axis of rotation = {Ax, Ay, Az} 

+// angle_of_rotation = theta

+//

+// s = sin(0.5 * theta)

+// c = cos(0.5 * theta)

+// Q = { s * Ax, s * Ay, s * Az, c }

+//

+//

+// 3x3 Matrix from Quaternion

+// --------------------------

+//

+//     |                                                                    |

+//     | 1 - 2 * (y^2 + z^2)   2 * (x * y + z * w)     2 * (y * w - x * z)  |

+//     |                                                                    |

+// M = | 2 * (x * y - z * w)   1 - 2 * (x^2 + z^2)     2 * (y * z + x * w)  |

+//     |                                                                    |

+//     | 2 * (x * z + y * w)   2 * (y * z - x * w)     1 - 2 * (x^2 + y^2)  |

+//     |                                                                    |

+

+#endif