1 /* Copyright (C) 2021-2024 Harry Godden (hgn) - All Rights Reserved
19 * 5.d Raycast & Spherecasts
29 #include "vg_stdint.h"
33 #define VG_PIf 3.14159265358979323846264338327950288f
34 #define VG_TAUf 6.28318530717958647692528676655900576f
37 * -----------------------------------------------------------------------------
38 * Section 0. Misc Operations
39 * -----------------------------------------------------------------------------
42 /* get the f32 as the raw bits in a u32 without converting */
43 static u32 vg_ftu32( f32 a )
45 u32 *ptr = (u32 *)(&a);
49 /* check if f32 is infinite */
50 static int vg_isinff( f32 a )
52 return ((vg_ftu32(a)) & 0x7FFFFFFFU) == 0x7F800000U;
55 /* check if f32 is not a number */
56 static int vg_isnanf( f32 a )
58 return !vg_isinff(a) && ((vg_ftu32(a)) & 0x7F800000U) == 0x7F800000U;
61 /* check if f32 is a number and is not infinite */
62 static int vg_validf( f32 a )
64 return ((vg_ftu32(a)) & 0x7F800000U) != 0x7F800000U;
67 static int v3_valid( v3f a ){
68 for( u32 i=0; i<3; i++ )
69 if( !vg_validf(a[i]) ) return 0;
74 * -----------------------------------------------------------------------------
75 * Section 1. Scalar Operations
76 * -----------------------------------------------------------------------------
79 static inline f32 vg_minf( f32 a, f32 b ){ return a < b? a: b; }
80 static inline f32 vg_maxf( f32 a, f32 b ){ return a > b? a: b; }
82 static inline int vg_min( int a, int b ){ return a < b? a: b; }
83 static inline int vg_max( int a, int b ){ return a > b? a: b; }
85 static inline f32 vg_clampf( f32 a, f32 min, f32 max )
87 return vg_minf( max, vg_maxf( a, min ) );
90 static inline f32 vg_signf( f32 a )
92 return a < 0.0f? -1.0f: 1.0f;
95 static inline f32 vg_fractf( f32 a )
97 return a - floorf( a );
100 static inline f64 vg_fractf64( f64 a ){
101 return a - floor( a );
104 static f32 vg_cfrictf( f32 velocity, f32 F )
106 return -vg_signf(velocity) * vg_minf( F, fabsf(velocity) );
109 static inline f32 vg_rad( f32 deg )
111 return deg * VG_PIf / 180.0f;
114 /* angle to reach b from a */
115 static f32 vg_angle_diff( f32 a, f32 b ){
116 f32 d = fmod(b,VG_TAUf)-fmodf(a,VG_TAUf);
117 if( fabsf(d) > VG_PIf )
118 d = -vg_signf(d) * (VG_TAUf - fabsf(d));
124 * quantize float to bit count
126 static u32 vg_quantf( f32 a, u32 bits, f32 min, f32 max ){
127 u32 mask = (0x1 << bits) - 1;
128 return vg_clampf((a - min) * ((f32)mask/(max-min)), 0.0f, mask );
132 * un-quantize discreet to float
134 static f32 vg_dequantf( u32 q, u32 bits, f32 min, f32 max ){
135 u32 mask = (0x1 << bits) - 1;
136 return min + (f32)q * ((max-min) / (f32)mask);
139 /* https://iquilezles.org/articles/functions/
141 * Use k to control the stretching of the function. Its maximum, which is 1,
142 * happens at exactly x = 1/k.
144 static f32 vg_exp_impulse( f32 x, f32 k ){
146 return h*expf(1.0f-h);
150 * -----------------------------------------------------------------------------
151 * Section 2.a 2D Vectors
152 * -----------------------------------------------------------------------------
155 static inline void v2_copy( v2f a, v2f d )
157 d[0] = a[0]; d[1] = a[1];
160 static inline void v2_zero( v2f a )
162 a[0] = 0.f; a[1] = 0.f;
165 static inline void v2_add( v2f a, v2f b, v2f d )
167 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
170 static inline void v2_sub( v2f a, v2f b, v2f d )
172 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
175 static inline void v2_minv( v2f a, v2f b, v2f dest )
177 dest[0] = vg_minf(a[0], b[0]);
178 dest[1] = vg_minf(a[1], b[1]);
181 static inline void v2_maxv( v2f a, v2f b, v2f dest )
183 dest[0] = vg_maxf(a[0], b[0]);
184 dest[1] = vg_maxf(a[1], b[1]);
187 static inline f32 v2_dot( v2f a, v2f b )
189 return a[0] * b[0] + a[1] * b[1];
192 static inline f32 v2_cross( v2f a, v2f b )
194 return a[0]*b[1] - a[1]*b[0];
197 static inline void v2_abs( v2f a, v2f d )
199 d[0] = fabsf( a[0] );
200 d[1] = fabsf( a[1] );
203 static inline void v2_muls( v2f a, f32 s, v2f d )
205 d[0] = a[0]*s; d[1] = a[1]*s;
208 static inline void v2_divs( v2f a, f32 s, v2f d )
210 d[0] = a[0]/s; d[1] = a[1]/s;
213 static inline void v2_mul( v2f a, v2f b, v2f d )
219 static inline void v2_div( v2f a, v2f b, v2f d )
221 d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
224 static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d )
226 d[0] = a[0]+b[0]*s[0];
227 d[1] = a[1]+b[1]*s[1];
230 static inline void v2_muladds( v2f a, v2f b, f32 s, v2f d )
236 static inline f32 v2_length2( v2f a )
238 return a[0]*a[0] + a[1]*a[1];
241 static inline f32 v2_length( v2f a )
243 return sqrtf( v2_length2( a ) );
246 static inline f32 v2_dist2( v2f a, v2f b )
249 v2_sub( a, b, delta );
250 return v2_length2( delta );
253 static inline f32 v2_dist( v2f a, v2f b )
255 return sqrtf( v2_dist2( a, b ) );
258 static inline void v2_lerp( v2f a, v2f b, f32 t, v2f d )
260 d[0] = a[0] + t*(b[0]-a[0]);
261 d[1] = a[1] + t*(b[1]-a[1]);
264 static inline void v2_normalize( v2f a )
266 v2_muls( a, 1.0f / v2_length( a ), a );
269 static void v2_normalize_clamp( v2f a )
271 f32 l2 = v2_length2( a );
273 v2_muls( a, 1.0f/sqrtf(l2), a );
276 static inline void v2_floor( v2f a, v2f b )
278 b[0] = floorf( a[0] );
279 b[1] = floorf( a[1] );
282 static inline void v2_fill( v2f a, f32 v )
288 static inline void v2_copysign( v2f a, v2f b )
290 a[0] = copysignf( a[0], b[0] );
291 a[1] = copysignf( a[1], b[1] );
295 * ---------------- */
297 static inline void v2i_copy( v2i a, v2i b )
299 b[0] = a[0]; b[1] = a[1];
302 static inline int v2i_eq( v2i a, v2i b )
304 return ((a[0] == b[0]) && (a[1] == b[1]));
307 static inline void v2i_add( v2i a, v2i b, v2i d )
309 d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
312 static inline void v2i_sub( v2i a, v2i b, v2i d )
314 d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
318 * -----------------------------------------------------------------------------
319 * Section 2.b 3D Vectors
320 * -----------------------------------------------------------------------------
323 static inline void v3_copy( v3f a, v3f b )
325 b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
328 static inline void v3_zero( v3f a )
330 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
333 static inline void v3_add( v3f a, v3f b, v3f d )
335 d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
338 static inline void v3i_add( v3i a, v3i b, v3i d )
340 d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
343 static inline void v3_sub( v3f a, v3f b, v3f d )
345 d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
348 static inline void v3i_sub( v3i a, v3i b, v3i d )
350 d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
353 static inline void v3_mul( v3f a, v3f b, v3f d )
355 d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
358 static inline void v3_div( v3f a, v3f b, v3f d )
360 d[0] = b[0]!=0.0f? a[0]/b[0]: INFINITY;
