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fteqw/engine/common/mathlib.c
Spoike 27a59a0cbc LOTS OF CHANGES. was hoping to get revision 5000 perfect, but really that's never going to happen. this has gone on for too long now. 
vulkan, wasapi, quake injector features added.
irc, avplug, cef plugins/drivers reworked/updated/added
openal reverb, doppler effects added.
'dir' console command now attempts to view clicked files.
lots of warning fixes, should now only be deprecation warnings for most targets (depending on compiler version anyway...).
SendEntity finally reworked to use flags properly.
effectinfo improved, other smc-targetted fixes.
mapcluster stuff now has support for linux.
.basebone+.baseframe now exist in ssqc.
qcc: -Fqccx supports qccx syntax, including qccx hacks. don't expect these to work in fteqw nor dp though.
qcc: rewrote function call handling to use refs rather than defs. this makes struct passing more efficient and makes the __out keyword usable with fields etc.
qccgui: can cope a little better with non-unicode files. can now represent most quake chars.
qcc: suppressed warnings from *extensions.qc

git-svn-id: https://svn.code.sf.net/p/fteqw/code/trunk@5000 fc73d0e0-1445-4013-8a0c-d673dee63da5
2016-07-12 00:40:13 +00:00

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/*
Copyright (C) 1996-1997 Id Software, Inc.
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"
#include <math.h>
vec3_t vec3_origin = {0,0,0};
/*-----------------------------------------------------------------*/
#define DEG2RAD( a ) ( a * M_PI ) / 180.0F
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 );
}
#ifdef _MSC_VER
#pragma optimize( "", off )
#endif
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];
}
}
#ifdef _MSC_VER
#pragma optimize( "", on )
#endif
/*-----------------------------------------------------------------*/
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 VARGS 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)
{
default:
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;
}
#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;
}
void VVPerpendicularVector(vec3_t dst, const vec3_t src)
{
if (!src[0] && !src[1])
{
if (src[2])
dst[1] = -1;
else
dst[1] = 0;
dst[0] = dst[2] = 0;
}
else
{
dst[0] = src[1];
dst[1] = -src[0];
dst[2] = 0;
VectorNormalize(dst);
}
}
void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
{
VVPerpendicularVector(right, forward);
CrossProduct(right, forward, up);
}
void QDECL VectorAngles(float *forward, float *up, float *result) //up may be NULL
{
float yaw, pitch, roll;
if (forward[1] == 0 && forward[0] == 0)
{
if (forward[2] > 0)
{
pitch = -M_PI * 0.5;
yaw = up ? atan2(-up[1], -up[0]) : 0;
}
else
{
pitch = M_PI * 0.5;
yaw = up ? atan2(up[1], up[0]) : 0;
}
roll = 0;
}
else
{
yaw = atan2(forward[1], forward[0]);
pitch = -atan2(forward[2], sqrt (forward[0]*forward[0] + forward[1]*forward[1]));
if (up)
{
vec_t cp = cos(pitch), sp = sin(pitch);
vec_t cy = cos(yaw), sy = sin(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;
roll = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
}
else
roll = 0;
}
pitch *= -180 / M_PI;
yaw *= 180 / M_PI;
roll *= 180 / M_PI;
if (pitch < 0)
pitch += 360;
if (yaw < 0)
yaw += 360;
if (roll < 0)
roll += 360;
result[0] = pitch;
result[1] = yaw;
result[2] = roll;
}
void QDECL AngleVectors (const 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);
if (forward)
{
forward[0] = cp*cy;
forward[1] = cp*sy;
forward[2] = -sp;
}
if (right)
{
right[0] = (-1*sr*sp*cy+-1*cr*-sy);
right[1] = (-1*sr*sp*sy+-1*cr*cy);
right[2] = -1*sr*cp;
}
if (up)
{
up[0] = (cr*sp*cy+-sr*-sy);
up[1] = (cr*sp*sy+-sr*cy);
up[2] = cr*cp;
}
}
void QDECL vectoangles(vec3_t fwd, vec3_t ang)
{
VectorAngles(fwd, NULL, ang);
}
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;
}
int Vector4Compare (const vec4_t v1, const vec4_t v2)
{
int i;
for (i=0 ; i<4 ; i++)
if (v1[i] != v2[i])
return 0;
return 1;
}
/*
void _VectorMA (const vec3_t veca, const float scale, const vec3_t vecb, vec3_t vecc)
{
vecc[0] = veca[0] + scale*vecb[0];
vecc[1] = veca[1] + scale*vecb[1];
vecc[2] = veca[2] + scale*vecb[2];
}
vec_t _DotProduct (vec3_t v1, vec3_t v2)
{
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}
void _VectorSubtract (vec3_t veca, 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 (vec3_t veca, 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 (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 Length(vec3_t v)
{
int i;
float length;
length = 0;
for (i=0 ; i< 3 ; i++)
length += v[i]*v[i];
length = sqrt (length); // FIXME
return length;
}
float Q_rsqrt(float number)
{
int i;
float x2, y;
const float threehalfs = 1.5F;
x2 = number * 0.5F;
y = number;
i = * (int *) &y; // evil floating point bit level hacking
i = 0x5f3759df - (i >> 1); // what the fuck?
