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, };
38 qboolean VectorIsOnAxis( vec3_t v ){
39 int i, zeroComponentCount;
41 zeroComponentCount = 0;
42 for ( i = 0; i < 3; i++ )
49 if ( zeroComponentCount > 1 ) {
50 // The zero vector will be on axis.
62 qboolean VectorIsOnAxialPlane( vec3_t v ){
65 for ( i = 0; i < 3; i++ )
68 // The zero vector will be on axial plane.
80 Given a normalized forward vector, create two
81 other perpendicular vectors
84 void MakeNormalVectors( vec3_t forward, vec3_t right, vec3_t up ){
87 // this rotate and negate guarantees a vector
88 // not colinear with the original
89 right[1] = -forward[0];
90 right[2] = forward[1];
91 right[0] = forward[2];
93 d = DotProduct( right, forward );
94 VectorMA( right, -d, forward, right );
95 VectorNormalize( right, right );
96 CrossProduct( right, forward, up );
99 vec_t VectorLength( const vec3_t v ){
104 for ( i = 0 ; i < 3 ; i++ )
105 length += v[i] * v[i];
106 length = (float)sqrt( length );
111 qboolean VectorCompare( const vec3_t v1, const vec3_t v2 ){
114 for ( i = 0 ; i < 3 ; i++ )
115 if ( fabs( v1[i] - v2[i] ) > EQUAL_EPSILON ) {
122 void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc ){
123 vc[0] = va[0] + scale * vb[0];
124 vc[1] = va[1] + scale * vb[1];
125 vc[2] = va[2] + scale * vb[2];
128 void _CrossProduct( vec3_t v1, vec3_t v2, vec3_t cross ){
129 cross[0] = v1[1] * v2[2] - v1[2] * v2[1];
130 cross[1] = v1[2] * v2[0] - v1[0] * v2[2];
131 cross[2] = v1[0] * v2[1] - v1[1] * v2[0];
134 vec_t _DotProduct( vec3_t v1, vec3_t v2 ){
135 return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
138 void _VectorSubtract( vec3_t va, vec3_t vb, vec3_t out ){
139 out[0] = va[0] - vb[0];
140 out[1] = va[1] - vb[1];
141 out[2] = va[2] - vb[2];
144 void _VectorAdd( vec3_t va, vec3_t vb, vec3_t out ){
145 out[0] = va[0] + vb[0];
146 out[1] = va[1] + vb[1];
147 out[2] = va[2] + vb[2];
150 void _VectorCopy( vec3_t in, vec3_t out ){
156 vec_t VectorAccurateNormalize( const vec3_t in, vec3_t out ) {
158 // The sqrt() function takes double as an input and returns double as an
159 // output according the the man pages on Debian and on FreeBSD. Therefore,
160 // I don't see a reason why using a double outright (instead of using the
161 // vec_accu_t alias for example) could possibly be frowned upon.
