quakespasm/Quake/mathlib.c

/*
Copyright (C) 1996-2001 Id Software, Inc.
Copyright (C) 2002-2009 John Fitzgibbons and others
Copyright (C) 2007-2008 Kristian Duske
Copyright (C) 2010-2014 QuakeSpasm developers

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

*/
// mathlib.c -- math primitives

#include "quakedef.h"

vec3_t vec3_origin = {0,0,0};

/*-----------------------------------------------------------------*/


void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
{
	float d;
	vec3_t n;
	float inv_denom;

	inv_denom = 1.0F / DotProduct( normal, normal );

	d = DotProduct( normal, p ) * inv_denom;

	n[0] = normal[0] * inv_denom;
	n[1] = normal[1] * inv_denom;
	n[2] = normal[2] * inv_denom;

	dst[0] = p[0] - d * n[0];
	dst[1] = p[1] - d * n[1];
	dst[2] = p[2] - d * n[2];
}

/*
** assumes "src" is normalized
*/
void PerpendicularVector( vec3_t dst, const vec3_t src )
{
	int	pos;
	int i;
	float minelem = 1.0F;
	vec3_t tempvec;

	/*
	** find the smallest magnitude axially aligned vector
	*/
	for ( pos = 0, i = 0; i < 3; i++ )
	{
		if ( fabs( src[i] ) < minelem )
		{
			pos = i;
			minelem = fabs( src[i] );
		}
	}
	tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
	tempvec[pos] = 1.0F;

	/*
	** project the point onto the plane defined by src
	*/
	ProjectPointOnPlane( dst, tempvec, src );

	/*
	** normalize the result
	*/
	VectorNormalize( dst );
}

//johnfitz -- removed RotatePointAroundVector() becuase it's no longer used and my compiler fucked it up anyway

//spike -- readded, because it is useful, and my version of gcc has never had a problem with it.
void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
{
	float	m[3][3];
	float	im[3][3];
	float	zrot[3][3];
	float	tmpmat[3][3];
	float	rot[3][3];
	int	i;
	vec3_t vr, vup, vf;

	vf[0] = dir[0];
	vf[1] = dir[1];
	vf[2] = dir[2];

	PerpendicularVector( vr, dir );
	CrossProduct( vr, vf, vup );

	m[0][0] = vr[0];
	m[1][0] = vr[1];
	m[2][0] = vr[2];

	m[0][1] = vup[0];
	m[1][1] = vup[1];
	m[2][1] = vup[2];

	m[0][2] = vf[0];
	m[1][2] = vf[1];
	m[2][2] = vf[2];

	memcpy( im, m, sizeof( im ) );

	im[0][1] = m[1][0];
	im[0][2] = m[2][0];
	im[1][0] = m[0][1];
	im[1][2] = m[2][1];
	im[2][0] = m[0][2];
	im[2][1] = m[1][2];

	memset( zrot, 0, sizeof( zrot ) );
	zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;

	zrot[0][0] = cos( DEG2RAD( degrees ) );
	zrot[0][1] = sin( DEG2RAD( degrees ) );
	zrot[1][0] = -sin( DEG2RAD( degrees ) );
	zrot[1][1] = cos( DEG2RAD( degrees ) );

	R_ConcatRotations( m, zrot, tmpmat );
	R_ConcatRotations( tmpmat, im, rot );

	for ( i = 0; i < 3; i++ )
	{
		dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];
	}
}
/*-----------------------------------------------------------------*/


float	anglemod(float a)
{
#if 0
	if (a >= 0)
		a -= 360*(int)(a/360);
	else
		a += 360*( 1 + (int)(-a/360) );
#endif
	a = (360.0/65536) * ((int)(a*(65536/360.0)) & 65535);
	return a;
}


/*
==================
BoxOnPlaneSide

Returns 1, 2, or 1 + 2
==================
*/
int BoxOnPlaneSide (vec3_t emins, vec3_t emaxs, mplane_t *p)
{
	float	dist1, dist2;
	int		sides;

