/*
===========================================================================
Copyright (C) 1999-2005 Id Software, Inc.
Copyright (C) 2002-2021 Q3Rally Team (Per Thormann - q3rally@gmail.com)
This file is part of q3rally source code.
q3rally source code 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.
q3rally source code 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 q3rally; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===========================================================================
*/
//
// q_math.c -- stateless support routines that are included in each code module
// Some of the vector functions are static inline in q_shared.h. q3asm
// doesn't understand static functions though, so we only want them in
// one file. That's what this is about.
#ifdef Q3_VM
#define __Q3_VM_MATH
#endif
#include "q_shared.h"
vec3_t vec3_origin = {0,0,0};
vec3_t axisDefault[3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } };
vec4_t colorBlack = {0, 0, 0, 1};
vec4_t colorRed = {1, 0, 0, 1};
vec4_t colorGreen = {0, 1, 0, 1};
vec4_t colorBlue = {0, 0, 1, 1};
vec4_t colorYellow = {1, 1, 0, 1};
vec4_t colorMagenta= {1, 0, 1, 1};
vec4_t colorCyan = {0, 1, 1, 1};
vec4_t colorWhite = {1, 1, 1, 1};
vec4_t colorLtGrey = {0.75, 0.75, 0.75, 1};
vec4_t colorMdGrey = {0.5, 0.5, 0.5, 1};
vec4_t colorDkGrey = {0.25, 0.25, 0.25, 1};
vec4_t g_color_table[8] =
{
{0.0, 0.0, 0.0, 1.0},
{1.0, 0.0, 0.0, 1.0},
{0.0, 1.0, 0.0, 1.0},
{1.0, 1.0, 0.0, 1.0},
{0.0, 0.0, 1.0, 1.0},
{0.0, 1.0, 1.0, 1.0},
{1.0, 0.0, 1.0, 1.0},
{1.0, 1.0, 1.0, 1.0},
};
vec3_t bytedirs[NUMVERTEXNORMALS] =
{
{-0.525731f, 0.000000f, 0.850651f}, {-0.442863f, 0.238856f, 0.864188f},
{-0.295242f, 0.000000f, 0.955423f}, {-0.309017f, 0.500000f, 0.809017f},
{-0.162460f, 0.262866f, 0.951056f}, {0.000000f, 0.000000f, 1.000000f},
{0.000000f, 0.850651f, 0.525731f}, {-0.147621f, 0.716567f, 0.681718f},
{0.147621f, 0.716567f, 0.681718f}, {0.000000f, 0.525731f, 0.850651f},
{0.309017f, 0.500000f, 0.809017f}, {0.525731f, 0.000000f, 0.850651f},
{0.295242f, 0.000000f, 0.955423f}, {0.442863f, 0.238856f, 0.864188f},
{0.162460f, 0.262866f, 0.951056f}, {-0.681718f, 0.147621f, 0.716567f},
{-0.809017f, 0.309017f, 0.500000f},{-0.587785f, 0.425325f, 0.688191f},
{-0.850651f, 0.525731f, 0.000000f},{-0.864188f, 0.442863f, 0.238856f},
{-0.716567f, 0.681718f, 0.147621f},{-0.688191f, 0.587785f, 0.425325f},
{-0.500000f, 0.809017f, 0.309017f}, {-0.238856f, 0.864188f, 0.442863f},
{-0.425325f, 0.688191f, 0.587785f}, {-0.716567f, 0.681718f, -0.147621f},
{-0.500000f, 0.809017f, -0.309017f}, {-0.525731f, 0.850651f, 0.000000f},
{0.000000f, 0.850651f, -0.525731f}, {-0.238856f, 0.864188f, -0.442863f},
{0.000000f, 0.955423f, -0.295242f}, {-0.262866f, 0.951056f, -0.162460f},
{0.000000f, 1.000000f, 0.000000f}, {0.000000f, 0.955423f, 0.295242f},
{-0.262866f, 0.951056f, 0.162460f}, {0.238856f, 0.864188f, 0.442863f},
{0.262866f, 0.951056f, 0.162460f}, {0.500000f, 0.809017f, 0.309017f},
{0.238856f, 0.864188f, -0.442863f},{0.262866f, 0.951056f, -0.162460f},
{0.500000f, 0.809017f, -0.309017f},{0.850651f, 0.525731f, 0.000000f},
{0.716567f, 0.681718f, 0.147621f}, {0.716567f, 0.681718f, -0.147621f},
{0.525731f, 0.850651f, 0.000000f}, {0.425325f, 0.688191f, 0.587785f},
{0.864188f, 0.442863f, 0.238856f}, {0.688191f, 0.587785f, 0.425325f},
{0.809017f, 0.309017f, 0.500000f}, {0.681718f, 0.147621f, 0.716567f},
{0.587785f, 0.425325f, 0.688191f}, {0.955423f, 0.295242f, 0.000000f},
{1.000000f, 0.000000f, 0.000000f}, {0.951056f, 0.162460f, 0.262866f},
{0.850651f, -0.525731f, 0.000000f},{0.955423f, -0.295242f, 0.000000f},
{0.864188f, -0.442863f, 0.238856f}, {0.951056f, -0.162460f, 0.262866f},
{0.809017f, -0.309017f, 0.500000f}, {0.681718f, -0.147621f, 0.716567f},
{0.850651f, 0.000000f, 0.525731f}, {0.864188f, 0.442863f, -0.238856f},
{0.809017f, 0.309017f, -0.500000f}, {0.951056f, 0.162460f, -0.262866f},
{0.525731f, 0.000000f, -0.850651f}, {0.681718f, 0.147621f, -0.716567f},
{0.681718f, -0.147621f, -0.716567f},{0.850651f, 0.000000f, -0.525731f},
{0.809017f, -0.309017f, -0.500000f}, {0.864188f, -0.442863f, -0.238856f},
{0.951056f, -0.162460f, -0.262866f}, {0.147621f, 0.716567f, -0.681718f},
{0.309017f, 0.500000f, -0.809017f}, {0.425325f, 0.688191f, -0.587785f},
{0.442863f, 0.238856f, -0.864188f}, {0.587785f, 0.425325f, -0.688191f},
{0.688191f, 0.587785f, -0.425325f}, {-0.147621f, 0.716567f, -0.681718f},
{-0.309017f, 0.500000f, -0.809017f}, {0.000000f, 0.525731f, -0.850651f},
{-0.525731f, 0.000000f, -0.850651f}, {-0.442863f, 0.238856f, -0.864188f},
{-0.295242f, 0.000000f, -0.955423f}, {-0.162460f, 0.262866f, -0.951056f},
{0.000000f, 0.000000f, -1.000000f}, {0.295242f, 0.000000f, -0.955423f},
{0.162460f, 0.262866f, -0.951056f}, {-0.442863f, -0.238856f, -0.864188f},
{-0.309017f, -0.500000f, -0.809017f}, {-0.162460f, -0.262866f, -0.951056f},
