fbb3c45317915d592d4fbb8120390027999944d9
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_abs( v2f a
, v2f d
)
151 d
[0] = fabsf( a
[0] );
152 d
[1] = fabsf( a
[1] );
155 static inline void v2_muls( v2f a
, float s
, v2f d
)
157 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
160 static inline void v2_divs( v2f a
, float s
, v2f d
)
162 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
165 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
171 static inline void v2_div( v2f a
, v2f b
, v2f d
)
173 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
176 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
178 d
[0] = a
[0]+b
[0]*s
[0];
179 d
[1] = a
[1]+b
[1]*s
[1];
182 static inline void v2_muladds( v2f a
, v2f b
, float s
, v2f d
)
188 static inline float v2_length2( v2f a
)
190 return a
[0]*a
[0] + a
[1]*a
[1];
193 static inline float v2_length( v2f a
)
195 return sqrtf( v2_length2( a
) );
198 static inline float v2_dist2( v2f a
, v2f b
)
201 v2_sub( a
, b
, delta
);
202 return v2_length2( delta
);
205 static inline float v2_dist( v2f a
, v2f b
)
207 return sqrtf( v2_dist2( a
, b
) );
210 static inline void v2_lerp( v2f a
, v2f b
, float t
, v2f d
)
212 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
213 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
216 static inline void v2_normalize( v2f a
)
218 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
221 static void v2_normalize_clamp( v2f a
)
223 float l2
= v2_length2( a
);
225 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
228 static inline void v2_floor( v2f a
, v2f b
)
230 b
[0] = floorf( a
[0] );
231 b
[1] = floorf( a
[1] );
234 static inline void v2_fill( v2f a
, float v
)
240 /* copysign of b to a */
241 static inline void v2_copysign( v2f a
, v2f b
)
243 a
[0] = copysignf( a
[0], b
[0] );
244 a
[1] = copysignf( a
[1], b
[1] );
250 static inline void v3_zero( v3f a
)
252 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
255 static inline void v3_copy( v3f a
, v3f b
)
257 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
260 static inline void v3_add( v3f a
, v3f b
, v3f d
)
262 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
265 static inline void v4_add( v4f a
, v4f b
, v4f d
)
273 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
275 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
278 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
280 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
283 static inline void v3_div( v3f a
, v3f b
, v3f d
)
285 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
286 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
287 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
290 static inline void v3_muls( v3f a
, float s
, v3f d
)
292 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
295 static inline void v3_fill( v3f a
, float v
)
302 static inline void v3_divs( v3f a
, float s
, v3f d
)
305 v3_fill( d
, INFINITY
);
314 static inline void v3_muladds( v3f a
, v3f b
, float s
, v3f d
)
316 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
319 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
321 d
[0] = a
[0]+b
[0]*s
[0];
322 d
[1] = a
[1]+b
[1]*s
[1];
323 d
[2] = a
[2]+b
[2]*s
[2];
326 static inline float v3_dot( v3f a
, v3f b
)
328 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
331 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
334 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
335 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
336 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
340 static inline float v3_length2( v3f a
)
342 return v3_dot( a
, a
);
345 static inline float v3_length( v3f a
)
347 return sqrtf( v3_length2( a
) );
350 static inline float v3_dist2( v3f a
, v3f b
)
353 v3_sub( a
, b
, delta
);
354 return v3_length2( delta
);
357 static inline float v3_dist( v3f a
, v3f b
)
359 return sqrtf( v3_dist2( a
, b
) );
362 static inline void v3_normalize( v3f a
)
364 v3_muls( a
, 1.f
/ v3_length( a
), a
);
367 static inline float vg_lerpf( float a
, float b
, float t
)
372 static inline double vg_lerp( double a
, double b
, double t
)
377 /* correctly lerp around circular period -pi -> pi */
378 static float vg_alerpf( float a
, float b
, float t
)
380 float d
= fmodf( b
-a
, VG_TAUf
),
381 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
385 static inline void v3_lerp( v3f a
, v3f b
, float t
, v3f d
)
387 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
388 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
389 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
392 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