#if 0	// this is done by the BOX_ON_PLANE_SIDE macro before calling this
		// function
// fast axial cases
	if (p->type < 3)
	{
		if (p->dist <= emins[p->type])
			return 1;
		if (p->dist >= emaxs[p->type])
			return 2;
		return 3;
	}
#endif

// general case
	switch (p->signbits)
	{
	case 0:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		break;
	case 1:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		break;
	case 2:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		break;
	case 3:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		break;
	case 4:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		break;
	case 5:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		break;
	case 6:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		break;
	case 7:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		break;
	default:
		dist1 = dist2 = 0;		// shut up compiler
		Sys_Error ("BoxOnPlaneSide:  Bad signbits");
		break;
	}

#if 0
	int		i;
	vec3_t	corners[2];

	for (i=0 ; i<3 ; i++)
	{
		if (plane->normal[i] < 0)
		{
			corners[0][i] = emins[i];
			corners[1][i] = emaxs[i];
		}
		else
		{
			corners[1][i] = emins[i];
			corners[0][i] = emaxs[i];
		}
	}
	dist = DotProduct (plane->normal, corners[0]) - plane->dist;
	dist2 = DotProduct (plane->normal, corners[1]) - plane->dist;
	sides = 0;
	if (dist1 >= 0)
		sides = 1;
	if (dist2 < 0)
		sides |= 2;
#endif

	sides = 0;
	if (dist1 >= p->dist)
		sides = 1;
	if (dist2 < p->dist)
		sides |= 2;

#ifdef PARANOID
	if (sides == 0)
		Sys_Error ("BoxOnPlaneSide: sides==0");
#endif

	return sides;
}

//johnfitz -- the opposite of AngleVectors.  this takes forward and generates pitch yaw roll
//Spike: take right and up vectors to properly set yaw and roll
void VectorAngles (const vec3_t forward, float *up, vec3_t angles)
{
	if (forward[0] == 0 && forward[1] == 0)
	{	//either vertically up or down
		if (forward[2] > 0)
		{
			angles[PITCH] = -90;
			angles[YAW] = up ? atan2(-up[1], -up[0]) / M_PI_DIV_180: 0;
		}
		else
		{
			angles[PITCH] = 90;
			angles[YAW] = up ? atan2(up[1], up[0]) / M_PI_DIV_180: 0;
		}
		angles[ROLL] = 0;
	}
	else
	{
		angles[PITCH] = -atan2(forward[2], sqrt(DotProduct2(forward,forward)));
		angles[YAW] = atan2(forward[1], forward[0]);

		if (up)
		{
			vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
			vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
			vec3_t tleft, tup;
			tleft[0] = -sy;
			tleft[1] = cy;
			tleft[2] = 0;
			tup[0] = sp*cy;
			tup[1] = sp*sy;
			tup[2] = cp;
			angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup)) / M_PI_DIV_180;
		}
		else angles[ROLL] = 0;

		angles[PITCH] /= M_PI_DIV_180;
		angles[YAW] /= M_PI_DIV_180;
	}
}

void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
{
	float		angle;
	float		sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI*2 / 360);
	sy = sin(angle);
	cy = cos(angle);
	angle = angles[PITCH] * (M_PI*2 / 360);
	sp = sin(angle);
	cp = cos(angle);
	angle = angles[ROLL] * (M_PI*2 / 360);
	sr = sin(angle);
	cr = cos(angle);

	forward[0] = cp*cy;
	forward[1] = cp*sy;
	forward[2] = -sp;
	right[0] = (-1*sr*sp*cy+-1*cr*-sy);
	right[1] = (-1*sr*sp*sy+-1*cr*cy);
	right[2] = -1*sr*cp;
	up[0] = (cr*sp*cy+-sr*-sy);
	up[1] = (cr*sp*sy+-sr*cy);
	up[2] = cr*cp;
}

