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/*
Copyright (C) 1999-2006 Id Software, Inc. and contributors.
For a list of contributors, see the accompanying CONTRIBUTORS file.
This file is part of GtkRadiant.
GtkRadiant 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.
GtkRadiant 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 GtkRadiant; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
// mathlib.c -- math primitives
#include "mathlib.h"
// we use memcpy and memset
#include <memory.h>
const vec3_t vec3_origin = {0.0f,0.0f,0.0f};
const vec3_t g_vec3_axis_x = { 1, 0, 0, };
const vec3_t g_vec3_axis_y = { 0, 1, 0, };
const vec3_t g_vec3_axis_z = { 0, 0, 1, };
/*
================
VectorIsOnAxis
================
*/
qboolean VectorIsOnAxis( vec3_t v ){
int i, zeroComponentCount;
zeroComponentCount = 0;
for ( i = 0; i < 3; i++ )
{
if ( v[i] == 0.0 ) {
zeroComponentCount++;
}
}
if ( zeroComponentCount > 1 ) {
// The zero vector will be on axis.
return qtrue;
}
return qfalse;
}
/*
================
VectorIsOnAxialPlane
================
*/
qboolean VectorIsOnAxialPlane( vec3_t v ){
int i;
for ( i = 0; i < 3; i++ )
{
if ( v[i] == 0.0 ) {
// The zero vector will be on axial plane.
return qtrue;
}
}
return qfalse;
}
/*
================
MakeNormalVectors
Given a normalized forward vector, create two
other perpendicular vectors
================
*/
void MakeNormalVectors( 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, right );
CrossProduct( right, forward, up );
}
vec_t VectorLength( const vec3_t v ){
int i;
float length;
length = 0.0f;
for ( i = 0; i < 3; i++ )
length += v[i] * v[i];
length = (float)sqrt( length );
return length;
}
qboolean 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 qfalse;
}
return qtrue;
}
void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc ){
vc[0] = va[0] + scale * vb[0];
vc[1] = va[1] + scale * vb[1];
vc[2] = va[2] + scale * vb[2];
}
void _CrossProduct( vec3_t v1, 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 _DotProduct( vec3_t v1, vec3_t v2 ){
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}
void _VectorSubtract( vec3_t va, vec3_t vb, vec3_t out ){
out[0] = va[0] - vb[0];
out[1] = va[1] - vb[1];
out[2] = va[2] - vb[2];
}
void _VectorAdd( vec3_t va, vec3_t vb, vec3_t out ){
out[0] = va[0] + vb[0];
out[1] = va[1] + vb[1];
out[2] = va[2] + vb[2];
}
void _VectorCopy( vec3_t in, vec3_t out ){
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
#if MATHLIB_VECTOR_NORMALIZE_PRECISION_FIX
// The sqrt() function takes double as an input and returns double as an
// output according the the man pages on Debian and on FreeBSD. Therefore,
// I don't see a reason why using a double outright (instead of using the
// vec_accu_t alias for example) could possibly be frowned upon.
double x, y, z, length;
x = (double) in[0];
y = (double) in[1];
z = (double) in[2];
length = sqrt( ( x * x ) + ( y * y ) + ( z * z ) );
if ( length == 0 ) {
VectorClear( out );
return 0;
}
out[0] = (vec_t) ( x / length );
out[1] = (vec_t) ( y / length );
out[2] = (vec_t) ( z / length );
return (vec_t) length;
#else
vec_t length, ilength;
length = (vec_t)sqrt( in[0] * in[0] + in[1] * in[1] + in[2] * in[2] );
if ( length == 0 ) {
VectorClear( out );
return 0;
}
ilength = 1.0f / length;
out[0] = in[0] * ilength;
out[1] = in[1] * ilength;
out[2] = in[2] * ilength;
return length;
#endif
}
vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
float max, scale;
max = in[0];
if ( in[1] > max ) {
max = in[1];
}
if ( in[2] > max ) {
max = in[2];
}
if ( max == 0 ) {
out[0] = out[1] = out[2] = 1.0;
return 0;
}
scale = 1.0f / max;
VectorScale( in, scale, out );
return max;
}
void VectorInverse( vec3_t v ){
v[0] = -v[0];
v[1] = -v[1];
v[2] = -v[2];
