path: root/indra/llmath/m4math.cpp

/** 
 * @file m4math.cpp
 * @brief LLMatrix4 class implementation.
 *
 * $LicenseInfo:firstyear=2000&license=viewergpl$
 * 
 * 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
 * 
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 * 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
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 */

#include "linden_common.h"

//#include "vmath.h"
#include "v3math.h"
#include "v4math.h"
#include "m4math.h"
#include "m3math.h"
#include "llquaternion.h"




// LLMatrix4

// Constructors


LLMatrix4::LLMatrix4(const F32 *mat)
{
	mMatrix[0][0] = mat[0];
	mMatrix[0][1] = mat[1];
	mMatrix[0][2] = mat[2];
	mMatrix[0][3] = mat[3];

	mMatrix[1][0] = mat[4];
	mMatrix[1][1] = mat[5];
	mMatrix[1][2] = mat[6];
	mMatrix[1][3] = mat[7];

	mMatrix[2][0] = mat[8];
	mMatrix[2][1] = mat[9];
	mMatrix[2][2] = mat[10];
	mMatrix[2][3] = mat[11];

	mMatrix[3][0] = mat[12];
	mMatrix[3][1] = mat[13];
	mMatrix[3][2] = mat[14];
	mMatrix[3][3] = mat[15];
}

LLMatrix4::LLMatrix4(const LLMatrix3 &mat, const LLVector4 &vec)
{
	mMatrix[0][0] = mat.mMatrix[0][0];
	mMatrix[0][1] = mat.mMatrix[0][1];
	mMatrix[0][2] = mat.mMatrix[0][2];
	mMatrix[0][3] = 0.f;

	mMatrix[1][0] = mat.mMatrix[1][0];
	mMatrix[1][1] = mat.mMatrix[1][1];
	mMatrix[1][2] = mat.mMatrix[1][2];
	mMatrix[1][3] = 0.f;

	mMatrix[2][0] = mat.mMatrix[2][0];
	mMatrix[2][1] = mat.mMatrix[2][1];
	mMatrix[2][2] = mat.mMatrix[2][2];
	mMatrix[2][3] = 0.f;

	mMatrix[3][0] = vec.mV[0];
	mMatrix[3][1] = vec.mV[1];
	mMatrix[3][2] = vec.mV[2];
	mMatrix[3][3] = 1.f;
}

LLMatrix4::LLMatrix4(const LLMatrix3 &mat)
{
	mMatrix[0][0] = mat.mMatrix[0][0];
	mMatrix[0][1] = mat.mMatrix[0][1];
	mMatrix[0][2] = mat.mMatrix[0][2];
	mMatrix[0][3] = 0.f;

	mMatrix[1][0] = mat.mMatrix[1][0];
	mMatrix[1][1] = mat.mMatrix[1][1];
	mMatrix[1][2] = mat.mMatrix[1][2];
	mMatrix[1][3] = 0.f;

	mMatrix[2][0] = mat.mMatrix[2][0];
	mMatrix[2][1] = mat.mMatrix[2][1];
	mMatrix[2][2] = mat.mMatrix[2][2];
	mMatrix[2][3] = 0.f;

	mMatrix[3][0] = 0.f;
	mMatrix[3][1] = 0.f;
	mMatrix[3][2] = 0.f;
	mMatrix[3][3] = 1.f;
}

LLMatrix4::LLMatrix4(const LLQuaternion &q)
{
	*this = initRotation(q);
}

LLMatrix4::LLMatrix4(const LLQuaternion &q, const LLVector4 &pos)
{
	*this = initRotTrans(q, pos);
}

LLMatrix4::LLMatrix4(const F32 angle, const LLVector4 &vec, const LLVector4 &pos)
{
	initRotTrans(LLQuaternion(angle, vec), pos);
}