int VectorCompare (const vec3_t v1, const vec3_t v2)
{
	int		i;

	for (i=0 ; i<3 ; i++)
		if (v1[i] != v2[i])
			return 0;

	return 1;
}

vec_t _DotProduct (const vec3_t v1, const vec3_t v2)
{
	return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}

void _VectorSubtract (const vec3_t veca, const vec3_t vecb, vec3_t out)
{
	out[0] = veca[0]-vecb[0];
	out[1] = veca[1]-vecb[1];
	out[2] = veca[2]-vecb[2];
}

void _VectorAdd (const vec3_t veca, const vec3_t vecb, vec3_t out)
{
	out[0] = veca[0]+vecb[0];
	out[1] = veca[1]+vecb[1];
	out[2] = veca[2]+vecb[2];
}

void _VectorCopy (const vec3_t in, vec3_t out)
{
	out[0] = in[0];
	out[1] = in[1];
	out[2] = in[2];
}

void CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
{
	cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
	cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
	cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
}

vec_t VectorLength(const vec3_t v)
{
	return sqrt(DotProduct(v,v));
}

float VectorNormalize (vec3_t v)
{
	float	length, ilength;

	length = sqrt(DotProduct(v,v));

	if (length)
	{
		ilength = 1/length;
		v[0] *= ilength;
		v[1] *= ilength;
		v[2] *= ilength;
	}

	return length;
}

void VectorInverse (vec3_t v)
{
	v[0] = -v[0];
	v[1] = -v[1];
	v[2] = -v[2];
}

void VectorScale (const vec3_t in, vec_t scale, vec3_t out)
{
	out[0] = in[0]*scale;
	out[1] = in[1]*scale;
	out[2] = in[2]*scale;
}


int Q_log2(int val)
{
	int answer=0;
	while (val>>=1)
		answer++;
	return answer;
}


/*
================
R_ConcatRotations
================
*/
void R_ConcatRotations (float in1[3][3], float in2[3][3], float out[3][3])
{
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
				in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
				in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
				in1[0][2] * in2[2][2];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
				in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
				in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
				in1[1][2] * in2[2][2];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
				in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
				in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
				in1[2][2] * in2[2][2];
}


/*
================
R_ConcatTransforms
================
*/
void R_ConcatTransforms (float in1[3][4], float in2[3][4], float out[3][4])
{
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
				in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
				in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
				in1[0][2] * in2[2][2];
	out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] +
				in1[0][2] * in2[2][3] + in1[0][3];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
				in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
				in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
				in1[1][2] * in2[2][2];
	out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] +
				in1[1][2] * in2[2][3] + in1[1][3];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
				in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
				in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
				in1[2][2] * in2[2][2];
	out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] +
				in1[2][2] * in2[2][3] + in1[2][3];
}


/*
===================
FloorDivMod

Returns mathematically correct (floor-based) quotient and remainder for
numer and denom, both of which should contain no fractional part. The
quotient must fit in 32 bits.
====================
*/

void FloorDivMod (double numer, double denom, int *quotient,
		int *rem)
{
	int		q, r;
	double	x;

#ifndef PARANOID
	if (denom <= 0.0)
		Sys_Error ("FloorDivMod: bad denominator %f\n", denom);

//	if ((floor(numer) != numer) || (floor(denom) != denom))
//		Sys_Error ("FloorDivMod: non-integer numer or denom %f %f\n",
//				numer, denom);
#endif

	if (numer >= 0.0)
	{

		x = floor(numer / denom);
		q = (int)x;
		r = (int)floor(numer - (x * denom));
	}
	else
	{
	//
	// perform operations with positive values, and fix mod to make floor-based
	//
		x = floor(-numer / denom);
		q = -(int)x;
		r = (int)floor(-numer - (x * denom));
		if (r != 0)
		{
			q--;
			r = (int)denom - r;
		}
	}