361 d[1] = b[1]!=0.0f? a[1]/b[1]: INFINITY;
362 d[2] = b[2]!=0.0f? a[2]/b[2]: INFINITY;
365 static inline void v3_muls( v3f a, f32 s, v3f d )
367 d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
370 static inline void v3_fill( v3f a, f32 v )
377 static inline void v3_divs( v3f a, f32 s, v3f d )
380 v3_fill( d, INFINITY );
389 static inline void v3_muladds( v3f a, v3f b, f32 s, v3f d )
391 d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
394 static inline void v3_muladd( v2f a, v2f b, v2f s, v2f d )
396 d[0] = a[0]+b[0]*s[0];
397 d[1] = a[1]+b[1]*s[1];
398 d[2] = a[2]+b[2]*s[2];
401 static inline f32 v3_dot( v3f a, v3f b )
403 return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
406 static inline void v3_cross( v3f a, v3f b, v3f dest )
409 d[0] = a[1]*b[2] - a[2]*b[1];
410 d[1] = a[2]*b[0] - a[0]*b[2];
411 d[2] = a[0]*b[1] - a[1]*b[0];
415 static inline f32 v3_length2( v3f a )
417 return v3_dot( a, a );
420 static inline f32 v3_length( v3f a )
422 return sqrtf( v3_length2( a ) );
425 static inline f32 v3_dist2( v3f a, v3f b )
428 v3_sub( a, b, delta );
429 return v3_length2( delta );
432 static inline f32 v3_dist( v3f a, v3f b )
434 return sqrtf( v3_dist2( a, b ) );
437 static inline void v3_normalize( v3f a )
439 v3_muls( a, 1.f / v3_length( a ), a );
442 static inline f32 vg_lerpf( f32 a, f32 b, f32 t ){
446 static inline f64 vg_lerp( f64 a, f64 b, f64 t )
451 static inline void vg_slewf( f32 *a, f32 b, f32 speed ){
452 f32 d = vg_signf( b-*a ),
454 *a = vg_minf( b*d, c*d ) * d;
457 static inline f32 vg_smoothstepf( f32 x ){
458 return x*x*(3.0f - 2.0f*x);
462 /* correctly lerp around circular period -pi -> pi */
463 static f32 vg_alerpf( f32 a, f32 b, f32 t )
465 f32 d = fmodf( b-a, VG_TAUf ),
466 s = fmodf( 2.0f*d, VG_TAUf ) - d;
470 static inline void v3_lerp( v3f a, v3f b, f32 t, v3f d )
472 d[0] = a[0] + t*(b[0]-a[0]);
473 d[1] = a[1] + t*(b[1]-a[1]);
474 d[2] = a[2] + t*(b[2]-a[2]);
477 static inline void v3_minv( v3f a, v3f b, v3f dest )
479 dest[0] = vg_minf(a[0], b[0]);
480 dest[1] = vg_minf(a[1], b[1]);
481 dest[2] = vg_minf(a[2], b[2]);
484 static inline void v3_maxv( v3f a, v3f b, v3f dest )
486 dest[0] = vg_maxf(a[0], b[0]);
487 dest[1] = vg_maxf(a[1], b[1]);
488 dest[2] = vg_maxf(a[2], b[2]);
491 static inline f32 v3_minf( v3f a )
493 return vg_minf( vg_minf( a[0], a[1] ), a[2] );
496 static inline f32 v3_maxf( v3f a )
498 return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
501 static inline void v3_floor( v3f a, v3f b )
503 b[0] = floorf( a[0] );
504 b[1] = floorf( a[1] );
505 b[2] = floorf( a[2] );
508 static inline void v3_ceil( v3f a, v3f b )
510 b[0] = ceilf( a[0] );
511 b[1] = ceilf( a[1] );
512 b[2] = ceilf( a[2] );
515 static inline void v3_negate( v3f a, v3f b )
522 static inline void v3_rotate( v3f v, f32 angle, v3f axis, v3f d )
533 v3_cross( k, v, v2 );
534 v3_muls( v2, s, v2 );
535 v3_add( v1, v2, v1 );
536 v3_muls( k, v3_dot(k, v) * (1.0f - c), v2);
540 static void v3_tangent_basis( v3f n, v3f tx, v3f ty ){
541 /* Compute tangent basis (box2d) */
542 if( fabsf( n[0] ) >= 0.57735027f ){
554 v3_cross( n, tx, ty );
558 * Compute yaw and pitch based of a normalized vector representing forward
560 * result -> (YAW,PITCH,0.0)
562 static void v3_angles( v3f v, v3f out_angles ){
563 float yaw = atan2f( v[0], -v[2] ),
567 v[0]*v[0] + v[2]*v[2]
572 out_angles[1] = pitch;
573 out_angles[2] = 0.0f;
577 * Compute the forward vector from (YAW,PITCH,ROLL)
580 static void v3_angles_vector( v3f angles, v3f out_v ){
581 out_v[0] = sinf( angles[0] ) * cosf( angles[1] );
582 out_v[1] = -sinf( angles[1] );
583 out_v[2] = -cosf( angles[0] ) * cosf( angles[1] );
587 * -----------------------------------------------------------------------------
588 * Section 2.c 4D Vectors
589 * -----------------------------------------------------------------------------
592 static inline void v4_copy( v4f a, v4f b )
594 b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
597 static inline void v4_add( v4f a, v4f b, v4f d )
605 static inline void v4_zero( v4f a )
607 a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
610 static inline void v4_muls( v4f a, f32 s, v4f d )
618 static inline void v4_muladds( v4f a, v4f b, f32 s, v4f d )
626 static inline void v4_lerp( v4f a, v4f b, f32 t, v4f d )
628 d[0] = a[0] + t*(b[0]-a[0]);
629 d[1] = a[1] + t*(b[1]-a[1]);
630 d[2] = a[2] + t*(b[2]-a[2]);
631 d[3] = a[3] + t*(b[3]-a[3]);
634 static inline f32 v4_dot( v4f a, v4f b )
636 return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + a[3]*b[3];
639 static inline f32 v4_length( v4f a )
641 return sqrtf( v4_dot(a,a) );
645 * -----------------------------------------------------------------------------
646 * Section 3 Quaternions
647 * -----------------------------------------------------------------------------
650 static inline void q_identity( v4f q )
652 q[0] = 0.0f; q[1] = 0.0f; q[2] = 0.0f; q[3] = 1.0f;
655 static inline void q_axis_angle( v4f q, v3f axis, f32 angle )
667 static inline void q_mul( v4f q, v4f q1, v4f d )
670 t[0] = q[3]*q1[0] + q[0]*q1[3] + q[1]*q1[2] - q[2]*q1[1];
671 t[1] = q[3]*q1[1] - q[0]*q1[2] + q[1]*q1[3] + q[2]*q1[0];
672 t[2] = q[3]*q1[2] + q[0]*q1[1] - q[1]*q1[0] + q[2]*q1[3];
673 t[3] = q[3]*q1[3] - q[0]*q1[0] - q[1]*q1[1] - q[2]*q1[2];
677 static inline void q_normalize( v4f q )
679 f32 l2 = v4_dot(q,q);
680 if( l2 < 0.00001f ) q_identity( q );
682 f32 s = 1.0f/sqrtf(l2);
690 static inline void q_inv( v4f q, v4f d )
692 f32 s = 1.0f / v4_dot(q,q);
699 static inline void q_nlerp( v4f a, v4f b, f32 t, v4f d ){
700 if( v4_dot(a,b) < 0.0f ){
702 v4_muls( b, -1.0f, c );
703 v4_lerp( a, c, t, d );
706 v4_lerp( a, b, t, d );
711 static inline void q_m3x3( v4f q, m3x3f d )
715 s = l > 0.0f? 2.0f/l: 0.0f,
717 xx = s*q[0]*q[0], xy = s*q[0]*q[1], wx = s*q[3]*q[0],
718 yy = s*q[1]*q[1], yz = s*q[1]*q[2], wy = s*q[3]*q[1],
719 zz = s*q[2]*q[2], xz = s*q[0]*q[2], wz = s*q[3]*q[2];
721 d[0][0] = 1.0f - yy - zz;
722 d[1][1] = 1.0f - xx - zz;
723 d[2][2] = 1.0f - xx - yy;
732 static void q_mulv( v4f q, v3f v, v3f d )
736 v3_muls( q, 2.0f*v3_dot(q,v), v1 );
737 v3_muls( v, q[3]*q[3] - v3_dot(q,q), v2 );
738 v3_add( v1, v2, v1 );
739 v3_cross( q, v, v2 );
740 v3_muls( v2, 2.0f*q[3], v2 );
744 static f32 q_dist( v4f q0, v4f q1 ){
745 return acosf( 2.0f * v4_dot(q0,q1) -1.0f );
749 * -----------------------------------------------------------------------------
750 * Section 4.a 2x2 matrices
751 * -----------------------------------------------------------------------------
754 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
757 #define M2X2_ZERO {{0.0f, 0.0f, }, \
760 static inline void m2x2_copy( m2x2f a, m2x2f b )
762 v2_copy( a[0], b[0] );
763 v2_copy( a[1], b[1] );
766 static inline void m2x2_identity( m2x2f a )
768 m2x2f id = M2X2_INDENTIY;
772 static inline void m2x2_create_rotation( m2x2f a, f32 theta )
785 static inline void m2x2_mulv( m2x2f m, v2f v, v2f d )
