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)
40 int i, zeroComponentCount;
42 zeroComponentCount = 0;
43 for (i = 0; i < 3; i++)
51 if (zeroComponentCount > 1)
53 // The zero vector will be on axis.
65 qboolean VectorIsOnAxialPlane(vec3_t v)
69 for (i = 0; i < 3; i++)
73 // The zero vector will be on axial plane.
86 qboolean VectorIsOnAxis(vec3_t v)
88 int i, zeroComponentCount;
90 zeroComponentCount = 0;
91 for (i = 0; i < 3; i++)
99 if (zeroComponentCount > 1)
101 // The zero vector will be on axis.
113 qboolean VectorIsOnAxialPlane(vec3_t v)
117 for (i = 0; i < 3; i++)
121 // The zero vector will be on axial plane.
133 Given a normalized forward vector, create two
134 other perpendicular vectors
137 void MakeNormalVectors (vec3_t forward, vec3_t right, vec3_t up)
141 // this rotate and negate guarantees a vector
142 // not colinear with the original
143 right[1] = -forward[0];
144 right[2] = forward[1];
145 right[0] = forward[2];
147 d = DotProduct (right, forward);
148 VectorMA (right, -d, forward, right);
149 VectorNormalize (right, right);
150 CrossProduct (right, forward, up);
153 vec_t VectorLength(const vec3_t v)
159 for (i=0 ; i< 3 ; i++)
161 length = (float)sqrt (length);
166 qboolean VectorCompare (const vec3_t v1, const vec3_t v2)
170 for (i=0 ; i<3 ; i++)
171 if (fabs(v1[i]-v2[i]) > EQUAL_EPSILON)
177 void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc )
179 vc[0] = va[0] + scale*vb[0];
180 vc[1] = va[1] + scale*vb[1];
181 vc[2] = va[2] + scale*vb[2];
184 void _CrossProduct (vec3_t v1, vec3_t v2, vec3_t cross)
186 cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
187 cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
188 cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
191 vec_t _DotProduct (vec3_t v1, vec3_t v2)
193 return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
196 void _VectorSubtract (vec3_t va, vec3_t vb, vec3_t out)
198 out[0] = va[0]-vb[0];
199 out[1] = va[1]-vb[1];
200 out[2] = va[2]-vb[2];
203 void _VectorAdd (vec3_t va, vec3_t vb, vec3_t out)
205 out[0] = va[0]+vb[0];
206 out[1] = va[1]+vb[1];
207 out[2] = va[2]+vb[2];
210 void _VectorCopy (vec3_t in, vec3_t out)
217 vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
219 #if MATHLIB_VECTOR_NORMALIZE_PRECISION_FIX
221 // The sqrt() function takes double as an input and returns double as an
222 // output according the the man pages on Debian and on FreeBSD. Therefore,
223 // I don't see a reason why using a double outright (instead of using the
224 // vec_accu_t alias for example) could possibly be frowned upon.
226 double x, y, z, length;
232 length = sqrt((x * x) + (y * y) + (z * z));
239 out[0] = (vec_t) (x / length);
240 out[1] = (vec_t) (y / length);
241 out[2] = (vec_t) (z / length);
243 return (vec_t) length;
247 vec_t length, ilength;
249 length = (vec_t)sqrt (in[0]*in[0] + in[1]*in[1] + in[2]*in[2]);
256 ilength = 1.0f/length;
257 out[0] = in[0]*ilength;
258 out[1] = in[1]*ilength;
259 out[2] = in[2]*ilength;
267 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
277 out[0] = out[1] = out[2] = 1.0;
283 VectorScale (in, scale, out);
288 void VectorInverse (vec3_t v)
296 void VectorScale (vec3_t v, vec_t scale, vec3_t out)
298 out[0] = v[0] * scale;
299 out[1] = v[1] * scale;
300 out[2] = v[2] * scale;
304 void VectorRotate (vec3_t vIn, vec3_t vRotation, vec3_t out)
311 VectorCopy(va, vWork);
312 nIndex[0][0] = 1; nIndex[0][1] = 2;
