2 Copyright (C) 1999-2006 Id Software, Inc. and contributors.
3 For a list of contributors, see the accompanying CONTRIBUTORS file.
5 This file is part of GtkRadiant.
7 GtkRadiant is free software; you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation; either version 2 of the License, or
10 (at your option) any later version.
12 GtkRadiant is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with GtkRadiant; if not, write to the Free Software
19 Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
22 // mathlib.c -- math primitives
24 // we use memcpy and memset
27 const vec3_t vec3_origin = {0.0f,0.0f,0.0f};
29 const vec3_t g_vec3_axis_x = { 1, 0, 0, };
30 const vec3_t g_vec3_axis_y = { 0, 1, 0, };
31 const vec3_t g_vec3_axis_z = { 0, 0, 1, };
37 Given a normalized forward vector, create two
38 other perpendicular vectors
41 void MakeNormalVectors (vec3_t forward, vec3_t right, vec3_t up)
45 // this rotate and negate guarantees a vector
46 // not colinear with the original
47 right[1] = -forward[0];
48 right[2] = forward[1];
49 right[0] = forward[2];
51 d = DotProduct (right, forward);
52 VectorMA (right, -d, forward, right);
53 VectorNormalize (right, right);
54 CrossProduct (right, forward, up);
57 vec_t VectorLength(const vec3_t v)
63 for (i=0 ; i< 3 ; i++)
65 length = (float)sqrt (length);
70 qboolean VectorCompare (const vec3_t v1, const vec3_t v2)
75 if (fabs(v1[i]-v2[i]) > EQUAL_EPSILON)
81 void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc )
83 vc[0] = va[0] + scale*vb[0];
84 vc[1] = va[1] + scale*vb[1];
85 vc[2] = va[2] + scale*vb[2];
88 void _CrossProduct (vec3_t v1, vec3_t v2, vec3_t cross)
90 cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
91 cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
92 cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
95 vec_t _DotProduct (vec3_t v1, vec3_t v2)
97 return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
100 void _VectorSubtract (vec3_t va, vec3_t vb, vec3_t out)
102 out[0] = va[0]-vb[0];
103 out[1] = va[1]-vb[1];
104 out[2] = va[2]-vb[2];
107 void _VectorAdd (vec3_t va, vec3_t vb, vec3_t out)
109 out[0] = va[0]+vb[0];
110 out[1] = va[1]+vb[1];
111 out[2] = va[2]+vb[2];
114 void _VectorCopy (vec3_t in, vec3_t out)
121 vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
124 length = (vec_t)sqrt (in[0]*in[0] + in[1]*in[1] + in[2]*in[2]);
131 out[0] = in[0]/length;
132 out[1] = in[1]/length;
133 out[2] = in[2]/length;
138 vec_t VectorSetLength(const vec3_t in, vec_t length, vec3_t out) {
141 origLength = (vec_t) sqrt((in[0] * in[0]) + (in[1] * in[1]) + (in[2] * in[2]));
148 VectorScale(in, length / origLength, out);
153 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
163 out[0] = out[1] = out[2] = 1.0;
169 VectorScale (in, scale, out);
174 void VectorInverse (vec3_t v)
182 void VectorScale (vec3_t v, vec_t scale, vec3_t out)
184 out[0] = v[0] * scale;
185 out[1] = v[1] * scale;
186 out[2] = v[2] * scale;
190 void VectorRotate (vec3_t vIn, vec3_t vRotation, vec3_t out)
197 VectorCopy(va, vWork);
198 nIndex[0][0] = 1; nIndex[0][1] = 2;
199 nIndex[1][0] = 2; nIndex[1][1] = 0;
200 nIndex[2][0] = 0; nIndex[2][1] = 1;
202 for (i = 0; i < 3; i++)
204 if (vRotation[i] != 0)
206 float dAngle = vRotation[i] * Q_PI / 180.0f;
207 float c = (vec_t)cos(dAngle);
208 float s = (vec_t)sin(dAngle);
209 vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
210 vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
212 VectorCopy(vWork, va);
214 VectorCopy(vWork, out);
217 void VectorRotateOrigin (vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out)
219 vec3_t vTemp, vTemp2;
221 VectorSubtract(vIn, vOrigin, vTemp);
222 VectorRotate(vTemp, vRotation, vTemp2);
223 VectorAdd(vTemp2, vOrigin, out);
226 void VectorPolar(vec3_t v, float radius, float theta, float phi)
228 v[0]=(float)(radius * cos(theta) * cos(phi));
229 v[1]=(float)(radius * sin(theta) * cos(phi));
230 v[2]=(float)(radius * sin(phi));
233 void VectorSnap(vec3_t v)
236 for (i = 0; i < 3; i++)
238 v[i] = (vec_t)FLOAT_TO_INTEGER(v[i]);
242 void VectorISnap(vec3_t point, int snap)
245 for (i = 0 ;i < 3 ; i++)
247 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
251 void VectorFSnap(vec3_t point, float snap)
254 for (i = 0 ;i < 3 ; i++)
256 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
260 void _Vector5Add (vec5_t va, vec5_t vb, vec5_t out)
262 out[0] = va[0]+vb[0];
263 out[1] = va[1]+vb[1];
264 out[2] = va[2]+vb[2];
265 out[3] = va[3]+vb[3];
266 out[4] = va[4]+vb[4];
269 void _Vector5Scale (vec5_t v, vec_t scale, vec5_t out)
271 out[0] = v[0] * scale;
272 out[1] = v[1] * scale;
273 out[2] = v[2] * scale;
274 out[3] = v[3] * scale;
275 out[4] = v[4] * scale;
278 void _Vector53Copy (vec5_t in, vec3_t out)
285 // NOTE: added these from Ritual's Q3Radiant
286 #define INVALID_BOUNDS 99999
287 void ClearBounds (vec3_t mins, vec3_t maxs)