789 res[0] = m[0][0]*v[0] + m[1][0]*v[1];
790 res[1] = m[0][1]*v[0] + m[1][1]*v[1];
796 * -----------------------------------------------------------------------------
797 * Section 4.b 3x3 matrices
798 * -----------------------------------------------------------------------------
801 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
802 { 0.0f, 1.0f, 0.0f, },\
803 { 0.0f, 0.0f, 1.0f, }}
805 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
806 { 0.0f, 0.0f, 0.0f, },\
807 { 0.0f, 0.0f, 0.0f, }}
810 static void euler_m3x3( v3f angles, m3x3f d )
812 f32 cosY = cosf( angles[0] ),
813 sinY = sinf( angles[0] ),
814 cosP = cosf( angles[1] ),
815 sinP = sinf( angles[1] ),
816 cosR = cosf( angles[2] ),
817 sinR = sinf( angles[2] );
819 d[2][0] = -sinY * cosP;
821 d[2][2] = cosY * cosP;
823 d[0][0] = cosY * cosR;
825 d[0][2] = sinY * cosR;
827 v3_cross( d[0], d[2], d[1] );
830 static void m3x3_q( m3x3f m, v4f q )
834 diag = m[0][0] + m[1][1] + m[2][2];
837 r = sqrtf( 1.0f + diag );
839 q[0] = rinv * (m[1][2] - m[2][1]);
840 q[1] = rinv * (m[2][0] - m[0][2]);
841 q[2] = rinv * (m[0][1] - m[1][0]);
844 else if( m[0][0] >= m[1][1] && m[0][0] >= m[2][2] )
846 r = sqrtf( 1.0f - m[1][1] - m[2][2] + m[0][0] );
849 q[1] = rinv * (m[0][1] + m[1][0]);
850 q[2] = rinv * (m[0][2] + m[2][0]);
851 q[3] = rinv * (m[1][2] - m[2][1]);
853 else if( m[1][1] >= m[2][2] )
855 r = sqrtf( 1.0f - m[0][0] - m[2][2] + m[1][1] );
857 q[0] = rinv * (m[0][1] + m[1][0]);
859 q[2] = rinv * (m[1][2] + m[2][1]);
860 q[3] = rinv * (m[2][0] - m[0][2]);
864 r = sqrtf( 1.0f - m[0][0] - m[1][1] + m[2][2] );
866 q[0] = rinv * (m[0][2] + m[2][0]);
867 q[1] = rinv * (m[1][2] + m[2][1]);
869 q[3] = rinv * (m[0][1] - m[1][0]);
873 /* a X b == [b]T a == ...*/
874 static void m3x3_skew_symetric( m3x3f a, v3f v )
887 /* aka kronecker product */
888 static void m3x3_outer_product( m3x3f out_m, v3f a, v3f b )
890 out_m[0][0] = a[0]*b[0];
891 out_m[0][1] = a[0]*b[1];
892 out_m[0][2] = a[0]*b[2];
893 out_m[1][0] = a[1]*b[0];
894 out_m[1][1] = a[1]*b[1];
895 out_m[1][2] = a[1]*b[2];
896 out_m[2][0] = a[2]*b[0];
897 out_m[2][1] = a[2]*b[1];
898 out_m[2][2] = a[2]*b[2];
901 static void m3x3_add( m3x3f a, m3x3f b, m3x3f d )
903 v3_add( a[0], b[0], d[0] );
904 v3_add( a[1], b[1], d[1] );
905 v3_add( a[2], b[2], d[2] );
908 static void m3x3_sub( m3x3f a, m3x3f b, m3x3f d )
910 v3_sub( a[0], b[0], d[0] );
911 v3_sub( a[1], b[1], d[1] );
912 v3_sub( a[2], b[2], d[2] );
915 static inline void m3x3_copy( m3x3f a, m3x3f b )
917 v3_copy( a[0], b[0] );
918 v3_copy( a[1], b[1] );
919 v3_copy( a[2], b[2] );
922 static inline void m3x3_identity( m3x3f a )
924 m3x3f id = M3X3_IDENTITY;
928 static void m3x3_diagonal( m3x3f out_a, f32 v )
930 m3x3_identity( out_a );
936 static void m3x3_setdiagonalv3( m3x3f a, v3f v )
943 static inline void m3x3_zero( m3x3f a )
949 static inline void m3x3_inv( m3x3f src, m3x3f dest )
951 f32 a = src[0][0], b = src[0][1], c = src[0][2],
952 d = src[1][0], e = src[1][1], f = src[1][2],
953 g = src[2][0], h = src[2][1], i = src[2][2];
960 dest[0][0] = (e*i-h*f)*det;
961 dest[0][1] = -(b*i-c*h)*det;
962 dest[0][2] = (b*f-c*e)*det;
963 dest[1][0] = -(d*i-f*g)*det;
964 dest[1][1] = (a*i-c*g)*det;
965 dest[1][2] = -(a*f-d*c)*det;
966 dest[2][0] = (d*h-g*e)*det;
967 dest[2][1] = -(a*h-g*b)*det;
968 dest[2][2] = (a*e-d*b)*det;
971 static f32 m3x3_det( m3x3f m )
973 return m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
974 - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
975 + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
978 static inline void m3x3_transpose( m3x3f src, m3x3f dest )
980 f32 a = src[0][0], b = src[0][1], c = src[0][2],
981 d = src[1][0], e = src[1][1], f = src[1][2],
982 g = src[2][0], h = src[2][1], i = src[2][2];
995 static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
997 f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
998 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
999 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
1001 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
1002 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
1003 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];
1005 d[0][0] = a00*b00 + a10*b01 + a20*b02;
1006 d[0][1] = a01*b00 + a11*b01 + a21*b02;
1007 d[0][2] = a02*b00 + a12*b01 + a22*b02;
1008 d[1][0] = a00*b10 + a10*b11 + a20*b12;
1009 d[1][1] = a01*b10 + a11*b11 + a21*b12;
1010 d[1][2] = a02*b10 + a12*b11 + a22*b12;
1011 d[2][0] = a00*b20 + a10*b21 + a20*b22;
1012 d[2][1] = a01*b20 + a11*b21 + a21*b22;
1013 d[2][2] = a02*b20 + a12*b21 + a22*b22;
1016 static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
1020 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
1021 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
1022 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
1027 static inline void m3x3_projection( m3x3f dst,
1028 f32 const left, f32 const right, f32 const bottom, f32 const top )
1034 rl = 1.0f / (right - left);
1035 tb = 1.0f / (top - bottom);
1037 dst[0][0] = 2.0f * rl;
1038 dst[1][1] = 2.0f * tb;
1042 static inline void m3x3_translate( m3x3f m, v3f v )
1044 m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
1045 m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
1046 m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
1049 static inline void m3x3_scale( m3x3f m, v3f v )
1051 v3_muls( m[0], v[0], m[0] );
1052 v3_muls( m[1], v[1], m[1] );
1053 v3_muls( m[2], v[2], m[2] );
1056 static inline void m3x3_scalef( m3x3f m, f32 f )
1063 static inline void m3x3_rotate( m3x3f m, f32 angle )
1065 f32 m00 = m[0][0], m10 = m[1][0],
1066 m01 = m[0][1], m11 = m[1][1],
1067 m02 = m[0][2], m12 = m[1][2];
1073 m[0][0] = m00 * c + m10 * s;
1074 m[0][1] = m01 * c + m11 * s;
1075 m[0][2] = m02 * c + m12 * s;
1077 m[1][0] = m00 * -s + m10 * c;
1078 m[1][1] = m01 * -s + m11 * c;
1079 m[1][2] = m02 * -s + m12 * c;
1083 * -----------------------------------------------------------------------------
1084 * Section 4.c 4x3 matrices
1085 * -----------------------------------------------------------------------------
1088 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
1089 { 0.0f, 1.0f, 0.0f, },\
1090 { 0.0f, 0.0f, 1.0f, },\
1091 { 0.0f, 0.0f, 0.0f }}
1093 static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
1095 v3_copy( a[0], b[0] );
1096 v3_copy( a[1], b[1] );
1097 v3_copy( a[2], b[2] );
1100 static inline void m4x3_invert_affine( m4x3f a, m4x3f b )
1102 m3x3_transpose( a, b );
1103 m3x3_mulv( b, a[3], b[3] );
1104 v3_negate( b[3], b[3] );
1107 static void m4x3_invert_full( m4x3f src, m4x3f dst )
1111 a = src[0][0], b = src[0][1], c = src[0][2],
1112 e = src[1][0], f = src[1][1], g = src[1][2],
1113 i = src[2][0], j = src[2][1], k = src[2][2],
1114 m = src[3][0], n = src[3][1], o = src[3][2];
1120 dst[0][0] = f*k - g*j;
1121 dst[1][0] =-(e*k - g*i);
