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
);
60 __attribute__ ((deprecated
))
61 static float stable_force( float current
, float diff
)
63 float fnew
= current
+ diff
;
65 if( fnew
* current
< 0.0f
)
71 static float vg_cfrictf( float current
, float F
)
73 return -vg_signf(current
) * vg_minf( F
, fabsf(current
) );
76 static inline int vg_min( int a
, int b
)
81 static inline int vg_max( int a
, int b
)
86 static inline float vg_rad( float deg
)
88 return deg
* VG_PIf
/ 180.0f
;
94 static inline void v2_copy( v2f a
, v2f b
)
96 b
[0] = a
[0]; b
[1] = a
[1];
99 static inline void v2_zero( v2f a
)
101 a
[0] = 0.f
; a
[1] = 0.f
;
104 static inline void v2i_copy( v2i a
, v2i b
)
106 b
[0] = a
[0]; b
[1] = a
[1];
109 static inline int v2i_eq( v2i a
, v2i b
)
111 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
114 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
116 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
119 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
121 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
124 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
126 dest
[0] = vg_minf(a
[0], b
[0]);
127 dest
[1] = vg_minf(a
[1], b
[1]);
130 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
132 dest
[0] = vg_maxf(a
[0], b
[0]);
133 dest
[1] = vg_maxf(a
[1], b
[1]);
136 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
138 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
141 static inline float v2_dot( v2f a
, v2f b
)
143 return a
[0] * b
[0] + a
[1] * b
[1];
146 static inline float v2_cross( v2f a
, v2f b
)
148 return a
[0]*b
[1] - a
[1]*b
[0];
151 static inline void v2_add( v2f a
, v2f b
, v2f d
)
153 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
156 static inline void v2_abs( v2f a
, v2f d
)
158 d
[0] = fabsf( a
[0] );
159 d
[1] = fabsf( a
[1] );
162 static inline void v2_muls( v2f a
, float s
, v2f d
)
164 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
167 static inline void v2_divs( v2f a
, float s
, v2f d
)
169 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
172 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
178 static inline void v2_div( v2f a
, v2f b
, v2f d
)
180 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
183 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
185 d
[0] = a
[0]+b
[0]*s
[0];
186 d
[1] = a
[1]+b
[1]*s
[1];
189 static inline void v2_muladds( v2f a
, v2f b
, float s
, v2f d
)
195 static inline float v2_length2( v2f a
)
197 return a
[0]*a
[0] + a
[1]*a
[1];
200 static inline float v2_length( v2f a
)
202 return sqrtf( v2_length2( a
) );
205 static inline float v2_dist2( v2f a
, v2f b
)
208 v2_sub( a
, b
, delta
);
209 return v2_length2( delta
);
212 static inline float v2_dist( v2f a
, v2f b
)
214 return sqrtf( v2_dist2( a
, b
) );
217 static inline void v2_lerp( v2f a
, v2f b
, float t
, v2f d
)
219 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
220 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
223 static inline void v2_normalize( v2f a
)
225 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
228 static void v2_normalize_clamp( v2f a
)
230 float l2
= v2_length2( a
);
232 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
235 static inline void v2_floor( v2f a
, v2f b
)
237 b
[0] = floorf( a
[0] );
238 b
[1] = floorf( a
[1] );
241 static inline void v2_fill( v2f a
, float v
)
247 /* copysign of b to a */
248 static inline void v2_copysign( v2f a
, v2f b
)
250 a
[0] = copysignf( a
[0], b
[0] );
251 a
[1] = copysignf( a
[1], b
[1] );
257 static inline void v3_zero( v3f a
)
259 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
262 static inline void v3_copy( v3f a
, v3f b
)
264 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
267 static inline void v3_add( v3f a
, v3f b
, v3f d
)
269 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
272 static inline void v4_add( v4f a
, v4f b
, v4f d
)
280 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
282 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
285 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
287 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
290 static inline void v3_div( v3f a
, v3f b
, v3f d
)
292 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
293 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
294 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
297 static inline void v3_muls( v3f a
, float s
, v3f d
)
299 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
302 static inline void v3_fill( v3f a
, float v
)
309 static inline void v3_divs( v3f a
, float s
, v3f d
)
312 v3_fill( d
, INFINITY
);
321 static inline void v3_muladds( v3f a
, v3f b
, float s
, v3f d
)
323 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
326 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
328 d
[0] = a
[0]+b
[0]*s
[0];
329 d
[1] = a
[1]+b
[1]*s
[1];
330 d
[2] = a
[2]+b
[2]*s
[2];
333 static inline float v3_dot( v3f a
, v3f b
)
335 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
338 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