LLMatrix4::LLMatrix4(const F32 angle, const LLVector4 &vec)
{
	initRotation(LLQuaternion(angle, vec));

	mMatrix[3][0] = 0.f;
	mMatrix[3][1] = 0.f;
	mMatrix[3][2] = 0.f;
	mMatrix[3][3] = 1.f;
}

LLMatrix4::LLMatrix4(const F32 roll, const F32 pitch, const F32 yaw, const LLVector4 &pos)
{
	LLMatrix3	mat(roll, pitch, yaw);
	initRotTrans(LLQuaternion(mat), pos);
}

LLMatrix4::LLMatrix4(const F32 roll, const F32 pitch, const F32 yaw)
{
	LLMatrix3	mat(roll, pitch, yaw);
	initRotation(LLQuaternion(mat));

	mMatrix[3][0] = 0.f;
	mMatrix[3][1] = 0.f;
	mMatrix[3][2] = 0.f;
	mMatrix[3][3] = 1.f;
}

LLMatrix4::~LLMatrix4(void)
{
}

// Clear and Assignment Functions

const LLMatrix4& LLMatrix4::setZero()
{
	mMatrix[0][0] = 0.f;
	mMatrix[0][1] = 0.f;
	mMatrix[0][2] = 0.f;
	mMatrix[0][3] = 0.f;

	mMatrix[1][0] = 0.f;
	mMatrix[1][1] = 0.f;
	mMatrix[1][2] = 0.f;
	mMatrix[1][3] = 0.f;

	mMatrix[2][0] = 0.f;
	mMatrix[2][1] = 0.f;
	mMatrix[2][2] = 0.f;
	mMatrix[2][3] = 0.f;

	mMatrix[3][0] = 0.f;
	mMatrix[3][1] = 0.f;
	mMatrix[3][2] = 0.f;
	mMatrix[3][3] = 0.f;
	return *this;
}


// various useful mMatrix functions

const LLMatrix4&	LLMatrix4::transpose()
{
	LLMatrix4 mat;
	mat.mMatrix[0][0] = mMatrix[0][0];
	mat.mMatrix[1][0] = mMatrix[0][1];
	mat.mMatrix[2][0] = mMatrix[0][2];
	mat.mMatrix[3][0] = mMatrix[0][3];

	mat.mMatrix[0][1] = mMatrix[1][0];
	mat.mMatrix[1][1] = mMatrix[1][1];
	mat.mMatrix[2][1] = mMatrix[1][2];
	mat.mMatrix[3][1] = mMatrix[1][3];

	mat.mMatrix[0][2] = mMatrix[2][0];
	mat.mMatrix[1][2] = mMatrix[2][1];
	mat.mMatrix[2][2] = mMatrix[2][2];
	mat.mMatrix[3][2] = mMatrix[2][3];

	mat.mMatrix[0][3] = mMatrix[3][0];
	mat.mMatrix[1][3] = mMatrix[3][1];
	mat.mMatrix[2][3] = mMatrix[3][2];
	mat.mMatrix[3][3] = mMatrix[3][3];

	*this = mat;
	return *this;
}


F32 LLMatrix4::determinant() const
{
	llerrs << "Not implemented!" << llendl;
	return 0.f;
}

// Only works for pure orthonormal, homogeneous transform matrices.
const LLMatrix4&	LLMatrix4::invert(void) 
{
	// transpose the rotation part
	F32 temp;
	temp = mMatrix[VX][VY]; mMatrix[VX][VY] = mMatrix[VY][VX]; mMatrix[VY][VX] = temp;
	temp = mMatrix[VX][VZ]; mMatrix[VX][VZ] = mMatrix[VZ][VX]; mMatrix[VZ][VX] = temp;
	temp = mMatrix[VY][VZ]; mMatrix[VY][VZ] = mMatrix[VZ][VY]; mMatrix[VZ][VY] = temp;

	// rotate the translation part by the new rotation 
	// (temporarily store in empty column of matrix)
	U32 j;
	for (j=0; j<3; j++)
	{
		mMatrix[j][VW] =  mMatrix[VW][VX] * mMatrix[VX][j] + 
						  mMatrix[VW][VY] * mMatrix[VY][j] +
						  mMatrix[VW][VZ] * mMatrix[VZ][j]; 
	}