1122 dst[2][0] = e*j - f*i;
1123 dst[3][0] =-(e*t2 - f*t4 + g*t5);
1125 dst[0][1] =-(b*k - c*j);
1126 dst[1][1] = a*k - c*i;
1127 dst[2][1] =-(a*j - b*i);
1128 dst[3][1] = a*t2 - b*t4 + c*t5;
1134 dst[0][2] = b*g - c*f ;
1135 dst[1][2] =-(a*g - c*e );
1136 dst[2][2] = a*f - b*e ;
1137 dst[3][2] =-(a*t2 - b*t4 + c * t5);
1139 det = 1.0f / (a * dst[0][0] + b * dst[1][0] + c * dst[2][0]);
1140 v3_muls( dst[0], det, dst[0] );
1141 v3_muls( dst[1], det, dst[1] );
1142 v3_muls( dst[2], det, dst[2] );
1143 v3_muls( dst[3], det, dst[3] );
1146 static inline void m4x3_copy( m4x3f a, m4x3f b )
1148 v3_copy( a[0], b[0] );
1149 v3_copy( a[1], b[1] );
1150 v3_copy( a[2], b[2] );
1151 v3_copy( a[3], b[3] );
1154 static inline void m4x3_identity( m4x3f a )
1156 m4x3f id = M4X3_IDENTITY;
1160 static void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
1163 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
1164 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
1165 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
1166 a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
1167 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
1168 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
1169 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
1170 b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
1172 d[0][0] = a00*b00 + a10*b01 + a20*b02;
1173 d[0][1] = a01*b00 + a11*b01 + a21*b02;
1174 d[0][2] = a02*b00 + a12*b01 + a22*b02;
1175 d[1][0] = a00*b10 + a10*b11 + a20*b12;
1176 d[1][1] = a01*b10 + a11*b11 + a21*b12;
1177 d[1][2] = a02*b10 + a12*b11 + a22*b12;
1178 d[2][0] = a00*b20 + a10*b21 + a20*b22;
1179 d[2][1] = a01*b20 + a11*b21 + a21*b22;
1180 d[2][2] = a02*b20 + a12*b21 + a22*b22;
1181 d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
1182 d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
1183 d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
1186 #if 0 /* shat appf mingw wstringop-overflow */
1189 static void m4x3_mulv( m4x3f m, v3f v, v3f d )
1193 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
1194 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
1195 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
1201 * Transform plane ( xyz, distance )
1203 static void m4x3_mulp( m4x3f m, v4f p, v4f d )
1207 v3_muls( p, p[3], o );
1208 m4x3_mulv( m, o, o );
1209 m3x3_mulv( m, p, d );
1211 d[3] = v3_dot( o, d );
1218 static void m4x3_translate( m4x3f m, v3f v )
1220 v3_muladds( m[3], m[0], v[0], m[3] );
1221 v3_muladds( m[3], m[1], v[1], m[3] );
1222 v3_muladds( m[3], m[2], v[2], m[3] );
1225 static void m4x3_rotate_x( m4x3f m, f32 angle )
1227 m4x3f t = M4X3_IDENTITY;
1238 m4x3_mul( m, t, m );
1241 static void m4x3_rotate_y( m4x3f m, f32 angle )
1243 m4x3f t = M4X3_IDENTITY;
1254 m4x3_mul( m, t, m );
1257 static void m4x3_rotate_z( m4x3f m, f32 angle )
1259 m4x3f t = M4X3_IDENTITY;
1270 m4x3_mul( m, t, m );
1273 static void m4x3_expand( m4x3f m, m4x4f d )
1275 v3_copy( m[0], d[0] );
1276 v3_copy( m[1], d[1] );
1277 v3_copy( m[2], d[2] );
1278 v3_copy( m[3], d[3] );
1285 static void m4x3_decompose( m4x3f m, v3f co, v4f q, v3f s )
1287 v3_copy( m[3], co );
1288 s[0] = v3_length(m[0]);
1289 s[1] = v3_length(m[1]);
1290 s[2] = v3_length(m[2]);
1293 v3_divs( m[0], s[0], rot[0] );
1294 v3_divs( m[1], s[1], rot[1] );
1295 v3_divs( m[2], s[2], rot[2] );
1300 static void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point ){
1302 m4x3_mulv( m, point, v );
1304 v3_minv( box[0], v, box[0] );
1305 v3_maxv( box[1], v, box[1] );
1308 static void m4x3_expand_aabb_aabb( m4x3f m, boxf boxa, boxf boxb ){
1310 v3_copy( boxb[0], a );
1311 v3_copy( boxb[1], b );
1312 m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], a[1], a[2] } );
1313 m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], b[1], a[2] } );
1314 m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], b[1], a[2] } );
1315 m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], a[1], a[2] } );
1316 m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], a[1], b[2] } );
1317 m4x3_expand_aabb_point( m, boxa, (v3f){ a[0], b[1], b[2] } );
1318 m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], b[1], b[2] } );
1319 m4x3_expand_aabb_point( m, boxa, (v3f){ b[0], a[1], b[2] } );
1321 static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up )
1324 v3_sub( target, pos, dir );
1325 v3_normalize( dir );
1327 v3_copy( dir, m[2] );
1329 v3_cross( up, m[2], m[0] );
1330 v3_normalize( m[0] );
1332 v3_cross( m[2], m[0], m[1] );
1333 v3_copy( pos, m[3] );
1337 * -----------------------------------------------------------------------------
1338 * Section 4.d 4x4 matrices
1339 * -----------------------------------------------------------------------------
1342 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1343 { 0.0f, 1.0f, 0.0f, 0.0f },\
1344 { 0.0f, 0.0f, 1.0f, 0.0f },\
1345 { 0.0f, 0.0f, 0.0f, 1.0f }}
1346 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1347 { 0.0f, 0.0f, 0.0f, 0.0f },\
1348 { 0.0f, 0.0f, 0.0f, 0.0f },\
1349 { 0.0f, 0.0f, 0.0f, 0.0f }}
1351 static void m4x4_projection( m4x4f m, f32 angle,
1352 f32 ratio, f32 fnear, f32 ffar )
1354 f32 scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * fnear,
1360 m[0][0] = 2.0f * fnear / (r - l);
1366 m[1][1] = 2.0f * fnear / (t - b);
1370 m[2][0] = (r + l) / (r - l);
1371 m[2][1] = (t + b) / (t - b);
1372 m[2][2] = -(ffar + fnear) / (ffar - fnear);
1377 m[3][2] = -2.0f * ffar * fnear / (ffar - fnear);
1381 static void m4x4_translate( m4x4f m, v3f v )
1383 v4_muladds( m[3], m[0], v[0], m[3] );
1384 v4_muladds( m[3], m[1], v[1], m[3] );
1385 v4_muladds( m[3], m[2], v[2], m[3] );
1388 static inline void m4x4_copy( m4x4f a, m4x4f b )
1390 v4_copy( a[0], b[0] );
1391 v4_copy( a[1], b[1] );
1392 v4_copy( a[2], b[2] );
1393 v4_copy( a[3], b[3] );
1396 static inline void m4x4_identity( m4x4f a )
1398 m4x4f id = M4X4_IDENTITY;
1402 static inline void m4x4_zero( m4x4f a )
1404 m4x4f zero = M4X4_ZERO;
1405 m4x4_copy( zero, a );
1408 static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d )
1410 f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
1411 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3],
1412 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3],
1413 a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3],
1415 b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], b03 = b[0][3],
1416 b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], b13 = b[1][3],
1417 b20 = b[2][0], b21 = b[2][1], b22 = b[2][2], b23 = b[2][3],
1418 b30 = b[3][0], b31 = b[3][1], b32 = b[3][2], b33 = b[3][3];
1420 d[0][0] = a00*b00 + a10*b01 + a20*b02 + a30*b03;
1421 d[0][1] = a01*b00 + a11*b01 + a21*b02 + a31*b03;
1422 d[0][2] = a02*b00 + a12*b01 + a22*b02 + a32*b03;
1423 d[0][3] = a03*b00 + a13*b01 + a23*b02 + a33*b03;
1424 d[1][0] = a00*b10 + a10*b11 + a20*b12 + a30*b13;
1425 d[1][1] = a01*b10 + a11*b11 + a21*b12 + a31*b13;
