1 /* Copyright (C) 2021-2022 Harry Godden (hgn) - All Rights Reserved */
6 #include "vg_platform.h"
10 #define VG_PIf 3.14159265358979323846264338327950288f
11 #define VG_TAUf 6.28318530717958647692528676655900576f
13 static u32
vg_ftu32( float a
)
15 u32
*ptr
= (u32
*)(&a
);
19 static int vg_isinff( float a
)
21 return ((vg_ftu32(a
)) & 0x7FFFFFFFU
) == 0x7F800000U
;
24 static int vg_isnanf( float a
)
26 return !vg_isinff(a
) && ((vg_ftu32(a
)) & 0x7F800000U
) == 0x7F800000U
;
29 static int vg_validf( float a
)
31 return ((vg_ftu32(a
)) & 0x7F800000U
) != 0x7F800000U
;
34 static inline float vg_minf( float a
, float b
)
39 static inline float vg_maxf( float a
, float b
)
44 static inline float vg_clampf( float a
, float min
, float max
)
46 return vg_minf( max
, vg_maxf( a
, min
) );
49 static inline float vg_signf( float a
)
51 return a
< 0.0f
? -1.0f
: 1.0f
;
54 static inline float vg_fractf( float a
)
56 return a
- floorf( a
);
59 static float stable_force( float current
, float diff
)
61 float fnew
= current
+ diff
;
63 if( fnew
* current
< 0.0f
)
69 static inline int vg_min( int a
, int b
)
74 static inline int vg_max( int a
, int b
)
79 static inline float vg_rad( float deg
)
81 return deg
* VG_PIf
/ 180.0f
;
87 static inline void v2_copy( v2f a
, v2f b
)
89 b
[0] = a
[0]; b
[1] = a
[1];
92 static inline void v2_zero( v2f a
)
94 a
[0] = 0.f
; a
[1] = 0.f
;
97 static inline void v2i_copy( v2i a
, v2i b
)
99 b
[0] = a
[0]; b
[1] = a
[1];
102 static inline int v2i_eq( v2i a
, v2i b
)
104 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
107 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
109 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
112 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
114 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
117 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
119 dest
[0] = vg_minf(a
[0], b
[0]);
120 dest
[1] = vg_minf(a
[1], b
[1]);
123 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
125 dest
[0] = vg_maxf(a
[0], b
[0]);
126 dest
[1] = vg_maxf(a
[1], b
[1]);
129 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
131 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
134 static inline float v2_dot( v2f a
, v2f b
)
136 return a
[0] * b
[0] + a
[1] * b
[1];
139 static inline float v2_cross( v2f a
, v2f b
)
141 return a
[0]*b
[1] - a
[1]*b
[0];
144 static inline void v2_add( v2f a
, v2f b
, v2f d
)
146 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
149 static inline void v2_muls( v2f a
, float s
, v2f d
)
151 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
154 static inline void v2_divs( v2f a
, float s
, v2f d
)
156 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
159 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
165 static inline void v2_div( v2f a
, v2f b
, v2f d
)
167 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
170 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
172 d
[0] = a
[0]+b
[0]*s
[0];
173 d
[1] = a
[1]+b
[1]*s
[1];
176 static inline void v2_muladds( v2f a
, v2f b
, float s
, v2f d
)
182 static inline float v2_length2( v2f a
)
184 return a
[0]*a
[0] + a
[1]*a
[1];
187 static inline float v2_length( v2f a
)
189 return sqrtf( v2_length2( a
) );
192 static inline float v2_dist2( v2f a
, v2f b
)
195 v2_sub( a
, b
, delta
);
196 return v2_length2( delta
);
199 static inline float v2_dist( v2f a
, v2f b
)
201 return sqrtf( v2_dist2( a
, b
) );
204 static inline void v2_lerp( v2f a
, v2f b
, float t
, v2f d
)
206 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
207 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
210 static inline void v2_normalize( v2f a
)
212 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
215 static void v2_normalize_clamp( v2f a
)
217 float l2
= v2_length2( a
);
219 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
222 static inline void v2_floor( v2f a
, v2f b
)
224 b
[0] = floorf( a
[0] );
225 b
[1] = floorf( a
[1] );
231 static inline void v3_zero( v3f a
)
233 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
236 static inline void v3_copy( v3f a
, v3f b
)
238 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
241 static inline void v3_add( v3f a
, v3f b
, v3f d
)
243 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
246 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
248 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
251 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
253 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
256 static inline void v3_div( v3f a
, v3f b
, v3f d
)
258 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
259 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
260 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
263 static inline void v3_muls( v3f a