y = * (float *) &i;
y = y * (threehalfs - (x2 * y * y)); // 1st iteration
// y = y * (threehalfs - (x2 * y * y)); // 2nd iteration, this can be removed
return y;
}
float QDECL VectorNormalize (vec3_t v)
{
float length;
float ilength;
length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
length = sqrt (length); // FIXME
if (length)
{
ilength = 1.0/length;
v[0] *= ilength;
v[1] *= ilength;
v[2] *= ilength;
}
return length;
}
void VectorNormalizeFast(vec3_t v)
{
float ilength;
ilength = Q_rsqrt(DotProduct(v, v));
v[0] *= ilength;
v[1] *= ilength;
v[2] *= ilength;
}
void VectorInverse (vec3_t v)
{
v[0] = -v[0];
v[1] = -v[1];
v[2] = -v[2];
}
int Q_log2(int val)
{
int answer=0;
while ((val>>=1) != 0)
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 QDECL 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];
}
void Matrix3x4_Multiply(const float *a, const float *b, float *out)
{
out[0] = a[0] * b[0] + a[4] * b[1] + a[8] * b[2];
out[1] = a[1] * b[0] + a[5] * b[1] + a[9] * b[2];
out[2] = a[2] * b[0] + a[6] * b[1] + a[10] * b[2];
out[3] = a[3] * b[0] + a[7] * b[1] + a[11] * b[2] + b[3];
out[4] = a[0] * b[4] + a[4] * b[5] + a[8] * b[6];
out[5] = a[1] * b[4] + a[5] * b[5] + a[9] * b[6];
out[6] = a[2] * b[4] + a[6] * b[5] + a[10] * b[6];
out[7] = a[3] * b[4] + a[7] * b[5] + a[11] * b[6] + b[7];
out[8] = a[0] * b[8] + a[4] * b[9] + a[8] * b[10];
out[9] = a[1] * b[8] + a[5] * b[9] + a[9] * b[10];
out[10] = a[2] * b[8] + a[6] * b[9] + a[10] * b[10];
out[11] = a[3] * b[8] + a[7] * b[9] + a[11] * b[10] + b[11];
}
void R_ConcatRotationsPad (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[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];
}
/*
===================
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;
#ifdef 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);
}
}
// TODO: move to nonintel.c
/*
===================
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);
}
void VectorTransform (const vec3_t in1, const matrix3x4 in2, vec3_t out)
{
out[0] = DotProduct(in1, in2[0]) + in2[0][3];
out[1] = DotProduct(in1, in2[1]) + in2[1][3];
out[2] = DotProduct(in1, in2[2]) + in2[2][3];
}
void Bones_To_PosQuat4(int numbones, const float *matrix, short *result)
{ //I ripped this function out of DP. tweaked slightly.
//http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
float origininvscale = 64;
float origin[3];
float quat[4];
float quatscale;
while (numbones --> 0)
{
float trace = matrix[0*4+0] + matrix[1*4+1] + matrix[2*4+2];
origin[0] = matrix[0*4+3];
origin[1] = matrix[1*4+3];
origin[2] = matrix[2*4+3];
if(trace > 0)
{
float r = sqrt(1.0f + trace), inv = 0.5f / r;
quat[0] = (matrix[2*4+1] - matrix[1*4+2]) * inv;
quat[1] = (matrix[0*4+2] - matrix[2*4+0]) * inv;
quat[2] = (matrix[1*4+0] - matrix[0*4+1]) * inv;
quat[3] = 0.5f * r;
}
else if(matrix[0*4+0] > matrix[1*4+1] && matrix[0*4+0] > matrix[2*4+2])
{
float r = sqrt(1.0f + matrix[0*4+0] - matrix[1*4+1] - matrix[2*4+2]), inv = 0.5f / r;
quat[0] = 0.5f * r;
quat[1] = (matrix[1*4+0] + matrix[0*4+1]) * inv;
quat[2] = (matrix[0*4+2] + matrix[2*4+0]) * inv;
quat[3] = (matrix[2*4+1] - matrix[1*4+2]) * inv;
}
else if(matrix[1*4+1] > matrix[2*4+2])
{
float r = sqrt(1.0f + matrix[1*4+1] - matrix[0*4+0] - matrix[2*4+2]), inv = 0.5f / r;
quat[0] = (matrix[1*4+0] + matrix[0*4+1]) * inv;
quat[1] = 0.5f * r;
quat[2] = (matrix[2*4+1] + matrix[1*4+2]) * inv;
quat[3] = (matrix[0*4+2] - matrix[2*4+0]) * inv;
}
else
{
float r = sqrt(1.0f + matrix[2*4+2] - matrix[0*4+0] - matrix[1*4+1]), inv = 0.5f / r;
quat[0] = (matrix[0*4+2] + matrix[2*4+0]) * inv;
quat[1] = (matrix[2*4+1] + matrix[1*4+2]) * inv;
quat[2] = 0.5f * r;
quat[3] = (matrix[1*4+0] - matrix[0*4+1]) * inv;
}
// normalize quaternion so that it is unit length