394 dest
[0] = vg_minf(a
[0], b
[0]);
395 dest
[1] = vg_minf(a
[1], b
[1]);
396 dest
[2] = vg_minf(a
[2], b
[2]);
399 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
401 dest
[0] = vg_maxf(a
[0], b
[0]);
402 dest
[1] = vg_maxf(a
[1], b
[1]);
403 dest
[2] = vg_maxf(a
[2], b
[2]);
406 static inline float v3_minf( v3f a
)
408 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
411 static inline float v3_maxf( v3f a
)
413 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
416 static inline void v3_floor( v3f a
, v3f b
)
418 b
[0] = floorf( a
[0] );
419 b
[1] = floorf( a
[1] );
420 b
[2] = floorf( a
[2] );
423 static inline void v3_ceil( v3f a
, v3f b
)
425 b
[0] = ceilf( a
[0] );
426 b
[1] = ceilf( a
[1] );
427 b
[2] = ceilf( a
[2] );
430 static inline void v3_negate( v3f a
, v3f b
)
437 static inline void v3_rotate( v3f v
, float angle
, v3f axis
, v3f d
)
448 v3_cross( k
, v
, v2
);
449 v3_muls( v2
, s
, v2
);
450 v3_add( v1
, v2
, v1
);
451 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
458 static inline void v4_copy( v4f a
, v4f b
)
460 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
463 static inline void v4_zero( v4f a
)
465 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
468 static inline void v4_muls( v4f a
, float s
, v4f d
)
476 static inline void v4_muladds( v4f a
, v4f b
, float s
, v4f d
)
484 static inline void v4_lerp( v4f a
, v4f b
, float t
, v4f d
)
486 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
487 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
488 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
489 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
492 static inline float v4_dot( v4f a
, v4f b
)
494 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
497 static inline float v4_length( v4f a
)
499 return sqrtf( v4_dot(a
,a
) );
506 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
509 #define M2X2_ZERO {{0.0f, 0.0f, }, \
512 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
514 v2_copy( a
[0], b
[0] );
515 v2_copy( a
[1], b
[1] );
518 static inline void m2x2_identity( m2x2f a
)
520 m2x2f id
= M2X2_INDENTIY
;
524 static inline void m2x2_create_rotation( m2x2f a
, float theta
)
541 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
542 { 0.0f, 1.0f, 0.0f, },\
543 { 0.0f, 0.0f, 1.0f, }}
545 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
546 { 0.0f, 0.0f, 0.0f, },\
547 { 0.0f, 0.0f, 0.0f, }}
550 /* a X b == [b]T a == ...*/
551 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
564 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
566 v3_add( a
[0], b
[0], d
[0] );
567 v3_add( a
[1], b
[1], d
[1] );
568 v3_add( a
[2], b
[2], d
[2] );
571 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
573 v3_copy( a
[0], b
[0] );
574 v3_copy( a
[1], b
[1] );
575 v3_copy( a
[2], b
[2] );
578 static inline void m3x3_identity( m3x3f a
)
580 m3x3f id
= M3X3_IDENTITY
;
584 static void m3x3_diagonal( m3x3f a
, float v
)
592 static inline void m3x3_zero( m3x3f a
)
598 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
600 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
601 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
602 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
609 dest
[0][0] = (e
*i
-h
*f
)*det
;
610 dest
[0][1] = -(b
*i
-c
*h
)*det
;
611 dest
[0][2] = (b
*f
-c
*e
)*det
;
612 dest
[1][0] = -(d
*i
-f
*g
)*det
;
613 dest
[1][1] = (a
*i
-c
*g
)*det
;
614 dest
[1][2] = -(a
*f
-d
*c
)*det
;
615 dest
[2][0] = (d
*h
-g
*e
)*det
;
616 dest
[2][1] = -(a
*h
-g
*b
)*det
;
617 dest
[2][2] = (a
*e
-d
*b
)*det
;
620 static float m3x3_det( m3x3f m
)
622 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
623 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
624 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
627 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
629 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
630 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
631 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
644 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
646 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
647 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
648 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
650 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
651 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
652 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
654 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
655 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
656 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
657 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