341 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
342 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
343 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
347 static inline float v3_length2( v3f a
)
349 return v3_dot( a
, a
);
352 static inline float v3_length( v3f a
)
354 return sqrtf( v3_length2( a
) );
357 static inline float v3_dist2( v3f a
, v3f b
)
360 v3_sub( a
, b
, delta
);
361 return v3_length2( delta
);
364 static inline float v3_dist( v3f a
, v3f b
)
366 return sqrtf( v3_dist2( a
, b
) );
369 static inline void v3_normalize( v3f a
)
371 v3_muls( a
, 1.f
/ v3_length( a
), a
);
374 static inline float vg_lerpf( float a
, float b
, float t
)
379 static inline double vg_lerp( double a
, double b
, double t
)
384 /* correctly lerp around circular period -pi -> pi */
385 static float vg_alerpf( float a
, float b
, float t
)
387 float d
= fmodf( b
-a
, VG_TAUf
),
388 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
392 static inline void v3_lerp( v3f a
, v3f b
, float t
, v3f d
)
394 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
395 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
396 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
399 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
401 dest
[0] = vg_minf(a
[0], b
[0]);
402 dest
[1] = vg_minf(a
[1], b
[1]);
403 dest
[2] = vg_minf(a
[2], b
[2]);
406 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
408 dest
[0] = vg_maxf(a
[0], b
[0]);
409 dest
[1] = vg_maxf(a
[1], b
[1]);
410 dest
[2] = vg_maxf(a
[2], b
[2]);
413 static inline float v3_minf( v3f a
)
415 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
418 static inline float v3_maxf( v3f a
)
420 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
423 static inline void v3_floor( v3f a
, v3f b
)
425 b
[0] = floorf( a
[0] );
426 b
[1] = floorf( a
[1] );
427 b
[2] = floorf( a
[2] );
430 static inline void v3_ceil( v3f a
, v3f b
)
432 b
[0] = ceilf( a
[0] );
433 b
[1] = ceilf( a
[1] );
434 b
[2] = ceilf( a
[2] );
437 static inline void v3_negate( v3f a
, v3f b
)
444 static inline void v3_rotate( v3f v
, float angle
, v3f axis
, v3f d
)
455 v3_cross( k
, v
, v2
);
456 v3_muls( v2
, s
, v2
);
457 v3_add( v1
, v2
, v1
);
458 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
465 static inline void v4_copy( v4f a
, v4f b
)
467 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
470 static inline void v4_zero( v4f a
)
472 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
475 static inline void v4_muls( v4f a
, float s
, v4f d
)
483 static inline void v4_muladds( v4f a
, v4f b
, float s
, v4f d
)
491 static inline void v4_lerp( v4f a
, v4f b
, float t
, v4f d
)
493 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
494 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
495 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
496 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
499 static inline float v4_dot( v4f a
, v4f b
)
501 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
504 static inline float v4_length( v4f a
)
506 return sqrtf( v4_dot(a
,a
) );
513 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
516 #define M2X2_ZERO {{0.0f, 0.0f, }, \
519 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
521 v2_copy( a
[0], b
[0] );
522 v2_copy( a
[1], b
[1] );
525 static inline void m2x2_identity( m2x2f a
)
527 m2x2f id
= M2X2_INDENTIY
;
531 static inline void m2x2_create_rotation( m2x2f a
, float theta
)
548 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
549 { 0.0f, 1.0f, 0.0f, },\
550 { 0.0f, 0.0f, 1.0f, }}
552 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
553 { 0.0f, 0.0f, 0.0f, },\
554 { 0.0f, 0.0f, 0.0f, }}
557 /* a X b == [b]T a == ...*/
558 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
571 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
573 v3_add( a
[0], b
[0], d
[0] );
574 v3_add( a
[1], b
[1], d
[1] );
575 v3_add( a
[2], b
[2], d
[2] );
578 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
580 v3_copy( a
[0], b
[0] );
581 v3_copy( a
[1], b
[1] );
582 v3_copy( a
[2], b
[2] );
585 static inline void m3x3_identity( m3x3f a
)
587 m3x3f id
= M3X3_IDENTITY
;
591 static void m3x3_diagonal( m3x3f a
, float v
)
599 static inline void m3x3_zero( m3x3f a
)
605 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
607 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
608 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
609 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
616 dest
[0][0] = (e
*i
-h
*f
)*det
;
617 dest
[0][1] = -(b
*i
-c
*h
)*det
;
618 dest
[0][2] = (b
*f
-c
*e
)*det
;
619 dest
[1][0] = -(d
*i
-f
*g
)*det
;
620 dest
[1][1] = (a
*i
-c
*g
)*det
;
621 dest
[1][2] = -(a
*f
-d
*c
)*det
;
622 dest
[2][0] = (d
*h
-g
*e
)*det
;
623 dest
[2][1] = -(a
*h
-g
*b
)*det
;
624 dest
[2][2] = (a
*e
-d
*b
)*det
;
627 static float m3x3_det( m3x3f m
)
629 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
630 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
631 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