quatscale = quat[0]*quat[0]+quat[1]*quat[1]+quat[2]*quat[2]+quat[3]*quat[3];
if (quatscale)
quatscale = (quat[3] >= 0 ? -32767.0f : 32767.0f) / sqrt(quatscale);
// use a negative scale on the quat because the above function produces a
// positive quat[3] and canonical quaternions have negative quat[3]
result[0] = origin[0] * origininvscale;
result[1] = origin[1] * origininvscale;
result[2] = origin[2] * origininvscale;
result[3] = quat[0] * quatscale;
result[4] = quat[1] * quatscale;
result[5] = quat[2] * quatscale;
result[6] = quat[3] * quatscale;
matrix += 12;
result += 7;
}
}
void QDECL GenMatrixPosQuat4Scale(const vec3_t pos, const vec4_t quat, const vec3_t scale, float result[12])
{
float xx, xy, xz, xw, yy, yz, yw, zz, zw;
float x2, y2, z2;
float s;
x2 = quat[0] + quat[0];
y2 = quat[1] + quat[1];
z2 = quat[2] + quat[2];
xx = quat[0] * x2; xy = quat[0] * y2; xz = quat[0] * z2;
yy = quat[1] * y2; yz = quat[1] * z2; zz = quat[2] * z2;
xw = quat[3] * x2; yw = quat[3] * y2; zw = quat[3] * z2;
s = scale[0];
result[0*4+0] = s*(1.0f - (yy + zz));
result[1*4+0] = s*(xy + zw);
result[2*4+0] = s*(xz - yw);
s = scale[1];
result[0*4+1] = s*(xy - zw);
result[1*4+1] = s*(1.0f - (xx + zz));
result[2*4+1] = s*(yz + xw);
s = scale[2];
result[0*4+2] = s*(xz + yw);
result[1*4+2] = s*(yz - xw);
result[2*4+2] = s*(1.0f - (xx + yy));
result[0*4+3] = pos[0];
result[1*4+3] = pos[1];
result[2*4+3] = pos[2];
}
#ifdef HALFLIFEMODELS
void AngleQuaternion( const vec3_t angles, vec4_t quaternion )
{
float angle;
float sr, sp, sy, cr, cp, cy;
// FIXME: rescale the inputs to 1/2 angle
angle = angles[2] * 0.5;
sy = sin(angle);
cy = cos(angle);
angle = angles[1] * 0.5;
sp = sin(angle);
cp = cos(angle);
angle = angles[0] * 0.5;
sr = sin(angle);
cr = cos(angle);
quaternion[0] = sr*cp*cy-cr*sp*sy; // X
quaternion[1] = cr*sp*cy+sr*cp*sy; // Y
quaternion[2] = cr*cp*sy-sr*sp*cy; // Z
quaternion[3] = cr*cp*cy+sr*sp*sy; // W
}
void QuaternionMatrix( const vec4_t quaternion, float (*matrix)[4] )
{
matrix[0][0] = 1.0 - 2.0 * quaternion[1] * quaternion[1] - 2.0 * quaternion[2] * quaternion[2];
matrix[1][0] = 2.0 * quaternion[0] * quaternion[1] + 2.0 * quaternion[3] * quaternion[2];
matrix[2][0] = 2.0 * quaternion[0] * quaternion[2] - 2.0 * quaternion[3] * quaternion[1];
matrix[0][1] = 2.0 * quaternion[0] * quaternion[1] - 2.0 * quaternion[3] * quaternion[2];
matrix[1][1] = 1.0 - 2.0 * quaternion[0] * quaternion[0] - 2.0 * quaternion[2] * quaternion[2];
matrix[2][1] = 2.0 * quaternion[1] * quaternion[2] + 2.0 * quaternion[3] * quaternion[0];
matrix[0][2] = 2.0 * quaternion[0] * quaternion[2] + 2.0 * quaternion[3] * quaternion[1];
matrix[1][2] = 2.0 * quaternion[1] * quaternion[2] - 2.0 * quaternion[3] * quaternion[0];
matrix[2][2] = 1.0 - 2.0 * quaternion[0] * quaternion[0] - 2.0 * quaternion[1] * quaternion[1];
}
#endif
void QuaternionSlerp( const vec4_t p, vec4_t q, float t, vec4_t qt )
{
int i;
float omega, cosom, sinom, sclp, sclq;
// decide if one of the quaternions is backwards
float a = 0;
float b = 0;
for (i = 0; i < 4; i++) {
a += (p[i]-q[i])*(p[i]-q[i]);
b += (p[i]+q[i])*(p[i]+q[i]);
}
if (a > b) {
for (i = 0; i < 4; i++) {
q[i] = -q[i];
}
}
cosom = p[0]*q[0] + p[1]*q[1] + p[2]*q[2] + p[3]*q[3];
if ((1.0 + cosom) > 0.00000001) {
if ((1.0 - cosom) > 0.00000001) {
omega = acos( cosom );
sinom = sin( omega );
sclp = sin( (1.0 - t)*omega) / sinom;
sclq = sin( t*omega ) / sinom;
}
else {
sclp = 1.0 - t;
sclq = t;
}
for (i = 0; i < 4; i++) {
qt[i] = sclp * p[i] + sclq * q[i];
}
}
else {
qt[0] = -p[1];
qt[1] = p[0];
qt[2] = -p[3];
qt[3] = p[2];
sclp = sin( (1.0 - t) * 0.5 * M_PI);
sclq = sin( t * 0.5 * M_PI);
for (i = 0; i < 3; i++) {
qt[i] = sclp * p[i] + sclq * qt[i];
}
}
}
//This function is GL stylie (use as 2nd arg to ML_MultMatrix4).