658 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
659 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
660 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
661 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
662 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
665 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
669 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
670 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
671 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
676 static inline void m3x3_projection( m3x3f dst
,
677 float const left
, float const right
, float const bottom
, float const top
)
683 rl
= 1.0f
/ (right
- left
);
684 tb
= 1.0f
/ (top
- bottom
);
686 dst
[0][0] = 2.0f
* rl
;
687 dst
[1][1] = 2.0f
* tb
;
691 static inline void m3x3_translate( m3x3f m
, v3f v
)
693 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
694 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
695 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
698 static inline void m3x3_scale( m3x3f m
, v3f v
)
700 m
[0][0] = m
[0][0] * v
[0];
701 m
[0][1] = m
[0][1] * v
[0];
702 m
[0][2] = m
[0][2] * v
[0];
704 m
[1][0] = m
[1][0] * v
[1];
705 m
[1][1] = m
[1][1] * v
[1];
706 m
[1][2] = m
[1][2] * v
[1];
709 static inline void m3x3_rotate( m3x3f m
, float angle
)
711 float m00
= m
[0][0], m10
= m
[1][0],
712 m01
= m
[0][1], m11
= m
[1][1],
713 m02
= m
[0][2], m12
= m
[1][2];
719 m
[0][0] = m00
* c
+ m10
* s
;
720 m
[0][1] = m01
* c
+ m11
* s
;
721 m
[0][2] = m02
* c
+ m12
* s
;
723 m
[1][0] = m00
* -s
+ m10
* c
;
724 m
[1][1] = m01
* -s
+ m11
* c
;
725 m
[1][2] = m02
* -s
+ m12
* c
;
732 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
733 { 0.0f, 1.0f, 0.0f, },\
734 { 0.0f, 0.0f, 1.0f, },\
735 { 0.0f, 0.0f, 0.0f }}
737 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
739 v3_copy( a
[0], b
[0] );
740 v3_copy( a
[1], b
[1] );
741 v3_copy( a
[2], b
[2] );
744 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
746 m3x3_transpose( a
, b
);
747 m3x3_mulv( b
, a
[3], b
[3] );
748 v3_negate( b
[3], b
[3] );
751 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
755 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
756 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
757 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
758 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
764 dst
[0][0] = f
*k
- g
*j
;
765 dst
[1][0] =-(e
*k
- g
*i
);
766 dst
[2][0] = e
*j
- f
*i
;
767 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
769 dst
[0][1] =-(b
*k
- c
*j
);
770 dst
[1][1] = a
*k
- c
*i
;
771 dst
[2][1] =-(a
*j
- b
*i
);
772 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
778 dst
[0][2] = b
*g
- c
*f
;
779 dst
[1][2] =-(a
*g
- c
*e
);
780 dst
[2][2] = a
*f
- b
*e
;
781 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
783 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
784 v3_muls( dst
[0], det
, dst
[0] );
785 v3_muls( dst
[1], det
, dst
[1] );
786 v3_muls( dst
[2], det
, dst
[2] );
787 v3_muls( dst
[3], det
, dst
[3] );
790 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
792 v3_copy( a
[0], b
[0] );
793 v3_copy( a
[1], b
[1] );
794 v3_copy( a
[2], b
[2] );
795 v3_copy( a
[3], b
[3] );
798 static inline void m4x3_identity( m4x3f a
)
800 m4x3f id
= M4X3_IDENTITY
;
804 static inline void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
807 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
808 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
809 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
810 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
811 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
812 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
813 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
814 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
816 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
817 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
818 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
819 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
820 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
821 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
822 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
823 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
824 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
825 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
826 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
827 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
830 static inline void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