, float s
, v3f d
)
265 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
268 static inline void v3_fill( v3f a
, float v
)
275 static inline void v3_divs( v3f a
, float s
, v3f d
)
278 v3_fill( d
, INFINITY
);
287 static inline void v3_muladds( v3f a
, v3f b
, float s
, v3f d
)
289 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
292 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
294 d
[0] = a
[0]+b
[0]*s
[0];
295 d
[1] = a
[1]+b
[1]*s
[1];
296 d
[2] = a
[2]+b
[2]*s
[2];
299 static inline float v3_dot( v3f a
, v3f b
)
301 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
304 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
307 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
308 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
309 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
313 static inline float v3_length2( v3f a
)
315 return v3_dot( a
, a
);
318 static inline float v3_length( v3f a
)
320 return sqrtf( v3_length2( a
) );
323 static inline float v3_dist2( v3f a
, v3f b
)
326 v3_sub( a
, b
, delta
);
327 return v3_length2( delta
);
330 static inline float v3_dist( v3f a
, v3f b
)
332 return sqrtf( v3_dist2( a
, b
) );
335 static inline void v3_normalize( v3f a
)
337 v3_muls( a
, 1.f
/ v3_length( a
), a
);
340 static inline float vg_lerpf( float a
, float b
, float t
)
345 static inline double vg_lerp( double a
, double b
, double t
)
350 /* correctly lerp around circular period -pi -> pi */
351 static float vg_alerpf( float a
, float b
, float t
)
353 float d
= fmodf( b
-a
, VG_TAUf
),
354 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
358 static inline void v3_lerp( v3f a
, v3f b
, float t
, v3f d
)
360 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
361 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
362 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
365 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
367 dest
[0] = vg_minf(a
[0], b
[0]);
368 dest
[1] = vg_minf(a
[1], b
[1]);
369 dest
[2] = vg_minf(a
[2], b
[2]);
372 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
374 dest
[0] = vg_maxf(a
[0], b
[0]);
375 dest
[1] = vg_maxf(a
[1], b
[1]);
376 dest
[2] = vg_maxf(a
[2], b
[2]);
379 static inline float v3_minf( v3f a
)
381 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
384 static inline float v3_maxf( v3f a
)
386 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
389 static inline void v3_floor( v3f a
, v3f b
)
391 b
[0] = floorf( a
[0] );
392 b
[1] = floorf( a
[1] );
393 b
[2] = floorf( a
[2] );
396 static inline void v3_ceil( v3f a
, v3f b
)
398 b
[0] = ceilf( a
[0] );
399 b
[1] = ceilf( a
[1] );
400 b
[2] = ceilf( a
[2] );
403 static inline void v3_negate( v3f a
, v3f b
)
410 static inline void v3_rotate( v3f v
, float angle
, v3f axis
, v3f d
)
421 v3_cross( k
, v
, v2
);
422 v3_muls( v2
, s
, v2
);
423 v3_add( v1
, v2
, v1
);
424 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
431 static inline void v4_copy( v4f a
, v4f b
)
433 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
436 static inline void v4_zero( v4f a
)
438 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
441 static inline void v4_muls( v4f a
, float s
, v4f d
)
449 static inline void v4_muladds( v4f a
, v4f b
, float s
, v4f d
)
457 static inline void v4_lerp( v4f a
, v4f b
, float t
, v4f d
)
459 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
460 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
461 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
462 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
465 static inline float v4_dot( v4f a
, v4f b
)
467 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
470 static inline float v4_length( v4f a
)
472 return sqrtf( v4_dot(a
,a
) );
479 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
482 #define M2X2_ZERO {{0.0f, 0.0f, }, \
485 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
487 v2_copy( a
[0], b
[0] );
488 v2_copy( a
[1], b
[1] );
491 static inline void m2x2_identity( m2x2f a
)
493 m2x2f id
= M2X2_INDENTIY
;
497 static inline void m2x2_create_rotation( m2x2f a
, float theta
)
514 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
515 { 0.0f, 1.0f, 0.0f, },\
516 { 0.0f, 0.0f, 1.0f, }}
518 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
519 { 0.0f, 0.0f, 0.0f, },\
520 { 0.0f, 0.0f, 0.0f, }}
523 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
525 v3_copy( a
[0], b
[0] );
526 v3_copy( a
[1], b
[1] );
527 v3_copy( a
[2], b
[2] );
530 static inline void m3x3_identity( m3x3f a
)
532 m3x3f id
= M3X3_IDENTITY
;
536 static inline void m3x3_zero( m3x3f a
)
542 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
544 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