163 double x, y, z, length;
169 length = sqrt( ( x * x ) + ( y * y ) + ( z * z ) );
175 out[0] = (vec_t) ( x / length );
176 out[1] = (vec_t) ( y / length );
177 out[2] = (vec_t) ( z / length );
179 return (vec_t) length;
182 vec_t VectorFastNormalize( const vec3_t in, vec3_t out ) {
184 // SmileTheory: This is ioquake3's VectorNormalize2
185 // for when accuracy matters less than speed
186 float length, ilength;
188 length = in[0] * in[0] + in[1] * in[1] + in[2] * in[2];
191 /* writing it this way allows gcc to recognize that rsqrt can be used */
192 ilength = 1 / (float)sqrt( length );
193 /* sqrt(length) = length * (1 / sqrt(length)) */
195 out[0] = in[0] * ilength;
196 out[1] = in[1] * ilength;
197 out[2] = in[2] * ilength;
206 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
218 out[0] = out[1] = out[2] = 1.0;
224 VectorScale( in, scale, out );
229 void VectorInverse( vec3_t v ){
236 void VectorScale (vec3_t v, vec_t scale, vec3_t out)
238 out[0] = v[0] * scale;
239 out[1] = v[1] * scale;
240 out[2] = v[2] * scale;
244 void VectorRotate( vec3_t vIn, vec3_t vRotation, vec3_t out ){
249 VectorCopy( vIn, va );
250 VectorCopy( va, vWork );
251 nIndex[0][0] = 1; nIndex[0][1] = 2;
252 nIndex[1][0] = 2; nIndex[1][1] = 0;
253 nIndex[2][0] = 0; nIndex[2][1] = 1;
255 for ( i = 0; i < 3; i++ )
257 if ( vRotation[i] != 0 ) {
258 float dAngle = vRotation[i] * Q_PI / 180.0f;
259 float c = (vec_t)cos( dAngle );
260 float s = (vec_t)sin( dAngle );
261 vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
262 vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
264 VectorCopy( vWork, va );
266 VectorCopy( vWork, out );
269 void VectorRotateOrigin( vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out ){
270 vec3_t vTemp, vTemp2;
272 VectorSubtract( vIn, vOrigin, vTemp );
273 VectorRotate( vTemp, vRotation, vTemp2 );
274 VectorAdd( vTemp2, vOrigin, out );
277 void VectorPolar( vec3_t v, float radius, float theta, float phi ){
278 v[0] = (float)( radius * cos( theta ) * cos( phi ) );
279 v[1] = (float)( radius * sin( theta ) * cos( phi ) );
280 v[2] = (float)( radius * sin( phi ) );
283 void VectorSnap( vec3_t v ){
285 for ( i = 0; i < 3; i++ )
287 v[i] = (vec_t)FLOAT_TO_INTEGER( v[i] );
291 void VectorISnap( vec3_t point, int snap ){
293 for ( i = 0 ; i < 3 ; i++ )
295 point[i] = (vec_t)FLOAT_SNAP( point[i], snap );
299 void VectorFSnap( vec3_t point, float snap ){
301 for ( i = 0 ; i < 3 ; i++ )
303 point[i] = (vec_t)FLOAT_SNAP( point[i], snap );
307 void _Vector5Add( vec5_t va, vec5_t vb, vec5_t out ){
308 out[0] = va[0] + vb[0];
309 out[1] = va[1] + vb[1];
310 out[2] = va[2] + vb[2];
311 out[3] = va[3] + vb[3];
312 out[4] = va[4] + vb[4];
315 void _Vector5Scale( vec5_t v, vec_t scale, vec5_t out ){
316 out[0] = v[0] * scale;
317 out[1] = v[1] * scale;
318 out[2] = v[2] * scale;
319 out[3] = v[3] * scale;
320 out[4] = v[4] * scale;
323 void _Vector53Copy( vec5_t in, vec3_t out ){
329 // NOTE: added these from Ritual's Q3Radiant
330 #define INVALID_BOUNDS 99999
331 void ClearBounds( vec3_t mins, vec3_t maxs ){
332 mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
333 maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
336 void AddPointToBounds( vec3_t v, vec3_t mins, vec3_t maxs ){
340 if ( mins[0] == +INVALID_BOUNDS ) {
341 if ( maxs[0] == -INVALID_BOUNDS ) {
342 VectorCopy( v, mins );
343 VectorCopy( v, maxs );
347 for ( i = 0 ; i < 3 ; i++ )
350 if ( val < mins[i] ) {
353 if ( val > maxs[i] ) {
359 void AngleVectors( vec3_t angles, vec3_t forward, vec3_t right, vec3_t up ){
361 static float sr, sp, sy, cr, cp, cy;
362 // static to help MS compiler fp bugs
364 angle = angles[YAW] * ( Q_PI * 2.0f / 360.0f );
365 sy = (vec_t)sin( angle );
366 cy = (vec_t)cos( angle );
367 angle = angles[PITCH] * ( Q_PI * 2.0f / 360.0f );
368 sp = (vec_t)sin( angle );
369 cp = (vec_t)cos( angle );
370 angle = angles[ROLL] * ( Q_PI * 2.0f / 360.0f );
371 sr = (vec_t)sin( angle );
372 cr = (vec_t)cos( angle );
375 forward[0] = cp * cy;
376 forward[1] = cp * sy;
380 right[0] = -sr * sp * cy + cr * sy;
381 right[1] = -sr * sp * sy - cr * cy;
385 up[0] = cr * sp * cy + sr * sy;
386 up[1] = cr * sp * sy - sr * cy;