1426 d[1][2] = a02*b10 + a12*b11 + a22*b12 + a32*b13;
1427 d[1][3] = a03*b10 + a13*b11 + a23*b12 + a33*b13;
1428 d[2][0] = a00*b20 + a10*b21 + a20*b22 + a30*b23;
1429 d[2][1] = a01*b20 + a11*b21 + a21*b22 + a31*b23;
1430 d[2][2] = a02*b20 + a12*b21 + a22*b22 + a32*b23;
1431 d[2][3] = a03*b20 + a13*b21 + a23*b22 + a33*b23;
1432 d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30*b33;
1433 d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31*b33;
1434 d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32*b33;
1435 d[3][3] = a03*b30 + a13*b31 + a23*b32 + a33*b33;
1438 static inline void m4x4_mulv( m4x4f m, v4f v, v4f d )
1442 res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]*v[3];
1443 res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]*v[3];
1444 res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]*v[3];
1445 res[3] = m[0][3]*v[0] + m[1][3]*v[1] + m[2][3]*v[2] + m[3][3]*v[3];
1450 static inline void m4x4_inv( m4x4f a, m4x4f d )
1452 f32 a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
1453 a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3],
1454 a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3],
1455 a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3],
1459 t[0] = a22*a33 - a32*a23;
1460 t[1] = a21*a33 - a31*a23;
1461 t[2] = a21*a32 - a31*a22;
1462 t[3] = a20*a33 - a30*a23;
1463 t[4] = a20*a32 - a30*a22;
1464 t[5] = a20*a31 - a30*a21;
1466 d[0][0] = a11*t[0] - a12*t[1] + a13*t[2];
1467 d[1][0] =-(a10*t[0] - a12*t[3] + a13*t[4]);
1468 d[2][0] = a10*t[1] - a11*t[3] + a13*t[5];
1469 d[3][0] =-(a10*t[2] - a11*t[4] + a12*t[5]);
1471 d[0][1] =-(a01*t[0] - a02*t[1] + a03*t[2]);
1472 d[1][1] = a00*t[0] - a02*t[3] + a03*t[4];
1473 d[2][1] =-(a00*t[1] - a01*t[3] + a03*t[5]);
1474 d[3][1] = a00*t[2] - a01*t[4] + a02*t[5];
1476 t[0] = a12*a33 - a32*a13;
1477 t[1] = a11*a33 - a31*a13;
1478 t[2] = a11*a32 - a31*a12;
1479 t[3] = a10*a33 - a30*a13;
1480 t[4] = a10*a32 - a30*a12;
1481 t[5] = a10*a31 - a30*a11;
1483 d[0][2] = a01*t[0] - a02*t[1] + a03*t[2];
1484 d[1][2] =-(a00*t[0] - a02*t[3] + a03*t[4]);
1485 d[2][2] = a00*t[1] - a01*t[3] + a03*t[5];
1486 d[3][2] =-(a00*t[2] - a01*t[4] + a02*t[5]);
1488 t[0] = a12*a23 - a22*a13;
1489 t[1] = a11*a23 - a21*a13;
1490 t[2] = a11*a22 - a21*a12;
1491 t[3] = a10*a23 - a20*a13;
1492 t[4] = a10*a22 - a20*a12;
1493 t[5] = a10*a21 - a20*a11;
1495 d[0][3] =-(a01*t[0] - a02*t[1] + a03*t[2]);
1496 d[1][3] = a00*t[0] - a02*t[3] + a03*t[4];
1497 d[2][3] =-(a00*t[1] - a01*t[3] + a03*t[5]);
1498 d[3][3] = a00*t[2] - a01*t[4] + a02*t[5];
1500 det = 1.0f / (a00*d[0][0] + a01*d[1][0] + a02*d[2][0] + a03*d[3][0]);
1501 v4_muls( d[0], det, d[0] );
1502 v4_muls( d[1], det, d[1] );
1503 v4_muls( d[2], det, d[2] );
1504 v4_muls( d[3], det, d[3] );
1508 * http://www.terathon.com/lengyel/Lengyel-Oblique.pdf
1510 static void m4x4_clip_projection( m4x4f mat, v4f plane ){
1513 (vg_signf(plane[0]) + mat[2][0]) / mat[0][0],
1514 (vg_signf(plane[1]) + mat[2][1]) / mat[1][1],
1516 (1.0f + mat[2][2]) / mat[3][2]
1519 v4_muls( plane, 2.0f / v4_dot(plane,c), c );
1523 mat[2][2] = c[2] + 1.0f;
1528 * Undoes the above operation
1530 static void m4x4_reset_clipping( m4x4f mat, float ffar, float fnear ){
1533 mat[2][2] = -(ffar + fnear) / (ffar - fnear);
1534 mat[3][2] = -2.0f * ffar * fnear / (ffar - fnear);
1538 * -----------------------------------------------------------------------------
1540 * -----------------------------------------------------------------------------
1543 static inline void box_addpt( boxf a, v3f pt )
1545 v3_minv( a[0], pt, a[0] );
1546 v3_maxv( a[1], pt, a[1] );
1549 static inline void box_concat( boxf a, boxf b )
1551 v3_minv( a[0], b[0], a[0] );
1552 v3_maxv( a[1], b[1], a[1] );
1555 static inline void box_copy( boxf a, boxf b )
1557 v3_copy( a[0], b[0] );
1558 v3_copy( a[1], b[1] );
1561 static inline int box_overlap( boxf a, boxf b )
1564 ( a[0][0] <= b[1][0] && a[1][0] >= b[0][0] ) &&
1565 ( a[0][1] <= b[1][1] && a[1][1] >= b[0][1] ) &&
1566 ( a[0][2] <= b[1][2] && a[1][2] >= b[0][2] )
1570 static int box_within( boxf greater, boxf lesser )
1573 v3_sub( lesser[0], greater[0], a );
1574 v3_sub( lesser[1], greater[1], b );
1576 if( (a[0] >= 0.0f) && (a[1] >= 0.0f) && (a[2] >= 0.0f) &&
1577 (b[0] <= 0.0f) && (b[1] <= 0.0f) && (b[2] <= 0.0f) )
1585 static inline void box_init_inf( boxf box ){
1586 v3_fill( box[0], INFINITY );
1587 v3_fill( box[1], -INFINITY );
1591 * -----------------------------------------------------------------------------
1592 * Section 5.b Planes
1593 * -----------------------------------------------------------------------------
1596 static inline void tri_to_plane( f64 a[3], f64 b[3],
1597 f64 c[3], f64 p[4] )
1603 edge0[0] = b[0] - a[0];
1604 edge0[1] = b[1] - a[1];
1605 edge0[2] = b[2] - a[2];
1607 edge1[0] = c[0] - a[0];
1608 edge1[1] = c[1] - a[1];
1609 edge1[2] = c[2] - a[2];
1611 p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
1612 p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
1613 p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
1615 l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
1616 p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
1623 static int plane_intersect3( v4f a, v4f b, v4f c, v3f p )
1625 f32 const epsilon = 1e-6f;
1628 v3_cross( a, b, x );
1629 f32 d = v3_dot( x, c );
1631 if( (d < epsilon) && (d > -epsilon) ) return 0;
1634 v3_cross( b, c, v0 );
1635 v3_cross( c, a, v1 );
1636 v3_cross( a, b, v2 );
1638 v3_muls( v0, a[3], p );
1639 v3_muladds( p, v1, b[3], p );
1640 v3_muladds( p, v2, c[3], p );
1646 static int plane_intersect2( v4f a, v4f b, v3f p, v3f n )
1648 f32 const epsilon = 1e-6f;
1651 v3_cross( a, b, c );
1652 f32 d = v3_length2( c );
1654 if( (d < epsilon) && (d > -epsilon) )
1658 v3_cross( c, b, v0 );
1659 v3_cross( a, c, v1 );
1661 v3_muls( v0, a[3], vx );
1662 v3_muladds( vx, v1, b[3], vx );
1663 v3_divs( vx, d, p );
1669 static int plane_segment( v4f plane, v3f a, v3f b, v3f co )
1671 f32 d0 = v3_dot( a, plane ) - plane[3],
1672 d1 = v3_dot( b, plane ) - plane[3];
1676 f32 tot = 1.0f/( fabsf(d0)+fabsf(d1) );
1678 v3_muls( a, fabsf(d1) * tot, co );
1679 v3_muladds( co, b, fabsf(d0) * tot, co );
1686 static inline f64 plane_polarity( f64 p[4], f64 a[3] )
1689 (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
1690 -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
1694 static f32 ray_plane( v4f plane, v3f co, v3f dir ){
1695 f32 d = v3_dot( plane, dir );
1696 if( fabsf(d) > 1e-6f ){
1698 v3_muls( plane, plane[3], v0 );
1699 v3_sub( v0, co, v0 );
1700 return v3_dot( v0, plane ) / d;
1702 else return INFINITY;
1706 * -----------------------------------------------------------------------------
1707 * Section 5.c Closest point functions
1708 * -----------------------------------------------------------------------------
1712 * These closest point tests were learned from Real-Time Collision Detection by
