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.
85 Given a normalized forward vector, create two
86 other perpendicular vectors
89 void MakeNormalVectors (vec3_t forward, vec3_t right, vec3_t up)
93 // this rotate and negate guarantees a vector
94 // not colinear with the original
95 right[1] = -forward[0];
96 right[2] = forward[1];
97 right[0] = forward[2];
99 d = DotProduct (right, forward);
100 VectorMA (right, -d, forward, right);
101 VectorNormalize (right, right);
102 CrossProduct (right, forward, up);
105 vec_t VectorLength(const vec3_t v)
111 for (i=0 ; i< 3 ; i++)
113 length = (float)sqrt (length);
118 qboolean VectorCompare (const vec3_t v1, const vec3_t v2)
122 for (i=0 ; i<3 ; i++)
123 if (fabs(v1[i]-v2[i]) > EQUAL_EPSILON)
129 void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc )
131 vc[0] = va[0] + scale*vb[0];
132 vc[1] = va[1] + scale*vb[1];
133 vc[2] = va[2] + scale*vb[2];
136 void _CrossProduct (vec3_t v1, vec3_t v2, vec3_t cross)
138 cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
139 cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
140 cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
143 vec_t _DotProduct (vec3_t v1, vec3_t v2)
145 return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
148 void _VectorSubtract (vec3_t va, vec3_t vb, vec3_t out)
150 out[0] = va[0]-vb[0];
151 out[1] = va[1]-vb[1];
152 out[2] = va[2]-vb[2];
155 void _VectorAdd (vec3_t va, vec3_t vb, vec3_t out)
157 out[0] = va[0]+vb[0];
158 out[1] = va[1]+vb[1];
159 out[2] = va[2]+vb[2];
162 void _VectorCopy (vec3_t in, vec3_t out)
169 vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
171 #if MATHLIB_VECTOR_NORMALIZE_PRECISION_FIX
173 // The sqrt() function takes double as an input and returns double as an
174 // output according the the man pages on Debian and on FreeBSD. Therefore,
175 // I don't see a reason why using a double outright (instead of using the
176 // vec_accu_t alias for example) could possibly be frowned upon.
178 double x, y, z, length;
184 length = sqrt((x * x) + (y * y) + (z * z));
191 out[0] = (vec_t) (x / length);
192 out[1] = (vec_t) (y / length);
193 out[2] = (vec_t) (z / length);
195 return (vec_t) length;
199 vec_t length, ilength;
201 length = (vec_t)sqrt (in[0]*in[0] + in[1]*in[1] + in[2]*in[2]);
208 ilength = 1.0f/length;
209 out[0] = in[0]*ilength;
210 out[1] = in[1]*ilength;
211 out[2] = in[2]*ilength;
219 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
229 out[0] = out[1] = out[2] = 1.0;
235 VectorScale (in, scale, out);
240 void VectorInverse (vec3_t v)
248 void VectorScale (vec3_t v, vec_t scale, vec3_t out)
250 out[0] = v[0] * scale;
251 out[1] = v[1] * scale;
252 out[2] = v[2] * scale;
256 void VectorRotate (vec3_t vIn, vec3_t vRotation, vec3_t out)
263 VectorCopy(va, vWork);
264 nIndex[0][0] = 1; nIndex[0][1] = 2;
265 nIndex[1][0] = 2; nIndex[1][1] = 0;
266 nIndex[2][0] = 0; nIndex[2][1] = 1;
268 for (i = 0; i < 3; i++)
270 if (vRotation[i] != 0)
272 float dAngle = vRotation[i] * Q_PI / 180.0f;
273 float c = (vec_t)cos(dAngle);
274 float s = (vec_t)sin(dAngle);
275 vWork[nIndex[i][0]] = va[nIndex[i][0]] * c - va[nIndex[i][1]] * s;
276 vWork[nIndex[i][1]] = va[nIndex[i][0]] * s + va[nIndex[i][1]] * c;
278 VectorCopy(vWork, va);
280 VectorCopy(vWork, out);
283 void VectorRotateOrigin (vec3_t vIn, vec3_t vRotation, vec3_t vOrigin, vec3_t out)
285 vec3_t vTemp, vTemp2;
287 VectorSubtract(vIn, vOrigin, vTemp);
288 VectorRotate(vTemp, vRotation, vTemp2);
289 VectorAdd(vTemp2, vOrigin, out);
292 void VectorPolar(vec3_t v, float radius, float theta, float phi)
294 v[0]=(float)(radius * cos(theta) * cos(phi));
295 v[1]=(float)(radius * sin(theta) * cos(phi));
296 v[2]=(float)(radius * sin(phi));
299 void VectorSnap(vec3_t v)
302 for (i = 0; i < 3; i++)
304 v[i] = (vec_t)FLOAT_TO_INTEGER(v[i]);
308 void VectorISnap(vec3_t point, int snap)
311 for (i = 0 ;i < 3 ; i++)
313 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
317 void VectorFSnap(vec3_t point, float snap)
320 for (i = 0 ;i < 3 ; i++)
322 point[i] = (vec_t)FLOAT_SNAP(point[i], snap);
326 void _Vector5Add (vec5_t va, vec5_t vb, vec5_t out)
328 out[0] = va[0]+vb[0];
329 out[1] = va[1]+vb[1];
330 out[2] = va[2]+vb[2];
331 out[3] = va[3]+vb[3];
332 out[4] = va[4]+vb[4];
335 void _Vector5Scale (vec5_t v, vec_t scale, vec5_t out)
337 out[0] = v[0] * scale;