834 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
835 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
836 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
842 * Transform plane ( xyz, distance )
844 static inline void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
848 v3_muls( p
, p
[3], o
);
849 m4x3_mulv( m
, o
, o
);
850 m3x3_mulv( m
, p
, d
);
852 d
[3] = v3_dot( o
, d
);
859 static inline void m4x3_translate( m4x3f m
, v3f v
)
861 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
862 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
863 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
866 static inline void m4x3_scale( m4x3f m
, float s
)
868 v3_muls( m
[0], s
, m
[0] );
869 v3_muls( m
[1], s
, m
[1] );
870 v3_muls( m
[2], s
, m
[2] );
873 static inline void m4x3_scalev( m4x3f m
, v3f v
)
875 v3_muls(m
[0], v
[0], m
[0]);
876 v3_muls(m
[1], v
[1], m
[1]);
877 v3_muls(m
[2], v
[2], m
[2]);
880 static inline void m4x3_rotate_x( m4x3f m
, float angle
)
882 m4x3f t
= M4X3_IDENTITY
;
896 static inline void m4x3_rotate_y( m4x3f m
, float angle
)
898 m4x3f t
= M4X3_IDENTITY
;
912 static inline void m4x3_rotate_z( m4x3f m
, float angle
)
914 m4x3f t
= M4X3_IDENTITY
;
928 static inline void m4x3_expand( m4x3f m
, m4x4f d
)
930 v3_copy( m
[0], d
[0] );
931 v3_copy( m
[1], d
[1] );
932 v3_copy( m
[2], d
[2] );
933 v3_copy( m
[3], d
[3] );
940 static inline void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
943 m4x3_mulv( m
, point
, v
);
945 v3_minv( box
[0], v
, box
[0] );
946 v3_maxv( box
[1], v
, box
[1] );
949 static inline void box_addpt( boxf a
, v3f pt
)
951 v3_minv( a
[0], pt
, a
[0] );
952 v3_maxv( a
[1], pt
, a
[1] );
955 static inline void box_concat( boxf a
, boxf b
)
957 v3_minv( a
[0], b
[0], a
[0] );
958 v3_maxv( a
[1], b
[1], a
[1] );
961 static inline void box_copy( boxf a
, boxf b
)
963 v3_copy( a
[0], b
[0] );
964 v3_copy( a
[1], b
[1] );
967 static inline int box_overlap( boxf a
, boxf b
)
970 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
971 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
972 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
976 static int box_within( boxf greater
, boxf lesser
)
979 v3_sub( lesser
[0], greater
[0], a
);
980 v3_sub( lesser
[1], greater
[1], b
);
982 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
983 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
991 static inline void box_init_inf( boxf box
)
993 v3_fill( box
[0], INFINITY
);
994 v3_fill( box
[1], -INFINITY
);
997 static inline void m4x3_transform_aabb( m4x3f m
, boxf box
)
1001 v3_copy( box
[0], a
);
1002 v3_copy( box
[1], b
);
1003 v3_fill( box
[0], INFINITY
);
1004 v3_fill( box
[1], -INFINITY
);
1006 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], a
[2] } );
1007 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
1008 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
1009 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
1011 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], b
[2] } );
1012 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
1013 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
1014 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
1017 int ray_aabb( boxf box
, v3f co
, v3f dir
, float dist
)
1022 v3_sub( box
[0], co
, v0
);
1023 v3_sub( box
[1], co
, v1
);
1025 v3_div( v0
, dir
, v0
);
1026 v3_div( v1
, dir
, v1
);
1028 tmin
= vg_minf( v0
[0], v1
[0] );
1029 tmax
= vg_maxf( v0
[0], v1
[0] );
1030 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
1031 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
1032 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
1033 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
1035 return tmax
>= tmin
&& tmin
< dist
&& tmax
> 0;
1038 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1041 v3_sub( target
, pos
, dir
);
1042 v3_normalize( dir
);
1044 v3_copy( dir
, m
[2] );
1046 v3_cross( up
, m
[2], m
[0] );
1047 v3_normalize( m
[0] );
1049 v3_cross( m
[2], m
[0], m
[1] );
1050 v3_copy( pos
, m
[3] );
1057 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1058 { 0.0f, 1.0f, 0.0f, 0.0f },\
1059 { 0.0f, 0.0f, 1.0f, 0.0f },\
1060 { 0.0f, 0.0f, 0.0f, 1.0f }}
1061 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1062 { 0.0f, 0.0f, 0.0f, 0.0f },\
1063 { 0.0f, 0.0f, 0.0f, 0.0f },\
1064 { 0.0f, 0.0f, 0.0f, 0.0f }}
1066 static void m4x4_projection( m4x4f m
, float angle
,
1067 float ratio
, float fnear
, float ffar
)
1069 float scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1075 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1081 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1085 m