313 nIndex[1][0] = 2; nIndex[1][1] = 0;
314 nIndex[2][0] = 0; nIndex[2][1] = 1;
316 for (i = 0; i < 3; i++)
318 if (vRotation[i] != 0)
320 float dAngle = vRotation[i] * Q_PI / 180.0f;
321 float c = (vec_t)cos(dAngle);
322 float s = (vec_t)sin(dAngle);
323 vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
324 vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
326 VectorCopy(vWork, va);
328 VectorCopy(vWork, out);
331 void VectorRotateOrigin (vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out)
333 vec3_t vTemp, vTemp2;
335 VectorSubtract(vIn, vOrigin, vTemp);
336 VectorRotate(vTemp, vRotation, vTemp2);
337 VectorAdd(vTemp2, vOrigin, out);
340 void VectorPolar(vec3_t v, float radius, float theta, float phi)
342 v[0]=(float)(radius * cos(theta) * cos(phi));
343 v[1]=(float)(radius * sin(theta) * cos(phi));
344 v[2]=(float)(radius * sin(phi));
347 void VectorSnap(vec3_t v)
350 for (i = 0; i < 3; i++)
352 v[i] = (vec_t)FLOAT_TO_INTEGER(v[i]);
356 void VectorISnap(vec3_t point, int snap)
359 for (i = 0 ;i < 3 ; i++)
361 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
365 void VectorFSnap(vec3_t point, float snap)
368 for (i = 0 ;i < 3 ; i++)
370 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
374 void _Vector5Add (vec5_t va, vec5_t vb, vec5_t out)
376 out[0] = va[0]+vb[0];
377 out[1] = va[1]+vb[1];
378 out[2] = va[2]+vb[2];
379 out[3] = va[3]+vb[3];
380 out[4] = va[4]+vb[4];
383 void _Vector5Scale (vec5_t v, vec_t scale, vec5_t out)
385 out[0] = v[0] * scale;
386 out[1] = v[1] * scale;
387 out[2] = v[2] * scale;
388 out[3] = v[3] * scale;
389 out[4] = v[4] * scale;
392 void _Vector53Copy (vec5_t in, vec3_t out)
399 // NOTE: added these from Ritual's Q3Radiant
400 #define INVALID_BOUNDS 99999
401 void ClearBounds (vec3_t mins, vec3_t maxs)
403 mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
404 maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
407 void AddPointToBounds (vec3_t v, vec3_t mins, vec3_t maxs)
412 if(mins[0] == +INVALID_BOUNDS)
413 if(maxs[0] == -INVALID_BOUNDS)
419 for (i=0 ; i<3 ; i++)
429 void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
432 static float sr, sp, sy, cr, cp, cy;
433 // static to help MS compiler fp bugs
435 angle = angles[YAW] * (Q_PI*2.0f / 360.0f);
436 sy = (vec_t)sin(angle);
437 cy = (vec_t)cos(angle);
438 angle = angles[PITCH] * (Q_PI*2.0f / 360.0f);
439 sp = (vec_t)sin(angle);
440 cp = (vec_t)cos(angle);
441 angle = angles[ROLL] * (Q_PI*2.0f / 360.0f);
442 sr = (vec_t)sin(angle);
443 cr = (vec_t)cos(angle);
453 right[0] = -sr*sp*cy+cr*sy;
454 right[1] = -sr*sp*sy-cr*cy;
459 up[0] = cr*sp*cy+sr*sy;
460 up[1] = cr*sp*sy-sr*cy;
465 void VectorToAngles( vec3_t vec, vec3_t angles )
470 if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) )
484 yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
490 forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
491 pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
504 =====================
507 Returns false if the triangle is degenrate.
508 The normal will point out of the clock for clockwise ordered points
509 =====================
511 qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
514 VectorSubtract( b, a, d1 );
515 VectorSubtract( c, a, d2 );
516 CrossProduct( d2, d1, plane );
517 if ( VectorNormalize( plane, plane ) == 0 ) {
521 plane[3] = DotProduct( a, plane );
528 ** We use two byte encoded normals in some space critical applications.