	// negate and copy the temporary vector back to the tranlation row
	mMatrix[VW][VX] = -mMatrix[VX][VW];
	mMatrix[VW][VY] = -mMatrix[VY][VW];
	mMatrix[VW][VZ] = -mMatrix[VZ][VW];

   	// zero the empty column again
	mMatrix[VX][VW] = mMatrix[VY][VW] = mMatrix[VZ][VW] = 0.0f;
	
	return *this;
}

LLVector4 LLMatrix4::getFwdRow4() const
{
	return LLVector4(mMatrix[VX][VX], mMatrix[VX][VY], mMatrix[VX][VZ], mMatrix[VX][VW]);
}

LLVector4 LLMatrix4::getLeftRow4() const
{
	return LLVector4(mMatrix[VY][VX], mMatrix[VY][VY], mMatrix[VY][VZ], mMatrix[VY][VW]);
}

LLVector4 LLMatrix4::getUpRow4() const
{
	return LLVector4(mMatrix[VZ][VX], mMatrix[VZ][VY], mMatrix[VZ][VZ], mMatrix[VZ][VW]);
}

// SJB: This code is correct for a logicly stored (non-transposed) matrix;
//		Our matrices are stored transposed, OpenGL style, so this generates the
//		INVERSE quaternion (-x, -y, -z, w)!
//		Because we use similar logic in LLQuaternion::getMatrix3,
//		we are internally consistant so everything works OK :)
LLQuaternion	LLMatrix4::quaternion() const
{
	LLQuaternion	quat;
	F32		tr, s, q[4];
	U32		i, j, k;
	U32		nxt[3] = {1, 2, 0};

	tr = mMatrix[0][0] + mMatrix[1][1] + mMatrix[2][2];

	// check the diagonal
	if (tr > 0.f) 
	{
		s = (F32)sqrt (tr + 1.f);
		quat.mQ[VS] = s / 2.f;
		s = 0.5f / s;
		quat.mQ[VX] = (mMatrix[1][2] - mMatrix[2][1]) * s;
		quat.mQ[VY] = (mMatrix[2][0] - mMatrix[0][2]) * s;
		quat.mQ[VZ] = (mMatrix[0][1] - mMatrix[1][0]) * s;
	} 
	else
	{		
		// diagonal is negative
		i = 0;
		if (mMatrix[1][1] > mMatrix[0][0]) 
			i = 1;
		if (mMatrix[2][2] > mMatrix[i][i]) 
			i = 2;

		j = nxt[i];
		k = nxt[j];


		s = (F32)sqrt ((mMatrix[i][i] - (mMatrix[j][j] + mMatrix[k][k])) + 1.f);

		q[i] = s * 0.5f;

		if (s != 0.f) 
			s = 0.5f / s;

		q[3] = (mMatrix[j][k] - mMatrix[k][j]) * s;
		q[j] = (mMatrix[i][j] + mMatrix[j][i]) * s;
		q[k] = (mMatrix[i][k] + mMatrix[k][i]) * s;

		quat.setQuat(q);
	}
	return quat;
}



void LLMatrix4::initRows(const LLVector4 &row0,
						 const LLVector4 &row1,
						 const LLVector4 &row2,
						 const LLVector4 &row3)
{
	mMatrix[0][0] = row0.mV[0];
	mMatrix[0][1] = row0.mV[1];
	mMatrix[0][2] = row0.mV[2];
	mMatrix[0][3] = row0.mV[3];

	mMatrix[1][0] = row1.mV[0];
	mMatrix[1][1] = row1.mV[1];
	mMatrix[1][2] = row1.mV[2];
	mMatrix[1][3] = row1.mV[3];