float *Matrix4x4_CM_NewRotation(float a, float x, float y, float z)
{
static float ret[16];
float c = cos(a* M_PI / 180.0);
float s = sin(a* M_PI / 180.0);
ret[0] = x*x*(1-c)+c;
ret[4] = x*y*(1-c)-z*s;
ret[8] = x*z*(1-c)+y*s;
ret[12] = 0;
ret[1] = y*x*(1-c)+z*s;
ret[5] = y*y*(1-c)+c;
ret[9] = y*z*(1-c)-x*s;
ret[13] = 0;
ret[2] = x*z*(1-c)-y*s;
ret[6] = y*z*(1-c)+x*s;
ret[10] = z*z*(1-c)+c;
ret[14] = 0;
ret[3] = 0;
ret[7] = 0;
ret[11] = 0;
ret[15] = 1;
return ret;
}
//This function is GL stylie (use as 2nd arg to ML_MultMatrix4).
float *Matrix4x4_CM_NewTranslation(float x, float y, float z)
{
static float ret[16];
ret[0] = 1;
ret[4] = 0;
ret[8] = 0;
ret[12] = x;
ret[1] = 0;
ret[5] = 1;
ret[9] = 0;
ret[13] = y;
ret[2] = 0;
ret[6] = 0;
ret[10] = 1;
ret[14] = z;
ret[3] = 0;
ret[7] = 0;
ret[11] = 0;
ret[15] = 1;
return ret;
}
//be aware that this generates two sorts of matricies depending on order of a+b
void Matrix4_Multiply(const float *a, const float *b, float *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];
}
void Matrix3x4_RM_Transform3(const float *matrix, const float *vector, float *product)
{
product[0] = matrix[0]*vector[0] + matrix[1]*vector[1] + matrix[2]*vector[2] + matrix[3];
product[1] = matrix[4]*vector[0] + matrix[5]*vector[1] + matrix[6]*vector[2] + matrix[7];
product[2] = matrix[8]*vector[0] + matrix[9]*vector[1] + matrix[10]*vector[2] + matrix[11];
}
//transform 4d vector by a 4d matrix.
void Matrix4x4_CM_Transform4(const float *matrix, const float *vector, float *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];
}
//ignore the entire right+bottom row/column of the 4*4 matrix
void Matrix4x4_CM_Transform3x3(const float *matrix, const float *vector, float *product)
{
product[0] = matrix[0]*vector[0] + matrix[4]*vector[1] + matrix[8]*vector[2];
product[1] = matrix[1]*vector[0] + matrix[5]*vector[1] + matrix[9]*vector[2];
product[2] = matrix[2]*vector[0] + matrix[6]*vector[1] + matrix[10]*vector[2];
}
//disregard the extra bit of the matrix
void Matrix4x4_CM_Transform3(const float *matrix, const float *vector, float *product)
{
product[0] = matrix[0]*vector[0] + matrix[4]*vector[1] + matrix[8]*vector[2] + matrix[12];
product[1] = matrix[1]*vector[0] + matrix[5]*vector[1] + matrix[9]*vector[2] + matrix[13];
product[2] = matrix[2]*vector[0] + matrix[6]*vector[1] + matrix[10]*vector[2] + matrix[14];
}
void Matrix4x4_CM_Transform34(const float *matrix, const vec3_t vector, vec4_t product)
{
//transform as though vector[3] == 1
product[0] = matrix[0]*vector[0] + matrix[4]*vector[1] + matrix[8]*vector[2] + matrix[12];
product[1] = matrix[1]*vector[0] + matrix[5]*vector[1] + matrix[9]*vector[2] + matrix[13];
product[2] = matrix[2]*vector[0] + matrix[6]*vector[1] + matrix[10]*vector[2] + matrix[14];
product[3] = matrix[3]*vector[0] + matrix[7]*vector[1] + matrix[11]*vector[2] + matrix[15];
}
void Matrix4x4_CM_ModelViewMatrix(float *modelview, const vec3_t viewangles, const vec3_t vieworg)
{
float tempmat[16];
//load identity.
memset(modelview, 0, sizeof(*modelview)*16);
#if FULLYGL
modelview[0] = 1;
modelview[5] = 1;
modelview[10] = 1;
modelview[15] = 1;
Matrix4_Multiply(modelview, Matrix4_CM_NewRotation(-90, 1, 0, 0), tempmat); // put Z going up
Matrix4_Multiply(tempmat, Matrix4_CM_NewRotation(90, 0, 0, 1), modelview); // put Z going up
#else
//use this lame wierd and crazy identity matrix..