338 out[1] = v[1] * scale;
339 out[2] = v[2] * scale;
340 out[3] = v[3] * scale;
341 out[4] = v[4] * scale;
344 void _Vector53Copy (vec5_t in, vec3_t out)
351 // NOTE: added these from Ritual's Q3Radiant
352 #define INVALID_BOUNDS 99999
353 void ClearBounds (vec3_t mins, vec3_t maxs)
355 mins[0] = mins[1] = mins[2] = +INVALID_BOUNDS;
356 maxs[0] = maxs[1] = maxs[2] = -INVALID_BOUNDS;
359 void AddPointToBounds (vec3_t v, vec3_t mins, vec3_t maxs)
364 if(mins[0] == +INVALID_BOUNDS)
365 if(maxs[0] == -INVALID_BOUNDS)
371 for (i=0 ; i<3 ; i++)
381 void AngleVectors (vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
384 static float sr, sp, sy, cr, cp, cy;
385 // static to help MS compiler fp bugs
387 angle = angles[YAW] * (Q_PI*2.0f / 360.0f);
388 sy = (vec_t)sin(angle);
389 cy = (vec_t)cos(angle);
390 angle = angles[PITCH] * (Q_PI*2.0f / 360.0f);
391 sp = (vec_t)sin(angle);
392 cp = (vec_t)cos(angle);
393 angle = angles[ROLL] * (Q_PI*2.0f / 360.0f);
394 sr = (vec_t)sin(angle);
395 cr = (vec_t)cos(angle);
405 right[0] = -sr*sp*cy+cr*sy;
406 right[1] = -sr*sp*sy-cr*cy;
411 up[0] = cr*sp*cy+sr*sy;
412 up[1] = cr*sp*sy-sr*cy;
417 void VectorToAngles( vec3_t vec, vec3_t angles )
422 if ( ( vec[ 0 ] == 0 ) && ( vec[ 1 ] == 0 ) )
436 yaw = (vec_t)atan2( vec[ 1 ], vec[ 0 ] ) * 180 / Q_PI;
442 forward = ( float )sqrt( vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] );
443 pitch = (vec_t)atan2( vec[ 2 ], forward ) * 180 / Q_PI;
456 =====================
459 Returns false if the triangle is degenrate.
460 The normal will point out of the clock for clockwise ordered points
461 =====================
463 qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) {
466 VectorSubtract( b, a, d1 );
467 VectorSubtract( c, a, d2 );
468 CrossProduct( d2, d1, plane );
469 if ( VectorNormalize( plane, plane ) == 0 ) {
473 plane[3] = DotProduct( a, plane );
480 ** We use two byte encoded normals in some space critical applications.
481 ** Lat = 0 at (1,0,0) to 360 (-1,0,0), encoded in 8-bit sine table format
482 ** Lng = 0 at (0,0,1) to 180 (0,0,-1), encoded in 8-bit sine table format
485 void NormalToLatLong( const vec3_t normal, byte bytes[2] ) {
486 // check for singularities
487 if ( normal[0] == 0 && normal[1] == 0 ) {
488 if ( normal[2] > 0 ) {
490 bytes[1] = 0; // lat = 0, long = 0
493 bytes[1] = 0; // lat = 0, long = 128
498 a = (int)( RAD2DEG( atan2( normal[1], normal[0] ) ) * (255.0f / 360.0f ) );
501 b = (int)( RAD2DEG( acos( normal[2] ) ) * ( 255.0f / 360.0f ) );
504 bytes[0] = b; // longitude
505 bytes[1] = a; // lattitude
514 int PlaneTypeForNormal (vec3_t normal) {
515 if (normal[0] == 1.0 || normal[0] == -1.0)
517 if (normal[1] == 1.0 || normal[1] == -1.0)
519 if (normal[2] == 1.0 || normal[2] == -1.0)
522 return PLANE_NON_AXIAL;
530 void MatrixMultiply(float in1[3][3], float in2[3][3], float out[3][3]) {
531 out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
532 in1[0][2] * in2[2][0];
533 out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
534 in1[0][2] * in2[2][1];
535 out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
536 in1[0][2] * in2[2][2];
537 out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
538 in1[1][2] * in2[2][0];
539 out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
540 in1[1][2] * in2[2][1];
541 out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
542 in1[1][2] * in2[2][2];
543 out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
544 in1[2][2] * in2[2][0];
545 out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
546 in1[2][2] * in2[2][1];
547 out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
548 in1[2][2] * in2[2][2];
551 void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal )
557 inv_denom = 1.0F / DotProduct( normal, normal );
559 d = DotProduct( normal, p ) * inv_denom;
561 n[0] = normal[0] * inv_denom;
562 n[1] = normal[1] * inv_denom;
563 n[2] = normal[2] * inv_denom;
565 dst[0] = p[0] - d * n[0];
566 dst[1] = p[1] - d * n[1];
567 dst[2] = p[2] - d * n[2];
571 ** assumes "src" is normalized
573 void PerpendicularVector( vec3_t dst, const vec3_t src )
577 vec_t minelem = 1.0F;
581 ** find the smallest magnitude axially aligned vector
583 for ( pos = 0, i = 0; i < 3; i++ )
585 if ( fabs( src[i] ) < minelem )
588 minelem = (vec_t)fabs( src[i] );
591 tempvec[0] = tempvec[1] = tempvec[2] = 0.0F;