1715 static f32 closest_segment_segment( v3f p1, v3f q1, v3f p2, v3f q2,
1716 f32 *s, f32 *t, v3f c1, v3f c2)
1719 v3_sub( q1, p1, d1 );
1720 v3_sub( q2, p2, d2 );
1721 v3_sub( p1, p2, r );
1723 f32 a = v3_length2( d1 ),
1724 e = v3_length2( d2 ),
1725 f = v3_dot( d2, r );
1727 const f32 kEpsilon = 0.0001f;
1729 if( a <= kEpsilon && e <= kEpsilon )
1737 v3_sub( c1, c2, v0 );
1739 return v3_length2( v0 );
1745 *t = vg_clampf( f / e, 0.0f, 1.0f );
1749 f32 c = v3_dot( d1, r );
1753 *s = vg_clampf( -c / a, 0.0f, 1.0f );
1757 f32 b = v3_dot(d1,d2),
1762 *s = vg_clampf((b*f - c*e)/d, 0.0f, 1.0f);
1769 *t = (b*(*s)+f) / e;
1774 *s = vg_clampf( -c / a, 0.0f, 1.0f );
1776 else if( *t > 1.0f )
1779 *s = vg_clampf((b-c)/a,0.0f,1.0f);
1784 v3_muladds( p1, d1, *s, c1 );
1785 v3_muladds( p2, d2, *t, c2 );
1788 v3_sub( c1, c2, v0 );
1789 return v3_length2( v0 );
1792 static int point_inside_aabb( boxf box, v3f point )
1794 if((point[0]<=box[1][0]) && (point[1]<=box[1][1]) && (point[2]<=box[1][2]) &&
1795 (point[0]>=box[0][0]) && (point[1]>=box[0][1]) && (point[2]>=box[0][2]) )
1801 static void closest_point_aabb( v3f p, boxf box, v3f dest )
1803 v3_maxv( p, box[0], dest );
1804 v3_minv( dest, box[1], dest );
1807 static void closest_point_obb( v3f p, boxf box,
1808 m4x3f mtx, m4x3f inv_mtx, v3f dest )
1811 m4x3_mulv( inv_mtx, p, local );
1812 closest_point_aabb( local, box, local );
1813 m4x3_mulv( mtx, local, dest );
1816 static f32 closest_point_segment( v3f a, v3f b, v3f point, v3f dest )
1820 v3_sub( point, a, v1 );
1822 f32 t = v3_dot( v1, v0 ) / v3_length2(v0);
1823 t = vg_clampf(t,0.0f,1.0f);
1824 v3_muladds( a, v0, t, dest );
1828 static void closest_on_triangle( v3f p, v3f tri[3], v3f dest )
1833 /* Region outside A */
1834 v3_sub( tri[1], tri[0], ab );
1835 v3_sub( tri[2], tri[0], ac );
1836 v3_sub( p, tri[0], ap );
1840 if( d1 <= 0.0f && d2 <= 0.0f )
1842 v3_copy( tri[0], dest );
1843 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1847 /* Region outside B */
1851 v3_sub( p, tri[1], bp );
1852 d3 = v3_dot( ab, bp );
1853 d4 = v3_dot( ac, bp );
1855 if( d3 >= 0.0f && d4 <= d3 )
1857 v3_copy( tri[1], dest );
1858 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1862 /* Edge region of AB */
1863 f32 vc = d1*d4 - d3*d2;
1864 if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
1866 f32 v = d1 / (d1-d3);
1867 v3_muladds( tri[0], ab, v, dest );
1868 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1872 /* Region outside C */
1875 v3_sub( p, tri[2], cp );
1876 d5 = v3_dot(ab, cp);
1877 d6 = v3_dot(ac, cp);
1879 if( d6 >= 0.0f && d5 <= d6 )
1881 v3_copy( tri[2], dest );
1882 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1887 f32 vb = d5*d2 - d1*d6;
1888 if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
1890 f32 w = d2 / (d2-d6);
1891 v3_muladds( tri[0], ac, w, dest );
1892 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1897 f32 va = d3*d6 - d5*d4;
1898 if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
1900 f32 w = (d4-d3) / ((d4-d3) + (d5-d6));
1902 v3_sub( tri[2], tri[1], bc );
1903 v3_muladds( tri[1], bc, w, dest );
1904 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
1908 /* P inside region, Q via barycentric coordinates uvw */
1909 f32 d = 1.0f/(va+vb+vc),
1913 v3_muladds( tri[0], ab, v, dest );
1914 v3_muladds( dest, ac, w, dest );
1919 k_contact_type_default,
1920 k_contact_type_disabled,
1924 static enum contact_type closest_on_triangle_1( v3f p, v3f tri[3], v3f dest )
1929 /* Region outside A */
1930 v3_sub( tri[1], tri[0], ab );
1931 v3_sub( tri[2], tri[0], ac );
1932 v3_sub( p, tri[0], ap );
1936 if( d1 <= 0.0f && d2 <= 0.0f )
1938 v3_copy( tri[0], dest );
1939 return k_contact_type_default;
1942 /* Region outside B */
1946 v3_sub( p, tri[1], bp );
1947 d3 = v3_dot( ab, bp );
1948 d4 = v3_dot( ac, bp );
1950 if( d3 >= 0.0f && d4 <= d3 )
1952 v3_copy( tri[1], dest );
1953 return k_contact_type_edge;
1956 /* Edge region of AB */
1957 f32 vc = d1*d4 - d3*d2;
1958 if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
1960 f32 v = d1 / (d1-d3);
1961 v3_muladds( tri[0], ab, v, dest );
1962 return k_contact_type_edge;
1965 /* Region outside C */
1968 v3_sub( p, tri[2], cp );
1969 d5 = v3_dot(ab, cp);
1970 d6 = v3_dot(ac, cp);
1972 if( d6 >= 0.0f && d5 <= d6 )
1974 v3_copy( tri[2], dest );
1975 return k_contact_type_edge;
1979 f32 vb = d5*d2 - d1*d6;
1980 if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
1982 f32 w = d2 / (d2-d6);
1983 v3_muladds( tri[0], ac, w, dest );
1984 return k_contact_type_edge;
1988 f32 va = d3*d6 - d5*d4;
1989 if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
1991 f32 w = (d4-d3) / ((d4-d3) + (d5-d6));
1993 v3_sub( tri[2], tri[1], bc );
1994 v3_muladds( tri[1], bc, w, dest );
1995 return k_contact_type_edge;
1998 /* P inside region, Q via barycentric coordinates uvw */
1999 f32 d = 1.0f/(va+vb+vc),
2003 v3_muladds( tri[0], ab, v, dest );
2004 v3_muladds( dest, ac, w, dest );
2006 return k_contact_type_default;
2009 static void closest_point_elipse( v2f p, v2f e, v2f o )
2011 v2f pabs, ei, e2, ve, t;
2014 v2_div( (v2f){ 1.0f, 1.0f }, e, ei );
2016 v2_mul( ei, (v2f){ e2[0]-e2[1], e2[1]-e2[0] }, ve );
2018 v2_fill( t, 0.70710678118654752f );
2020 for( int i=0; i<3; i++ ){
2023 v2_mul( ve, t, v ); /* ve*t*t*t */
2027 v2_sub( pabs, v, u );
2031 v2_sub( ud, v, ud );
2033 v2_muls( u, v2_length( ud ), u );
2038 v2_maxv( (v2f){0.0f,0.0f}, w, t );
2043 v2_copysign( o, p );
2047 * -----------------------------------------------------------------------------
2048 * Section 5.d Raycasts & Spherecasts
2049 * -----------------------------------------------------------------------------
2052 static int ray_aabb1( boxf box, v3f co, v3f dir_inv, f32 dist )
2057 v3_sub( box[0], co, v0 );
2058 v3_sub( box[1], co, v1 );
2060 v3_mul( v0, dir_inv, v0 );
2061 v3_mul( v1, dir_inv, v1 );
2063 tmin = vg_minf( v0[0], v1[0] );
2064 tmax = vg_maxf( v0[0], v1[0] );
2065 tmin = vg_maxf( tmin, vg_minf( v0[1], v1[1] ));
2066 tmax = vg_minf( tmax, vg_maxf( v0[1], v1[1] ));
2067 tmin = vg_maxf( tmin, vg_minf( v0[2], v1[2] ));
2068 tmax = vg_minf( tmax, vg_maxf( v0[2], v1[2] ));
2070 return (tmax >= tmin) && (tmin <= dist) && (tmax >= 0.0f);
2073 /* Time of intersection with ray vs triangle */
2074 static int ray_tri( v3f tri[3], v3f co,
2075 v3f dir, f32 *dist, int backfaces )
2077 f32 const kEpsilon = 0.00001f;
2079 v3f v0, v1, h, s, q, n;
2086 v3_sub( pb, pa, v0 );
2087 v3_sub( pc, pa, v1 );
2088 v3_cross( dir, v1, h );
2089 v3_cross( v0, v1, n );
2091 if( (v3_dot( n, dir ) > 0.0f) && !backfaces ) /* Backface culling */
2095 a = v3_dot( v0, h );
2097 if( a > -kEpsilon && a < kEpsilon )
2101 v3_sub( co, pa, s );
2103 u = f * v3_dot(s, h);
2104 if( u < 0.0f || u > 1.0f )
2107 v3_cross( s, v0, q );
2108 v = f * v3_dot( dir, q );
2109 if( v < 0.0f || u+v > 1.0f )
2112 t = f * v3_dot(v1, q);
2121 /* time of intersection with ray vs sphere */