	*quotient = q;
	*rem = r;
}


/*
===================
GreatestCommonDivisor
====================
*/
int GreatestCommonDivisor (int i1, int i2)
{
	if (i1 > i2)
	{
		if (i2 == 0)
			return (i1);
		return GreatestCommonDivisor (i2, i1 % i2);
	}
	else
	{
		if (i1 == 0)
			return (i2);
		return GreatestCommonDivisor (i1, i2 % i1);
	}
}


/*
===================
Invert24To16

Inverts an 8.24 value to a 16.16 value
====================
*/

fixed16_t Invert24To16(fixed16_t val)
{
	if (val < 256)
		return (0xFFFFFFFF);

	return (fixed16_t)
			(((double)0x10000 * (double)0x1000000 / (double)val) + 0.5);
}

/*
===================
Various 4*4 matrix functions.
===================
*/
void Matrix4_Transform4(const mat4_t matrix, const vec4_t vector, vec4_t product)
{
	product[0] = matrix[0]*vector[0] + matrix[4]*vector[1] + matrix[8]*vector[2] + matrix[12]*vector[3];
	product[1] = matrix[1]*vector[0] + matrix[5]*vector[1] + matrix[9]*vector[2] + matrix[13]*vector[3];
	product[2] = matrix[2]*vector[0] + matrix[6]*vector[1] + matrix[10]*vector[2] + matrix[14]*vector[3];
	product[3] = matrix[3]*vector[0] + matrix[7]*vector[1] + matrix[11]*vector[2] + matrix[15]*vector[3];
}
void Matrix4_Multiply(const mat4_t a, const mat4_t b, mat4_t out)
{
	out[0]  = a[0] * b[0] + a[4] * b[1] + a[8] * b[2] + a[12] * b[3];
	out[1]  = a[1] * b[0] + a[5] * b[1] + a[9] * b[2] + a[13] * b[3];
	out[2]  = a[2] * b[0] + a[6] * b[1] + a[10] * b[2] + a[14] * b[3];
	out[3]  = a[3] * b[0] + a[7] * b[1] + a[11] * b[2] + a[15] * b[3];

	out[4]  = a[0] * b[4] + a[4] * b[5] + a[8] * b[6] + a[12] * b[7];
	out[5]  = a[1] * b[4] + a[5] * b[5] + a[9] * b[6] + a[13] * b[7];
	out[6]  = a[2] * b[4] + a[6] * b[5] + a[10] * b[6] + a[14] * b[7];
	out[7]  = a[3] * b[4] + a[7] * b[5] + a[11] * b[6] + a[15] * b[7];

	out[8]  = a[0] * b[8] + a[4] * b[9] + a[8] * b[10] + a[12] * b[11];
	out[9]  = a[1] * b[8] + a[5] * b[9] + a[9] * b[10] + a[13] * b[11];
	out[10] = a[2] * b[8] + a[6] * b[9] + a[10] * b[10] + a[14] * b[11];
	out[11] = a[3] * b[8] + a[7] * b[9] + a[11] * b[10] + a[15] * b[11];

	out[12] = a[0] * b[12] + a[4] * b[13] + a[8] * b[14] + a[12] * b[15];
	out[13] = a[1] * b[12] + a[5] * b[13] + a[9] * b[14] + a[13] * b[15];
	out[14] = a[2] * b[12] + a[6] * b[13] + a[10] * b[14] + a[14] * b[15];
	out[15] = a[3] * b[12] + a[7] * b[13] + a[11] * b[14] + a[15] * b[15];
}
/*
 * Compute inverse of 4x4 transformation matrix.
 * Code contributed by Jacques Leroy jle@star.be
 * Return true for success, false for failure (singular matrix)
 * Spike: This comes from mesa's GLU.
 */
qboolean Matrix4_Invert(const float *m, float *out)
{
/* NB. OpenGL Matrices are COLUMN major. */
#define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]

   float wtmp[4][8];
   float m0, m1, m2, m3, s;
   float *r0, *r1, *r2, *r3;

   r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];

   r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
      r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
      r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
      r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
      r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
      r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
      r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
      r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
      r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
      r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
      r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
      r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;