	mMatrix[2][0] = row2.mV[0];
	mMatrix[2][1] = row2.mV[1];
	mMatrix[2][2] = row2.mV[2];
	mMatrix[2][3] = row2.mV[3];

	mMatrix[3][0] = row3.mV[0];
	mMatrix[3][1] = row3.mV[1];
	mMatrix[3][2] = row3.mV[2];
	mMatrix[3][3] = row3.mV[3];
}


const LLMatrix4& 	LLMatrix4::initRotation(const F32 angle, const F32 x, const F32 y, const F32 z)
{
	LLMatrix3	mat(angle, x, y, z);
	return initMatrix(mat);
}


const LLMatrix4& 	LLMatrix4::initRotation(F32 angle, const LLVector4 &vec)
{
	LLMatrix3	mat(angle, vec);
	return initMatrix(mat);
}


const LLMatrix4& 	LLMatrix4::initRotation(const F32 roll, const F32 pitch, const F32 yaw)
{
	LLMatrix3	mat(roll, pitch, yaw);
	return initMatrix(mat);
}


const LLMatrix4&  	LLMatrix4::initRotation(const LLQuaternion &q)
{
	LLMatrix3	mat(q);
	return initMatrix(mat);
}


// Position and Rotation
const LLMatrix4&  	LLMatrix4::initRotTrans(const F32 angle, const F32 rx, const F32 ry, const F32 rz,
											const F32 tx, const F32 ty, const F32 tz)
{
	LLMatrix3	mat(angle, rx, ry, rz);
	LLVector3	translation(tx, ty, tz);
	initMatrix(mat);
	setTranslation(translation);
	return (*this);
}

const LLMatrix4&  	LLMatrix4::initRotTrans(const F32 angle, const LLVector3 &axis, const LLVector3&translation)
{
	LLMatrix3	mat(angle, axis);
	initMatrix(mat);
	setTranslation(translation);
	return (*this);
}

const LLMatrix4&  	LLMatrix4::initRotTrans(const F32 roll, const F32 pitch, const F32 yaw, const LLVector4 &translation)
{
	LLMatrix3	mat(roll, pitch, yaw);
	initMatrix(mat);
	setTranslation(translation);
	return (*this);
}

/*
const LLMatrix4&  	LLMatrix4::initRotTrans(const LLVector4 &fwd, 
											const LLVector4 &left, 
											const LLVector4 &up, 
											const LLVector4 &translation)
{
	LLMatrix3 mat(fwd, left, up);
	initMatrix(mat);
	setTranslation(translation);
	return (*this);
}
*/

const LLMatrix4&  	LLMatrix4::initRotTrans(const LLQuaternion &q, const LLVector4 &translation)
{
	LLMatrix3	mat(q);
	initMatrix(mat);
	setTranslation(translation);
	return (*this);
}

const LLMatrix4& LLMatrix4::initAll(const LLVector3 &scale, const LLQuaternion &q, const LLVector3 &pos)
{
	F32		sx, sy, sz;
	F32		xx, xy, xz, xw, yy, yz, yw, zz, zw;

	sx      = scale.mV[0];
	sy      = scale.mV[1];
	sz      = scale.mV[2];

    xx      = q.mQ[VX] * q.mQ[VX];
    xy      = q.mQ[VX] * q.mQ[VY];
    xz      = q.mQ[VX] * q.mQ[VZ];
    xw      = q.mQ[VX] * q.mQ[VW];

    yy      = q.mQ[VY] * q.mQ[VY];
    yz      = q.mQ[VY] * q.mQ[VZ];
    yw      = q.mQ[VY] * q.mQ[VW];

    zz      = q.mQ[VZ] * q.mQ[VZ];
    zw      = q.mQ[VZ] * q.mQ[VW];

    mMatrix[0][0]  = (1.f - 2.f * ( yy + zz )) *sx;
    mMatrix[0][1]  = (	    2.f * ( xy + zw )) *sx;
    mMatrix[0][2]  = (	    2.f * ( xz - yw )) *sx;

