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quakeforge/libs/util/mathlib.c

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/*
mathlib.c
math primitives
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:
Free Software Foundation, Inc.
59 Temple Place - Suite 330
Boston, MA 02111-1307, USA
*/
#ifdef HAVE_CONFIG_H
# include "config.h"
#endif
#ifdef HAVE_STRING_H
# include <string.h>
#endif
#ifdef HAVE_STRINGS_H
# include <strings.h>
#endif
#include <math.h>
#define IMPLEMENT_R_Cull
#define IMPLEMENT_VectorNormalize
#include "QF/mathlib.h"
#include "QF/qtypes.h"
#include "QF/sys.h"
VISIBLE int nanmask = 255 << 23;
static plane_t _frustum[4];
VISIBLE plane_t *const frustum = _frustum;
static vec3_t _vec3_origin = { 0, 0, 0 };
VISIBLE const vec_t * const vec3_origin = _vec3_origin;
static vec3_t _quat_origin = { 0, 0, 0 };
VISIBLE const vec_t * const quat_origin = _quat_origin;
#define DEG2RAD(a) (a * (M_PI / 180.0))
#define FMANTBITS 23
#define FMANTMASK ((1 << FMANTBITS) - 1)
#define FEXPBITS 8
#define FEXPMASK ((1 << FEXPBITS) - 1)
#define FBIAS (1 << (FEXPBITS - 1))
#define FEXPMAX ((1 << FEXPBITS) - 1)
#define HMANTBITS 10
#define HMANTMASK ((1 << HMANTBITS) - 1)
#define HEXPBITS 5
#define HEXPMASK ((1 << HEXPBITS) - 1)
#define HBIAS (1 << (HEXPBITS - 1))
#define HEXPMAX ((1 << HEXPBITS) - 1)
int16_t
FloatToHalf (float x)
{
union {
float f;
uint32_t u;
} uf;
unsigned sign;
int exp;
unsigned mant;
int16_t half;
uf.f = x;
sign = (uf.u >> (FEXPBITS + FMANTBITS)) & 1;
exp = ((uf.u >> FMANTBITS) & FEXPMASK) - FBIAS + HBIAS;
mant = (uf.u & FMANTMASK) >> (FMANTBITS - HMANTBITS);
if (exp <= 0) {
mant |= 1 << HMANTBITS;
mant >>= min (1 - exp, HMANTBITS + 1);
exp = 0;
} else if (exp >= HEXPMAX) {
mant = 0;
exp = HEXPMAX;
}
half = (sign << (HEXPBITS + HMANTBITS)) | (exp << HMANTBITS) | mant;
return half;
}
float
HalfToFloat (int16_t x)
{
union {
float f;
uint32_t u;
} uf;
unsigned sign;
int exp;
unsigned mant;
sign = (x >> (HEXPBITS + HMANTBITS)) & 1;
exp = ((x >> HMANTBITS) & HEXPMASK);
mant = (x & HMANTMASK) << (FMANTBITS - HMANTBITS);
if (exp == 0) {
if (mant) {
while (mant < (1 << FMANTBITS)) {
mant <<= 1;
exp--;
}
mant &= (1 << FMANTBITS) - 1;
exp += FBIAS - HBIAS + 1;
}
} else if (exp == HEXPMAX) {
exp = FEXPMAX;
} else {
exp += FBIAS - HBIAS;
}
uf.u = (sign << (FEXPBITS + FMANTBITS)) | (exp << FMANTBITS) | mant;
return uf.f;
}
static void
ProjectPointOnPlane (vec3_t dst, const vec3_t p, const vec3_t normal)
{
float inv_denom, d;
vec3_t n;
inv_denom = 1.0F / DotProduct (normal, normal);
d = DotProduct (normal, p) * inv_denom;
VectorScale (normal, inv_denom * d, n);
VectorSubtract (p, n, dst);
}
// assumes "src" is normalized
static void
PerpendicularVector (vec3_t dst, const vec3_t src)
{
int pos, 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]);
}
}
VectorZero (tempvec);
tempvec[pos] = 1.0F;
/* project the point onto the plane defined by src */