545 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
546 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
553 dest
[0][0] = (e
*i
-h
*f
)*det
;
554 dest
[0][1] = -(b
*i
-c
*h
)*det
;
555 dest
[0][2] = (b
*f
-c
*e
)*det
;
556 dest
[1][0] = -(d
*i
-f
*g
)*det
;
557 dest
[1][1] = (a
*i
-c
*g
)*det
;
558 dest
[1][2] = -(a
*f
-d
*c
)*det
;
559 dest
[2][0] = (d
*h
-g
*e
)*det
;
560 dest
[2][1] = -(a
*h
-g
*b
)*det
;
561 dest
[2][2] = (a
*e
-d
*b
)*det
;
564 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
566 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
567 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
568 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
581 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
583 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
584 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
585 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
587 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
588 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
589 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
591 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
592 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
593 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
594 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
595 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
596 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
597 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
598 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
599 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
602 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
606 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
607 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
608 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
613 static inline void m3x3_projection( m3x3f dst
,
614 float const left
, float const right
, float const bottom
, float const top
)
620 rl
= 1.0f
/ (right
- left
);
621 tb
= 1.0f
/ (top
- bottom
);
623 dst
[0][0] = 2.0f
* rl
;
624 dst
[1][1] = 2.0f
* tb
;
628 static inline void m3x3_translate( m3x3f m
, v3f v
)
630 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
631 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
632 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
635 static inline void m3x3_scale( m3x3f m
, v3f v
)
637 m
[0][0] = m
[0][0] * v
[0];
638 m
[0][1] = m
[0][1] * v
[0];
639 m
[0][2] = m
[0][2] * v
[0];
641 m
[1][0] = m
[1][0] * v
[1];
642 m
[1][1] = m
[1][1] * v
[1];
643 m
[1][2] = m
[1][2] * v
[1];
646 static inline void m3x3_rotate( m3x3f m
, float angle
)
648 float m00
= m
[0][0], m10
= m
[1][0],
649 m01
= m
[0][1], m11
= m
[1][1],
650 m02
= m
[0][2], m12
= m
[1][2];
656 m
[0][0] = m00
* c
+ m10
* s
;
657 m
[0][1] = m01
* c
+ m11
* s
;
658 m
[0][2] = m02
* c
+ m12
* s
;
660 m
[1][0] = m00
* -s
+ m10
* c
;
661 m
[1][1] = m01
* -s
+ m11
* c
;
662 m
[1][2] = m02
* -s
+ m12
* c
;
669 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
670 { 0.0f, 1.0f, 0.0f, },\
671 { 0.0f, 0.0f, 1.0f, },\
672 { 0.0f, 0.0f, 0.0f }}
674 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
676 v3_copy( a
[0], b
[0] );
677 v3_copy( a
[1], b
[1] );
678 v3_copy( a
[2], b
[2] );
681 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
683 m3x3_transpose( a
, b
);
684 m3x3_mulv( b
, a
[3], b
[3] );
685 v3_negate( b
[3], b
[3] );
688 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
692 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
693 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
694 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
695 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
701 dst
[0][0] = f
*k
- g
*j
;
702 dst
[1][0] =-(e
*k
- g
*i
);
703 dst
[2][0] = e
*j
- f
*i
;
704 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
706 dst
[0][1] =-(b
*k
- c
*j
);
707 dst
[1][1] = a
*k
- c
*i
;
708 dst
[2][1] =-(a
*j
- b
*i
);
709 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
715 dst
[0][2] = b
*g
- c
*f
;
716 dst
[1][2] =-(a
*g
- c
*e
);
717 dst
[2][2] = a
*f
- b
*e
;
718 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
720 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
721 v3_muls( dst
[0], det
, dst
[0] );
722 v3_muls( dst
[1], det
, dst
[1] );
723 v3_muls( dst
[2], det
, dst
[2] );
724 v3_muls( dst
[3], det
, dst
[3] );
727 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
729 v3_copy( a
[0], b
[0] );
730 v3_copy( a
[1], b
[1] );
731 v3_copy( a
[2], b
[2] );
732 v3_copy( a
[3], b
[3] );
735 static inline void m4x3_identity( m4x3f a
)
737 m4x3f id
= M4X3_IDENTITY
;
741 static inline void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
744 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
