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quakespasm/Quake/mathlib.c

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/*
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;
}
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