{0.000000f, -0.850651f, -0.525731f}, {-0.147621f, -0.716567f, -0.681718f},
{0.147621f, -0.716567f, -0.681718f}, {0.000000f, -0.525731f, -0.850651f},
{0.309017f, -0.500000f, -0.809017f}, {0.442863f, -0.238856f, -0.864188f},
{0.162460f, -0.262866f, -0.951056f}, {0.238856f, -0.864188f, -0.442863f},
{0.500000f, -0.809017f, -0.309017f}, {0.425325f, -0.688191f, -0.587785f},
{0.716567f, -0.681718f, -0.147621f}, {0.688191f, -0.587785f, -0.425325f},
{0.587785f, -0.425325f, -0.688191f}, {0.000000f, -0.955423f, -0.295242f},
{0.000000f, -1.000000f, 0.000000f}, {0.262866f, -0.951056f, -0.162460f},
{0.000000f, -0.850651f, 0.525731f}, {0.000000f, -0.955423f, 0.295242f},
{0.238856f, -0.864188f, 0.442863f}, {0.262866f, -0.951056f, 0.162460f},
{0.500000f, -0.809017f, 0.309017f}, {0.716567f, -0.681718f, 0.147621f},
{0.525731f, -0.850651f, 0.000000f}, {-0.238856f, -0.864188f, -0.442863f},
{-0.500000f, -0.809017f, -0.309017f}, {-0.262866f, -0.951056f, -0.162460f},
{-0.850651f, -0.525731f, 0.000000f}, {-0.716567f, -0.681718f, -0.147621f},
{-0.716567f, -0.681718f, 0.147621f}, {-0.525731f, -0.850651f, 0.000000f},
{-0.500000f, -0.809017f, 0.309017f}, {-0.238856f, -0.864188f, 0.442863f},
{-0.262866f, -0.951056f, 0.162460f}, {-0.864188f, -0.442863f, 0.238856f},
{-0.809017f, -0.309017f, 0.500000f}, {-0.688191f, -0.587785f, 0.425325f},
{-0.681718f, -0.147621f, 0.716567f}, {-0.442863f, -0.238856f, 0.864188f},
{-0.587785f, -0.425325f, 0.688191f}, {-0.309017f, -0.500000f, 0.809017f},
{-0.147621f, -0.716567f, 0.681718f}, {-0.425325f, -0.688191f, 0.587785f},
{-0.162460f, -0.262866f, 0.951056f}, {0.442863f, -0.238856f, 0.864188f},
{0.162460f, -0.262866f, 0.951056f}, {0.309017f, -0.500000f, 0.809017f},
{0.147621f, -0.716567f, 0.681718f}, {0.000000f, -0.525731f, 0.850651f},
{0.425325f, -0.688191f, 0.587785f}, {0.587785f, -0.425325f, 0.688191f},
{0.688191f, -0.587785f, 0.425325f}, {-0.955423f, 0.295242f, 0.000000f},
{-0.951056f, 0.162460f, 0.262866f}, {-1.000000f, 0.000000f, 0.000000f},
{-0.850651f, 0.000000f, 0.525731f}, {-0.955423f, -0.295242f, 0.000000f},
{-0.951056f, -0.162460f, 0.262866f}, {-0.864188f, 0.442863f, -0.238856f},
{-0.951056f, 0.162460f, -0.262866f}, {-0.809017f, 0.309017f, -0.500000f},
{-0.864188f, -0.442863f, -0.238856f}, {-0.951056f, -0.162460f, -0.262866f},
{-0.809017f, -0.309017f, -0.500000f}, {-0.681718f, 0.147621f, -0.716567f},
{-0.681718f, -0.147621f, -0.716567f}, {-0.850651f, 0.000000f, -0.525731f},
{-0.688191f, 0.587785f, -0.425325f}, {-0.587785f, 0.425325f, -0.688191f},
{-0.425325f, 0.688191f, -0.587785f}, {-0.425325f, -0.688191f, -0.587785f},
{-0.587785f, -0.425325f, -0.688191f}, {-0.688191f, -0.587785f, -0.425325f}
};
//==============================================================
int Q_rand( int *seed ) {
*seed = (69069U * *seed + 1U);
return *seed;
}
float Q_random( int *seed ) {
return ( Q_rand( seed ) & 0xffff ) / (float)0x10000;
}
float Q_crandom( int *seed ) {
return 2.0 * ( Q_random( seed ) - 0.5 );
}
//=======================================================
signed char ClampChar( int i ) {
if ( i < -128 ) {
return -128;
}
if ( i > 127 ) {
return 127;
}
return i;
}
signed short ClampShort( int i ) {
if ( i < -32768 ) {
return -32768;
}
if ( i > 0x7fff ) {
return 0x7fff;
}
return i;
}
// this isn't a real cheap function to call!
int DirToByte( vec3_t dir ) {
int i, best;
float d, bestd;
if ( !dir ) {
return 0;
}
bestd = 0;
best = 0;
for (i=0 ; i<NUMVERTEXNORMALS ; i++)
{
d = DotProduct (dir, bytedirs[i]);
if (d > bestd)
{
bestd = d;
best = i;
}
}
return best;
}
void ByteToDir( int b, vec3_t dir ) {
if ( b < 0 || b >= NUMVERTEXNORMALS ) {
VectorCopy( vec3_origin, dir );
return;
}
VectorCopy (bytedirs[b], dir);
}
unsigned ColorBytes3 (float r, float g, float b) {
unsigned i;
( (byte *)&i )[0] = r * 255;
( (byte *)&i )[1] = g * 255;
( (byte *)&i )[2] = b * 255;
return i;
}
unsigned ColorBytes4 (float r, float g, float b, float a) {
unsigned i;
( (byte *)&i )[0] = r * 255;
( (byte *)&i )[1] = g * 255;
( (byte *)&i )[2] = b * 255;
( (byte *)&i )[3] = a * 255;
return i;
}
float NormalizeColor( const vec3_t in, vec3_t out ) {
float max;
max = in[0];
if ( in[1] > max ) {
max = in[1];
}
if ( in[2] > max ) {
max = in[2];
}
if ( !max ) {
VectorClear( out );
} else {
out[0] = in[0] / max;
out[1] = in[1] / max;
out[2] = in[2] / max;
}
return max;
}
/*
=====================
PlaneFromPoints
Returns false if the triangle is degenrate.
The normal will point out of the clock for clockwise ordered points
=====================
*/
qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
vec3_t d1, d2;
VectorSubtract( b, a, d1 );
VectorSubtract( c, a, d2 );
CrossProduct( d2, d1, plane );
if ( VectorNormalize( plane ) == 0 ) {
return qfalse;
}
plane[3] = DotProduct( a, plane );
return qtrue;
}
/*
===============
RotatePointAroundVector
This is not implemented very well...