745 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
746 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
747 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
748 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
749 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
750 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
751 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
753 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
754 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
755 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
756 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
757 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
758 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
759 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
760 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
761 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
762 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
763 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
764 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
767 static inline void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
771 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
772 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
773 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
779 * Transform plane ( xyz, distance )
781 static inline void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
785 v3_muls( p
, p
[3], o
);
786 m4x3_mulv( m
, o
, o
);
787 m3x3_mulv( m
, p
, d
);
789 d
[3] = v3_dot( o
, d
);
796 static inline void m4x3_translate( m4x3f m
, v3f v
)
798 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
799 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
800 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
803 static inline void m4x3_scale( m4x3f m
, float s
)
805 v3_muls( m
[0], s
, m
[0] );
806 v3_muls( m
[1], s
, m
[1] );
807 v3_muls( m
[2], s
, m
[2] );
810 static inline void m4x3_scalev( m4x3f m
, v3f v
)
812 v3_muls(m
[0], v
[0], m
[0]);
813 v3_muls(m
[1], v
[1], m
[1]);
814 v3_muls(m
[2], v
[2], m
[2]);
817 static inline void m4x3_rotate_x( m4x3f m
, float angle
)
819 m4x3f t
= M4X3_IDENTITY
;
833 static inline void m4x3_rotate_y( m4x3f m
, float angle
)
835 m4x3f t
= M4X3_IDENTITY
;
849 static inline void m4x3_rotate_z( m4x3f m
, float angle
)
851 m4x3f t
= M4X3_IDENTITY
;
865 static inline void m4x3_expand( m4x3f m
, m4x4f d
)
867 v3_copy( m
[0], d
[0] );
868 v3_copy( m
[1], d
[1] );
869 v3_copy( m
[2], d
[2] );
870 v3_copy( m
[3], d
[3] );
877 static inline void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
880 m4x3_mulv( m
, point
, v
);
882 v3_minv( box
[0], v
, box
[0] );
883 v3_maxv( box
[1], v
, box
[1] );
886 static inline void box_addpt( boxf a
, v3f pt
)
888 v3_minv( a
[0], pt
, a
[0] );
889 v3_maxv( a
[1], pt
, a
[1] );
892 static inline void box_concat( boxf a
, boxf b
)
894 v3_minv( a
[0], b
[0], a
[0] );
895 v3_maxv( a
[1], b
[1], a
[1] );
898 static inline void box_copy( boxf a
, boxf b
)
900 v3_copy( a
[0], b
[0] );
901 v3_copy( a
[1], b
[1] );
904 static inline int box_overlap( boxf a
, boxf b
)
907 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
908 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
909 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
913 static int box_within( boxf greater
, boxf lesser
)
916 v3_sub( lesser
[0], greater
[0], a
);
917 v3_sub( lesser
[1], greater
[1], b
);
919 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
920 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
928 static inline void box_init_inf( boxf box
)
930 v3_fill( box
[0], INFINITY
);
931 v3_fill( box
[1], -INFINITY
);
934 static inline void m4x3_transform_aabb( m4x3f m
, boxf box
)
938 v3_copy( box
[0], a
);
939 v3_copy( box
[1], b
);
940 v3_fill( box
[0], INFINITY
);
941 v3_fill( box
[1], -INFINITY
);
943 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], a
[2] } );
944 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
945 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
946 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
948 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], b
[2] } );
949 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
950 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
951 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
954 int ray_aabb( boxf box
, v3f co
, v3f dir
, float dist
)
959 v3_sub( box
[0], co
, v0
);
960 v3_sub( box
[1], co
, v1
);
962 v3_div( v0
, dir
, v0
);
963 v3_div( v1
, dir
, v1
);
965 tmin
= vg_minf( v0
[0], v1
[0] );
966 tmax
= vg_maxf( v0
[0], v1
[0] );
967 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
968 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