modelview[2] = -1;
modelview[4] = -1;
modelview[9] = 1;
modelview[15] = 1;
#endif
//figure out the current modelview matrix
//I would if some of these, but then I'd still need a couple of copys
Matrix4_Multiply(modelview, Matrix4x4_CM_NewRotation(-viewangles[2], 1, 0, 0), tempmat);
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewRotation(-viewangles[0], 0, 1, 0), modelview);
Matrix4_Multiply(modelview, Matrix4x4_CM_NewRotation(-viewangles[1], 0, 0, 1), tempmat);
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewTranslation(-vieworg[0], -vieworg[1], -vieworg[2]), modelview); // put Z going up
}
void Matrix4x4_CM_CreateTranslate (float *out, float x, float y, float z)
{
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = x;
out[13] = y;
out[14] = z;
out[15] = 1;
}
void Matrix4x4_RM_CreateTranslate (float *out, float x, float y, float z)
{
out[0] = 1;
out[4] = 0;
out[8] = 0;
out[12] = 0;
out[1] = 0;
out[5] = 1;
out[9] = 0;
out[13] = 0;
out[2] = 0;
out[6] = 0;
out[10] = 1;
out[14] = 0;
out[3] = x;
out[7] = y;
out[11] = z;
out[15] = 1;
}
void Matrix4x4_CM_LightMatrixFromAxis(float *modelview, const vec3_t px, const vec3_t py, const vec3_t pz, const vec3_t org)
{
modelview[ 0] = px[0];
modelview[ 1] = py[0];
modelview[ 2] = pz[0];
modelview[ 3] = 0;
modelview[ 4] = px[1];
modelview[ 5] = py[1];
modelview[ 6] = pz[1];
modelview[ 7] = 0;
modelview[ 8] = px[2];
modelview[ 9] = py[2];
modelview[10] = pz[2];
modelview[11] = 0;
modelview[12] = -(px[0]*org[0] + px[1]*org[1] + px[2]*org[2]);
modelview[13] = -(py[0]*org[0] + py[1]*org[1] + py[2]*org[2]);
modelview[14] = -(pz[0]*org[0] + pz[1]*org[1] + pz[2]*org[2]);
modelview[15] = 1;
}
void Matrix4x4_CM_ModelViewMatrixFromAxis(float *modelview, const vec3_t pn, const vec3_t right, const vec3_t up, const vec3_t vieworg)
{
float tempmat[16];
tempmat[ 0] = right[0];
tempmat[ 1] = up[0];
tempmat[ 2] = -pn[0];
tempmat[ 3] = 0;
tempmat[ 4] = right[1];
tempmat[ 5] = up[1];
tempmat[ 6] = -pn[1];
tempmat[ 7] = 0;
tempmat[ 8] = right[2];
tempmat[ 9] = up[2];
tempmat[10] = -pn[2];
tempmat[11] = 0;
tempmat[12] = 0;
tempmat[13] = 0;
tempmat[14] = 0;
tempmat[15] = 1;
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewTranslation(-vieworg[0], -vieworg[1], -vieworg[2]), modelview); // put Z going up
}
void Matrix3x4_RM_ToVectors(const float *in, float vx[3], float vy[3], float vz[3], float t[3])
{
vx[0] = in[0];
vx[1] = in[4];
vx[2] = in[8];
vy[0] = in[1];
vy[1] = in[5];
vy[2] = in[9];
vz[0] = in[2];
vz[1] = in[6];
vz[2] = in[10];
t [0] = in[3];
t [1] = in[7];
t [2] = in[11];
}
void Matrix4x4_RM_FromVectors(float *out, const float vx[3], const float vy[3], const float vz[3], const float t[3])
{
out[0] = vx[0];
out[1] = vy[0];
out[2] = vz[0];
out[3] = t[0];
out[4] = vx[1];
out[5] = vy[1];
out[6] = vz[1];
out[7] = t[1];
out[8] = vx[2];
out[9] = vy[2];
out[10] = vz[2];
out[11] = t[2];
out[12] = 0.0f;
out[13] = 0.0f;
out[14] = 0.0f;
out[15] = 1.0f;
}
void Matrix3x4_RM_FromVectors(float *out, const float vx[3], const float vy[3], const float vz[3], const float t[3])
{
out[0] = vx[0];
out[1] = vy[0];
out[2] = vz[0];
out[3] = t[0];
out[4] = vx[1];
out[5] = vy[1];
out[6] = vz[1];
out[7] = t[1];
out[8] = vx[2];
out[9] = vy[2];
out[10] = vz[2];
out[11] = t[2];
}
void Matrix4x4_CM_ModelMatrixFromAxis(float *modelview, const vec3_t pn, const vec3_t right, const vec3_t up, const vec3_t vieworg)
{
float tempmat[16];
tempmat[ 0] = pn[0];
tempmat[ 1] = pn[1];
tempmat[ 2] = pn[2];
tempmat[ 3] = 0;
tempmat[ 4] = right[0];
tempmat[ 5] = right[1];
tempmat[ 6] = right[2];
tempmat[ 7] = 0;
tempmat[ 8] = up[0];
tempmat[ 9] = up[1];
tempmat[10] = up[2];
tempmat[11] = 0;
tempmat[12] = 0;
tempmat[13] = 0;
tempmat[14] = 0;
tempmat[15] = 1;
Matrix4_Multiply(Matrix4x4_CM_NewTranslation(vieworg[0], vieworg[1], vieworg[2]), tempmat, modelview); // put Z going up
}
void Matrix4x4_CM_ModelMatrix(float *modelview, vec_t x, vec_t y, vec_t z, vec_t pitch, vec_t yaw, vec_t roll, vec_t scale)
{
float tempmat[16];
//load identity.