   /* choose pivot - or die */
   if (fabs(r3[0]) > fabs(r2[0]))
      SWAP_ROWS(r3, r2)
   if (fabs(r2[0]) > fabs(r1[0]))
      SWAP_ROWS(r2, r1)
   if (fabs(r1[0]) > fabs(r0[0]))
      SWAP_ROWS(r1, r0)
   if (0.0 == r0[0])
      return false;

   /* eliminate first variable     */
   m1 = r1[0] / r0[0];
   m2 = r2[0] / r0[0];
   m3 = r3[0] / r0[0];
   s = r0[1];
   r1[1] -= m1 * s;
   r2[1] -= m2 * s;
   r3[1] -= m3 * s;
   s = r0[2];
   r1[2] -= m1 * s;
   r2[2] -= m2 * s;
   r3[2] -= m3 * s;
   s = r0[3];
   r1[3] -= m1 * s;
   r2[3] -= m2 * s;
   r3[3] -= m3 * s;
   s = r0[4];
   if (s != 0.0) {
      r1[4] -= m1 * s;
      r2[4] -= m2 * s;
      r3[4] -= m3 * s;
   }
   s = r0[5];
   if (s != 0.0) {
      r1[5] -= m1 * s;
      r2[5] -= m2 * s;
      r3[5] -= m3 * s;
   }
   s = r0[6];
   if (s != 0.0) {
      r1[6] -= m1 * s;
      r2[6] -= m2 * s;
      r3[6] -= m3 * s;
   }
   s = r0[7];
   if (s != 0.0) {
      r1[7] -= m1 * s;
      r2[7] -= m2 * s;
      r3[7] -= m3 * s;
   }

   /* choose pivot - or die */
   if (fabs(r3[1]) > fabs(r2[1]))
      SWAP_ROWS(r3, r2)
   if (fabs(r2[1]) > fabs(r1[1]))
      SWAP_ROWS(r2, r1)
   if (0.0 == r1[1])
      return false;

   /* eliminate second variable */
   m2 = r2[1] / r1[1];
   m3 = r3[1] / r1[1];
   r2[2] -= m2 * r1[2];
   r3[2] -= m3 * r1[2];
   r2[3] -= m2 * r1[3];
   r3[3] -= m3 * r1[3];
   s = r1[4];
   if (0.0 != s) {
      r2[4] -= m2 * s;
      r3[4] -= m3 * s;
   }
   s = r1[5];
   if (0.0 != s) {
      r2[5] -= m2 * s;
      r3[5] -= m3 * s;
   }
   s = r1[6];
   if (0.0 != s) {
      r2[6] -= m2 * s;
      r3[6] -= m3 * s;
   }
   s = r1[7];
   if (0.0 != s) {
      r2[7] -= m2 * s;
      r3[7] -= m3 * s;
   }

   /* choose pivot - or die */
   if (fabs(r3[2]) > fabs(r2[2]))
      SWAP_ROWS(r3, r2)
   if (0.0 == r2[2])
      return false;

   /* eliminate third variable */
   m3 = r3[2] / r2[2];
   r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
      r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];

   /* last check */
   if (0.0 == r3[3])
      return false;

   s = 1.0 / r3[3];             /* now back substitute row 3 */
   r3[4] *= s;
   r3[5] *= s;
   r3[6] *= s;
   r3[7] *= s;

   m2 = r2[3];                  /* now back substitute row 2 */
   s = 1.0 / r2[2];
   r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
      r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
   m1 = r1[3];
   r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
      r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
   m0 = r0[3];
   r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
      r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;

   m1 = r1[2];                  /* now back substitute row 1 */
   s = 1.0 / r1[1];
   r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
      r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
   m0 = r0[2];
   r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
      r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;

   m0 = r0[1];                  /* now back substitute row 0 */
   s = 1.0 / r0[0];
   r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
      r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);