}
/*
void VectorScale (vec3_t v, vec_t scale, vec3_t out)
{
out[0] = v[0] * scale;
out[1] = v[1] * scale;
out[2] = v[2] * scale;
}
*/
void VectorRotate( vec3_t vIn, vec3_t vRotation, vec3_t out ){
vec3_t vWork, va;
int nIndex[3][2];
int i;
VectorCopy( vIn, va );
VectorCopy( va, vWork );
nIndex[0][0] = 1; nIndex[0][1] = 2;
nIndex[1][0] = 2; nIndex[1][1] = 0;
nIndex[2][0] = 0; nIndex[2][1] = 1;
for ( i = 0; i < 3; i++ )
{
if ( vRotation[i] != 0 ) {
float dAngle = vRotation[i] * Q_PI / 180.0f;
float c = (vec_t)cos( dAngle );
float s = (vec_t)sin( dAngle );
vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
}
VectorCopy( vWork, va );
}
VectorCopy( vWork, out );
}
void VectorRotateOrigin( vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out ){
vec3_t vTemp, vTemp2;
VectorSubtract( vIn, vOrigin, vTemp );
VectorRotate( vTemp, vRotation, vTemp2 );
VectorAdd( vTemp2, vOrigin, out );
}
void VectorPolar( vec3_t v, float radius, float theta, float phi ){
v[0] = (float)( radius * cos( theta ) * cos( phi ) );
v[1] = (float)( radius * sin( theta ) * cos( phi ) );
v[2] = (float)( radius * sin( phi ) );
}
void VectorSnap( vec3_t v ){
int i;
for ( i = 0; i < 3; i++ )
{
v[i] = (vec_t)FLOAT_TO_INTEGER( v[i] );
}
}
void VectorISnap( vec3_t point, int snap ){
int i;
for ( i = 0; i < 3; i++ )
{
point[i] = (vec_t)FLOAT_SNAP( point[i], snap );
}
}
void VectorFSnap( vec3_t point, float snap ){
int i;
for ( i = 0; i < 3; i++ )
{
point[i] = (vec_t)FLOAT_SNAP( point[i], snap );
}
}
void _Vector5Add( vec5_t va, vec5_t vb, vec5_t out ){
out[0] = va[0] + vb[0];
out[1] = va[1] + vb[1];
out[2] = va[2] + vb[2];
out[3] = va[3] + vb[3];
out[4] = va[4] + vb[4];
}
void _Vector5Scale( vec5_t v, vec_t scale, vec5_t out ){
out[0] = v[0] * scale;
out[1] = v[1] * scale;
out[2] = v[2] * scale;
out[3] = v[3] * scale;
out[4] = v[4] * scale;
}
void _Vector53Copy( vec5_t in, vec3_t out ){
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
// NOTE: added these from Ritual's Q3Radiant
const int INVALID_BOUNDS = 99999;
void ClearBounds( vec3_t mins, vec3_t maxs ){
mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
}
void AddPointToBounds( vec3_t v, vec3_t mins, vec3_t maxs ){
int i;
vec_t val;
if ( mins[0] == +INVALID_BOUNDS ) {
if ( maxs[0] == -INVALID_BOUNDS ) {
VectorCopy( v, mins );
VectorCopy( v, maxs );
}
}
for ( i = 0; i < 3; i++ )
{
val = v[i];
if ( val < mins[i] ) {
mins[i] = val;
}
if ( val > maxs[i] ) {
maxs[i] = val;
}
}
}
void AngleVectors( 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
angle = angles[YAW] * ( Q_PI * 2.0f / 360.0f );
sy = (vec_t)sin( angle );
cy = (vec_t)cos( angle );
angle = angles[PITCH] * ( Q_PI * 2.0f / 360.0f );
sp = (vec_t)sin( angle );
cp = (vec_t)cos( angle );
angle = angles[ROLL] * ( Q_PI * 2.0f / 360.0f );
sr = (vec_t)sin( angle );
cr = (vec_t)cos( angle );
if ( forward ) {
forward[0] = cp * cy;
forward[1] = cp * sy;
forward[2] = -sp;
}
if ( right ) {
right[0] = -sr * sp * cy + cr * sy;
right[1] = -sr * sp * sy - cr * cy;
right[2] = -sr * cp;
}
if ( up ) {
up[0] = cr * sp * cy + sr * sy;
up[1] = cr * sp * sy - sr * cy;
up[2] = cr * cp;
}
}
void VectorToAngles( vec3_t vec, vec3_t angles ){
float forward;
float yaw, pitch;
if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) ) {
yaw = 0;
if ( vec[ 2 ] > 0 ) {
pitch = 90;
}
else
{
pitch = 270;
}
}
else
{
yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
if ( yaw < 0 ) {
yaw += 360;
}
forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
if ( pitch < 0 ) {
pitch += 360;
}
}
angles[ 0 ] = pitch;
angles[ 1 ] = yaw;
angles[ 2 ] = 0;
}
/*
=====================
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, plane ) == 0 ) {
return qfalse;
}
plane[3] = DotProduct( a, plane );
return qtrue;