969 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
970 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
972 return tmax
>= tmin
&& tmin
< dist
&& tmax
> 0;
975 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
978 v3_sub( target
, pos
, dir
);
981 v3_copy( dir
, m
[2] );
983 v3_cross( up
, m
[2], m
[0] );
984 v3_normalize( m
[0] );
986 v3_cross( m
[2], m
[0], m
[1] );
987 v3_copy( pos
, m
[3] );
994 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
995 { 0.0f, 1.0f, 0.0f, 0.0f },\
996 { 0.0f, 0.0f, 1.0f, 0.0f },\
997 { 0.0f, 0.0f, 0.0f, 1.0f }}
998 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
999 { 0.0f, 0.0f, 0.0f, 0.0f },\
1000 { 0.0f, 0.0f, 0.0f, 0.0f },\
1001 { 0.0f, 0.0f, 0.0f, 0.0f }}
1003 static void m4x4_projection( m4x4f m
, float angle
,
1004 float ratio
, float fnear
, float ffar
)
1006 float scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1012 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1018 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1022 m
[2][0] = (r
+ l
) / (r
- l
);
1023 m
[2][1] = (t
+ b
) / (t
- b
);
1024 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1029 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1033 static void m4x4_translate( m4x4f m
, v3f v
)
1035 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1036 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1037 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1040 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1042 v4_copy( a
[0], b
[0] );
1043 v4_copy( a
[1], b
[1] );
1044 v4_copy( a
[2], b
[2] );
1045 v4_copy( a
[3], b
[3] );
1048 static inline void m4x4_identity( m4x4f a
)
1050 m4x4f id
= M4X4_IDENTITY
;
1054 static inline void m4x4_zero( m4x4f a
)
1056 m4x4f zero
= M4X4_ZERO
;
1057 m4x4_copy( zero
, a
);
1060 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1062 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1063 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1064 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1065 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1067 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1068 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1069 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1070 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1072 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1073 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1074 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1075 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1076 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1077 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1078 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1079 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1080 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1081 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1082 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1083 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1084 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1085 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1086 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1087 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1090 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1094 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1095 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1096 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1097 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1102 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1104 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1105 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1106 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1107 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1111 t
[0] = a22
*a33
- a32
*a23
;
1112 t
[1] = a21
*a33
- a31
*a23
;
1113 t
[2] = a21
*a32
- a31
*a22
;
1114 t
[3] = a20
*a33
- a30
*a23
;
1115 t
[4] = a20
*a32
- a30
*a22
;
1116 t
[5] = a20
*a31
- a30
*a21
;
1118 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1119 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1120 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1121 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1123 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1124 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1125 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1126 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1128 t
[0] = a12
*a33
- a32
*a13
;
1129 t
[1] = a11
*a33
- a31
*a13
;
1130 t
[2] = a11
*a32
- a31
*a12
;
1131 t
[3] = a10
*a33
- a30
*a13
;
1132 t
[4] = a10
*a32
- a30
*a12
;
1133 t
[5] = a10
*a31
- a30
*a11
;