595 ** project the point onto the plane defined by src
597 ProjectPointOnPlane( dst, tempvec, src );
600 ** normalize the result
602 VectorNormalize( dst, dst );
607 RotatePointAroundVector
609 This is not implemented very well...
612 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point,
627 PerpendicularVector( vr, dir );
628 CrossProduct( vr, vf, vup );
642 memcpy( im, m, sizeof( im ) );
651 memset( zrot, 0, sizeof( zrot ) );
652 zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F;
654 rad = (float)DEG2RAD( degrees );
655 zrot[0][0] = (vec_t)cos( rad );
656 zrot[0][1] = (vec_t)sin( rad );
657 zrot[1][0] = (vec_t)-sin( rad );
658 zrot[1][1] = (vec_t)cos( rad );
660 MatrixMultiply( m, zrot, tmpmat );
661 MatrixMultiply( tmpmat, im, rot );
663 for ( i = 0; i < 3; i++ ) {
664 dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2];
669 ////////////////////////////////////////////////////////////////////////////////
670 // Below is double-precision math stuff. This was initially needed by the new
671 // "base winding" code in q3map2 brush processing in order to fix the famous
672 // "disappearing triangles" issue. These definitions can be used wherever extra
673 // precision is needed.
674 ////////////////////////////////////////////////////////////////////////////////
681 vec_accu_t VectorLengthAccu(const vec3_accu_t v)
683 return (vec_accu_t) sqrt((v[0] * v[0]) + (v[1] * v[1]) + (v[2] * v[2]));
691 vec_accu_t DotProductAccu(const vec3_accu_t a, const vec3_accu_t b)
693 return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);
701 void VectorSubtractAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
703 out[0] = a[0] - b[0];
704 out[1] = a[1] - b[1];
705 out[2] = a[2] - b[2];
713 void VectorAddAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
715 out[0] = a[0] + b[0];
716 out[1] = a[1] + b[1];
717 out[2] = a[2] + b[2];
725 void VectorCopyAccu(const vec3_accu_t in, vec3_accu_t out)
737 void VectorScaleAccu(const vec3_accu_t in, vec_accu_t scaleFactor, vec3_accu_t out)
739 out[0] = in[0] * scaleFactor;
740 out[1] = in[1] * scaleFactor;
741 out[2] = in[2] * scaleFactor;
749 void CrossProductAccu(const vec3_accu_t a, const vec3_accu_t b, vec3_accu_t out)
751 out[0] = (a[1] * b[2]) - (a[2] * b[1]);
752 out[1] = (a[2] * b[0]) - (a[0] * b[2]);
753 out[2] = (a[0] * b[1]) - (a[1] * b[0]);
761 vec_accu_t Q_rintAccu(vec_accu_t val)
763 return (vec_accu_t) floor(val + 0.5);
768 VectorCopyAccuToRegular
771 void VectorCopyAccuToRegular(const vec3_accu_t in, vec3_t out)
773 out[0] = (vec_t) in[0];
774 out[1] = (vec_t) in[1];
775 out[2] = (vec_t) in[2];
780 VectorCopyRegularToAccu
783 void VectorCopyRegularToAccu(const vec3_t in, vec3_accu_t out)
785 out[0] = (vec_accu_t) in[0];
786 out[1] = (vec_accu_t) in[1];
787 out[2] = (vec_accu_t) in[2];
795 vec_accu_t VectorNormalizeAccu(const vec3_accu_t in, vec3_accu_t out)
797 // The sqrt() function takes double as an input and returns double as an
798 // output according the the man pages on Debian and on FreeBSD. Therefore,
799 // I don't see a reason why using a double outright (instead of using the
800 // vec_accu_t alias for example) could possibly be frowned upon.
804 length = (vec_accu_t) sqrt((in[0] * in[0]) + (in[1] * in[1]) + (in[2] * in[2]));
811 out[0] = in[0] / length;
812 out[1] = in[1] / length;
813 out[2] = in[2] / length;