    mMatrix[1][0]  = ( 	    2.f * ( xy - zw )) *sy;
    mMatrix[1][1]  = (1.f - 2.f * ( xx + zz )) *sy;
    mMatrix[1][2]  = (      2.f * ( yz + xw )) *sy;

    mMatrix[2][0]  = (	    2.f * ( xz + yw )) *sz;
    mMatrix[2][1]  = ( 	    2.f * ( yz - xw )) *sz;
    mMatrix[2][2]  = (1.f - 2.f * ( xx + yy )) *sz;

	mMatrix[3][0]  = pos.mV[0];
	mMatrix[3][1]  = pos.mV[1];
	mMatrix[3][2]  = pos.mV[2];
	mMatrix[3][3]  = 1.0;

	// TODO -- should we set the translation portion to zero?
	return (*this);
}

// Rotate exisitng mMatrix
const LLMatrix4&  	LLMatrix4::rotate(const F32 angle, const F32 x, const F32 y, const F32 z)
{
	LLVector4	vec4(x, y, z);
	LLMatrix4	mat(angle, vec4);
	*this *= mat;
	return *this;
}

const LLMatrix4&  	LLMatrix4::rotate(const F32 angle, const LLVector4 &vec)
{
	LLMatrix4	mat(angle, vec);
	*this *= mat;
	return *this;
}

const LLMatrix4&  	LLMatrix4::rotate(const F32 roll, const F32 pitch, const F32 yaw)
{
	LLMatrix4	mat(roll, pitch, yaw);
	*this *= mat;
	return *this;
}

const LLMatrix4&  	LLMatrix4::rotate(const LLQuaternion &q)
{
	LLMatrix4	mat(q);
	*this *= mat;
	return *this;
}


const LLMatrix4&  	LLMatrix4::translate(const LLVector3 &vec)
{
	mMatrix[3][0] += vec.mV[0];
	mMatrix[3][1] += vec.mV[1];
	mMatrix[3][2] += vec.mV[2];
	return (*this);
}


void LLMatrix4::setFwdRow(const LLVector3 &row)
{
	mMatrix[VX][VX] = row.mV[VX];
	mMatrix[VX][VY] = row.mV[VY];
	mMatrix[VX][VZ] = row.mV[VZ];
}

void LLMatrix4::setLeftRow(const LLVector3 &row)
{
	mMatrix[VY][VX] = row.mV[VX];
	mMatrix[VY][VY] = row.mV[VY];
	mMatrix[VY][VZ] = row.mV[VZ];
}

void LLMatrix4::setUpRow(const LLVector3 &row)
{
	mMatrix[VZ][VX] = row.mV[VX];
	mMatrix[VZ][VY] = row.mV[VY];
	mMatrix[VZ][VZ] = row.mV[VZ];
}


void LLMatrix4::setFwdCol(const LLVector3 &col)
{
	mMatrix[VX][VX] = col.mV[VX];
	mMatrix[VY][VX] = col.mV[VY];
	mMatrix[VZ][VX] = col.mV[VZ];
}

void LLMatrix4::setLeftCol(const LLVector3 &col)
{
	mMatrix[VX][VY] = col.mV[VX];
	mMatrix[VY][VY] = col.mV[VY];
	mMatrix[VZ][VY] = col.mV[VZ];
}

void LLMatrix4::setUpCol(const LLVector3 &col)
{
	mMatrix[VX][VZ] = col.mV[VX];
	mMatrix[VY][VZ] = col.mV[VY];
	mMatrix[VZ][VZ] = col.mV[VZ];
}


const LLMatrix4&  	LLMatrix4::setTranslation(const F32 tx, const F32 ty, const F32 tz)
{
	mMatrix[VW][VX] = tx;
	mMatrix[VW][VY] = ty;
	mMatrix[VW][VZ] = tz;
	return (*this);
}

const LLMatrix4&  	LLMatrix4::setTranslation(const LLVector3 &translation)
{
	mMatrix[VW][VX] = translation.mV[VX];
	mMatrix[VW][VY] = translation.mV[VY];
	mMatrix[VW][VZ] = translation.mV[VZ];
	return (*this);
}

const LLMatrix4&  	LLMatrix4::setTranslation(const LLVector4 &translation)
{
	mMatrix[VW][VX] = translation.mV[VX];
	mMatrix[VW][VY] = translation.mV[VY];
	mMatrix[VW][VZ] = translation.mV[VZ];
	return (*this);
}

