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 ) {
122 vec_t length, ilength;
124 length = (vec_t)sqrt (in[0]*in[0] + in[1]*in[1] + in[2]*in[2]);
131 ilength = 1.0f/length;
132 out[0] = in[0]*ilength;
133 out[1] = in[1]*ilength;
134 out[2] = in[2]*ilength;
139 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
149 out[0] = out[1] = out[2] = 1.0;
155 VectorScale (in, scale, out);
160 void VectorInverse (vec3_t v)
168 void VectorScale (vec3_t v, vec_t scale, vec3_t out)
170 out[0] = v[0] * scale;
171 out[1] = v[1] * scale;
172 out[2] = v[2] * scale;
176 void VectorRotate (vec3_t vIn, vec3_t vRotation, vec3_t out)
183 VectorCopy(va, vWork);
184 nIndex[0][0] = 1; nIndex[0][1] = 2;
185 nIndex[1][0] = 2; nIndex[1][1] = 0;
186 nIndex[2][0] = 0; nIndex[2][1] = 1;
188 for (i = 0; i < 3; i++)
190 if (vRotation[i] != 0)
192 float dAngle = vRotation[i] * Q_PI / 180.0f;
193 float c = (vec_t)cos(dAngle);
194 float s = (vec_t)sin(dAngle);
195 vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
196 vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
198 VectorCopy(vWork, va);
200 VectorCopy(vWork, out);
203 void VectorRotateOrigin (vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out)
205 vec3_t vTemp, vTemp2;
207 VectorSubtract(vIn, vOrigin, vTemp);
208 VectorRotate(vTemp, vRotation, vTemp2);
209 VectorAdd(vTemp2, vOrigin, out);
212 void VectorPolar(vec3_t v, float radius, float theta, float phi)
214 v[0]=(float)(radius * cos(theta) * cos(phi));
215 v[1]=(float)(radius * sin(theta) * cos(phi));
216 v[2]=(float)(radius * sin(phi));
219 void VectorSnap(vec3_t v)
222 for (i = 0; i < 3; i++)
224 v[i] = (vec_t)FLOAT_TO_INTEGER(v[i]);
228 void VectorISnap(vec3_t point, int snap)
231 for (i = 0 ;i < 3 ; i++)
233 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
237 void VectorFSnap(vec3_t point, float snap)
240 for (i = 0 ;i < 3 ; i++)
242 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
246 void _Vector5Add (vec5_t va, vec5_t vb, vec5_t out)
248 out[0] = va[0]+vb[0];
249 out[1] = va[1]+vb[1];
250 out[2] = va[2]+vb[2];
251 out[3] = va[3]+vb[3];
252 out[4] = va[4]+vb[4];
255 void _Vector5Scale (vec5_t v, vec_t scale, vec5_t out)
257 out[0] = v[0] * scale;
258 out[1] = v[1] * scale;
259 out[2] = v[2] * scale;
260 out[3] = v[3] * scale;
261 out[4] = v[4] * scale;
264 void _Vector53Copy (vec5_t in, vec3_t out)
271 // NOTE: added these from Ritual's Q3Radiant
272 #define INVALID_BOUNDS 99999
273 void ClearBounds (vec3_t mins, vec3_t maxs)
275 mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
276 maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
279 void AddPointToBounds (vec3_t v, vec3_t mins, vec3_t maxs)
284 if(mins[0] == +INVALID_BOUNDS)
285 if(maxs[0] == -INVALID_BOUNDS)
291 for (i=0 ; i<3 ; i++)
301 void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
304 static float sr, sp, sy, cr, cp, cy;
305 // static to help MS compiler fp bugs
307 angle = angles[YAW] * (Q_PI*2.0f / 360.0f);
308 sy = (vec_t)sin(angle);
309 cy = (vec_t)cos(angle);
310 angle = angles[PITCH] * (Q_PI*2.0f / 360.0f);
311 sp = (vec_t)sin(angle);
312 cp = (vec_t)cos(angle);
313 angle = angles[ROLL] * (Q_PI*2.0f / 360.0f);
314 sr = (vec_t)sin(angle);
315 cr = (vec_t)cos(angle);
325 right[0] = -sr*sp*cy+cr*sy;
326 right[1] = -sr*sp*sy-cr*cy;
331 up[0] = cr*sp*cy+sr*sy;
332 up[1] = cr*sp*sy-sr*cy;
337 void VectorToAngles( vec3_t vec, vec3_t angles )
342 if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) )