529 ** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
530 ** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
533 void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
534 // check for singularities
535 if ( normal[0] == 0 && normal[1] == 0 ) {
536 if ( normal[2] > 0 ) {
538 bytes[1] = 0; // lat = 0, long = 0
541 bytes[1] = 0; // lat = 0, long = 128
546 a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * (255.0f / 360.0f ) );
549 b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
552 bytes[0] = b; // longitude
553 bytes[1] = a; // lattitude
562 int PlaneTypeForNormal (vec3_t normal) {
563 if (normal[0] == 1.0 || normal[0] == -1.0)
565 if (normal[1] == 1.0 || normal[1] == -1.0)
567 if (normal[2] == 1.0 || normal[2] == -1.0)
570 return PLANE_NON_AXIAL;
578 void MatrixMultiply(float in1[3][3], float in2[3][3], float out[3][3]) {
579 out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
580 in1[0][2] * in2[2][0];
581 out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
582 in1[0][2] * in2[2][1];
583 out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
584 in1[0][2] * in2[2][2];
585 out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
586 in1[1][2] * in2[2][0];
587 out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
588 in1[1][2] * in2[2][1];
589 out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
590 in1[1][2] * in2[2][2];
591 out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
592 in1[2][2] * in2[2][0];
593 out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
594 in1[2][2] * in2[2][1];
595 out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
596 in1[2][2] * in2[2][2];
599 void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
605 inv_denom = 1.0F / DotProduct( normal, normal );
607 d = DotProduct( normal, p ) * inv_denom;
609 n[0] = normal[0] * inv_denom;
610 n[1] = normal[1] * inv_denom;
611 n[2] = normal[2] * inv_denom;
613 dst[0] = p[0] - d * n[0];
614 dst[1] = p[1] - d * n[1];
615 dst[2] = p[2] - d * n[2];
619 ** assumes "src" is normalized
621 void PerpendicularVector( vec3_t dst, const vec3_t src )
625 vec_t minelem = 1.0F;
629 ** find the smallest magnitude axially aligned vector
631 for ( pos = 0, i = 0; i < 3; i++ )
633 if ( fabs( src[i] ) < minelem )
636 minelem = (vec_t)fabs( src[i] );
639 tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
643 ** project the point onto the plane defined by src
645 ProjectPointOnPlane( dst, tempvec, src );
648 ** normalize the result
650 VectorNormalize( dst, dst );
655 RotatePointAroundVector
657 This is not implemented very well...
660 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
675 PerpendicularVector( vr, dir );
676 CrossProduct( vr, vf, vup );
690 memcpy( im, m, sizeof( im ) );
699 memset( zrot, 0, sizeof( zrot ) );
700 zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
702 rad = (float)DEG2RAD( degrees );
703 zrot[0][0] = (vec_t)cos( rad );
704 zrot[0][1] = (vec_t)sin( rad );
705 zrot[1][0] = (vec_t)-sin( rad );
706 zrot[1][1] = (vec_t)cos( rad );
708 MatrixMultiply( m, zrot, tmpmat );
709 MatrixMultiply( tmpmat, im, rot );
711 for ( i = 0; i < 3; i++ ) {
712 dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];
717 ////////////////////////////////////////////////////////////////////////////////
718 // Below is double-precision math stuff. This was initially needed by the new
719 // "base winding" code in q3map2 brush processing in order to fix the famous
720 // "disappearing triangles" issue. These definitions can be used wherever extra
721 // precision is needed.
722 ////////////////////////////////////////////////////////////////////////////////
729 vec_accu_t VectorLengthAccu(const vec3_accu_t v)
731 return (vec_accu_t) sqrt((v[0] * v[0]) + (v[1] * v[1]) + (v[2] * v[2]));
739 vec_accu_t DotProductAccu(const vec3_accu_t a, const vec3_accu_t b)
741 return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);
749 void VectorSubtractAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
751 out[0] = a[0] - b[0];
752 out[1] = a[1] - b[1];
753 out[2] = a[2] - b[2];
761 void VectorAddAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
763 out[0] = a[0] + b[0];
764 out[1] = a[1] + b[1];
765 out[2] = a[2] + b[2];
773 void VectorCopyAccu(const vec3_accu_t in, vec3_accu_t out)
785 void VectorScaleAccu(const vec3_accu_t in, vec_accu_t scaleFactor, vec3_accu_t out)
787 out[0] = in[0] * scaleFactor;
788 out[1] = in[1] * scaleFactor;
789 out[2] = in[2] * scaleFactor;
797 void CrossProductAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
799 out[0] = (a[1] * b[2]) - (a[2] * b[1]);
800 out[1] = (a[2] * b[0]) - (a[0] * b[2]);
801 out[2] = (a[0] * b[1]) - (a[1] * b[0]);
809 vec_accu_t Q_rintAccu(vec_accu_t val)
811 return (vec_accu_t) floor(val + 0.5);
816 VectorCopyAccuToRegular
819 void VectorCopyAccuToRegular(const vec3_accu_t in, vec3_t out)
821 out[0] = (vec_t) in[0];
822 out[1] = (vec_t) in[1];
823 out[2] = (vec_t) in[2];
828 VectorCopyRegularToAccu
831 void VectorCopyRegularToAccu(const vec3_t in, vec3_accu_t out)
833 out[0] = (vec_accu_t) in[0];
834 out[1] = (vec_accu_t) in[1];
835 out[2] = (vec_accu_t) in[2];
843 vec_accu_t VectorNormalizeAccu(const vec3_accu_t in, vec3_accu_t out)
845 // The sqrt() function takes double as an input and returns double as an
846 // output according the the man pages on Debian and on FreeBSD. Therefore,
847 // I don't see a reason why using a double outright (instead of using the
848 // vec_accu_t alias for example) could possibly be frowned upon.