// LLMatrix3 Extraction and Setting
LLMatrix3  	LLMatrix4::getMat3() const
{
	LLMatrix3 retmat;

	retmat.mMatrix[0][0] = mMatrix[0][0];
	retmat.mMatrix[0][1] = mMatrix[0][1];
	retmat.mMatrix[0][2] = mMatrix[0][2];

	retmat.mMatrix[1][0] = mMatrix[1][0];
	retmat.mMatrix[1][1] = mMatrix[1][1];
	retmat.mMatrix[1][2] = mMatrix[1][2];

	retmat.mMatrix[2][0] = mMatrix[2][0];
	retmat.mMatrix[2][1] = mMatrix[2][1];
	retmat.mMatrix[2][2] = mMatrix[2][2];

	return retmat;
}

const LLMatrix4&  	LLMatrix4::initMatrix(const LLMatrix3 &mat)
{
	mMatrix[0][0] = mat.mMatrix[0][0];
	mMatrix[0][1] = mat.mMatrix[0][1];
	mMatrix[0][2] = mat.mMatrix[0][2];
	mMatrix[0][3] = 0.f;

	mMatrix[1][0] = mat.mMatrix[1][0];
	mMatrix[1][1] = mat.mMatrix[1][1];
	mMatrix[1][2] = mat.mMatrix[1][2];
	mMatrix[1][3] = 0.f;

	mMatrix[2][0] = mat.mMatrix[2][0];
	mMatrix[2][1] = mat.mMatrix[2][1];
	mMatrix[2][2] = mat.mMatrix[2][2];
	mMatrix[2][3] = 0.f;

	mMatrix[3][0] = 0.f;
	mMatrix[3][1] = 0.f;
	mMatrix[3][2] = 0.f;
	mMatrix[3][3] = 1.f;
	return (*this);
}

const LLMatrix4&  	LLMatrix4::initMatrix(const LLMatrix3 &mat, const LLVector4 &translation)
{
	mMatrix[0][0] = mat.mMatrix[0][0];
	mMatrix[0][1] = mat.mMatrix[0][1];
	mMatrix[0][2] = mat.mMatrix[0][2];
	mMatrix[0][3] = 0.f;

	mMatrix[1][0] = mat.mMatrix[1][0];
	mMatrix[1][1] = mat.mMatrix[1][1];
	mMatrix[1][2] = mat.mMatrix[1][2];
	mMatrix[1][3] = 0.f;

	mMatrix[2][0] = mat.mMatrix[2][0];
	mMatrix[2][1] = mat.mMatrix[2][1];
	mMatrix[2][2] = mat.mMatrix[2][2];
	mMatrix[2][3] = 0.f;

	mMatrix[3][0] = translation.mV[0];
	mMatrix[3][1] = translation.mV[1];
	mMatrix[3][2] = translation.mV[2];
	mMatrix[3][3] = 1.f;
	return (*this);
}