391 void VectorToAngles( vec3_t vec, vec3_t angles ){
395 if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) ) {
397 if ( vec[ 2 ] > 0 ) {
407 yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
412 forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
413 pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
425 =====================
428 Returns false if the triangle is degenrate.
429 The normal will point out of the clock for clockwise ordered points
430 =====================
432 qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
435 VectorSubtract( b, a, d1 );
436 VectorSubtract( c, a, d2 );
437 CrossProduct( d2, d1, plane );
438 if ( VectorNormalize( plane, plane ) == 0 ) {
442 plane[3] = DotProduct( a, plane );
449 ** We use two byte encoded normals in some space critical applications.
450 ** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
451 ** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
454 void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
455 // check for singularities
456 if ( normal[0] == 0 && normal[1] == 0 ) {
457 if ( normal[2] > 0 ) {
459 bytes[1] = 0; // lat = 0, long = 0
463 bytes[1] = 0; // lat = 0, long = 128
469 a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * ( 255.0f / 360.0f ) );
472 b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
475 bytes[0] = b; // longitude
476 bytes[1] = a; // lattitude
485 int PlaneTypeForNormal( vec3_t normal ) {
486 if ( normal[0] == 1.0 || normal[0] == -1.0 ) {
489 if ( normal[1] == 1.0 || normal[1] == -1.0 ) {
492 if ( normal[2] == 1.0 || normal[2] == -1.0 ) {
496 return PLANE_NON_AXIAL;
504 void MatrixMultiply( float in1[3][3], float in2[3][3], float out[3][3] ) {
505 out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
506 in1[0][2] * in2[2][0];
507 out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
508 in1[0][2] * in2[2][1];
509 out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
510 in1[0][2] * in2[2][2];
511 out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
512 in1[1][2] * in2[2][0];
513 out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
514 in1[1][2] * in2[2][1];
515 out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
516 in1[1][2] * in2[2][2];
517 out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
518 in1[2][2] * in2[2][0];
519 out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
520 in1[2][2] * in2[2][1];
521 out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
522 in1[2][2] * in2[2][2];
525 void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal ){
530 inv_denom = 1.0F / DotProduct( normal, normal );
532 d = DotProduct( normal, p ) * inv_denom;
534 n[0] = normal[0] * inv_denom;
535 n[1] = normal[1] * inv_denom;
536 n[2] = normal[2] * inv_denom;
538 dst[0] = p[0] - d * n[0];
539 dst[1] = p[1] - d * n[1];
540 dst[2] = p[2] - d * n[2];
544 ** assumes "src" is normalized
546 void PerpendicularVector( vec3_t dst, const vec3_t src ){
549 vec_t minelem = 1.0F;
553 ** find the smallest magnitude axially aligned vector
555 for ( pos = 0, i = 0; i < 3; i++ )
557 if ( fabs( src[i] ) < minelem ) {
559 minelem = (vec_t)fabs( src[i] );