===============
*/
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;
float rad;
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;
rad = DEG2RAD( degrees );
zrot[0][0] = cos( rad );
zrot[0][1] = sin( rad );
zrot[1][0] = -sin( rad );
zrot[1][1] = cos( rad );
MatrixMultiply( m, zrot, tmpmat );
MatrixMultiply( 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];
}
}
/*
===============
RotateAroundDirection
===============
*/
void RotateAroundDirection( vec3_t axis[3], float yaw ) {
// create an arbitrary axis[1]
PerpendicularVector( axis[1], axis[0] );
// rotate it around axis[0] by yaw
if ( yaw ) {
vec3_t temp;
VectorCopy( axis[1], temp );
RotatePointAroundVector( axis[1], axis[0], temp, yaw );
}
// cross to get axis[2]
CrossProduct( axis[0], axis[1], axis[2] );
}
void vectoangles( const vec3_t value1, vec3_t angles ) {
float forward;
float yaw, pitch;
if ( value1[1] == 0 && value1[0] == 0 ) {
yaw = 0;
if ( value1[2] > 0 ) {
pitch = 90;
}
else {
pitch = 270;
}
}
else {
if ( value1[0] ) {
// STONELANCE
// yaw = ( atan2 ( value1[1], value1[0] ) * 180 / M_PI );
yaw = ( atan2 ( value1[1], value1[0] ) * M_180_PI );
// END
}
else if ( value1[1] > 0 ) {
yaw = 90;
}
else {
yaw = 270;
}
if ( yaw < 0 ) {
yaw += 360;
}
forward = sqrt ( value1[0]*value1[0] + value1[1]*value1[1] );
// STONELANCE
// pitch = ( atan2(value1[2], forward) * 180 / M_PI );
pitch = ( atan2(value1[2], forward) * M_180_PI );
// END
if ( pitch < 0 ) {
pitch += 360;
}
}
angles[PITCH] = -pitch;
angles[YAW] = yaw;
angles[ROLL] = 0;
}
/*
=================
AnglesToAxis
=================
*/
void AnglesToAxis( const vec3_t angles, vec3_t axis[3] ) {
vec3_t right;
// angle vectors returns "right" instead of "y axis"
AngleVectors( angles, axis[0], right, axis[2] );
VectorSubtract( vec3_origin, right, axis[1] );
}
void AxisClear( vec3_t axis[3] ) {
axis[0][0] = 1;
axis[0][1] = 0;
axis[0][2] = 0;
axis[1][0] = 0;
axis[1][1] = 1;
axis[1][2] = 0;
axis[2][0] = 0;
axis[2][1] = 0;
axis[2][2] = 1;
}
void AxisCopy( vec3_t in[3], vec3_t out[3] ) {
VectorCopy( in[0], out[0] );
VectorCopy( in[1], out[1] );
VectorCopy( in[2], out[2] );
}
void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
{
float d;
vec3_t n;
float inv_denom;
inv_denom = DotProduct( normal, normal );
#ifndef Q3_VM
assert( Q_fabs(inv_denom) != 0.0f ); // zero vectors get here
#endif
inv_denom = 1.0f / inv_denom;
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];
}
/*
================
MakeNormalVectors
Given a normalized forward vector, create two
other perpendicular vectors
================
*/
void MakeNormalVectors( const vec3_t forward, vec3_t right, vec3_t up) {
float d;
// this rotate and negate 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);
}
void VectorRotate( vec3_t in, vec3_t matrix[3], vec3_t out )
{
out[0] = DotProduct( in, matrix[0] );
out[1] = DotProduct( in, matrix[1] );
out[2] = DotProduct( in, matrix[2] );
}
//============================================================================
#if !idppc
/*
** float q_rsqrt( float number )
*/
float Q_rsqrt( float number )
{
floatint_t t;
float x2, y;
const float threehalfs = 1.5F;
x2 = number * 0.5F;
t.f = number;
t.i = 0x5f3759df - ( t.i >> 1 ); // what the fuck?
y = t.f;
y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration
// y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed
return y;
}
float Q_fabs( float f ) {
floatint_t fi;
fi.f = f;
fi.i &= 0x7FFFFFFF;
return fi.f;
}
#endif
//============================================================
/*
===============
LerpAngle
===============
*/
float LerpAngle (float from, float to, float frac) {
float a;
if ( to - from > 180 ) {
to -= 360;
}
if ( to - from < -180 ) {
to += 360;
}
a = from + frac * (to - from);
return a;
}
/*
=================
AngleSubtract
Always returns a value from -180 to 180
=================
*/
float AngleSubtract( float a1, float a2 ) {
float a;
a = a1 - a2;
while ( a > 180 ) {
a -= 360;
}
while ( a < -180 ) {
a += 360;
}
return a;
}
void AnglesSubtract( vec3_t v1, vec3_t v2, vec3_t v3 ) {
v3[0] = AngleSubtract( v1[0], v2[0] );
v3[1] = AngleSubtract( v1[1], v2[1] );
v3[2] = AngleSubtract( v1[2], v2[2] );
}
float AngleMod(float a) {
a = (360.0/65536) * ((int)(a*(65536/360.0)) & 65535);
return a;
}
/*
=================
AngleNormalize360
returns angle normalized to the range [0 <= angle < 360]
=================
*/
float AngleNormalize360 ( float angle ) {
return (360.0 / 65536) * ((int)(angle * (65536 / 360.0)) & 65535);
}
/*
=================
AngleNormalize180
returns angle normalized to the range [-180 < angle <= 180]
=================
*/
float AngleNormalize180 ( float angle ) {
angle = AngleNormalize360( angle );
if ( angle > 180.0 ) {
angle -= 360.0;
}
return angle;
}
/*
=================
AngleDelta
returns the normalized delta from angle1 to angle2
=================
*/
float AngleDelta ( float angle1, float angle2 ) {
return AngleNormalize180( angle1 - angle2 );
}
//============================================================
/*
=================
SetPlaneSignbits
=================
*/
void SetPlaneSignbits (cplane_t *out) {
int bits, j;
// for fast box on planeside test
bits = 0;
for (j=0 ; j<3 ; j++) {
if (out->normal[j] < 0) {
bits |= 1<<j;
}
}
out->signbits = bits;
}
/*
==================
BoxOnPlaneSide
Returns 1, 2, or 1 + 2
==================
*/
int BoxOnPlaneSide(vec3_t emins, vec3_t emaxs, struct cplane_s *p)
{
float dist[2];
int sides, b, i;
// 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;
}
// general case
dist[0] = dist[1] = 0;
if (p->signbits < 8) // >= 8: default case is original code (dist[0]=dist[1]=0)
{
for (i=0 ; i<3 ; i++)
{
b = (p->signbits >> i) & 1;
dist[ b] += p->normal[i]*emaxs[i];
dist[!b] += p->normal[i]*emins[i];
}
}
sides = 0;
if (dist[0] >= p->dist)
sides = 1;
if (dist[1] < p->dist)
sides |= 2;
return sides;
}
/*
=================
RadiusFromBounds
=================
*/
float RadiusFromBounds( const vec3_t mins, const vec3_t maxs ) {
int i;
vec3_t corner;
float a, b;
for (i=0 ; i<3 ; i++) {
a = fabs( mins[i] );
b = fabs( maxs[i] );
corner[i] = a > b ? a : b;
}
return VectorLength (corner);
}
void ClearBounds( vec3_t mins, vec3_t maxs ) {
mins[0] = mins[1] = mins[2] = 99999;
maxs[0] = maxs[1] = maxs[2] = -99999;
}
void AddPointToBounds( const vec3_t v, vec3_t mins, vec3_t maxs ) {
if ( v[0] < mins[0] ) {
mins[0] = v[0];
}
if ( v[0] > maxs[0]) {
maxs[0] = v[0];
}
if ( v[1] < mins[1] ) {
mins[1] = v[1];
}
if ( v[1] > maxs[1]) {
maxs[1] = v[1];
}
if ( v[2] < mins[2] ) {
mins[2] = v[2];
}
if ( v[2] > maxs[2]) {
maxs[2] = v[2];
}
}
qboolean BoundsIntersect(const vec3_t mins, const vec3_t maxs,
const vec3_t mins2, const vec3_t maxs2)
{
if ( maxs[0] < mins2[0] ||
maxs[1] < mins2[1] ||
maxs[2] < mins2[2] ||
mins[0] > maxs2[0] ||
mins[1] > maxs2[1] ||
mins[2] > maxs2[2])
{
return qfalse;
}
return qtrue;
}
qboolean BoundsIntersectSphere(const vec3_t mins, const vec3_t maxs,
const vec3_t origin, vec_t radius)
{
if ( origin[0] - radius > maxs[0] ||
origin[0] + radius < mins[0] ||
origin[1] - radius > maxs[1] ||
origin[1] + radius < mins[1] ||
origin[2] - radius > maxs[2] ||
origin[2] + radius < mins[2])
{
return qfalse;
}
return qtrue;
}
qboolean BoundsIntersectPoint(const vec3_t mins, const vec3_t maxs,
const vec3_t origin)
{
if ( origin[0] > maxs[0] ||
origin[0] < mins[0] ||
origin[1] > maxs[1] ||
origin[1] < mins[1] ||
origin[2] > maxs[2] ||
origin[2] < mins[2])
{
return qfalse;
}
return qtrue;
}
vec_t VectorNormalize( vec3_t v ) {
// NOTE: TTimo - Apple G4 altivec source uses double?