// LLMatrix4 Operators


/* Not implemented to help enforce code consistency with the syntax of
   row-major notation.  This is a Good Thing.
LLVector4 operator*(const LLMatrix4 &a, const LLVector4 &b)
{
	// Operate "to the right" on column-vector b
	LLVector4	vec;
	vec.mV[VX] = a.mMatrix[VX][VX] * b.mV[VX] + 
				 a.mMatrix[VY][VX] * b.mV[VY] + 
 				 a.mMatrix[VZ][VX] * b.mV[VZ] +
				 a.mMatrix[VW][VX] * b.mV[VW];

	vec.mV[VY] = a.mMatrix[VX][VY] * b.mV[VX] + 
				 a.mMatrix[VY][VY] * b.mV[VY] + 
				 a.mMatrix[VZ][VY] * b.mV[VZ] +
				 a.mMatrix[VW][VY] * b.mV[VW];

	vec.mV[VZ] = a.mMatrix[VX][VZ] * b.mV[VX] + 
			  	 a.mMatrix[VY][VZ] * b.mV[VY] + 
				 a.mMatrix[VZ][VZ] * b.mV[VZ] +
				 a.mMatrix[VW][VZ] * b.mV[VW];

	vec.mV[VW] = a.mMatrix[VX][VW] * b.mV[VX] + 
				 a.mMatrix[VY][VW] * b.mV[VY] + 
				 a.mMatrix[VZ][VW] * b.mV[VZ] +
				 a.mMatrix[VW][VW] * b.mV[VW];
	return vec;
}
*/

// Operates "to the left" on row-vector a
//
// This used to be in the header file but was not actually inlined in practice.
// When avatar vertex programs are off, this function is a hot spot in profiles
// due to software skinning in LLViewerJointMesh::updateGeometry().  JC
LLVector3 operator*(const LLVector3 &a, const LLMatrix4 &b)
{
	// This is better than making a temporary LLVector3.  This eliminates an
	// unnecessary LLVector3() constructor and also helps the compiler to
	// realize that the output floats do not alias the input floats, hence
	// eliminating redundant loads of a.mV[0], etc.  JC
	return LLVector3(a.mV[VX] * b.mMatrix[VX][VX] + 
					 a.mV[VY] * b.mMatrix[VY][VX] + 
					 a.mV[VZ] * b.mMatrix[VZ][VX] +
					 b.mMatrix[VW][VX],
					 
					 a.mV[VX] * b.mMatrix[VX][VY] + 
					 a.mV[VY] * b.mMatrix[VY][VY] + 
					 a.mV[VZ] * b.mMatrix[VZ][VY] +
					 b.mMatrix[VW][VY],
					 
					 a.mV[VX] * b.mMatrix[VX][VZ] + 
					 a.mV[VY] * b.mMatrix[VY][VZ] + 
					 a.mV[VZ] * b.mMatrix[VZ][VZ] +
					 b.mMatrix[VW][VZ]);
}

LLVector4 operator*(const LLVector4 &a, const LLMatrix4 &b)
{
	// Operate "to the left" on row-vector a
	return LLVector4(a.mV[VX] * b.mMatrix[VX][VX] + 
					 a.mV[VY] * b.mMatrix[VY][VX] + 
					 a.mV[VZ] * b.mMatrix[VZ][VX] +
					 a.mV[VW] * b.mMatrix[VW][VX],

					 a.mV[VX] * b.mMatrix[VX][VY] + 
					 a.mV[VY] * b.mMatrix[VY][VY] + 
					 a.mV[VZ] * b.mMatrix[VZ][VY] +
					 a.mV[VW] * b.mMatrix[VW][VY],

					 a.mV[VX] * b.mMatrix[VX][VZ] + 
					 a.mV[VY] * b.mMatrix[VY][VZ] + 
					 a.mV[VZ] * b.mMatrix[VZ][VZ] +
					 a.mV[VW] * b.mMatrix[VW][VZ],

					 a.mV[VX] * b.mMatrix[VX][VW] + 
					 a.mV[VY] * b.mMatrix[VY][VW] + 
					 a.mV[VZ] * b.mMatrix[VZ][VW] +
					 a.mV[VW] * b.mMatrix[VW][VW]);
}