1135 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1136 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1137 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1138 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1140 t
[0] = a12
*a23
- a22
*a13
;
1141 t
[1] = a11
*a23
- a21
*a13
;
1142 t
[2] = a11
*a22
- a21
*a12
;
1143 t
[3] = a10
*a23
- a20
*a13
;
1144 t
[4] = a10
*a22
- a20
*a12
;
1145 t
[5] = a10
*a21
- a20
*a11
;
1147 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1148 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1149 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1150 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1152 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1153 v4_muls( d
[0], det
, d
[0] );
1154 v4_muls( d
[1], det
, d
[1] );
1155 v4_muls( d
[2], det
, d
[2] );
1156 v4_muls( d
[3], det
, d
[3] );
1160 * Planes (double precision)
1162 static inline void tri_to_plane( double a
[3], double b
[3],
1163 double c
[3], double p
[4] )
1169 edge0
[0] = b
[0] - a
[0];
1170 edge0
[1] = b
[1] - a
[1];
1171 edge0
[2] = b
[2] - a
[2];
1173 edge1
[0] = c
[0] - a
[0];
1174 edge1
[1] = c
[1] - a
[1];
1175 edge1
[2] = c
[2] - a
[2];
1177 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1178 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1179 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1181 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1182 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1189 static inline int plane_intersect( double a
[4], double b
[4],
1190 double c
[4], double p
[4] )
1192 double const epsilon
= 1e-8f
;
1197 x
[0] = a
[1] * b
[2] - a
[2] * b
[1];
1198 x
[1] = a
[2] * b
[0] - a
[0] * b
[2];
1199 x
[2] = a
[0] * b
[1] - a
[1] * b
[0];
1201 d
= x
[0] * c
[0] + x
[1] * c
[1] + x
[2] * c
[2];
1203 if( d
< epsilon
&& d
> -epsilon
) return 0;
1205 p
[0] = (b
[1] * c
[2] - b
[2] * c
[1]) * -a
[3];
1206 p
[1] = (b
[2] * c
[0] - b
[0] * c
[2]) * -a
[3];
1207 p
[2] = (b
[0] * c
[1] - b
[1] * c
[0]) * -a
[3];
1209 p
[0] += (c
[1] * a
[2] - c
[2] * a
[1]) * -b
[3];
1210 p
[1] += (c
[2] * a
[0] - c
[0] * a
[2]) * -b
[3];
1211 p
[2] += (c
[0] * a
[1] - c
[1] * a
[0]) * -b
[3];
1213 p
[0] += (a
[1] * b
[2] - a
[2] * b
[1]) * -c
[3];
1214 p
[1] += (a
[2] * b
[0] - a
[0] * b
[2]) * -c
[3];
1215 p
[2] += (a
[0] * b
[1] - a
[1] * b
[0]) * -c
[3];
1224 static inline double plane_polarity( double p
[4], double a
[3] )
1227 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1228 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1234 static inline void q_identity( v4f q
)
1236 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
1239 static inline void q_axis_angle( v4f q
, v3f axis
, float angle
)
1241 float a
= angle
*0.5f
,
1251 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
1254 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
1255 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
1256 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
1257 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
1261 static inline void q_normalize( v4f q
)
1263 float s
= 1.0f
/ sqrtf(v4_dot(q
,q
));
1270 static inline void q_inv( v4f q
, v4f d
)
1272 float s
= 1.0f
/ v4_dot(q
,q
);
1279 static inline void q_nlerp( v4f a
, v4f b
, float t
, v4f d
)
1281 if( v4_dot(a
,b
) < 0.0f
)
1283 v4_muls( b
, -1.0f
, d
);
1284 v4_lerp( a
, d
, t
, d
);
1287 v4_lerp( a
, b
, t
, d
);
1292 static inline void q_m3x3( v4f q
, m3x3f d
)
1296 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
1298 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
1299 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
1300 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
1302 d
[0][0] = 1.0f
- yy
- zz
;
1303 d
[1][1] = 1.0f
- xx
- zz
;
1304 d
[2][2] = 1.0f
- xx
- yy
;
1313 static void m3x3_q( m3x3f m
, v4f q
)
1315 float diag
, r
, rinv
;
1317 diag
= m
[0][0] + m
[1][1] + m
[2][2];
1320 r
= sqrtf( 1.0f
+ diag
);
1322 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
1323 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
1324 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
1327 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
1329 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
1332 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
1333 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
1334 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
1336 else if( m
[1][1] >= m
[2][2] )
1338 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
1340 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
1342 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
1343 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
1347 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
1349 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