[2][0] = (r
+ l
) / (r
- l
);
1086 m
[2][1] = (t
+ b
) / (t
- b
);
1087 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1092 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1096 static void m4x4_translate( m4x4f m
, v3f v
)
1098 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1099 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1100 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1103 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1105 v4_copy( a
[0], b
[0] );
1106 v4_copy( a
[1], b
[1] );
1107 v4_copy( a
[2], b
[2] );
1108 v4_copy( a
[3], b
[3] );
1111 static inline void m4x4_identity( m4x4f a
)
1113 m4x4f id
= M4X4_IDENTITY
;
1117 static inline void m4x4_zero( m4x4f a
)
1119 m4x4f zero
= M4X4_ZERO
;
1120 m4x4_copy( zero
, a
);
1123 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1125 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1126 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1127 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1128 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1130 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1131 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1132 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1133 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1135 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1136 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1137 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1138 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1139 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1140 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1141 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1142 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1143 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1144 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1145 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1146 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1147 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1148 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1149 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1150 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1153 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1157 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1158 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1159 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1160 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1165 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1167 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1168 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1169 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1170 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1174 t
[0] = a22
*a33
- a32
*a23
;
1175 t
[1] = a21
*a33
- a31
*a23
;
1176 t
[2] = a21
*a32
- a31
*a22
;
1177 t
[3] = a20
*a33
- a30
*a23
;
1178 t
[4] = a20
*a32
- a30
*a22
;
1179 t
[5] = a20
*a31
- a30
*a21
;
1181 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1182 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1183 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1184 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1186 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1187 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1188 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1189 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1191 t
[0] = a12
*a33
- a32
*a13
;
1192 t
[1] = a11
*a33
- a31
*a13
;
1193 t
[2] = a11
*a32
- a31
*a12
;
1194 t
[3] = a10
*a33
- a30
*a13
;
1195 t
[4] = a10
*a32
- a30
*a12
;
1196 t
[5] = a10
*a31
- a30
*a11
;
1198 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1199 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1200 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1201 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1203 t
[0] = a12
*a23
- a22
*a13
;
1204 t
[1] = a11
*a23
- a21
*a13
;
1205 t
[2] = a11
*a22
- a21
*a12
;
1206 t
[3] = a10
*a23
- a20
*a13
;
1207 t
[4] = a10
*a22
- a20
*a12
;
1208 t
[5] = a10
*a21
- a20
*a11
;
1210 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1211 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1212 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1213 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1215 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1216 v4_muls( d
[0], det
, d
[0] );
1217 v4_muls( d
[1], det
, d
[1] );
1218 v4_muls( d
[2], det
, d
[2] );
1219 v4_muls( d
[3], det
, d
[3] );
1223 * Planes (double precision)
1225 static inline void tri_to_plane( double a