LLVector4 rotate_vector(const LLVector4 &a, const LLMatrix4 &b)
{
	// Rotates but does not translate
	// Operate "to the left" on row-vector a
	LLVector4	vec;
	vec.mV[VX] = a.mV[VX] * b.mMatrix[VX][VX] + 
				 a.mV[VY] * b.mMatrix[VY][VX] + 
				 a.mV[VZ] * b.mMatrix[VZ][VX];

	vec.mV[VY] = a.mV[VX] * b.mMatrix[VX][VY] + 
				 a.mV[VY] * b.mMatrix[VY][VY] + 
				 a.mV[VZ] * b.mMatrix[VZ][VY];

	vec.mV[VZ] = a.mV[VX] * b.mMatrix[VX][VZ] + 
				 a.mV[VY] * b.mMatrix[VY][VZ] + 
				 a.mV[VZ] * b.mMatrix[VZ][VZ];

//	vec.mV[VW] = a.mV[VX] * b.mMatrix[VX][VW] + 
//				 a.mV[VY] * b.mMatrix[VY][VW] + 
//				 a.mV[VZ] * b.mMatrix[VZ][VW] +
	vec.mV[VW] = a.mV[VW];
	return vec;
}

LLVector3 rotate_vector(const LLVector3 &a, const LLMatrix4 &b)
{
	// Rotates but does not translate
	// Operate "to the left" on row-vector a
	LLVector3	vec;
	vec.mV[VX] = a.mV[VX] * b.mMatrix[VX][VX] + 
				 a.mV[VY] * b.mMatrix[VY][VX] + 
				 a.mV[VZ] * b.mMatrix[VZ][VX];

	vec.mV[VY] = a.mV[VX] * b.mMatrix[VX][VY] + 
				 a.mV[VY] * b.mMatrix[VY][VY] + 
				 a.mV[VZ] * b.mMatrix[VZ][VY];

	vec.mV[VZ] = a.mV[VX] * b.mMatrix[VX][VZ] + 
				 a.mV[VY] * b.mMatrix[VY][VZ] + 
				 a.mV[VZ] * b.mMatrix[VZ][VZ];
	return vec;
}

bool operator==(const LLMatrix4 &a, const LLMatrix4 &b)
{
	U32		i, j;
	for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
	{
		for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
		{
			if (a.mMatrix[j][i] != b.mMatrix[j][i])
				return FALSE;
		}
	}
	return TRUE;
}

bool operator!=(const LLMatrix4 &a, const LLMatrix4 &b)
{
	U32		i, j;
	for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
	{
		for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
		{
			if (a.mMatrix[j][i] != b.mMatrix[j][i])
				return TRUE;
		}
	}
	return FALSE;
}

const LLMatrix4& operator*=(LLMatrix4 &a, F32 k)
{
	U32		i, j;
	for (i = 0; i < NUM_VALUES_IN_MAT4; i++)
	{
		for (j = 0; j < NUM_VALUES_IN_MAT4; j++)
		{
			a.mMatrix[j][i] *= k;
		}
	}
	return a;
}

std::ostream& operator<<(std::ostream& s, const LLMatrix4 &a) 
{
	s << "{ " 
		<< a.mMatrix[VX][VX] << ", " 
		<< a.mMatrix[VX][VY] << ", " 
		<< a.mMatrix[VX][VZ] << ", " 
		<< a.mMatrix[VX][VW] 
		<< "; "
		<< a.mMatrix[VY][VX] << ", " 
		<< a.mMatrix[VY][VY] << ", " 
		<< a.mMatrix[VY][VZ] << ", " 
		<< a.mMatrix[VY][VW] 
		<< "; "
		<< a.mMatrix[VZ][VX] << ", " 
		<< a.mMatrix[VZ][VY] << ", " 
		<< a.mMatrix[VZ][VZ] << ", " 
		<< a.mMatrix[VZ][VW] 
		<< "; "
		<< a.mMatrix[VW][VX] << ", " 
		<< a.mMatrix[VW][VY] << ", " 
		<< a.mMatrix[VW][VZ] << ", " 
		<< a.mMatrix[VW][VW] 
	  << " }";
	return s;
}