1350 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
1352 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
1358 k_contact_type_default
,
1359 k_contact_type_disabled
,
1364 * -----------------------------------------------------------------------------
1365 * Closest point functions
1366 * -----------------------------------------------------------------------------
1370 * These closest point tests were learned from Real-Time Collision Detection by
1373 VG_STATIC
float closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1374 float *s
, float *t
, v3f c1
, v3f c2
)
1377 v3_sub( q1
, p1
, d1
);
1378 v3_sub( q2
, p2
, d2
);
1379 v3_sub( p1
, p2
, r
);
1381 float a
= v3_length2( d1
),
1382 e
= v3_length2( d2
),
1383 f
= v3_dot( d2
, r
);
1385 const float kEpsilon
= 0.0001f
;
1387 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1395 v3_sub( c1
, c2
, v0
);
1397 return v3_length2( v0
);
1403 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1407 float c
= v3_dot( d1
, r
);
1411 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1415 float b
= v3_dot(d1
,d2
),
1420 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1427 *t
= (b
*(*s
)+f
) / e
;
1432 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1434 else if( *t
> 1.0f
)
1437 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1442 v3_muladds( p1
, d1
, *s
, c1
);
1443 v3_muladds( p2
, d2
, *t
, c2
);
1446 v3_sub( c1
, c2
, v0
);
1447 return v3_length2( v0
);
1450 VG_STATIC
void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1452 v3_maxv( p
, box
[0], dest
);
1453 v3_minv( dest
, box
[1], dest
);
1456 VG_STATIC
void closest_point_obb( v3f p
, boxf box
,
1457 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1460 m4x3_mulv( inv_mtx
, p
, local
);
1461 closest_point_aabb( local
, box
, local
);
1462 m4x3_mulv( mtx
, local
, dest
);
1465 VG_STATIC
float closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1469 v3_sub( point
, a
, v1
);
1471 float t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1472 t
= vg_clampf(t
,0.0f
,1.0f
);
1473 v3_muladds( a
, v0
, t
, dest
);
1477 VG_STATIC
void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1482 /* Region outside A */
1483 v3_sub( tri
[1], tri
[0], ab
);
1484 v3_sub( tri
[2], tri
[0], ac
);
1485 v3_sub( p
, tri
[0], ap
);
1489 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1491 v3_copy( tri
[0], dest
);
1492 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1496 /* Region outside B */
1500 v3_sub( p
, tri
[1], bp
);
1501 d3
= v3_dot( ab
, bp
);
1502 d4
= v3_dot( ac
, bp
);
1504 if( d3
>= 0.0f
&& d4
<= d3
)
1506 v3_copy( tri
[1], dest
);
1507 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1511 /* Edge region of AB */
1512 float vc
= d1
*d4
- d3
*d2
;
1513 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1515 float v
= d1
/ (d1
-d3
);
1516 v3_muladds( tri
[0], ab
, v
, dest
);
1517 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1521 /* Region outside C */
1524 v3_sub( p
, tri
[2], cp
);
1525 d5
= v3_dot(ab
, cp
);
1526 d6
= v3_dot(ac
, cp
);
1528 if( d6
>= 0.0f
&& d5
<= d6
)
1530 v3_copy( tri
[2], dest
);
1531 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1536 float vb
= d5
*d2
- d1
*d6
;
1537 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1539 float w
= d2
/ (d2
-d6
);
1540 v3_muladds( tri
[0], ac
, w
, dest
);
1541 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1546 float va
= d3
*d6
- d5
*d4
;
1547 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1549 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1551 v3_sub( tri
[2], tri
[1], bc
);
1552 v3_muladds( tri
[1], bc
, w
, dest
);
1553 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1557 /* P inside region, Q via barycentric coordinates uvw */
1558 float d
= 1.0f
/(va
+vb
+vc
),
1562 v3_muladds( tri
[0], ab
, v
, dest
);
1563 v3_muladds( dest
, ac
, w
, dest
);
1566 VG_STATIC
enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1571 /* Region outside A */
1572 v3_sub( tri
[1], tri
[0], ab
);
1573 v3_sub( tri
[2], tri
[0], ac
);
1574 v3_sub( p
, tri
[0], ap
);
1578 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1580 v3_copy( tri
[0], dest
);
1581 return k_contact_type_default
;
1584 /* Region outside B */
1588 v3_sub( p
, tri
[1], bp
);
1589 d3
= v3_dot( ab
, bp
);
1590 d4
= v3_dot( ac
, bp
);
1592 if( d3
>= 0.0f
&& d4
<= d3
)
1594 v3_copy( tri
[1], dest
);
1595 return k_contact_type_edge
;
1598 /* Edge region of AB */
1599 float vc
= d1
*d4
- d3
*d2
;
1600 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1602 float v
= d1
/ (d1
-d3
);
1603 v3_muladds( tri
[0], ab
, v
, dest
);
1604 return k_contact_type_edge
;
1607 /* Region outside C */
1610 v3_sub( p
, tri
[2], cp
);
1611 d5
= v3_dot(ab
, cp
);
1612 d6
= v3_dot(ac
, cp
);
1614 if( d6