}
/*
** NormalToLatLong
**
** We use two byte encoded normals in some space critical applications.
** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
**
*/
void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
// check for singularities
if ( normal[0] == 0 && normal[1] == 0 ) {
if ( normal[2] > 0 ) {
bytes[0] = 0;
bytes[1] = 0; // lat = 0, long = 0
}
else {
bytes[0] = 128;
bytes[1] = 0; // lat = 0, long = 128
}
}
else {
int a, b;
a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * ( 255.0f / 360.0f ) );
a &= 0xff;
b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
b &= 0xff;
bytes[0] = b; // longitude
bytes[1] = a; // lattitude
}
}
/*
=================
PlaneTypeForNormal
=================
*/
int PlaneTypeForNormal( vec3_t normal ) {
if ( normal[0] == 1.0 || normal[0] == -1.0 ) {
return PLANE_X;
}
if ( normal[1] == 1.0 || normal[1] == -1.0 ) {
return PLANE_Y;
}
if ( normal[2] == 1.0 || normal[2] == -1.0 ) {
return PLANE_Z;
}
return PLANE_NON_AXIAL;
}
/*
================
MatrixMultiply
================
*/
void MatrixMultiply( 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];
}
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;
vec_t 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 = (vec_t)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, dst );
}
/*
===============
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 = (float)DEG2RAD( degrees );
zrot[0][0] = (vec_t)cos( rad );
zrot[0][1] = (vec_t)sin( rad );
zrot[1][0] = (vec_t)-sin( rad );
zrot[1][1] = (vec_t)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];
}
}
////////////////////////////////////////////////////////////////////////////////
// Below is double-precision math stuff. This was initially needed by the new
// "base winding" code in q3map2 brush processing in order to fix the famous
// "disappearing triangles" issue. These definitions can be used wherever extra
// precision is needed.
////////////////////////////////////////////////////////////////////////////////
/*
=================
VectorLengthAccu
=================
*/
vec_accu_t VectorLengthAccu( const vec3_accu_t v ){
return (vec_accu_t) sqrt( ( v[0] * v[0] ) + ( v[1] * v[1] ) + ( v[2] * v[2] ) );
}
/*
=================
DotProductAccu
=================
*/
vec_accu_t DotProductAccu( const vec3_accu_t a, const vec3_accu_t b ){
return ( a[0] * b[0] ) + ( a[1] * b[1] ) + ( a[2] * b[2] );
}
/*
=================
VectorSubtractAccu
=================
*/
void VectorSubtractAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
}
/*
=================
VectorAddAccu
=================
*/
void VectorAddAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
out[0] = a[0] + b[0];
out[1] = a[1] + b[1];
out[2] = a[2] + b[2];
}
/*
=================
VectorCopyAccu
=================
*/
void VectorCopyAccu( const vec3_accu_t in, vec3_accu_t out ){
out[0] = in[0];
out[1] = in[1];
out[2] = in[2];
}
/*
=================
VectorScaleAccu
=================
*/
void VectorScaleAccu( const vec3_accu_t in, vec_accu_t scaleFactor, vec3_accu_t out ){
out[0] = in[0] * scaleFactor;
out[1] = in[1] * scaleFactor;
out[2] = in[2] * scaleFactor;
}
/*
=================
CrossProductAccu
=================
*/
void CrossProductAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
out[0] = ( a[1] * b[2] ) - ( a[2] * b[1] );
out[1] = ( a[2] * b[0] ) - ( a[0] * b[2] );
out[2] = ( a[0] * b[1] ) - ( a[1] * b[0] );
}
/*
=================
Q_rintAccu
=================
*/
vec_accu_t Q_rintAccu( vec_accu_t val ){
return (vec_accu_t) floor( val + 0.5 );
}
/*
=================
VectorCopyAccuToRegular
=================
*/
void VectorCopyAccuToRegular( const vec3_accu_t in, vec3_t out ){
out[0] = (vec_t) in[0];
out[1] = (vec_t) in[1];
out[2] = (vec_t) in[2];
}
/*
=================
VectorCopyRegularToAccu
=================
*/
void VectorCopyRegularToAccu( const vec3_t in, vec3_accu_t out ){
out[0] = (vec_accu_t) in[0];
out[1] = (vec_accu_t) in[1];
out[2] = (vec_accu_t) in[2];
}
/*
=================
VectorNormalizeAccu
=================
*/
vec_accu_t VectorNormalizeAccu( const vec3_accu_t in, vec3_accu_t out ){
// The sqrt() function takes double as an input and returns double as an
// output according the the man pages on Debian and on FreeBSD. Therefore,
// I don't see a reason why using a double outright (instead of using the
// vec_accu_t alias for example) could possibly be frowned upon.
vec_accu_t length;
length = (vec_accu_t) sqrt( ( in[0] * in[0] ) + ( in[1] * in[1] ) + ( in[2] * in[2] ) );
if ( length == 0 ) {
VectorClear( out );
return 0;
}
out[0] = in[0] / length;
out[1] = in[1] / length;
out[2] = in[2] / length;
return length;
}
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