[3], double b
[3],
1226 double c
[3], double p
[4] )
1232 edge0
[0] = b
[0] - a
[0];
1233 edge0
[1] = b
[1] - a
[1];
1234 edge0
[2] = b
[2] - a
[2];
1236 edge1
[0] = c
[0] - a
[0];
1237 edge1
[1] = c
[1] - a
[1];
1238 edge1
[2] = c
[2] - a
[2];
1240 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1241 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1242 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1244 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1245 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1252 static inline int plane_intersect( double a
[4], double b
[4],
1253 double c
[4], double p
[4] )
1255 double const epsilon
= 1e-8f
;
1260 x
[0] = a
[1] * b
[2] - a
[2] * b
[1];
1261 x
[1] = a
[2] * b
[0] - a
[0] * b
[2];
1262 x
[2] = a
[0] * b
[1] - a
[1] * b
[0];
1264 d
= x
[0] * c
[0] + x
[1] * c
[1] + x
[2] * c
[2];
1266 if( d
< epsilon
&& d
> -epsilon
) return 0;
1268 p
[0] = (b
[1] * c
[2] - b
[2] * c
[1]) * -a
[3];
1269 p
[1] = (b
[2] * c
[0] - b
[0] * c
[2]) * -a
[3];
1270 p
[2] = (b
[0] * c
[1] - b
[1] * c
[0]) * -a
[3];
1272 p
[0] += (c
[1] * a
[2] - c
[2] * a
[1]) * -b
[3];
1273 p
[1] += (c
[2] * a
[0] - c
[0] * a
[2]) * -b
[3];
1274 p
[2] += (c
[0] * a
[1] - c
[1] * a
[0]) * -b
[3];
1276 p
[0] += (a
[1] * b
[2] - a
[2] * b
[1]) * -c
[3];
1277 p
[1] += (a
[2] * b
[0] - a
[0] * b
[2]) * -c
[3];
1278 p
[2] += (a
[0] * b
[1] - a
[1] * b
[0]) * -c
[3];
1287 static inline double plane_polarity( double p
[4], double a
[3] )
1290 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1291 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1297 static inline void q_identity( v4f q
)
1299 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
1302 static inline void q_axis_angle( v4f q
, v3f axis
, float angle
)
1304 float a
= angle
*0.5f
,
1314 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
1317 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
1318 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
1319 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
1320 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
1324 static inline void q_normalize( v4f q
)
1326 float s
= 1.0f
/ sqrtf(v4_dot(q
,q
));
1333 static inline void q_inv( v4f q
, v4f d
)
1335 float s
= 1.0f
/ v4_dot(q
,q
);
1342 static inline void q_nlerp( v4f a
, v4f b
, float t
, v4f d
)
1344 if( v4_dot(a
,b
) < 0.0f
)
1346 v4_muls( b
, -1.0f
, d
);
1347 v4_lerp( a
, d
, t
, d
);
1350 v4_lerp( a
, b
, t
, d
);
1355 static inline void q_m3x3( v4f q
, m3x3f d
)
1359 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
1361 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
1362 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
1363 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
1365 d
[0][0] = 1.0f
- yy
- zz
;
1366 d
[1][1] = 1.0f
- xx
- zz
;
1367 d
[2][2] = 1.0f
- xx
- yy
;
1376 static void m3x3_q( m3x3f m
, v4f q
)
1378 float diag
, r
, rinv
;
1380 diag
= m
[0][0] + m
[1][1] + m
[2][2];
1383 r
= sqrtf( 1.0f
+ diag
);
1385 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
1386 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
1387 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
1390 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
1392 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
1395 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
1396 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
1397 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
1399 else if( m
[1][1] >= m
[2][2] )
1401 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
1403 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
1405 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
1406 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
1410 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
1412 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
1413 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
1415 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
1421 k_contact_type_default
,
1422 k_contact_type_disabled
,
1427 * -----------------------------------------------------------------------------
1428 * Closest point functions
1429 * -----------------------------------------------------------------------------
1433 * These closest point tests were learned from Real-Time Collision Detection by
1436 VG_STATIC
float closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1437 float *s
, float *t
, v3f c1
, v3f c2
)
1440 v3_sub( q1
, p1
, d1
);
1441 v3_sub( q2
, p2
, d2
);
1442 v3_sub( p1
, p2
, r
);
1444 float a
= v3_length2( d1
),
1445 e
= v3_length2( d2
),
1446 f
= v3_dot( d2
, r
);
1448 const float kEpsilon