memset(modelview, 0, sizeof(*modelview)*16);
#if FULLYGL
modelview[0] = 1;
modelview[5] = 1;
modelview[10] = 1;
modelview[15] = 1;
Matrix4_Multiply(modelview, Matrix4x4_CM_NewRotation(-90, 1, 0, 0), tempmat); // put Z going up
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewRotation(90, 0, 0, 1), modelview); // put Z going up
#else
//use this lame wierd and crazy identity matrix..
modelview[2] = -1;
modelview[4] = -1;
modelview[9] = 1;
modelview[15] = 1;
#endif
//figure out the current modelview matrix
//I would if some of these, but then I'd still need a couple of copys
Matrix4_Multiply(modelview, Matrix4x4_CM_NewRotation(-roll, 1, 0, 0), tempmat);
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewRotation(-pitch, 0, 1, 0), modelview);
Matrix4_Multiply(modelview, Matrix4x4_CM_NewRotation(-yaw, 0, 0, 1), tempmat);
Matrix4_Multiply(tempmat, Matrix4x4_CM_NewTranslation(x, y, z), modelview);
}
void Matrix4x4_Identity(float *outm)
{
outm[ 0] = 1;
outm[ 1] = 0;
outm[ 2] = 0;
outm[ 3] = 0;
outm[ 4] = 0;
outm[ 5] = 1;
outm[ 6] = 0;
outm[ 7] = 0;
outm[ 8] = 0;
outm[ 9] = 0;
outm[10] = 1;
outm[11] = 0;
outm[12] = 0;
outm[13] = 0;
outm[14] = 0;
outm[15] = 1;
}
void Matrix4x4_CM_Projection_Far(float *proj, float fovx, float fovy, float neard, float fard)
{
double xmin, xmax, ymin, ymax;
//proj
ymax = neard * tan( fovy * M_PI / 360.0 );
ymin = -ymax;
if (fovx == fovy)
{
xmax = ymax;
xmin = ymin;
}
else
{
xmax = neard * tan( fovx * M_PI / 360.0 );
xmin = -xmax;
}
proj[0] = (2*neard) / (xmax - xmin);
proj[4] = 0;
proj[8] = (xmax + xmin) / (xmax - xmin);
proj[12] = 0;
proj[1] = 0;
proj[5] = (2*neard) / (ymax - ymin);
proj[9] = (ymax + ymin) / (ymax - ymin);
proj[13] = 0;
proj[2] = 0;
proj[6] = 0;
proj[10] = (fard+neard)/(neard-fard);
proj[14] = (2*fard*neard)/(neard-fard);
proj[3] = 0;
proj[7] = 0;
proj[11] = -1;
proj[15] = 0;
}
void Matrix4x4_CM_Projection_Inf(float *proj, float fovx, float fovy, float neard)
{
float xmin, xmax, ymin, ymax;
float nudge = 1;
//proj
ymax = neard * tan( fovy * M_PI / 360.0 );
ymin = -ymax;
if (fovx == fovy)
{
xmax = ymax;
xmin = ymin;
}
else
{
xmax = neard * tan( fovx * M_PI / 360.0 );
xmin = -xmax;
}
proj[0] = (2*neard) / (xmax - xmin);
proj[4] = 0;
proj[8] = (xmax + xmin) / (xmax - xmin);
proj[12] = 0;
proj[1] = 0;
proj[5] = (2*neard) / (ymax - ymin);
proj[9] = (ymax + ymin) / (ymax - ymin);
proj[13] = 0;
proj[2] = 0;
proj[6] = 0;
proj[10] = -1 * ((float)(1<<21)/(1<<22));
proj[14] = -2*neard * nudge;
proj[3] = 0;
proj[7] = 0;
proj[11] = -1;
proj[15] = 0;
}
void Matrix4x4_CM_Projection2(float *proj, float fovx, float fovy, float neard)
{
float xmin, xmax, ymin, ymax;
float nudge = 1;
//proj
ymax = neard * tan( fovy * M_PI / 360.0 );
ymin = -ymax;
xmax = neard * tan( fovx * M_PI / 360.0 );
xmin = -xmax;
proj[0] = (2*neard) / (xmax - xmin);
proj[4] = 0;
proj[8] = (xmax + xmin) / (xmax - xmin);
proj[12] = 0;
proj[1] = 0;
proj[5] = (2*neard) / (ymax - ymin);
proj[9] = (ymax + ymin) / (ymax - ymin);
proj[13] = 0;
proj[2] = 0;
proj[6] = 0;
proj[10] = -1 * nudge;
proj[14] = -2*neard * nudge;
proj[3] = 0;
proj[7] = 0;
proj[11] = -1;
proj[15] = 0;
}
void Matrix4x4_CM_Orthographic(float *proj, float xmin, float xmax, float ymin, float ymax,
float znear, float zfar)
{
proj[0] = 2/(xmax-xmin);
proj[4] = 0;
proj[8] = 0;
proj[12] = -(xmax+xmin)/(xmax-xmin);
proj[1] = 0;
proj[5] = 2/(ymax-ymin);
proj[9] = 0;
proj[13] = -(ymax+ymin)/(ymax-ymin);
proj[2] = 0;
proj[6] = 0;
proj[10] = -2/(zfar-znear);
proj[14] = -(zfar+znear)/(zfar-znear);
proj[3] = 0;
proj[7] = 0;
proj[11] = 0;
proj[15] = 1;
}
void Matrix4x4_CM_OrthographicD3D(float *proj, float xmin, float xmax, float ymax, float ymin,
float znear, float zfar)
{
proj[0] = 2/(xmax-xmin);
proj[4] = 0;
proj[8] = 0;
proj[12] = (xmax+xmin)/(xmin-xmax);
proj[1] = 0;
proj[5] = 2/(ymax-ymin);
proj[9] = 0;
proj[13] = (ymax+ymin)/(ymin-ymax);
proj[2] = 0;
proj[6] = 0;
proj[10] = 1/(znear-zfar);
proj[14] = znear/(znear-zfar);
proj[3] = 0;
proj[7] = 0;
proj[11] = 0;
proj[15] = 1;
}
/*
* Compute inverse of 4x4 transformation matrix.