289 mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
290 maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
293 void AddPointToBounds (vec3_t v, vec3_t mins, vec3_t maxs)
298 if(mins[0] == +INVALID_BOUNDS)
299 if(maxs[0] == -INVALID_BOUNDS)
305 for (i=0 ; i<3 ; i++)
315 void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
318 static float sr, sp, sy, cr, cp, cy;
319 // static to help MS compiler fp bugs
321 angle = angles[YAW] * (Q_PI*2.0f / 360.0f);
322 sy = (vec_t)sin(angle);
323 cy = (vec_t)cos(angle);
324 angle = angles[PITCH] * (Q_PI*2.0f / 360.0f);
325 sp = (vec_t)sin(angle);
326 cp = (vec_t)cos(angle);
327 angle = angles[ROLL] * (Q_PI*2.0f / 360.0f);
328 sr = (vec_t)sin(angle);
329 cr = (vec_t)cos(angle);
339 right[0] = -sr*sp*cy+cr*sy;
340 right[1] = -sr*sp*sy-cr*cy;
345 up[0] = cr*sp*cy+sr*sy;
346 up[1] = cr*sp*sy-sr*cy;
351 void VectorToAngles( vec3_t vec, vec3_t angles )
356 if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) )
370 yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
376 forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
377 pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
390 =====================
393 Returns false if the triangle is degenrate.
394 The normal will point out of the clock for clockwise ordered points
395 =====================
397 qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
400 VectorSubtract( b, a, d1 );
401 VectorSubtract( c, a, d2 );
402 CrossProduct( d2, d1, plane );
403 if ( VectorNormalize( plane, plane ) == 0 ) {
407 plane[3] = DotProduct( a, plane );
414 ** We use two byte encoded normals in some space critical applications.
415 ** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
416 ** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
419 void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
420 // check for singularities
421 if ( normal[0] == 0 && normal[1] == 0 ) {
422 if ( normal[2] > 0 ) {
424 bytes[1] = 0; // lat = 0, long = 0
427 bytes[1] = 0; // lat = 0, long = 128
432 a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * (255.0f / 360.0f ) );
435 b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
438 bytes[0] = b; // longitude
439 bytes[1] = a; // lattitude
448 int PlaneTypeForNormal (vec3_t normal) {
449 if (normal[0] == 1.0 || normal[0] == -1.0)
451 if (normal[1] == 1.0 || normal[1] == -1.0)
453 if (normal[2] == 1.0 || normal[2] == -1.0)
456 return PLANE_NON_AXIAL;
464 void MatrixMultiply(float in1[3][3], float in2[3][3], float out[3][3]) {
465 out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
466 in1[0][2] * in2[2][0];
467 out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
468 in1[0][2] * in2[2][1];
469 out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
470 in1[0][2] * in2[2][2];
471 out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
472 in1[1][2] * in2[2][0];
473 out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
474 in1[1][2] * in2[2][1];
475 out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
476 in1[1][2] * in2[2][2];
477 out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
478 in1[2][2] * in2[2][0];
479 out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
480 in1[2][2] * in2[2][1];
481 out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
482 in1[2][2] * in2[2][2];
485 void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
491 inv_denom = 1.0F / DotProduct( normal, normal );
493 d = DotProduct( normal, p ) * inv_denom;
495 n[0] = normal[0] * inv_denom;
496 n[1] = normal[1] * inv_denom;
497 n[2] = normal[2] * inv_denom;
499 dst[0] = p[0] - d * n[0];
500 dst[1] = p[1] - d * n[1];
501 dst[2] = p[2] - d * n[2];
505 ** assumes "src" is normalized
507 void PerpendicularVector( vec3_t dst, const vec3_t src )
511 vec_t minelem = 1.0F;
515 ** find the smallest magnitude axially aligned vector
517 for ( pos = 0, i = 0; i < 3; i++ )
519 if ( fabs( src[i] ) < minelem )
522 minelem = (vec_t)fabs( src[i] );
525 tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
529 ** project the point onto the plane defined by src
531 ProjectPointOnPlane( dst, tempvec, src );
534 ** normalize the result
536 VectorNormalize( dst, dst );
541 RotatePointAroundVector
543 This is not implemented very well...
546 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
561 PerpendicularVector( vr, dir );
562 CrossProduct( vr, vf, vup );
576 memcpy( im, m, sizeof( im ) );
585 memset( zrot, 0, sizeof( zrot ) );
586 zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
588 rad = (float)DEG2RAD( degrees );
589 zrot[0][0] = (vec_t)cos( rad );
590 zrot[0][1] = (vec_t)sin( rad );
591 zrot[1][0] = (vec_t)-sin( rad );
592 zrot[1][1] = (vec_t)cos( rad );
594 MatrixMultiply( m, zrot, tmpmat );
595 MatrixMultiply( tmpmat, im, rot );
597 for ( i = 0; i < 3; i++ ) {
598 dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];