float length, ilength;
length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
if ( length ) {
/* writing it this way allows gcc to recognize that rsqrt can be used */
ilength = 1/(float)sqrt (length);
/* sqrt(length) = length * (1 / sqrt(length)) */
length *= ilength;
v[0] *= ilength;
v[1] *= ilength;
v[2] *= ilength;
}
return length;
}
vec_t 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)
{
/* writing it this way allows gcc to recognize that rsqrt can be used */
ilength = 1/(float)sqrt (length);
/* sqrt(length) = length * (1 / sqrt(length)) */
length *= ilength;
out[0] = v[0]*ilength;
out[1] = v[1]*ilength;
out[2] = v[2]*ilength;
} else {
VectorClear( out );
}
return length;
}
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];
}
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 _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;
}
void Vector4Scale( const vec4_t in, vec_t scale, vec4_t out ) {
out[0] = in[0]*scale;
out[1] = in[1]*scale;
out[2] = in[2]*scale;
out[3] = in[3]*scale;
}
int Q_log2( int val ) {
int answer;
answer = 0;
while ( ( val>>=1 ) != 0 ) {
answer++;
}
return answer;
}
/*
=================
PlaneTypeForNormal
=================
*/
/*
int PlaneTypeForNormal (vec3_t normal) {
if ( normal[0] == 1.0 )
return PLANE_X;
if ( normal[1] == 1.0 )
return PLANE_Y;
if ( normal[2] == 1.0 )
return PLANE_Z;
return PLANE_NON_AXIAL;
}
*/
// STONELANCE
/*
================================================================================
VectorNAN
================================================================================
*/
qboolean VectorNAN( const vec3_t vec ){
if (IS_NAN(vec[0]) || IS_NAN(vec[1]) || IS_NAN(vec[2])){
return qtrue;
}
return qfalse;
}
/*
================
MatrixMultiply
================
*/
void MatrixMultiply( float in1[3][3], float in2[3][3], float out[3][3]) {
if( in1 == out || in2 == out )
{
float temp[3][3];
temp[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
in1[0][2] * in2[2][0];
temp[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
in1[0][2] * in2[2][1];
temp[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
in1[0][2] * in2[2][2];
temp[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
in1[1][2] * in2[2][0];
temp[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
in1[1][2] * in2[2][1];
temp[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
in1[1][2] * in2[2][2];
temp[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
in1[2][2] * in2[2][0];
temp[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
in1[2][2] * in2[2][1];
temp[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
in1[2][2] * in2[2][2];
out[0][0] = temp[0][0];
out[0][1] = temp[0][1];
out[0][2] = temp[0][2];
out[1][0] = temp[1][0];
out[1][1] = temp[1][1];
out[1][2] = temp[1][2];
out[2][0] = temp[2][0];
out[2][1] = temp[2][1];
out[2][2] = temp[2][2];
}
else
{
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];
}
}
/*
================
MatrixTranspose
Cant do MatrixTranspose(m, m);
================
*/
void MatrixTranspose( float in[3][3], float out[3][3] ) {
out[0][0] = in[0][0];
out[0][1] = in[1][0];
out[0][2] = in[2][0];
out[1][0] = in[0][1];
out[1][1] = in[1][1];
out[1][2] = in[2][1];
out[2][0] = in[0][2];
out[2][1] = in[1][2];
out[2][2] = in[2][2];
}
/*
================
MatrixAdd
================
*/
void MatrixAdd( float in1[3][3], float in2[3][3], float out[3][3] ) {
out[0][0] = in1[0][0] + in2[0][0];
out[0][1] = in1[0][1] + in2[0][1];
out[0][2] = in1[0][2] + in2[0][2];
out[1][0] = in1[1][0] + in2[1][0];
out[1][1] = in1[1][1] + in2[1][1];
out[1][2] = in1[1][2] + in2[1][2];
out[2][0] = in1[2][0] + in2[2][0];
out[2][1] = in1[2][1] + in2[2][1];
out[2][2] = in1[2][2] + in2[2][2];
}
/*
================
MatrixScale
================
*/
void MatrixScale( float in[3][3], float s, float out[3][3] ) {
out[0][0] = in[0][0] * s;
out[0][1] = in[0][1] * s;
out[0][2] = in[0][2] * s;
out[1][0] = in[1][0] * s;
out[1][1] = in[1][1] * s;
out[1][2] = in[1][2] * s;
out[2][0] = in[2][0] * s;
out[2][1] = in[2][1] * s;
out[2][2] = in[2][2] * s;
}
/*
================
AnglesToOrientation
Converts car angles to an orientation matrix
================
*/
void AnglesToOrientation( const vec3_t angles, float t[3][3] ) {
float angle;
static float sr, sp, sy, cr, cp, cy;
// static to help MS compiler fp bugs
angle = angles[YAW] * M_PI_180;
sy = sin(angle);
cy = cos(angle);
angle = angles[PITCH] * M_PI_180;
sp = sin(angle);
cp = cos(angle);
angle = angles[ROLL] * M_PI_180;
sr = sin(angle);
cr = cos(angle);
t[0][0] = (-1*sr*sp*cy+-1*cr*-sy); t[1][0] = (-1*sr*sp*sy+-1*cr*cy); t[2][0] = -1*sr*cp;
t[0][1] = cp*cy; t[1][1] = cp*sy; t[2][1] = -sp;
t[0][2] = (cr*sp*cy+-sr*-sy); t[1][2] = (cr*sp*sy+-sr*cy); t[2][2] = cr*cp;
}
/*
================
OrientationToVectors
Converts orientation matrix to angle vectors
================
*/
void OrientationToVectors( float t[3][3], vec3_t forward, vec3_t right, vec3_t up ) {
right[0] = t[0][0]; right[1] = t[1][0]; right[2] = t[2][0];
forward[0] = t[0][1]; forward[1] = t[1][1]; forward[2] = t[2][1];
up[0] = t[0][2]; up[1] = t[1][2]; up[2] = t[2][2];
// VectorNormalize(right);
// VectorNormalize(forward);
// VectorNormalize(up);
}
/*
================
AnglesToDeltaAngles
Converts orientation matrix to car angles
================
*/
void AnglesToDeltaAngles( vec3_t angles, const vec3_t w, vec3_t deltaAngles ) {
/*
float cr, cy;
float sr, sy;
float aaa;
sy = sin( angles[YAW] * M_180_PI );
cy = cos( angles[YAW] * M_180_PI );