852 length = (vec_accu_t) sqrt((in[0] * in[0]) + (in[1] * in[1]) + (in[2] * in[2]));
859 out[0] = in[0] / length;
860 out[1] = in[1] / length;
861 out[2] = in[2] / length;
867 ////////////////////////////////////////////////////////////////////////////////
868 // Below is double-precision math stuff. This was initially needed by the new
869 // "base winding" code in q3map2 brush processing in order to fix the famous
870 // "disappearing triangles" issue. These definitions can be used wherever extra
871 // precision is needed.
872 ////////////////////////////////////////////////////////////////////////////////
879 vec_accu_t VectorLengthAccu(const vec3_accu_t v)
881 return (vec_accu_t) sqrt((v[0] * v[0]) + (v[1] * v[1]) + (v[2] * v[2]));
889 vec_accu_t DotProductAccu(const vec3_accu_t a, const vec3_accu_t b)
891 return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);
899 void VectorSubtractAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
901 out[0] = a[0] - b[0];
902 out[1] = a[1] - b[1];
903 out[2] = a[2] - b[2];
911 void VectorAddAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
913 out[0] = a[0] + b[0];
914 out[1] = a[1] + b[1];
915 out[2] = a[2] + b[2];
923 void VectorCopyAccu(const vec3_accu_t in, vec3_accu_t out)
935 void VectorScaleAccu(const vec3_accu_t in, vec_accu_t scaleFactor, vec3_accu_t out)
937 out[0] = in[0] * scaleFactor;
938 out[1] = in[1] * scaleFactor;
939 out[2] = in[2] * scaleFactor;
947 void CrossProductAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
949 out[0] = (a[1] * b[2]) - (a[2] * b[1]);
950 out[1] = (a[2] * b[0]) - (a[0] * b[2]);
951 out[2] = (a[0] * b[1]) - (a[1] * b[0]);
959 vec_accu_t Q_rintAccu(vec_accu_t val)
961 return (vec_accu_t) floor(val + 0.5);
966 VectorCopyAccuToRegular
969 void VectorCopyAccuToRegular(const vec3_accu_t in, vec3_t out)
971 out[0] = (vec_t) in[0];
972 out[1] = (vec_t) in[1];
973 out[2] = (vec_t) in[2];
978 VectorCopyRegularToAccu
981 void VectorCopyRegularToAccu(const vec3_t in, vec3_accu_t out)
983 out[0] = (vec_accu_t) in[0];
984 out[1] = (vec_accu_t) in[1];
985 out[2] = (vec_accu_t) in[2];
993 vec_accu_t VectorNormalizeAccu(const vec3_accu_t in, vec3_accu_t out)
995 // The sqrt() function takes double as an input and returns double as an
996 // output according the the man pages on Debian and on FreeBSD. Therefore,
997 // I don't see a reason why using a double outright (instead of using the
998 // vec_accu_t alias for example) could possibly be frowned upon.
1002 length = (vec_accu_t) sqrt((in[0] * in[0]) + (in[1] * in[1]) + (in[2] * in[2]));
1009 out[0] = in[0] / length;
1010 out[1] = in[1] / length;
1011 out[2] = in[2] / length;