562 tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
566 ** project the point onto the plane defined by src
568 ProjectPointOnPlane( dst, tempvec, src );
571 ** normalize the result
573 VectorNormalize( dst, dst );
578 RotatePointAroundVector
580 This is not implemented very well...
583 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
598 PerpendicularVector( vr, dir );
599 CrossProduct( vr, vf, vup );
613 memcpy( im, m, sizeof( im ) );
622 memset( zrot, 0, sizeof( zrot ) );
623 zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
625 rad = (float)DEG2RAD( degrees );
626 zrot[0][0] = (vec_t)cos( rad );
627 zrot[0][1] = (vec_t)sin( rad );
628 zrot[1][0] = (vec_t)-sin( rad );
629 zrot[1][1] = (vec_t)cos( rad );
631 MatrixMultiply( m, zrot, tmpmat );
632 MatrixMultiply( tmpmat, im, rot );
634 for ( i = 0; i < 3; i++ ) {
635 dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];
640 ////////////////////////////////////////////////////////////////////////////////
641 // Below is double-precision math stuff. This was initially needed by the new
642 // "base winding" code in q3map2 brush processing in order to fix the famous
643 // "disappearing triangles" issue. These definitions can be used wherever extra
644 // precision is needed.
645 ////////////////////////////////////////////////////////////////////////////////
652 vec_accu_t VectorLengthAccu( const vec3_accu_t v ){
653 return (vec_accu_t) sqrt( ( v[0] * v[0] ) + ( v[1] * v[1] ) + ( v[2] * v[2] ) );
661 vec_accu_t DotProductAccu( const vec3_accu_t a, const vec3_accu_t b ){
662 return ( a[0] * b[0] ) + ( a[1] * b[1] ) + ( a[2] * b[2] );
670 void VectorSubtractAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
671 out[0] = a[0] - b[0];
672 out[1] = a[1] - b[1];
673 out[2] = a[2] - b[2];
681 void VectorAddAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
682 out[0] = a[0] + b[0];
683 out[1] = a[1] + b[1];
684 out[2] = a[2] + b[2];
692 void VectorCopyAccu( const vec3_accu_t in, vec3_accu_t out ){
703 void VectorScaleAccu( const vec3_accu_t in, vec_accu_t scaleFactor, vec3_accu_t out ){
704 out[0] = in[0] * scaleFactor;
705 out[1] = in[1] * scaleFactor;
706 out[2] = in[2] * scaleFactor;
714 void CrossProductAccu( const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out ){
715 out[0] = ( a[1] * b[2] ) - ( a[2] * b[1] );
716 out[1] = ( a[2] * b[0] ) - ( a[0] * b[2] );
717 out[2] = ( a[0] * b[1] ) - ( a[1] * b[0] );
725 vec_accu_t Q_rintAccu( vec_accu_t val ){
726 return (vec_accu_t) floor( val + 0.5 );
731 VectorCopyAccuToRegular
734 void VectorCopyAccuToRegular( const vec3_accu_t in, vec3_t out ){
735 out[0] = (vec_t) in[0];
736 out[1] = (vec_t) in[1];
737 out[2] = (vec_t) in[2];
742 VectorCopyRegularToAccu
745 void VectorCopyRegularToAccu( const vec3_t in, vec3_accu_t out ){
746 out[0] = (vec_accu_t) in[0];
747 out[1] = (vec_accu_t) in[1];
748 out[2] = (vec_accu_t) in[2];
756 vec_accu_t VectorNormalizeAccu( const vec3_accu_t in, vec3_accu_t out ){
757 // The sqrt() function takes double as an input and returns double as an
758 // output according the the man pages on Debian and on FreeBSD. Therefore,
759 // I don't see a reason why using a double outright (instead of using the
760 // vec_accu_t alias for example) could possibly be frowned upon.
764 length = (vec_accu_t) sqrt( ( in[0] * in[0] ) + ( in[1] * in[1] ) + ( in[2] * in[2] ) );
770 out[0] = in[0] / length;
771 out[1] = in[1] / length;
772 out[2] = in[2] / length;