2122 static int ray_sphere( v3f c, f32 r,
2123 v3f co, v3f dir, f32 *t )
2128 f32 b = v3_dot( m, dir ),
2129 c1 = v3_dot( m, m ) - r*r;
2131 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
2132 if( c1 > 0.0f && b > 0.0f )
2135 f32 discr = b*b - c1;
2137 /* A negative discriminant corresponds to ray missing sphere */
2142 * Ray now found to intersect sphere, compute smallest t value of
2145 *t = -b - sqrtf( discr );
2147 /* If t is negative, ray started inside sphere so clamp t to zero */
2155 * time of intersection of ray vs cylinder
2156 * The cylinder does not have caps but is finite
2158 * Heavily adapted from regular segment vs cylinder from:
2159 * Real-Time Collision Detection
2161 static int ray_uncapped_finite_cylinder( v3f q, v3f p, f32 r,
2162 v3f co, v3f dir, f32 *t )
2165 v3_muladds( co, dir, 1.0f, sb );
2169 v3_sub( sb, co, n );
2171 f32 md = v3_dot( m, d ),
2172 nd = v3_dot( n, d ),
2173 dd = v3_dot( d, d ),
2174 nn = v3_dot( n, n ),
2175 mn = v3_dot( m, n ),
2177 k = v3_dot( m, m ) - r*r,
2180 if( fabsf(a) < 0.00001f )
2182 /* Segment runs parallel to cylinder axis */
2186 f32 b = dd*mn - nd*md,
2190 return 0; /* No real roots; no intersection */
2192 *t = (-b - sqrtf(discr)) / a;
2194 return 0; /* Intersection behind ray */
2196 /* Check within cylinder segment */
2197 if( md + (*t)*nd < 0.0f )
2200 if( md + (*t)*nd > dd )
2203 /* Segment intersects cylinder between the endcaps; t is correct */
2208 * Time of intersection of sphere and triangle. Origin must be outside the
2209 * colliding area. This is a fairly long procedure.
2211 static int spherecast_triangle( v3f tri[3],
2212 v3f co, v3f dir, f32 r, f32 *t, v3f n )
2217 v3_sub( tri[1], tri[0], v0 );
2218 v3_sub( tri[2], tri[0], v1 );
2219 v3_cross( v0, v1, n );
2221 v3_muladds( tri[0], n, r, sum[0] );
2222 v3_muladds( tri[1], n, r, sum[1] );
2223 v3_muladds( tri[2], n, r, sum[2] );
2226 f32 t_min = INFINITY,
2229 if( ray_tri( sum, co, dir, &t1, 0 ) ){
2230 t_min = vg_minf( t_min, t1 );
2235 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2238 for( int i=0; i<3; i++ ){
2239 if( ray_sphere( tri[i], r, co, dir, &t1 ) ){
2240 t_min = vg_minf( t_min, t1 );
2246 for( int i=0; i<3; i++ ){
2250 if( ray_uncapped_finite_cylinder( tri[i0], tri[i1], r, co, dir, &t1 ) ){
2255 v3_add( dir, co, co1 );
2256 v3_lerp( co, co1, t_min, ct );
2258 closest_point_segment( tri[i0], tri[i1], ct, cx );
2259 v3_sub( ct, cx, n );
2272 * -----------------------------------------------------------------------------
2273 * Section 5.e Curves
2274 * -----------------------------------------------------------------------------
2277 static void eval_bezier_time( v3f p0, v3f p1, v3f h0, v3f h1, f32 t, v3f p )
2282 v3_muls( p1, ttt, p );
2283 v3_muladds( p, h1, 3.0f*tt -3.0f*ttt, p );
2284 v3_muladds( p, h0, 3.0f*ttt -6.0f*tt +3.0f*t, p );
2285 v3_muladds( p, p0, 3.0f*tt -ttt -3.0f*t +1.0f, p );
2288 static void eval_bezier3( v3f p0, v3f p1, v3f p2, f32 t, v3f p )
2292 v3_muls( p0, u*u, p );
2293 v3_muladds( p, p1, 2.0f*u*t, p );
2294 v3_muladds( p, p2, t*t, p );
2298 * -----------------------------------------------------------------------------
2299 * Section 5.f Volumes
2300 * -----------------------------------------------------------------------------
2303 static f32 vg_sphere_volume( f32 r ){
2304 return (4.0f/3.0f) * VG_PIf * r*r*r;
2307 static f32 vg_box_volume( boxf box ){
2309 v3_sub( box[1], box[0], e );
2310 return e[0]*e[1]*e[2];
2313 static f32 vg_cylinder_volume( f32 r, f32 h ){
2314 return VG_PIf * r*r * h;
2317 static f32 vg_capsule_volume( f32 r, f32 h ){
2318 return vg_sphere_volume( r ) + vg_cylinder_volume( r, h-r*2.0f );
2321 static void vg_sphere_bound( f32 r, boxf out_box ){
2322 v3_fill( out_box[0], -r );
2323 v3_fill( out_box[1], r );
2326 static void vg_capsule_bound( f32 r, f32 h, boxf out_box ){
2327 v3_copy( (v3f){-r,-h*0.5f,r}, out_box[0] );
2328 v3_copy( (v3f){-r, h*0.5f,r}, out_box[1] );
2333 * -----------------------------------------------------------------------------
2334 * Section 5.g Inertia Tensors
2335 * -----------------------------------------------------------------------------
2339 * Translate existing inertia tensor
2341 static void vg_translate_inertia( m3x3f inout_inertia, f32 mass, v3f d ){
2343 * I = I_0 + m*[(d.d)E_3 - d(X)d]
2346 * I_0: original tensor
2348 * d: translation vector
2349 * (X): outer product
2350 * E_3: identity matrix
2352 m3x3f t, outer, scale;
2353 m3x3_diagonal( t, v3_dot(d,d) );
2354 m3x3_outer_product( outer, d, d );
2355 m3x3_sub( t, outer, t );
2356 m3x3_diagonal( scale, mass );
2357 m3x3_mul( scale, t, t );
2358 m3x3_add( inout_inertia, t, inout_inertia );
2362 * Rotate existing inertia tensor
2364 static void vg_rotate_inertia( m3x3f inout_inertia, m3x3f rotation ){
2369 * I_0: original tensor
2370 * R: rotation matrix
2371 * R^T: tranposed rotation matrix
2375 m3x3_transpose( rotation, Rt );
2376 m3x3_mul( rotation, inout_inertia, inout_inertia );
2377 m3x3_mul( inout_inertia, Rt, inout_inertia );
2380 * Create inertia tensor for box
2382 static void vg_box_inertia( boxf box, f32 mass, m3x3f out_inertia ){
2384 v3_sub( box[1], box[0], e );
2385 v3_muladds( box[0], e, 0.5f, com );
2387 f32 ex2 = e[0]*e[0],
2390 ix = (ey2+ez2) * mass * (1.0f/12.0f),
2391 iy = (ex2+ez2) * mass * (1.0f/12.0f),
2392 iz = (ex2+ey2) * mass * (1.0f/12.0f);
2394 m3x3_identity( out_inertia );
2395 m3x3_setdiagonalv3( out_inertia, (v3f){ ix, iy, iz } );
2396 vg_translate_inertia( out_inertia, mass, com );
2400 * Create inertia tensor for sphere
2402 static void vg_sphere_inertia( f32 r, f32 mass, m3x3f out_inertia ){
2403 f32 ixyz = r*r * mass * (2.0f/5.0f);
2405 m3x3_identity( out_inertia );
2406 m3x3_setdiagonalv3( out_inertia, (v3f){ ixyz, ixyz, ixyz } );
2410 * Create inertia tensor for capsule
2412 static void vg_capsule_inertia( f32 r, f32 h, f32 mass, m3x3f out_inertia ){
2413 f32 density = mass / vg_capsule_volume( r, h ),
2414 ch = h-r*2.0f, /* cylinder height */
2415 cm = VG_PIf * ch*r*r * density, /* cylinder mass */
2416 hm = VG_TAUf * (1.0f/3.0f) * r*r*r * density, /* hemisphere mass */
2419 ixz = iy * 0.5f + cm*ch*ch*(1.0f/12.0f),
2421 aux0= (hm*2.0f*r*r)/5.0f;
2426 aux2= aux0 + hm*(aux1*aux1 + 3.0f*(1.0f/8.0f)*ch*r);
2430 m3x3_identity( out_inertia );
2431 m3x3_setdiagonalv3( out_inertia, (v3f){ ixz, iy, ixz } );
2435 * -----------------------------------------------------------------------------
2436 * Section 6.a PSRNG and some distributions
2437 * -----------------------------------------------------------------------------
2440 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2441 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2442 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2443 * equidistributed uniform pseudorandom number generator," ACM
2444 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2445 * January pp.3-30 1998.