>= 0.0f
&& d5
<= d6
)
1616 v3_copy( tri
[2], dest
);
1617 return k_contact_type_edge
;
1621 float vb
= d5
*d2
- d1
*d6
;
1622 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1624 float w
= d2
/ (d2
-d6
);
1625 v3_muladds( tri
[0], ac
, w
, dest
);
1626 return k_contact_type_edge
;
1630 float va
= d3
*d6
- d5
*d4
;
1631 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1633 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1635 v3_sub( tri
[2], tri
[1], bc
);
1636 v3_muladds( tri
[1], bc
, w
, dest
);
1637 return k_contact_type_edge
;
1640 /* P inside region, Q via barycentric coordinates uvw */
1641 float d
= 1.0f
/(va
+vb
+vc
),
1645 v3_muladds( tri
[0], ab
, v
, dest
);
1646 v3_muladds( dest
, ac
, w
, dest
);
1648 return k_contact_type_default
;
1655 /* Time of intersection with ray vs triangle */
1656 static int ray_tri( v3f tri
[3], v3f co
,
1657 v3f dir
, float *dist
)
1659 float const kEpsilon
= 0.00001f
;
1661 v3f v0
, v1
, h
, s
, q
, n
;
1668 v3_sub( pb
, pa
, v0
);
1669 v3_sub( pc
, pa
, v1
);
1670 v3_cross( dir
, v1
, h
);
1671 v3_cross( v0
, v1
, n
);
1673 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
1677 a
= v3_dot( v0
, h
);
1678 if( a
> -kEpsilon
&& a
< kEpsilon
)
1682 v3_sub( co
, pa
, s
);
1684 u
= f
* v3_dot(s
, h
);
1685 if( u
< 0.0f
|| u
> 1.0f
)
1688 v3_cross( s
, v0
, q
);
1689 v
= f
* v3_dot( dir
, q
);
1690 if( v
< 0.0f
|| u
+v
> 1.0f
)
1693 t
= f
* v3_dot(v1
, q
);
1702 /* time of intersection with ray vs sphere */
1703 static int ray_sphere( v3f c
, float r
,
1704 v3f co
, v3f dir
, float *t
)
1709 float b
= v3_dot( m
, dir
),
1710 c1
= v3_dot( m
, m
) - r
*r
;
1712 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
1713 if( c1
> 0.0f
&& b
> 0.0f
)
1716 float discr
= b
*b
- c1
;
1718 /* A negative discriminant corresponds to ray missing sphere */
1723 * Ray now found to intersect sphere, compute smallest t value of
1726 *t
= -b
- sqrtf( discr
);
1728 /* If t is negative, ray started inside sphere so clamp t to zero */
1736 * time of intersection of ray vs cylinder
1737 * The cylinder does not have caps but is finite
1739 * Heavily adapted from regular segment vs cylinder from:
1740 * Real-Time Collision Detection
1742 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, float r
,
1743 v3f co
, v3f dir
, float *t
)
1746 v3_muladds( co
, dir
, 1.0f
, sb
);
1750 v3_sub( sb
, co
, n
);
1752 float md
= v3_dot( m
, d
),
1753 nd
= v3_dot( n
, d
),
1754 dd
= v3_dot( d
, d
),
1755 nn
= v3_dot( n
, n
),
1756 mn
= v3_dot( m
, n
),
1758 k
= v3_dot( m
, m
) - r
*r
,
1761 if( fabsf(a
) < 0.00001f
)
1763 /* Segment runs parallel to cylinder axis */
1767 float b
= dd
*mn
- nd
*md
,
1771 return 0; /* No real roots; no intersection */
1773 *t
= (-b
- sqrtf(discr
)) / a
;
1775 return 0; /* Intersection behind ray */
1777 /* Check within cylinder segment */
1778 if( md
+ (*t
)*nd
< 0.0f
)
1781 if( md
+ (*t
)*nd
> dd
)
1784 /* Segment intersects cylinder between the endcaps; t is correct */
1789 * Time of intersection of sphere and triangle. Origin must be outside the
1790 * colliding area. This is a fairly long procedure.
1792 static int spherecast_triangle( v3f tri
[3],
1793 v3f co
, v3f dir
, float r
, float *t
, v3f n
)
1798 v3_sub( tri
[1], tri
[0], v0
);
1799 v3_sub( tri
[2], tri
[0], v1
);
1800 v3_cross( v0
, v1
, n
);
1802 v3_muladds( tri
[0], n
, r
, sum
[0] );
1803 v3_muladds( tri
[1], n
, r
, sum
[1] );
1804 v3_muladds( tri
[2], n
, r
, sum
[2] );
1807 float t_min
= INFINITY
,
1810 if( ray_tri( sum
, co
, dir
, &t1
) )
1812 t_min
= vg_minf( t_min
, t1
);
1817 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
1820 for( int i
=0; i
<3; i
++ )
1822 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) )
1824 t_min
= vg_minf( t_min
, t1
);
1830 for( int i
=0; i
<3; i
++ )
1835 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) )
1842 v3_add( dir
, co
, co1
);
1843 v3_lerp( co
, co1
, t_min
, ct
);
1845 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
1846 v3_sub( ct
, cx
, n
);
1858 static inline float vg_randf(void)
1860 return (float)rand()/(float)(RAND_MAX
);
1863 static inline void vg_rand_dir(v3f dir
)
1865 dir
[0] = vg_randf();
1866 dir
[1] = vg_randf();
1867 dir
[2] = vg_randf();
1869 v3_muls( dir
, 2.0f
, dir
);
1870 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
1872 v3_normalize( dir
);
1875 static inline void vg_rand_sphere( v3f co
)
1878 v3_muls( co
, cbrtf( vg_randf() ), co
);
1881 static inline int vg_randint(int max
)
1886 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, float t
, v3f p
)
1891 v3_muls( p1
, ttt
, p
);
1892 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
1893 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
1894 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);