634 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
636 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
637 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
638 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
651 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
653 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
654 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
655 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
657 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
658 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
659 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
661 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
662 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
663 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
664 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
665 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
666 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
667 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
668 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
669 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
672 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
676 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
677 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
678 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
683 static inline void m3x3_projection( m3x3f dst
,
684 float const left
, float const right
, float const bottom
, float const top
)
690 rl
= 1.0f
/ (right
- left
);
691 tb
= 1.0f
/ (top
- bottom
);
693 dst
[0][0] = 2.0f
* rl
;
694 dst
[1][1] = 2.0f
* tb
;
698 static inline void m3x3_translate( m3x3f m
, v3f v
)
700 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
701 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
702 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
705 static inline void m3x3_scale( m3x3f m
, v3f v
)
707 m
[0][0] = m
[0][0] * v
[0];
708 m
[0][1] = m
[0][1] * v
[0];
709 m
[0][2] = m
[0][2] * v
[0];
711 m
[1][0] = m
[1][0] * v
[1];
712 m
[1][1] = m
[1][1] * v
[1];
713 m
[1][2] = m
[1][2] * v
[1];
716 static inline void m3x3_rotate( m3x3f m
, float angle
)
718 float m00
= m
[0][0], m10
= m
[1][0],
719 m01
= m
[0][1], m11
= m
[1][1],
720 m02
= m
[0][2], m12
= m
[1][2];
726 m
[0][0] = m00
* c
+ m10
* s
;
727 m
[0][1] = m01
* c
+ m11
* s
;
728 m
[0][2] = m02
* c
+ m12
* s
;
730 m
[1][0] = m00
* -s
+ m10
* c
;
731 m
[1][1] = m01
* -s
+ m11
* c
;
732 m
[1][2] = m02
* -s
+ m12
* c
;
739 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
740 { 0.0f, 1.0f, 0.0f, },\
741 { 0.0f, 0.0f, 1.0f, },\
742 { 0.0f, 0.0f, 0.0f }}
744 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
746 v3_copy( a
[0], b
[0] );
747 v3_copy( a
[1], b
[1] );
748 v3_copy( a
[2], b
[2] );
751 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
753 m3x3_transpose( a
, b
);
754 m3x3_mulv( b
, a
[3], b
[3] );
755 v3_negate( b
[3], b
[3] );
758 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
762 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
763 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
764 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
765 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
771 dst
[0][0] = f
*k
- g
*j
;
772 dst
[1][0] =-(e
*k
- g
*i
);
773 dst
[2][0] = e
*j
- f
*i
;
774 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
776 dst
[0][1] =-(b
*k
- c
*j
);
777 dst
[1][1] = a
*k
- c
*i
;
778 dst
[2][1] =-(a
*j
- b
*i
);
779 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
785 dst
[0][2] = b
*g
- c
*f
;
786 dst
[1][2] =-(a
*g
- c
*e
);
787 dst
[2][2] = a
*f
- b
*e
;
788 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
790 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
791 v3_muls( dst
[0], det
, dst
[0] );
792 v3_muls( dst
[1], det
, dst
[1] );
793 v3_muls( dst
[2], det
, dst
[2] );
794 v3_muls( dst
[3], det
, dst
[3] );
797 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
799 v3_copy( a
[0], b
[0] );
800 v3_copy( a
[1], b
[1] );
801 v3_copy( a
[2], b
[2] );
802 v3_copy( a
[3], b
[3] );
805 static inline void m4x3_identity( m4x3f a
)
807 m4x3f id
= M4X3_IDENTITY
;
811 static inline void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
814 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
815 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
816 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
817 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
818 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
819 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
820 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
821 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
823 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
824 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
825 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
826 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
827 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