356 yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
362 forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
363 pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
376 =====================
379 Returns false if the triangle is degenrate.
380 The normal will point out of the clock for clockwise ordered points
381 =====================
383 qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
386 VectorSubtract( b, a, d1 );
387 VectorSubtract( c, a, d2 );
388 CrossProduct( d2, d1, plane );
389 if ( VectorNormalize( plane, plane ) == 0 ) {
393 plane[3] = DotProduct( a, plane );
400 ** We use two byte encoded normals in some space critical applications.
401 ** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
402 ** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
405 void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
406 // check for singularities
407 if ( normal[0] == 0 && normal[1] == 0 ) {
408 if ( normal[2] > 0 ) {
410 bytes[1] = 0; // lat = 0, long = 0
413 bytes[1] = 0; // lat = 0, long = 128
418 a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * (255.0f / 360.0f ) );
421 b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
424 bytes[0] = b; // longitude
425 bytes[1] = a; // lattitude
434 int PlaneTypeForNormal (vec3_t normal) {
435 if (normal[0] == 1.0 || normal[0] == -1.0)
437 if (normal[1] == 1.0 || normal[1] == -1.0)
439 if (normal[2] == 1.0 || normal[2] == -1.0)
442 return PLANE_NON_AXIAL;
450 void MatrixMultiply(float in1[3][3], float in2[3][3], float out[3][3]) {
451 out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
452 in1[0][2] * in2[2][0];
453 out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
454 in1[0][2] * in2[2][1];
455 out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
456 in1[0][2] * in2[2][2];
457 out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
458 in1[1][2] * in2[2][0];
459 out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
460 in1[1][2] * in2[2][1];
461 out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
462 in1[1][2] * in2[2][2];
463 out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
464 in1[2][2] * in2[2][0];
465 out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
466 in1[2][2] * in2[2][1];
467 out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
468 in1[2][2] * in2[2][2];
471 void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
477 inv_denom = 1.0F / DotProduct( normal, normal );
479 d = DotProduct( normal, p ) * inv_denom;
481 n[0] = normal[0] * inv_denom;
482 n[1] = normal[1] * inv_denom;
483 n[2] = normal[2] * inv_denom;
485 dst[0] = p[0] - d * n[0];
486 dst[1] = p[1] - d * n[1];
487 dst[2] = p[2] - d * n[2];
491 ** assumes "src" is normalized
493 void PerpendicularVector( vec3_t dst, const vec3_t src )
497 vec_t minelem = 1.0F;
501 ** find the smallest magnitude axially aligned vector
503 for ( pos = 0, i = 0; i < 3; i++ )
505 if ( fabs( src[i] ) < minelem )
508 minelem = (vec_t)fabs( src[i] );
511 tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
515 ** project the point onto the plane defined by src
517 ProjectPointOnPlane( dst, tempvec, src );
520 ** normalize the result
522 VectorNormalize( dst, dst );
527 RotatePointAroundVector
529 This is not implemented very well...
532 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
547 PerpendicularVector( vr, dir );
548 CrossProduct( vr, vf, vup );
562 memcpy( im, m, sizeof( im ) );
571 memset( zrot, 0, sizeof( zrot ) );
572 zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
574 rad = (float)DEG2RAD( degrees );
575 zrot[0][0] = (vec_t)cos( rad );
576 zrot[0][1] = (vec_t)sin( rad );
577 zrot[1][0] = (vec_t)-sin( rad );
578 zrot[1][1] = (vec_t)cos( rad );
580 MatrixMultiply( m, zrot, tmpmat );
581 MatrixMultiply( tmpmat, im, rot );
583 for ( i = 0; i < 3; i++ ) {
584 dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];