ProjectPointOnPlane (dst, tempvec, src);
/* normalize the result */
VectorNormalize (dst);
}
#if defined(_WIN32) && !defined(__GNUC__)
# pragma optimize( "", off )
#endif
VISIBLE void
VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
{
float d;
right[0] = forward[2];
right[1] = -forward[0];
right[2] = forward[1];
d = DotProduct(forward, right);
VectorMultSub (right, d, forward, right);
VectorNormalize (right);
CrossProduct(right, forward, up);
}
VISIBLE void
RotatePointAroundVector (vec3_t dst, const vec3_t axis, 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;
VectorCopy (axis, vf);
PerpendicularVector (vr, axis);
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] = DotProduct (rot[i], point);
}
}
VISIBLE void
QuatMult (const quat_t q1, const quat_t q2, quat_t out)
{
vec_t s;
vec3_t v;
s = q1[0] * q2[0] - DotProduct (q1 + 1, q2 + 1);
CrossProduct (q1 + 1, q2 + 1, v);
VectorMultAdd (v, q1[0], q2 + 1, v);
VectorMultAdd (v, q2[0], q1 + 1, out + 1);
out[0] = s;
}
VISIBLE void
QuatMultVec (const quat_t q, const vec3_t v, vec3_t out)
{
vec_t s;
vec3_t tv;
s = -DotProduct (q + 1, v);
CrossProduct (q + 1, v, tv);
VectorMultAdd (tv, q[0], v, tv);
CrossProduct (q + 1, tv, out);
VectorMultSub (out, s, q + 1, out);
VectorMultAdd (out, q[0], tv, out);
}
VISIBLE void
QuatInverse (const quat_t in, quat_t out)
{
quat_t q;
vec_t m;
m = QDotProduct (in, in); // in * in*
QuatConj (in, q);
QuatScale (q, 1 / m, out);
}
VISIBLE void
QuatExp (const quat_t a, quat_t b)
{
vec3_t n;
vec_t th;
vec_t r;
vec_t c, s;
VectorCopy (a + 1, n);
th = VectorNormalize (n);
r = expf (a[0]);
c = cosf (th);
s = sinf (th);
VectorScale (n, r * s, b + 1);
b[0] = r * c;
}
VISIBLE void
QuatToMatrix (const quat_t q, vec_t *m, int homogenous, int vertical)
{
vec_t aa, ab, ac, ad, bb, bc, bd, cc, cd, dd;
vec_t *_m[4] = {
m + (homogenous ? 0 : 0),
m + (homogenous ? 4 : 3),
m + (homogenous ? 8 : 6),
m + (homogenous ? 12 : 9),
};
aa = q[0] * q[0];
ab = q[0] * q[1];
ac = q[0] * q[2];
ad = q[0] * q[3];
bb = q[1] * q[1];
bc = q[1] * q[2];
bd = q[1] * q[3];
cc = q[2] * q[2];
cd = q[2] * q[3];
dd = q[3] * q[3];
if (vertical) {
VectorSet (aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac), _m[0]);
VectorSet (2 * (bc - ad), aa - bb + cc - dd, 2 * (cd + ab), _m[1]);
VectorSet (2 * (bd + ac), 2 * (cd - ab), aa - bb - cc + dd, _m[2]);
} else {
VectorSet (aa + bb - cc - dd, 2 * (bc - ad), 2 * (bd + ac), _m[0]);
VectorSet (2 * (bc + ad), aa - bb + cc - dd, 2 * (cd - ab), _m[1]);
VectorSet (2 * (bd - ac), 2 * (cd + ab), aa - bb - cc + dd, _m[2]);
}
if (homogenous) {
_m[0][3] = 0;
_m[1][3] = 0;
_m[2][3] = 0;
VectorZero (_m[3]);
_m[3][3] = 1;
}
}
#if defined(_WIN32) && !defined(__GNUC__)
# pragma optimize( "", on )
#endif
VISIBLE float
anglemod (float a)
{
a = (360.0 / 65536) * ((int) (a * (65536 / 360.0)) & 65535);
return a;
}
/*
BOPS_Error
Split out like this for ASM to call.