= 0.0001f
;
1450 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1458 v3_sub( c1
, c2
, v0
);
1460 return v3_length2( v0
);
1466 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1470 float c
= v3_dot( d1
, r
);
1474 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1478 float b
= v3_dot(d1
,d2
),
1483 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1490 *t
= (b
*(*s
)+f
) / e
;
1495 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1497 else if( *t
> 1.0f
)
1500 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1505 v3_muladds( p1
, d1
, *s
, c1
);
1506 v3_muladds( p2
, d2
, *t
, c2
);
1509 v3_sub( c1
, c2
, v0
);
1510 return v3_length2( v0
);
1513 VG_STATIC
void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1515 v3_maxv( p
, box
[0], dest
);
1516 v3_minv( dest
, box
[1], dest
);
1519 VG_STATIC
void closest_point_obb( v3f p
, boxf box
,
1520 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1523 m4x3_mulv( inv_mtx
, p
, local
);
1524 closest_point_aabb( local
, box
, local
);
1525 m4x3_mulv( mtx
, local
, dest
);
1528 VG_STATIC
float closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1532 v3_sub( point
, a
, v1
);
1534 float t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1535 t
= vg_clampf(t
,0.0f
,1.0f
);
1536 v3_muladds( a
, v0
, t
, dest
);
1540 VG_STATIC
void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1545 /* Region outside A */
1546 v3_sub( tri
[1], tri
[0], ab
);
1547 v3_sub( tri
[2], tri
[0], ac
);
1548 v3_sub( p
, tri
[0], ap
);
1552 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1554 v3_copy( tri
[0], dest
);
1555 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1559 /* Region outside B */
1563 v3_sub( p
, tri
[1], bp
);
1564 d3
= v3_dot( ab
, bp
);
1565 d4
= v3_dot( ac
, bp
);
1567 if( d3
>= 0.0f
&& d4
<= d3
)
1569 v3_copy( tri
[1], dest
);
1570 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1574 /* Edge region of AB */
1575 float vc
= d1
*d4
- d3
*d2
;
1576 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1578 float v
= d1
/ (d1
-d3
);
1579 v3_muladds( tri
[0], ab
, v
, dest
);
1580 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1584 /* Region outside C */
1587 v3_sub( p
, tri
[2], cp
);
1588 d5
= v3_dot(ab
, cp
);
1589 d6
= v3_dot(ac
, cp
);
1591 if( d6
>= 0.0f
&& d5
<= d6
)
1593 v3_copy( tri
[2], dest
);
1594 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1599 float vb
= d5
*d2
- d1
*d6
;
1600 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1602 float w
= d2
/ (d2
-d6
);
1603 v3_muladds( tri
[0], ac
, w
, dest
);
1604 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1609 float va
= d3
*d6
- d5
*d4
;
1610 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1612 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1614 v3_sub( tri
[2], tri
[1], bc
);
1615 v3_muladds( tri
[1], bc
, w
, dest
);
1616 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1620 /* P inside region, Q via barycentric coordinates uvw */
1621 float d
= 1.0f
/(va
+vb
+vc
),
1625 v3_muladds( tri
[0], ab
, v
, dest
);
1626 v3_muladds( dest
, ac
, w
, dest
);
1629 VG_STATIC
enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1634 /* Region outside A */
1635 v3_sub( tri
[1], tri
[0], ab
);
1636 v3_sub( tri
[2], tri
[0], ac
);
1637 v3_sub( p
, tri
[0], ap
);
1641 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1643 v3_copy( tri
[0], dest
);
1644 return k_contact_type_default
;
1647 /* Region outside B */
1651 v3_sub( p
, tri
[1], bp
);
1652 d3
= v3_dot( ab
, bp
);
1653 d4
= v3_dot( ac
, bp
);
1655 if( d3
>= 0.0f
&& d4
<= d3
)
1657 v3_copy( tri
[1], dest
);
1658 return k_contact_type_edge
;
1661 /* Edge region of AB */
1662 float vc
= d1
*d4
- d3
*d2
;
1663 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1665 float v
= d1
/ (d1
-d3
);
1666 v3_muladds( tri
[0], ab
, v
, dest
);
1667 return k_contact_type_edge
;
1670 /* Region outside C */
1673 v3_sub( p
, tri
[2], cp
);
1674 d5
= v3_dot(ab
, cp
);
1675 d6
= v3_dot(ac
, cp
);
1677 if( d6
>= 0.0f
&& d5
<= d6
)
1679 v3_copy( tri
[2], dest
);
1680 return k_contact_type_edge
;
1684 float vb
= d5
*d2
- d1
*d6
;
1685 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1687 float w
= d2
/ (d2
-d6
);
1688 v3_muladds( tri
[0], ac
, w
, dest
);
1689 return k_contact_type_edge
;
1693 float va
= d3
*d6
- d5
*d4
;
1694 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1696 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1698 v3_sub( tri
[2], tri
[1], bc
);
1699 v3_muladds( tri
[1], bc
, w
, dest
);
1700 return k_contact_type_edge
;
1703 /* P inside region, Q via barycentric coordinates uvw */
1704 float d
= 1.0f
/(va
+vb