* Code contributed by Jacques Leroy jle@star.be
* Return true for success, false for failure (singular matrix)
* This came to FTE via 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 Matrix3x3_RM_Invert_Simple (const vec3_t in1[3], vec3_t out[3])
{
// we only support uniform scaling, so assume the first row is enough
// (note the lack of sqrt here, because we're trying to undo the scaling,
// this means multiplying by the inverse scale twice - squaring it, which
// makes the sqrt a waste of time)
#if 1
double scale = 1.0 / (in1[0][0] * in1[0][0] + in1[0][1] * in1[0][1] + in1[0][2] * in1[0][2]);
#else
double scale = 3.0 / sqrt
(in1->m[0][0] * in1->m[0][0] + in1->m[0][1] * in1->m[0][1] + in1->m[0][2] * in1->m[0][2]
+ in1->m[1][0] * in1->m[1][0] + in1->m[1][1] * in1->m[1][1] + in1->m[1][2] * in1->m[1][2]
+ in1->m[2][0] * in1->m[2][0] + in1->m[2][1] * in1->m[2][1] + in1->m[2][2] * in1->m[2][2]);
scale *= scale;
#endif
// invert the rotation by transposing and multiplying by the squared
// recipricol of the input matrix scale as described above
out[0][0] = in1[0][0] * scale;
out[0][1] = in1[1][0] * scale;
out[0][2] = in1[2][0] * scale;
out[1][0] = in1[0][1] * scale;
out[1][1] = in1[1][1] * scale;
out[1][2] = in1[2][1] * scale;
out[2][0] = in1[0][2] * scale;
out[2][1] = in1[1][2] * scale;
out[2][2] = in1[2][2] * scale;
}
void Matrix3x4_Invert (const float *in1, float *out)
{
vec3_t a, b, c, trans;
VectorSet (a, in1[0], in1[4], in1[8]);
VectorSet (b, in1[1], in1[5], in1[9]);
VectorSet (c, in1[2], in1[6], in1[10]);
VectorScale (a, 1 / DotProduct (a, a), a);
VectorScale (b, 1 / DotProduct (b, b), b);
VectorScale (c, 1 / DotProduct (c, c), c);
VectorSet (trans, in1[3], in1[7], in1[11]);
Vector4Set (out+0, a[0], a[1], a[2], -DotProduct (a, trans));
Vector4Set (out+4, b[0], b[1], b[2], -DotProduct (b, trans));
Vector4Set (out+8, c[0], c[1], c[2], -DotProduct (c, trans));
}
void QDECL Matrix3x4_Invert_Simple (const float *in1, float *out)
{
// we only support uniform scaling, so assume the first row is enough
// (note the lack of sqrt here, because we're trying to undo the scaling,
// this means multiplying by the inverse scale twice - squaring it, which
// makes the sqrt a waste of time)
#if 1
double scale = 1.0 / (in1[0] * in1[0] + in1[1] * in1[1] + in1[2] * in1[2]);
#else
double scale = 3.0 / sqrt
(in1->m[0][0] * in1->m[0][0] + in1->m[0][1] * in1->m[0][1] + in1->m[0][2] * in1->m[0][2]
+ in1->m[1][0] * in1->m[1][0] + in1->m[1][1] * in1->m[1][1] + in1->m[1][2] * in1->m[1][2]
+ in1->m[2][0] * in1->m[2][0] + in1->m[2][1] * in1->m[2][1] + in1->m[2][2] * in1->m[2][2]);
scale *= scale;
#endif
// invert the rotation by transposing and multiplying by the squared
// recipricol of the input matrix scale as described above
out[0] = in1[0] * scale;
out[1] = in1[4] * scale;
out[2] = in1[8] * scale;
out[4] = in1[1] * scale;
out[5] = in1[5] * scale;
out[6] = in1[9] * scale;
out[8] = in1[2] * scale;
out[9] = in1[6] * scale;
out[10] = in1[10] * scale;
// invert the translate
out[3] = -(in1[3] * out[0] + in1[7] * out[1] + in1[11] * out[2]);
out[7] = -(in1[3] * out[4] + in1[7] * out[5] + in1[11] * out[6]);
out[11] = -(in1[3] * out[8] + in1[7] * out[9] + in1[11] * out[10]);
}
void Matrix3x4_InvertTo4x4_Simple (const float *in1, float *out)
{
Matrix3x4_Invert_Simple(in1, out);
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
}
void Matrix3x4_InvertTo3x3(const float *in, float *result)
{
float t1[16], tr[16];
memcpy(t1, in, sizeof(float)*12);
t1[12] = 0;
t1[13] = 0;
t1[14] = 0;
t1[15] = 1;
Matrix4_Invert(t1, tr);