*/
void __attribute__ ((noreturn)) BOPS_Error (void);
VISIBLE void __attribute__ ((noreturn))
BOPS_Error (void)
{
Sys_Error ("BoxOnPlaneSide: Bad signbits");
}
#ifndef USE_INTEL_ASM
/*
BoxOnPlaneSide
Returns 1, 2, or 1 + 2
*/
VISIBLE int
BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs, plane_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:
BOPS_Error ();
}
#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;
}
#endif
/*
angles is a left(?) handed system: 'pitch yaw roll' with x (pitch) axis to
the right, y (yaw) axis up and z (roll) axis forward.
the math in AngleVectors has the entity frame as left handed with x
(forward) axis forward, y (right) axis to the right and z (up) up. However,
the world is a right handed system with x to the right, y forward and
z up.
pitch =
cp 0 -sp
0 1 0
sp 0 cp
yaw =
cy sy 0
-sy cy 0
0 0 1
roll =
1 0 0
0 cr sr
0 -sr cr
final = roll * (pitch * yaw)
final =
[forward]
[-right] -ve due to left handed to right handed conversion
[up]
*/
VISIBLE void
AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
{
float angle, 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;
// need to flip right because it's a left handed system in a right handed
// world
right[0] = -1 * (sr * sp * cy + cr * -sy);
right[1] = -1 * (sr * sp * sy + 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;
}
VISIBLE void
AngleQuat (const vec3_t angles, quat_t q)
{
float alpha, sr, sp, sy, cr, cp, cy;
// alpha is half the angle
alpha = angles[YAW] * (M_PI / 360);
sy = sin (alpha);
cy = cos (alpha);
alpha = angles[PITCH] * (M_PI / 360);
sp = sin (alpha);
cp = cos (alpha);
alpha = angles[ROLL] * (M_PI / 360);
sr = sin (alpha);
cr = cos (alpha);
QuatSet (cy * cp * cr + sy * sp * sr,
cy * cp * sr - sy * sp * cr,
cy * sp * cr + sy * cp * sr,
sy * cp * cr - cy * sp * sr,
q);
}
VISIBLE int
_VectorCompare (const vec3_t v1, const vec3_t v2)
{
int i;
for (i = 0; i < 3; i++)
if (fabs (v1[i] - v2[i]) > EQUAL_EPSILON)
return 0;
return 1;
}
VISIBLE void
_VectorMA (const vec3_t veca, 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];
}
VISIBLE vec_t
_DotProduct (const vec3_t v1, const vec3_t v2)
{
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}
VISIBLE 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];
}
VISIBLE 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];
}
VISIBLE void
_VectorCopy (const vec3_t in, vec3_t out)
{
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
VISIBLE void
CrossProduct (const vec3_t v1, const vec3_t v2, vec3_t cross)
{
float v10 = v1[0];
float v11 = v1[1];
float v12 = v1[2];
float v20 = v2[0];
float v21 = v2[1];
float v22 = v2[2];
cross[0] = v11 * v22 - v12 * v21;
cross[1] = v12 * v20 - v10 * v22;
cross[2] = v10 * v21 - v11 * v20;
}
VISIBLE vec_t
_VectorLength (const vec3_t v)
{
float length;
length = sqrt (DotProduct (v, v));
return length;
}
VISIBLE vec_t
_VectorNormalize (vec3_t v)
{
int i;
double length;
length = 0;
for (i = 0; i < 3; i++)
length += v[i] * v[i];
length = sqrt (length);
if (length == 0)
return 0;
for (i = 0; i < 3; i++)
v[i] /= length;
return length;
}
VISIBLE 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;
}
VISIBLE int
Q_log2 (int val)
{
int answer = 0;
while ((val >>= 1) != 0)
answer++;
return answer;
}
VISIBLE 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];
}
VISIBLE 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.