   MAT(out, 0, 0) = r0[4];
   MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
   MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
   MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
   MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
   MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
   MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
   MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
   MAT(out, 3, 3) = r3[7];

   return true;

#undef MAT
#undef SWAP_ROWS
}

void Matrix4_ViewMatrix(const vec3_t viewangles, const vec3_t vieworg, mat4_t out)
{	//directly compute a view matrix. this is not the same as a model matrix (in part because the values are all negated).
	float cp = cos(-viewangles[0] * M_PI / 180.0);
	float sp = sin(-viewangles[0] * M_PI / 180.0);
	float cy = cos(-viewangles[1] * M_PI / 180.0);
	float sy = sin(-viewangles[1] * M_PI / 180.0);
	float cr = cos(-viewangles[2] * M_PI / 180.0);
	float sr = sin(-viewangles[2] * M_PI / 180.0);

	out[0]  = -sr*sp*cy - cr*sy;
	out[1]  = -cr*sp*cy + sr*sy;
	out[2]  = -cp*cy;
	out[3]  = 0;
	out[4]  = sr*sp*sy - cr*cy;
	out[5]  = cr*sp*sy + sr*cy;
	out[6]  = cp*sy;
	out[7]  = 0;
	out[8]  = sr*cp;
	out[9]  = cr*cp;
	out[10] = -sp;
	out[11] = 0;
	out[12] =   - out[0]*vieworg[0] - out[4]*vieworg[1] - out[ 8]*vieworg[2];
	out[13] =   - out[1]*vieworg[0] - out[5]*vieworg[1] - out[ 9]*vieworg[2];
	out[14] =   - out[2]*vieworg[0] - out[6]*vieworg[1] - out[10]*vieworg[2];
	out[15] = 1 - out[3]*vieworg[0] - out[7]*vieworg[1] - out[11]*vieworg[2];
}
//computes an orthographic projection matrix (mostly equivelent to glFrustum)
void Matrix4_ProjectionMatrix(float fovx, float fovy, float neard, float fard, qboolean d3d, float xskew, float yskew, mat4_t out)
{
	double xmin, xmax, ymin, ymax;
	double dn = (d3d?0:-1), df = 1;

	xmax = neard * tan( fovx * M_PI / 360.0 );
	xmin = -xmax;
	ymax = neard * tan( fovy * M_PI / 360.0 );
	ymin = -ymax;

	xmax += xskew;	//this stuff for r_stereo
	xmin += xskew;
	ymax += yskew;
	ymin += yskew;

	out[0] = (2*neard) / (xmax - xmin);
	out[4] = 0;
	out[8] = (xmax + xmin) / (xmax - xmin);
	out[12] = 0;

	out[1] = 0;
	out[5] = (2*neard) / (ymax - ymin);
	out[9] = (ymax + ymin) / (ymax - ymin);
	out[13] = 0;

	out[2] = 0;
	out[6] = 0;
	if (fard < neard)
	{	//fiddle with the far clip plane to make it rather large
		//depth precision is non-linear, decaying with distance relative to the near clip plane, a closer near plane degrades precision faster, so an 'infinite' far clip plane doesn't actually hurt typical precision all that much, at least with a 24bit depth buffer.
		const double epsilon = 1.0/(1<<22);
		out[10] = epsilon-1;
		out[14] = (epsilon-(df-dn))*neard;
	}
	else
	{
		out[10] = (fard*df-neard*dn)/(neard-fard);
		out[14] = ((df-dn)*fard*neard)/(neard-fard);
	}

	out[3] = 0;
	out[7] = 0;
	out[11] = -1;
	out[15] = 0;
}