VectorCopy(tr+0, result+0);
VectorCopy(tr+4, result+3);
VectorCopy(tr+8, result+6);
return;
/*
#define A(x,y) in[x+y*4]
#define result(x,y) result[x+y*3]
double determinant = +A(0,0)*(A(1,1)*A(2,2)-A(2,1)*A(1,2))
-A(0,1)*(A(1,0)*A(2,2)-A(1,2)*A(2,0))
+A(0,2)*(A(1,0)*A(2,1)-A(1,1)*A(2,0));
double invdet = 1/determinant;
result(0,0) = (A(1,1)*A(2,2)-A(2,1)*A(1,2))*invdet;
result(1,0) = -(A(0,1)*A(2,2)-A(0,2)*A(2,1))*invdet;
result(2,0) = (A(0,1)*A(1,2)-A(0,2)*A(1,1))*invdet;
result(0,1) = -(A(1,0)*A(2,2)-A(1,2)*A(2,0))*invdet;
result(1,1) = (A(0,0)*A(2,2)-A(0,2)*A(2,0))*invdet;
result(2,1) = -(A(0,0)*A(1,2)-A(1,0)*A(0,2))*invdet;
result(0,2) = (A(1,0)*A(2,1)-A(2,0)*A(1,1))*invdet;
result(1,2) = -(A(0,0)*A(2,1)-A(2,0)*A(0,1))*invdet;
result(2,2) = (A(0,0)*A(1,1)-A(1,0)*A(0,1))*invdet;
*/
}
//screen->3d
void Matrix4x4_CM_UnProject(const vec3_t in, vec3_t out, const vec3_t viewangles, const vec3_t vieworg, float fovx, float fovy)
{
float modelview[16];
float proj[16];
float tempm[16];
Matrix4x4_CM_ModelViewMatrix(modelview, viewangles, vieworg);
Matrix4x4_CM_Projection_Inf(proj, fovx, fovy, 4);
Matrix4_Multiply(proj, modelview, tempm);
Matrix4_Invert(tempm, proj);
{
float v[4], tempv[4];
v[0] = in[0]*2-1;
v[1] = in[1]*2-1;
v[2] = in[2];
v[3] = 1;
//don't use 1, because the far clip plane really is an infinite distance away
if (v[2] >= 1)
v[2] = 0.999999;
Matrix4x4_CM_Transform4(proj, v, tempv);
out[0] = tempv[0]/tempv[3];
out[1] = tempv[1]/tempv[3];
out[2] = tempv[2]/tempv[3];
}
}
//returns fractions of screen.
//uses GL style rotations and translations and stuff.
//3d -> screen (fixme: offscreen return values needed)
//returns false if the 2d point is offscreen.
qboolean Matrix4x4_CM_Project (const vec3_t in, vec3_t out, const vec3_t viewangles, const vec3_t vieworg, float fovx, float fovy)
{
qboolean result = true;
float modelview[16];
float proj[16];
Matrix4x4_CM_ModelViewMatrix(modelview, viewangles, vieworg);
Matrix4x4_CM_Projection_Inf(proj, fovx, fovy, 4);
{
float v[4], tempv[4];
v[0] = in[0];
v[1] = in[1];
v[2] = in[2];
v[3] = 1;
Matrix4x4_CM_Transform4(modelview, v, tempv);
Matrix4x4_CM_Transform4(proj, tempv, v);
v[0] /= v[3];
v[1] /= v[3];
if (v[2] < 0)
result = false; //too close to the view
v[2] /= v[3];
out[0] = (1+v[0])/2;
out[1] = (1+v[1])/2;
out[2] = (1+v[2])/2;
if (out[2] > 1)
result = false; //beyond far clip plane
}
return result;
}
//I much prefer it to take float*...
void Matrix3_Multiply (vec3_t *in1, vec3_t *in2, vec3_t *out)
{
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];
}
vec_t QDECL VectorNormalize2 (const vec3_t v, vec3_t out)
{
float length, ilength;
length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
if (length)
{
length = sqrt (length); // FIXME
ilength = 1/length;
out[0] = v[0]*ilength;
out[1] = v[1]*ilength;
out[2] = v[2]*ilength;
}
else
{
VectorClear (out);
}
return length;
}
float ColorNormalize (vec3_t in, vec3_t out)
{
float f = max (max (in[0], in[1]), in[2]);
if ( f > 1.0 ) {
f = 1.0 / f;
out[0] = in[0] * f;
out[1] = in[1] * f;
out[2] = in[2] * f;
} else {
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
return f;
}
void MakeNormalVectors (vec3_t forward, vec3_t right, vec3_t up)
{
float d;
// this rotate and negat guarantees a vector
// not colinear with the original
right[1] = -forward[0];
right[2] = forward[1];
right[0] = forward[2];
d = DotProduct (right, forward);
VectorMA (right, -d, forward, right);
VectorNormalize (right);
CrossProduct (right, forward, up);
}
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