+vc
),
1708 v3_muladds( tri
[0], ab
, v
, dest
);
1709 v3_muladds( dest
, ac
, w
, dest
);
1711 return k_contact_type_default
;
1715 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1717 v2f pabs
, ei
, e2
, ve
, t
;
1720 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1722 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1724 v2_fill( t
, 0.70710678118654752f
);
1726 for( int i
=0; i
<3; i
++ )
1730 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1734 v2_sub( pabs
, v
, u
);
1738 v2_sub( ud
, v
, ud
);
1740 v2_muls( u
, v2_length( ud
), u
);
1745 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1750 v2_copysign( o
, p
);
1757 /* Time of intersection with ray vs triangle */
1758 static int ray_tri( v3f tri
[3], v3f co
,
1759 v3f dir
, float *dist
)
1761 float const kEpsilon
= 0.00001f
;
1763 v3f v0
, v1
, h
, s
, q
, n
;
1770 v3_sub( pb
, pa
, v0
);
1771 v3_sub( pc
, pa
, v1
);
1772 v3_cross( dir
, v1
, h
);
1773 v3_cross( v0
, v1
, n
);
1775 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
1779 a
= v3_dot( v0
, h
);
1780 if( a
> -kEpsilon
&& a
< kEpsilon
)
1784 v3_sub( co
, pa
, s
);
1786 u
= f
* v3_dot(s
, h
);
1787 if( u
< 0.0f
|| u
> 1.0f
)
1790 v3_cross( s
, v0
, q
);
1791 v
= f
* v3_dot( dir
, q
);
1792 if( v
< 0.0f
|| u
+v
> 1.0f
)
1795 t
= f
* v3_dot(v1
, q
);
1804 /* time of intersection with ray vs sphere */
1805 static int ray_sphere( v3f c
, float r
,
1806 v3f co
, v3f dir
, float *t
)
1811 float b
= v3_dot( m
, dir
),
1812 c1
= v3_dot( m
, m
) - r
*r
;
1814 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
1815 if( c1
> 0.0f
&& b
> 0.0f
)
1818 float discr
= b
*b
- c1
;
1820 /* A negative discriminant corresponds to ray missing sphere */
1825 * Ray now found to intersect sphere, compute smallest t value of
1828 *t
= -b
- sqrtf( discr
);
1830 /* If t is negative, ray started inside sphere so clamp t to zero */
1838 * time of intersection of ray vs cylinder
1839 * The cylinder does not have caps but is finite
1841 * Heavily adapted from regular segment vs cylinder from:
1842 * Real-Time Collision Detection
1844 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, float r
,
1845 v3f co
, v3f dir
, float *t
)
1848 v3_muladds( co
, dir
, 1.0f
, sb
);
1852 v3_sub( sb
, co
, n
);
1854 float md
= v3_dot( m
, d
),
1855 nd
= v3_dot( n
, d
),
1856 dd
= v3_dot( d
, d
),
1857 nn
= v3_dot( n
, n
),
1858 mn
= v3_dot( m
, n
),
1860 k
= v3_dot( m
, m
) - r
*r
,
1863 if( fabsf(a
) < 0.00001f
)
1865 /* Segment runs parallel to cylinder axis */
1869 float b
= dd
*mn
- nd
*md
,
1873 return 0; /* No real roots; no intersection */
1875 *t
= (-b
- sqrtf(discr
)) / a
;
1877 return 0; /* Intersection behind ray */
1879 /* Check within cylinder segment */
1880 if( md
+ (*t
)*nd
< 0.0f
)
1883 if( md
+ (*t
)*nd
> dd
)
1886 /* Segment intersects cylinder between the endcaps; t is correct */
1891 * Time of intersection of sphere and triangle. Origin must be outside the
1892 * colliding area. This is a fairly long procedure.
1894 static int spherecast_triangle( v3f tri
[3],
1895 v3f co
, v3f dir
, float r
, float *t
, v3f n
)
1900 v3_sub( tri
[1], tri
[0], v0
);
1901 v3_sub( tri
[2], tri
[0], v1
);
1902 v3_cross( v0
, v1
, n
);
1904 v3_muladds( tri
[0], n
, r
, sum
[0] );
1905 v3_muladds( tri
[1], n
, r
, sum
[1] );
1906 v3_muladds( tri
[2], n
, r
, sum
[2] );
1909 float t_min
= INFINITY
,
1912 if( ray_tri( sum
, co
, dir
, &t1
) )
1914 t_min
= vg_minf( t_min
, t1
);
1919 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
1922 for( int i
=0; i
<3; i
++ )
1924 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) )
1926 t_min
= vg_minf( t_min
, t1
);
1932 for( int i
=0; i
<3; i
++ )
1937 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) )
1944 v3_add( dir
, co
, co1
);
1945 v3_lerp( co
, co1
, t_min
, ct
);
1947 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
1948 v3_sub( ct
, cx
, n
);
1960 static inline float vg_randf(void)
1962 return (float)rand()/(float)(RAND_MAX
);
1965 static inline void vg_rand_dir(v3f dir
)
1967 dir
[0] = vg_randf();
1968 dir
[1] = vg_randf();
1969 dir
[2] = vg_randf();
1971 v3_muls( dir
, 2.0f
, dir
);
1972 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
1974 v3_normalize( dir
);
1977 static inline void vg_rand_sphere( v3f co
)
1980 v3_muls( co
, cbrtf( vg_randf() ), co
);
1983 static inline int vg_randint(int max
)
1988 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, float t
, v3f p
)
1993 v3_muls( p1
, ttt
, p
);
1994 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
1995 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
1996 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);