2447 * http://www.sultanik.com/Mersenne_twister
2448 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2451 #define MT_UPPER_MASK 0x80000000
2452 #define MT_LOWER_MASK 0x7fffffff
2453 #define MT_TEMPERING_MASK_B 0x9d2c5680
2454 #define MT_TEMPERING_MASK_C 0xefc60000
2456 #define MT_STATE_VECTOR_LENGTH 624
2458 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2459 #define MT_STATE_VECTOR_M 397
2461 typedef struct vg_rand vg_rand;
2463 u32 mt[MT_STATE_VECTOR_LENGTH];
2467 static void vg_rand_seed( vg_rand *rand, unsigned long seed ) {
2468 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2469 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2470 * Programming," Vol. 2 (2nd Ed.) pp.102.
2472 rand->mt[0] = seed & 0xffffffff;
2473 for( rand->index=1; rand->index<MT_STATE_VECTOR_LENGTH; rand->index++){
2474 rand->mt[rand->index] = (6069 * rand->mt[rand->index-1]) & 0xffffffff;
2479 * Generates a pseudo-randomly generated long.
2481 static u32 vg_randu32( vg_rand *rand ) {
2483 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2484 static u32 mag[2] = {0x0, 0x9908b0df};
2485 if( rand->index >= MT_STATE_VECTOR_LENGTH || rand->index < 0 ){
2486 /* generate STATE_VECTOR_LENGTH words at a time */
2488 if( rand->index >= MT_STATE_VECTOR_LENGTH+1 || rand->index < 0 ){
2489 vg_rand_seed( rand, 4357 );
2491 for( kk=0; kk<MT_STATE_VECTOR_LENGTH-MT_STATE_VECTOR_M; kk++ ){
2492 y = (rand->mt[kk] & MT_UPPER_MASK) |
2493 (rand->mt[kk+1] & MT_LOWER_MASK);
2494 rand->mt[kk] = rand->mt[kk+MT_STATE_VECTOR_M] ^ (y>>1) ^ mag[y & 0x1];
2496 for( ; kk<MT_STATE_VECTOR_LENGTH-1; kk++ ){
2497 y = (rand->mt[kk] & MT_UPPER_MASK) |
2498 (rand->mt[kk+1] & MT_LOWER_MASK);
2500 rand->mt[ kk+(MT_STATE_VECTOR_M-MT_STATE_VECTOR_LENGTH)] ^
2501 (y >> 1) ^ mag[y & 0x1];
2503 y = (rand->mt[MT_STATE_VECTOR_LENGTH-1] & MT_UPPER_MASK) |
2504 (rand->mt[0] & MT_LOWER_MASK);
2505 rand->mt[MT_STATE_VECTOR_LENGTH-1] =
2506 rand->mt[MT_STATE_VECTOR_M-1] ^ (y >> 1) ^ mag[y & 0x1];
2509 y = rand->mt[rand->index++];
2511 y ^= (y << 7) & MT_TEMPERING_MASK_B;
2512 y ^= (y << 15) & MT_TEMPERING_MASK_C;
2518 * Generates a pseudo-randomly generated f64 in the range [0..1].
2520 static inline f64 vg_randf64( vg_rand *rand ){
2521 return (f64)vg_randu32(rand)/(f64)0xffffffff;
2524 static inline f64 vg_randf64_range( vg_rand *rand, f64 min, f64 max ){
2525 return vg_lerp( min, max, (f64)vg_randf64(rand) );
2528 static inline void vg_rand_dir( vg_rand *rand, v3f dir ){
2529 dir[0] = vg_randf64(rand);
2530 dir[1] = vg_randf64(rand);
2531 dir[2] = vg_randf64(rand);
2533 /* warning: *could* be 0 length.
2534 * very unlikely.. 1 in (2^32)^3. but its mathematically wrong. */
2536 v3_muls( dir, 2.0f, dir );
2537 v3_sub( dir, (v3f){1.0f,1.0f,1.0f}, dir );
2539 v3_normalize( dir );
2542 static inline void vg_rand_sphere( vg_rand *rand, v3f co ){
2543 vg_rand_dir(rand,co);
2544 v3_muls( co, cbrtf( vg_randf64(rand) ), co );
2547 static void vg_rand_disc( vg_rand *rand, v2f co ){
2548 f32 a = vg_randf64(rand) * VG_TAUf;
2551 v2_muls( co, sqrtf( vg_randf64(rand) ), co );
2554 static void vg_rand_cone( vg_rand *rand, v3f out_dir, f32 angle ){
2555 f32 r = sqrtf(vg_randf64(rand)) * angle * 0.5f,
2556 a = vg_randf64(rand) * VG_TAUf;
2558 out_dir[0] = sinf(a) * sinf(r);
2559 out_dir[1] = cosf(a) * sinf(r);
2560 out_dir[2] = cosf(r);
2563 static void vg_hsv_rgb( v3f hsv, v3f rgb ){
2564 i32 i = floorf( hsv[0]*6.0f );
2566 f = hsv[0] * 6.0f - (f32)i,
2567 p = v * (1.0f-hsv[1]),
2568 q = v * (1.0f-f*hsv[1]),
2569 t = v * (1.0f-(1.0f-f)*hsv[1]);
2572 case 0: rgb[0] = v; rgb[1] = t; rgb[2] = p; break;
2573 case 1: rgb[0] = q; rgb[1] = v; rgb[2] = p; break;
2574 case 2: rgb[0] = p; rgb[1] = v; rgb[2] = t; break;
2575 case 3: rgb[0] = p; rgb[1] = q; rgb[2] = v; break;
2576 case 4: rgb[0] = t; rgb[1] = p; rgb[2] = v; break;
2577 case 5: rgb[0] = v; rgb[1] = p; rgb[2] = q; break;
2581 static void vg_rgb_hsv( v3f rgb, v3f hsv ){
2582 f32 min = v3_minf( rgb ),
2583 max = v3_maxf( rgb ),
2585 k_epsilon = 0.00001f;
2588 if( range < k_epsilon ){
2594 if( max > k_epsilon ){
2604 hsv[0] = (rgb[1]-rgb[2])/range;
2605 else if( max == rgb[1] )
2606 hsv[0] = 2.0f+(rgb[2]-rgb[0])/range;
2608 hsv[0] = 4.0f+(rgb[0]-rgb[1])/range;
2610 hsv[0] = vg_fractf( hsv[0] * (60.0f/360.0f) );