sr = sin( angles[ROLL] * M_180_PI );
cr = cos( angles[ROLL] * M_180_PI );
// [ dpsi dtheta dphi ]T = M-1(theta,phi) * Omega
//
// M-1(theta,phi) = [ cos(phi)/cos(theta) sin(phi)/cos(theta) 0 ]
// [ -sin(phi) cos(phi) 0 ]
// [ cos(phi)*sin(theta)/cos(theta) sin(phi)*sin(theta)/cos(theta) 1 ]
aaa = ( cr + sr ) / cy;
delta_angles[0] = ( aaa ) * w[0];
delta_angles[1] = ( cr - sr ) * w[1];
delta_angles[2] = ( aaa * sy + 1 ) * w[2];
*/
float c1, c2, c3, s1, s2, s3;
float p, sp;
c1 = cos( angles[0] * M_PI_180 );
c2 = cos( angles[1] * M_PI_180 );
c3 = cos( angles[2] * M_PI_180 );
s1 = sin( angles[0] * M_PI_180 );
s2 = sin( angles[1] * M_PI_180 );
s3 = sin( angles[2] * M_PI_180 );
p = 2.0f * Q_acos( c1*c2*c3 - s1*s2*s3 );
sp = p / sin( p / 2.0f ) ;
deltaAngles[0] = (c1*s2*c3 + s1*c2*c3) * sp * M_180_PI;
deltaAngles[1] = (s1*s2*c3 + c1*s2*s3) * sp * M_180_PI;
deltaAngles[2] = (c1*c2*s3 + s1*s2*c3) * sp * M_180_PI;
}
/*
================
OrientationToDeltaAngles
Converts orientation matrix to car angles
================
*/
void OrientationToDeltaAngles( float t[3][3], const vec3_t w, vec3_t delta_angles ) {
// vec3_t forward, right, up;
// float cp, as;
// OrientationToVectors(t, forward, right, up);
/*
forward[0] = -w[2] * t[1][1] + w[1] * t[1][2];
forward[1] = w[2] * t[1][0] + w[0] * t[1][2];
forward[2] = -w[1] * t[1][0] + w[0] * t[1][1];
up[2] = -w[1] * t[2][0] + w[0] * t[2][1];
right[2] = -w[1] * t[0][0] + w[0] * t[0][1];
delta_angles[PITCH] = Q_asin( -forward[2] ) * M_180_PI;
if (up[2] < 0.0f)
delta_angles[PITCH] = 180 - delta_angles[PITCH];
cp = cos( delta_angles[PITCH] * M_PI_180 );
if (cp){
// fix small floating point errors that would cause it to
// have asin() of a number > 1.00
as = forward[1] / cp > 1.00f ? 1.00f : forward[1] / cp;
as = as < -1.00f ? -1.00f : as;
delta_angles[YAW] = Q_asin(as) * M_180_PI;
if (forward[0] < 0.0f)
delta_angles[YAW] = 180 - delta_angles[YAW];
if (up[2] < 0.0f)
delta_angles[YAW] = 180 - delta_angles[YAW];
as = -right[2] / cp > 1.00f ? 1.00f : -right[2] / cp;
as = as < -1.00f ? -1.00f : as;
delta_angles[ROLL] = Q_asin(as) * M_180_PI;
}
else {
delta_angles[YAW]=0;
delta_angles[ROLL]=0;
}
// we still want yaw to be facing the front of the car so spin yaw
// 180 and adjust pitch and roll to keep car in the same position
if (fabs(delta_angles[PITCH]) > 90){
delta_angles[YAW] += 180;
delta_angles[PITCH] = 180 - delta_angles[PITCH];
delta_angles[ROLL] += 180;
}
*/
}
/*
================
OrientationToAngles
Converts orientation matrix to car angles
================
*/
void OrientationToAngles( float t[3][3], vec3_t angles ) {
vec3_t forward, right, up;
float cp, as;
OrientationToVectors(t, forward, right, up);
angles[PITCH] = Q_asin(-forward[2]) * M_180_PI;
if (up[2] < 0.0f)
angles[PITCH] = 180 - angles[PITCH];
cp = cos(angles[PITCH] * M_PI_180 );
if (cp){
// fix small floating point errors that would cause it to
// have asin() of a number > 1.00
as = forward[1] / cp > 1.00f ? 1.00f : forward[1] / cp;
as = as < -1.00f ? -1.00f : as;
angles[YAW] = Q_asin(as) * M_180_PI;
if (forward[0] < 0.0f)
angles[YAW] = 180 - angles[YAW];
if (up[2] < 0.0f)
angles[YAW] = 180 - angles[YAW];
as = -right[2] / cp > 1.00f ? 1.00f : -right[2] / cp;
as = as < -1.00f ? -1.00f : as;
angles[ROLL] = Q_asin(as) * M_180_PI;
}
else {
angles[YAW]=0;
angles[ROLL]=0;
}
// we still want yaw to be facing the front of the car so spin yaw
// 180 and adjust pitch and roll to keep car in the same position
if (fabs(angles[PITCH]) > 90){
angles[YAW] += 180;
angles[PITCH] = 180 - angles[PITCH];
angles[ROLL] += 180;
}
}
/*
================
OrthonormalizeOrientation
Normalizes orientation matrix
================
*/
void OrthonormalizeOrientation( float t[3][3] ){
vec3_t x, y, z;
VectorSet(x, t[0][0], t[1][0], t[2][0]);
VectorSet(y, t[0][1], t[1][1], t[2][1]);
// FIXME: check for 0 length?
VectorNormalize(x);
CrossProduct(x, y, z);
VectorNormalize(z);
CrossProduct(z, x, y);
VectorNormalize(y);
t[0][0] = x[0]; t[0][1] = y[0]; t[0][2] = z[0];
t[1][0] = x[1]; t[1][1] = y[1]; t[1][2] = z[1];
t[2][0] = x[2]; t[2][1] = y[2]; t[2][2] = z[2];
}
/*
================
QuaternionLengthSquared
Returns the DotProduct(q, q)
================
*/
float QuaternionLengthSquared( const vec4_t q ){
return q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
}
/*
================
QuaternionLength
Returns the sqrt( DotProduct(q, q) )
================
*/
float QuaternionLength( const vec4_t q ){
return sqrt( q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3] );
}
/*
================
QuaternionFastNormalize
Normalizes quat avoiding a sqrt
returns squared length of quaternion;
Quaternion function code from racer
================
*/
float QuaternionFastNormalize( vec4_t quat )
{
// Check if quaternion needs normalizing
float len = QuaternionLengthSquared( quat );
if ( len == 0.0f )
{
// TODO: Make w 0 instead of this?
quat[3] = 1.0f;
quat[0] = quat[1] = quat[2] = 0.0f;
}
else if( len < 0.9999f || len > 1.0001f )
{
// Push quat back to 1.0 (avoid a sqrt())
float n = ( len + 1.0f ) / ( 2.0f * len );
quat[0] *= n;
quat[1] *= n;
quat[2] *= n;
quat[3] *= n;
}
return len;
}
/*
================
QuaternionNormalize
Normalizes a quat using the normal sqrt method
returns length of quaternion;
Quaternion function code from racer
================
*/
float QuaternionNormalize( vec4_t quat )
{
float tmp, len;
len = QuaternionLength( quat );
if ( len == 0.0f )
{
// TODO: Make w 0 instead of this?