*/
VISIBLE void
FloorDivMod (double numer, double denom, int *quotient, int *rem)
{
double x;
int q, r;
#ifndef PARANOID
if (denom <= 0.0)
Sys_Error ("FloorDivMod: bad denominator %f", denom);
// if ((floor(numer) != numer) || (floor(denom) != denom))
// Sys_Error ("FloorDivMod: non-integer numer or denom %f %f",
// 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;
}
VISIBLE 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);
}
}
#ifndef USE_INTEL_ASM
/*
Invert24To16
Inverts an 8.24 value to a 16.16 value
*/
VISIBLE fixed16_t
Invert24To16 (fixed16_t val)
{
if (val < 256)
return (0xFFFFFFFF);
return (fixed16_t)
(((double) 0x10000 * (double) 0x1000000 / (double) val) + 0.5);
}
#endif
void
Mat4Transpose (const mat4_t a, mat4_t b)
{
vec_t t;
int i, j;
for (i = 0; i < 3; i++) {
b[i * 4 + i] = a[i * 4 + i]; // in case b != a
for (j = i + 1; j < 4; j++) {
t = a[i * 4 + j]; // in case b == a
b[i * 4 + j] = a[j * 4 + i];
b[j * 4 + i] = t;
}
}
b[i * 4 + i] = a[i * 4 + i]; // in case b != a
}
void
Mat4Mult (const mat4_t a, const mat4_t b, mat4_t c)
{
mat4_t ta, tb; // in case c == b or c == a
int i, j, k;
Mat4Transpose (a, ta); // transpose so we can use dot
Mat4Copy (b, tb);
k = 0;
for (i = 0; i < 4; i++) {
for (j = 0; j < 4; j++) {
c[k++] = QDotProduct (ta + 4 * j, tb + 4 * i);
}
}
}
int
MatDecompose (const mat4_t m, quat_t rot, vec3_t scale, vec3_t shear,
vec3_t trans)
{
vec3_t row[3], shr, scl;
vec_t l, t;
int i, j;
if (trans)
VectorCopy (m + 12, trans);
for (i = 0; i < 3; i++)
for (j = 0; i < 3; j++)
row[j][i] = m[i * 4 + j];
l = DotProduct (row[0], row[0]);
if (l < 1e-5)
return 0;
scl[0] = sqrt (l);
VectorScale (row[0], 1/scl[0], row[0]);
shr[0] = DotProduct (row[0], row[1]);
VectorMultSub (row[1], shr[0], row[0], row[1]);
l = DotProduct (row[1], row[1]);
if (l < 1e-5)
return 0;
scl[1] = sqrt (l);
shr[0] /= scl[1];
VectorScale (row[1], 1/scl[1], row[1]);
shr[1] = DotProduct (row[0], row[2]);
VectorMultSub (row[2], shr[1], row[0], row[2]);
shr[2] = DotProduct (row[1], row[2]);
l = DotProduct (row[2], row[2]);
if (l < 1e-5)
return 0;
scl[2] = sqrt (l);
shr[1] /= scl[2];
shr[2] /= scl[2];
VectorScale (row[0], 1/scl[2], row[0]);
if (scale)
VectorCopy (scl, scale);
if (shear)
VectorCopy (shr, shear);
if (!rot)
return 1;
t = 1 + row[0][0] + row[1][1] + row[2][2];
if (t >= 1e-5) {
vec_t s = sqrt (t);
rot[0] = s / 4;
rot[1] = (row[1][2] - row[2][1]) / s;
rot[2] = (row[2][0] - row[0][2]) / s;
rot[3] = (row[0][1] - row[1][4]) / s;
} else {
if (row[0][0] > row[1][1] && row[0][0] > row[2][2]) {
vec_t s = sqrt (1 + row[0][0] - row[1][1] - row[2][2]);
rot[0] = (row[1][2] - row[2][1]) / s;
rot[1] = s / 4;
rot[2] = (row[2][0] - row[0][2]) / s;
rot[3] = (row[0][1] - row[1][0]) / s;
} else if (row[1][1] > row[2][2]) {
vec_t s = sqrt (1 + row[1][1] - row[0][0] - row[2][2]);
rot[0] = (row[2][0] - row[0][2]) / s;
rot[1] = (row[1][2] - row[2][1]) / s;
rot[2] = s / 4;
rot[3] = (row[0][1] - row[1][0]) / s;
} else {
vec_t s = sqrt (1 + row[2][2] - row[0][0] - row[1][1]);
rot[0] = (row[0][1] - row[1][0]) / s;
rot[1] = (row[1][2] - row[2][1]) / s;
rot[2] = (row[2][0] - row[0][2]) / s;
rot[3] = s / 4;
}
}
return 1;
}
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