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-rwxr-xr-xcommon/mathlib.c434
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+/*
+===========================================================================
+Copyright (C) 1999-2005 Id Software, Inc.
+
+This file is part of Quake III Arena source code.
+
+Quake III Arena 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.
+
+Quake III Arena 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 Foobar; if not, write to the Free Software
+Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+===========================================================================
+*/
+// mathlib.c -- math primitives
+
+#include "cmdlib.h"
+#include "mathlib.h"
+
+#ifdef _WIN32
+//Improve floating-point consistency.
+//without this option weird floating point issues occur
+#pragma optimize( "p", on )
+#endif
+
+
+vec3_t vec3_origin = {0,0,0};
+
+/*
+** 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 = RAD2DEG( atan2( normal[1], normal[0] ) ) * (255.0f / 360.0f );
+ a &= 0xff;
+
+ b = RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f );
+ b &= 0xff;
+
+ bytes[0] = b; // longitude
+ bytes[1] = a; // lattitude
+ }
+}
+
+/*
+=====================
+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;
+}
+
+/*
+================
+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);
+}
+
+
+void Vec10Copy( vec_t *in, vec_t *out ) {
+ out[0] = in[0];
+ out[1] = in[1];
+ out[2] = in[2];
+ out[3] = in[3];
+ out[4] = in[4];
+ out[5] = in[5];
+ out[6] = in[6];
+ out[7] = in[7];
+ out[8] = in[8];
+ out[9] = in[9];
+}
+
+
+void VectorRotate3x3( vec3_t v, float r[3][3], vec3_t d )
+{
+ d[0] = v[0] * r[0][0] + v[1] * r[1][0] + v[2] * r[2][0];
+ d[1] = v[0] * r[0][1] + v[1] * r[1][1] + v[2] * r[2][1];
+ d[2] = v[0] * r[0][2] + v[1] * r[1][2] + v[2] * r[2][2];
+}
+
+double VectorLength( const vec3_t v ) {
+ int i;
+ double length;
+
+ length = 0;
+ for (i=0 ; i< 3 ; i++)
+ length += v[i]*v[i];
+ length = sqrt (length); // FIXME
+
+ 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;
+}
+
+vec_t Q_rint (vec_t in)
+{
+ return floor (in + 0.5);
+}
+
+void VectorMA( const vec3_t va, double 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( 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 _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];
+}
+
+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;
+}
+
+vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
+ vec_t length, ilength;
+
+ length = sqrt (in[0]*in[0] + in[1]*in[1] + in[2]*in[2]);
+ if (length == 0)
+ {
+ VectorClear (out);
+ return 0;
+ }
+
+ ilength = 1.0/length;
+ out[0] = in[0]*ilength;
+ out[1] = in[1]*ilength;
+ out[2] = in[2]*ilength;
+
+ return length;
+}
+
+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 = 1.0 / 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 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 ) {
+ int i;
+ vec_t val;
+
+ for (i=0 ; i<3 ; i++)
+ {
+ val = v[i];
+ if (val < mins[i])
+ mins[i] = val;
+ if (val > maxs[i])
+ maxs[i] = val;
+ }
+}
+
+
+/*
+=================
+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;
+ 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, 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 = 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];
+ }
+}
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