quat[3] = 1.0f;
quat[0] = quat[1] = quat[2] = 0.0f;
return len;
}
tmp = 1.0f / len;
quat[3] *= tmp;
quat[0] *= tmp;
quat[1] *= tmp;
quat[2] *= tmp;
return len;
}
/*
================
QuaternionMultiply
Multiplies two quaternions together
Quaternion function code from skwid
================
*/
void QuaternionMultiply(const vec4_t in1, const vec4_t in2, vec4_t out){
/*
// from racer
w = in1[3] * in2[3] - in1[0] * in2[0] - in1[1] * in2[1] - in1[2] * in2[2];
x = in1[3] * in2[0] + in1[0] * in2[3] + in1[1] * in2[2] - in1[2] * in2[1];
y = in1[3] * in2[1] - in1[0] * in2[2] + in1[1] * in2[3] + in1[2] * in2[0];
z = in1[3] * in2[2] + in1[0] * in2[1] - in1[1] * in2[0] + in1[2] * in2[3];
*/
/* this crap doesnt work
float A, B, C, D, E, F, G, H;
A = (q1[3] + q1[0]) * (q2[3] + q2[0]);
B = (q1[2] - q1[1]) * (q2[1] - q2[2]);
C = (q1[3] - q1[0]) * (q2[1] + q2[2]);
D = (q1[1] + q1[2]) * (q2[3] - q2[0]);
E = (q1[0] + q1[2]) * (q2[0] + q2[1]);
F = (q1[0] - q1[2]) * (q2[0] - q2[1]);
G = (q1[3] + q1[1]) * (q2[3] - q2[2]);
H = (q1[3] - q1[1]) * (q2[3] + q2[2]);
res[0] = A - (E + F + G + H)/2;
res[1] = C + (E - F + G - H)/2;
res[2] = D + (E - F - G + H)/2;
res[3] = B + (-E - F + G + H) /2;
*/
vec3_t temp; // in case of mulp(a, b, a)
temp[0] = (in1[1] * in2[2] - in1[2] * in2[1]) + in2[3] * in1[0] + in1[3] * in2[0];
temp[1] = (in1[2] * in2[0] - in1[0] * in2[2]) + in2[3] * in1[1] + in1[3] * in2[1];
temp[2] = (in1[0] * in2[1] - in1[1] * in2[0]) + in2[3] * in1[2] + in1[3] * in2[2];
out[3] = in1[3] * in2[3] - (in1[0] * in2[0] + in1[1] * in2[1] + in1[2] * in2[2]);
out[0] = temp[0];
out[1] = temp[1];
out[2] = temp[2];
}
/*
================
QuaternionRotate
Rotates quat by the amount specified in w*time
w in body coords
Note: out cannot be the same as quat
================
*/
void QuaternionRotate( const vec4_t quat, const vec3_t w, const float time, vec4_t out){
vec3_t tempVec;
// divide by 2.0f is part of quaternion derivative calculation
VectorScale( w, time / 2.0f, tempVec );
out[0] = quat[0] + ( quat[3]*tempVec[0] - quat[2]*tempVec[1] + quat[1]*tempVec[2] );
out[1] = quat[1] + ( quat[2]*tempVec[0] + quat[3]*tempVec[1] - quat[0]*tempVec[2] );
out[2] = quat[2] + (-quat[1]*tempVec[0] + quat[0]*tempVec[1] + quat[3]*tempVec[2] );
out[3] = quat[3] + (-quat[0]*tempVec[0] - quat[1]*tempVec[1] - quat[2]*tempVec[2] );
}
/*
================
QuaternionSLERP
4D Spherically lerps from one quarternion to another.
'from' and 'to' need to be normalized
t = fraction of move from start quarternion to end quarternion [0 .. 1]
================
*/
void QuaternionSLERP(const vec4_t from, const vec4_t to, float t, vec4_t res){
/*
// from racer
float theta, costheta, w1, w2, sintheta;
costheta = from[0] * to[0] + from[1] * to[1] + from[2] * to[2] + from[3] * to[3];
// OPTIMIZE: If costheta was squared then i could use the sin(t)^2 = 1-cos(t)^s
// Is sintheta ever negative? If not then sin(t)^2 > 0 == sin(t) > 0
theta = Q_acos( costheta );
sintheta = sin( theta );
if( sintheta > 0.0f )
{
w1 = sin( (1.0f - t) * theta ) / sintheta;
w2 = sin( t * theta ) / sintheta;
}
else
{
// They're the same quaternion, so who cares?
w1 = 1.0f;
w2 = 0.0f;
}
res[0] = w1 * from[0] + w2 * to[0];
res[1] = w1 * from[1] + w2 * to[1];
res[2] = w1 * from[2] + w2 * to[2];
res[3] = w1 * from[3] + w2 * to[3];
*/
/*
// Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick
vec4_t to1;
double omega, cosom, sinom, scale0, scale1;
// calc cosine
cosom = from[0] * to[0] + from[1] * to[1] + from[2] * to[2] + from[3] * to[3];
// adjust signs (if necessary)
if ( cosom < 0.0 ){
cosom = -cosom;
to1[0] = -to[0];
to1[1] = -to[1];
to1[2] = -to[2];
to1[3] = -to[3];
} else {
to1[0] = to[0];
to1[1] = to[1];
to1[2] = to[2];
to1[3] = to[3];
}
// calculate coefficients
if ( (1.0 - cosom) > 0.1f ) {
// standard case (slerp)
omega = Q_acos(cosom);
sinom = sin(omega);
scale0 = sin((1.0 - t) * omega) / sinom;
scale1 = sin(t * omega) / sinom;
} else {
// "from" and "to" quaternions are very close
// ... so we can do a linear interpolation
scale0 = 1.0 - t;
scale1 = t;
}
// calculate final values
res[0] = scale0 * from[0] + scale1 * to1[0];
res[1] = scale0 * from[1] + scale1 * to1[1];
res[2] = scale0 * from[2] + scale1 * to1[2];
res[3] = scale0 * from[3] + scale1 * to1[3];
*/
}
/*
================
AnglesToQuaternion
Converts euler angles to a quaternion
================
*/
void AnglesToQuaternion( const vec3_t angles, vec4_t quat){
float t[3][3];
// OPTIMIZE: See if this can be simplified
AnglesToOrientation( angles, t );
OrientationToQuaternion( t, quat );
// based on Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick
/*
float cr, cp, cy, sr, sp, sy, spcy, spsy;
float tr, s;
int i, j, k;
vec3_t t[3];
// calculate trig identities
cr = cos(angles[ROLL] * M_PI / 180.0f);
cp = cos(angles[PITCH] * M_PI / 180.0f);
cy = cos(angles[YAW] * M_PI / 180.0f);
sr = sin(angles[ROLL] * M_PI / 180.0f);
sp = sin(angles[PITCH] * M_PI / 180.0f);
sy = sin(angles[YAW] * M_PI / 180.0f);
spcy = sp * cy;
spsy = sp * sy;
t[0][0] = (-sr*spcy + cr*sy); t[1][0] = (-sr*spsy - cr*cy); t[2][0] = -sr*cp;
t[0][1] = cp*cy; t[1][1] = cp*sy; t[2][1] = -sp;
t[0][2] = (cr*spcy + sr*sy); t[1][2] = (cr*spsy - sr*cy); t[2][2] = cr*cp;
*/
/*
tr = t[0][0] + t[1][1] + t[2][2];
// check the diagonal
if (tr > 0.0) {
s = sqrt (tr + 1.0);
quat[3] = s / 2.0;
s = 0.5 / s;
quat[0] = (t[1][2] - t[2][1]) * s;
quat[1] = (t[2][0] - t[0][2]) * s;
quat[2] = (t[0][1] - t[1][0]) * s;
} else {
// diagonal is negative
i = 0;
if (t[1][1] > t[0][0]) i = 1;
if (t[2][2] > t[i][i]) i = 2;
j = (i+1) % 3;
k = (j+1) % 3;
s = sqrt ((t[i][i] - (t[j][j] + t[k][k])) + 1.0);
quat[i] = s * 0.5;
if (s != 0.0) s = 0.5 / s;
quat[3] = (t[j][k] - t[k][j]) * s;
quat[j] = (t[i][j] + t[j][i]) * s;
quat[k] = (t[i][k] + t[k][i]) * s;
}
*/
/*
// Quaternion function code from skwid
vec4_t qy = { 0, sin(angles[YAW] * M_PI / 180.0f), 0, cos(angles[YAW] * M_PI / 180.0f) };
vec4_t qp = { sin(angles[PITCH] * M_PI / 180.0f), 0, 0, cos(angles[PITCH] * M_PI / 180.0f) };
vec4_t qr = { 0, 0, sin(angles[ROLL] * M_PI / 180.0f), cos(angles[ROLL] * M_PI / 180.0f) };
Com_Printf("qy %f %f %f %f\n", qy[0], qy[1], qy[2], qy[3]);
Com_Printf("qp %f %f %f %f\n", qp[0], qp[1], qp[2], qp[3]);
Com_Printf("qr %f %f %f %f\n", qr[0], qr[1], qr[2], qr[3]);
QuaternionMultiply( qy, qp, quat );
Com_Printf("quat %f %f %f %f\n", quat[0], quat[1], quat[2], quat[3]);
QuaternionMultiply( quat, qr, quat );
*/
}
/*
================
QuaternionToAngles
Converts a quaternion to angles
================
*/
void QuaternionToAngles( const vec4_t quat, vec3_t angles ){
float t[3][3];
// OPTIMIZE: See if this can be simplified, some parts of t dont need to be calculated
QuaternionToOrientation( quat, t );
OrientationToAngles( t, angles );
/*
float wx, wy, wz, xx, yy, yz, xy, xz, zz;
float x2, y2, z2;
vec3_t f, r, u;
float cp, as;
// calculate coefficients
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;
wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2;
right[0] = 1.0 - (yy + zz); right[1] = xy - wz; right[2] = xz + wy;
forward[0] = xy + wz; forward[1] = 1.0 - (xx + zz); forward[2] = yz - wx;
up[0] = xz - wy; up[1] = yz + wx; up[2] = 1.0 - (xx + yy);
*/
/*
// Quaternion function code based on skwids
float wx, wy, wz, xx, yy, yz, xy, xz, zz;
float x2, y2, z2;
vec3_t f, r, u;
float cp, as;
float s = 2 / QuaternionNormal( quat );
xx = quat[0] * quat[0]; xy = quat[0] * quat[1]; xz = quat[0] * quat[2];
yy = quat[1] * quat[1]; yz = quat[1] * quat[2]; zz = quat[2] * quat[2];
wx = quat[3] * quat[0]; wy = quat[3] * quat[1]; wz = quat[3] * quat[2];
// r[0] = 1 - s * (yy + zz); r[1] = s * (xy - wz);
r[2] = s * (xz + wy);
f[0] = s * (xy + wz); f[1] = 1 - s * (xx + zz); f[2] = s * (yz - wx);
// u[0] = s * (xz - wy); u[1] = s * (yz + wx);
u[2] = 1 - s * (xx + yy);
angles[PITCH] = Q_asin(-f[2]) * 180.0f / M_PI;
if (u[2] < 0.0f)
angles[PITCH] = 180 - angles[PITCH];
cp = cos(angles[PITCH] / 180.0f * M_PI);
if (cp){
// fix small floating point errors that would cause it to
// have asin() of a number > 1.00
as = f[1] / cp > 1.00f ? 1.00f : f[1] / cp;
as = as < -1.00f ? -1.00f : as;
angles[YAW] = Q_asin(as) * 180.0f / M_PI;
if (f[0] < 0.0f)
angles[YAW] = 180 - angles[YAW];
if (u[2] < 0.0f)
angles[YAW] = 180 - angles[YAW];
as = -r[2] / cp > 1.00f ? 1.00f : -r[2] / cp;
as = as < -1.00f ? -1.00f : as;
angles[ROLL] = Q_asin(as) * 180 / M_PI;
}
else {
angles[YAW]=0;
angles[ROLL]=0;
}
// we still want yaw to be facing the front of the car so spin yaw
// 180 and adjust pitch and roll to keep car in the same position
if (fabs(angles[PITCH]) > 90){
angles[YAW] += 180;
angles[PITCH] = 180 - angles[PITCH];
angles[ROLL] += 180;
}
*/
}
/*
================
OrientationToQuaternion
Converts orientation matrix to a quaternion
================
*/
void OrientationToQuaternion( float t[3][3], vec4_t quat ){
// from racer
int i;
float qw2, qx2, qy2, qz2, tmp;
// Quaternion components squared
qw2 = 0.25 * (t[0][0] + t[1][1] + t[2][2] + 1.0);
qx2 = qw2 - 0.5 * (t[1][1] + t[2][2]);
qy2 = qw2 - 0.5 * (t[2][2] + t[0][0]);
qz2 = qw2 - 0.5 * (t[0][0] + t[1][1]);
// Decide maximum magnitude component
i = ( qw2 > qx2 ) ?
( ( qw2 > qy2 ) ? (( qw2 > qz2 ) ? 0 : 3) : (( qy2 > qz2 ) ? 2 : 3)) :
( ( qx2 > qy2 ) ? (( qx2 > qz2 ) ? 1 : 3) : (( qy2 > qz2 ) ? 2 : 3));
// Compute signed quat components using numerically stable method
switch( i )
{
case 0:
quat[3] = sqrt(qw2); tmp = 0.25f / quat[3];
quat[0] = (t[1][2] - t[2][1]) * tmp;
quat[1] = (t[2][0] - t[0][2]) * tmp;
quat[2] = (t[0][1] - t[1][0]) * tmp;
break;
case 1:
quat[0] = sqrt(qx2); tmp = 0.25f / quat[0];
quat[3] = (t[1][2] - t[2][1]) * tmp;
quat[1] = (t[1][0] + t[0][1]) * tmp;
quat[2] = (t[0][2] + t[2][0]) * tmp;
break;
case 2:
quat[1] = sqrt(qy2); tmp = 0.25f / quat[1];
quat[3] = (t[2][0] - t[0][2]) * tmp;
quat[0] = (t[1][0] + t[0][1]) * tmp;
quat[2] = (t[2][1] + t[1][2]) * tmp;
break;
case 3:
quat[2] = sqrt(qz2); tmp = 0.25f / quat[2];
quat[3] = (t[0][1] - t[1][0]) * tmp;
quat[0] = (t[2][0] + t[0][2]) * tmp;
quat[1] = (t[2][1] + t[1][2]) * tmp;
break;
}
// Always keep all components positive
// (note that scalar*quat is equivalent to quat, so q==-q)
if ( i && quat[3] < 0.0f )
{
quat[3] = -quat[3];
quat[0] = -quat[0];
quat[1] = -quat[1];
quat[2] = -quat[2];
}
// Normalize it to be safe
QuaternionFastNormalize( quat );
// tmp = 1.0f / sqrt( quat[3]*quat[3] + quat[0]*quat[0] + quat[1]*quat[1] + quat[2]*quat[2] );
// quat[3] *= tmp;
// quat[0] *= tmp;
// quat[1] *= tmp;
// quat[2] *= tmp;
// Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick
/*
float tr, s;
int i, j, k;
int nxt[3] = {1, 2, 0};
tr = t[0][0] + t[1][1] + t[2][2];
// check the diagonal
if (tr > 0.0) {
s = sqrt (tr + 1.0);
quat[3] = s / 2.0;
s = 0.5 / s;
quat[0] = (t[1][2] - t[2][1]) * s;
quat[1] = (t[2][0] - t[0][2]) * s;
quat[2] = (t[0][1] - t[1][0]) * s;
} else {
// diagonal is negative
i = 0;
if (t[1][1] > t[0][0]) i = 1;
if (t[2][2] > t[i][i]) i = 2;
j = nxt[i];
k = nxt[j];
s = sqrt ((t[i][i] - (t[j][j] + t[k][k])) + 1.0);
quat[i] = s * 0.5;
if (s != 0.0) s = 0.5 / s;
quat[3] = (t[j][k] - t[k][j]) * s;
quat[j] = (t[i][j] + t[j][i]) * s;
quat[k] = (t[i][k] + t[k][i]) * s;
}
*/
/*
// thanks to skwid for the equations
quat[3] = 0.5f * sqrt( t[0][0] + t[1][1] + t[2][2] + 1.0f );
quat[0] = (t[1][2] - t[2][1]) / (4 * quat[3]);
quat[1] = (t[2][0] - t[0][2]) / (4 * quat[3]);
quat[2] = (t[0][1] - t[1][0]) / (4 * quat[3]);
*/
}
/*
================
QuaternionToOrientation
Converts normalized quaternion to a orientation matrix
================
*/
void QuaternionToOrientation( const vec4_t quat, float t[3][3] ){
float xy, wz, xz, wy, yz, wx, x2, y2, z2;
// based on code from racer
x2 = quat[0] * quat[0];
y2 = quat[1] * quat[1];
z2 = quat[2] * quat[2];
xy = quat[0] * quat[1];
wz = quat[3] * quat[2];
xz = quat[0] * quat[2];
wy = quat[3] * quat[1];
yz = quat[1] * quat[2];
wx = quat[3] * quat[0];
t[0][0] = 1.0f - 2.0f * (y2 + z2);
t[1][0] = 2.0f * (xy - wz);
t[2][0] = 2.0f * (xz + wy);
t[0][1] = 2.0f * (xy + wz);
t[1][1] = 1.0f - 2.0f * (z2 + x2);
t[2][1] = 2.0f * (yz - wx);
t[0][2] = 2.0f * (xz - wy);
t[1][2] = 2.0f * (yz + wx);
t[2][2] = 1.0f - 2.0f * (x2 + y2);
/*
Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick
float x2, y2, z2;
// calculate coefficients
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;
wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2;
t[0][0] = 1.0 - (yy + zz); t[1][0] = xy - wz; t[2][0] = xz + wy;
t[0][1] = xy + wz; t[1][1] = 1.0 - (xx + zz); t[2][1] = yz - wx;
t[0][2] = xz - wy; t[1][2] = yz + wx; t[2][2] = 1.0 - (xx + yy);
*/
/*
// Quaternion function code based on skwids
float s = 2 / QuaternionNormal( quat );
xx = quat[0] * quat[0]; xy = quat[0] * quat[1]; xz = quat[0] * quat[2];
yy = quat[1] * quat[1]; yz = quat[1] * quat[2]; zz = quat[2] * quat[2];
wx = quat[3] * quat[0]; wy = quat[3] * quat[1]; wz = quat[3] * quat[2];
t[0][0] = 1 - s * (yy + zz); t[1][0] = s * (xy - wz); t[2][0] = s * (xz + wy);
t[0][1] = s * (xy + wz); t[1][1] = 1 - s * (xx + zz); t[2][1] = s * (yz - wx);
t[0][2] = s * (xz - wy); t[1][2] = s * (yz + wx); t[2][2] = 1 - s * (xx + yy);
*/
}
/*
================
QuaternionL2ToOrientation
Converts non-normalize quaternion to a orientation matrix
'l2' is the squared length of the quaternion, used to get 't' orthogonal
================
*/
void QuaternionL2ToOrientation( const vec4_t quat, const float l2, float t[3][3] ){
float xy, wz, xz, wy, yz, wx, x2, y2, z2, s;
// based on code from racer
x2 = quat[0] * quat[0];
y2 = quat[1] * quat[1];
z2 = quat[2] * quat[2];
xy = quat[0] * quat[1];
wz = quat[3] * quat[2];
xz = quat[0] * quat[2];
wy = quat[3] * quat[1];
yz = quat[1] * quat[2];
wx = quat[3] * quat[0];
s = 2.0f / l2;
t[0][0] = 1.0f - s * (y2 + z2);
t[1][0] = s * (xy - wz);
t[2][0] = s * (xz + wy);
t[0][1] = s * (xy + wz);
t[1][1] = 1.0f - s * (z2 + x2);
t[2][1] = s * (yz - wx);
t[0][2] = s * (xz - wy);
t[1][2] = s * (yz + wx);
t[2][2] = 1.0f - s * (x2 + y2);
}
/*
================
QuaternionToVectors
Converts a quaternion to angle vectors
================
*/
void QuaternionToVectors( const vec4_t quat, vec3_t forward, vec3_t right, vec3_t up ) {
float t[3][3];
QuaternionToOrientation( quat, t );
OrientationToVectors( t, forward, right, up );
/*
float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
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;
wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2;
right[0] = 1.0 - (yy + zz); right[1] = xy - wz; right[2] = xz + wy;
forward[0] = xy + wz; forward[1] = 1.0 - (xx + zz); forward[2] = yz - wx;
up[0] = xz - wy; up[1] = yz + wx; up[2] = 1.0 - (xx + yy);
VectorNormalize(right);
VectorNormalize(forward);
VectorNormalize(up);
*/
}
// END
void AngleVectors( const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up) {
float angle;
static float sr, sp, sy, cr, cp, cy;
// static to help MS compiler fp bugs
// STONELANCE
// angle = angles[YAW] * (M_PI*2 / 360);
angle = angles[YAW] * M_PI_180;
// END
sy = sin(angle);
cy = cos(angle);
// STONELANCE
// angle = angles[PITCH] * (M_PI*2 / 360);
angle = angles[PITCH] * M_PI_180;
// END
sp = sin(angle);
cp = cos(angle);
// STONELANCE
// angle = angles[ROLL] * (M_PI*2 / 360);
angle = angles[ROLL] * M_PI_180;
// END
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;
}
}
/*
** 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 );
}
/*
================
Q_isnan
Don't pass doubles to this
================
*/
int Q_isnan( float x )
{
floatint_t fi;
fi.f = x;
fi.ui &= 0x7FFFFFFF;
fi.ui = 0x7F800000 - fi.ui;
return (int)( (unsigned int)fi.ui >> 31 );
}
//------------------------------------------------------------------------
#ifndef Q3_VM
/*
=====================
Q_acos
the msvc acos doesn't always return a value between 0 and PI:
int i;
i = 1065353246;
acos(*(float*) &i) == -1.#IND0
=====================
*/
float Q_acos(float c) {
float angle;
angle = acos(c);
if (angle > M_PI) {
return M_PI;
}
if (angle < 0.0f) {
return 0.0f;
}
return angle;
}
/*
=====================
Q_asin
the msvc asin probably has same type of behavior as acos
=====================
*/
float Q_asin(float c) {
float angle;
angle = asin(c);
if (angle > M_PI_2) {
return M_PI_2;
}
if (angle < -M_PI_2) {
return -M_PI_2;
}
return angle;
}
#endif