828 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
829 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
830 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
831 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
832 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
833 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
834 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
837 static inline void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
841 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
842 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
843 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
849 * Transform plane ( xyz, distance )
851 static inline void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
855 v3_muls( p
, p
[3], o
);
856 m4x3_mulv( m
, o
, o
);
857 m3x3_mulv( m
, p
, d
);
859 d
[3] = v3_dot( o
, d
);
866 static inline void m4x3_translate( m4x3f m
, v3f v
)
868 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
869 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
870 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
873 static inline void m4x3_scale( m4x3f m
, float s
)
875 v3_muls( m
[0], s
, m
[0] );
876 v3_muls( m
[1], s
, m
[1] );
877 v3_muls( m
[2], s
, m
[2] );
880 static inline void m4x3_scalev( m4x3f m
, v3f v
)
882 v3_muls(m
[0], v
[0], m
[0]);
883 v3_muls(m
[1], v
[1], m
[1]);
884 v3_muls(m
[2], v
[2], m
[2]);
887 static inline void m4x3_rotate_x( m4x3f m
, float angle
)
889 m4x3f t
= M4X3_IDENTITY
;
903 static inline void m4x3_rotate_y( m4x3f m
, float angle
)
905 m4x3f t
= M4X3_IDENTITY
;
919 static inline void m4x3_rotate_z( m4x3f m
, float angle
)
921 m4x3f t
= M4X3_IDENTITY
;
935 static inline void m4x3_expand( m4x3f m
, m4x4f d
)
937 v3_copy( m
[0], d
[0] );
938 v3_copy( m
[1], d
[1] );
939 v3_copy( m
[2], d
[2] );
940 v3_copy( m
[3], d
[3] );
947 static inline void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
950 m4x3_mulv( m
, point
, v
);
952 v3_minv( box
[0], v
, box
[0] );
953 v3_maxv( box
[1], v
, box
[1] );
956 static inline void box_addpt( boxf a
, v3f pt
)
958 v3_minv( a
[0], pt
, a
[0] );
959 v3_maxv( a
[1], pt
, a
[1] );
962 static inline void box_concat( boxf a
, boxf b
)
964 v3_minv( a
[0], b
[0], a
[0] );
965 v3_maxv( a
[1], b
[1], a
[1] );
968 static inline void box_copy( boxf a
, boxf b
)
970 v3_copy( a
[0], b
[0] );
971 v3_copy( a
[1], b
[1] );
974 static inline int box_overlap( boxf a
, boxf b
)
977 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
978 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
979 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
983 static int box_within( boxf greater
, boxf lesser
)
986 v3_sub( lesser
[0], greater
[0], a
);
987 v3_sub( lesser
[1], greater
[1], b
);
989 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
990 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
998 static inline void box_init_inf( boxf box
)
1000 v3_fill( box
[0], INFINITY
);
1001 v3_fill( box
[1], -INFINITY
);
1004 static inline void m4x3_transform_aabb( m4x3f m
, boxf box
)
1008 v3_copy( box
[0], a
);
1009 v3_copy( box
[1], b
);
1010 v3_fill( box
[0], INFINITY
);
1011 v3_fill( box
[1], -INFINITY
);
1013 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], a
[2] } );
1014 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
1015 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
1016 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
1018 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], b
[2] } );
1019 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
1020 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
1021 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
1024 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, float dist
)
1029 v3_sub( box
[0], co
, v0
);
1030 v3_sub( box
[1], co
, v1
);
1032 v3_mul( v0
, dir_inv
, v0
);
1033 v3_mul( v1
, dir_inv
, v1
);
1035 tmin
= vg_minf( v0
[0], v1
[0] );
1036 tmax
= vg_maxf( v0
[0], v1
[0] );
1037 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
1038 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
1039 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
1040 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
1042 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
1045 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1048 v3_sub( target
, pos
, dir
);
1049 v3_normalize( dir
);
1051 v3_copy( dir
, m
[2] );
1053 v3_cross( up
, m
[2], m
[0] );
1054 v3_normalize( m
[0] );
1056 v3_cross( m
[2], m
[0], m
[1] );
1057 v3_copy( pos
, m
[3] );
1064 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1065 { 0.0f, 1.0f, 0.0f, 0.0f },\
1066 { 0.0f, 0.0f, 1.0f, 0.0f },\
1067 { 0.0f, 0.0f, 0.0f, 1.0f }}
1068 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1069 { 0.0f, 0.0f, 0.0f, 0.0f },\
1070 { 0.0f, 0.0f, 0.0f, 0.0f },\
1071 { 0.0f, 0.0f, 0.0f, 0.0f }}
1073 static void m4x4_projection( m4x4f m
, float angle
,
1074 float ratio
, float fnear
, float ffar
)
1076 float scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1082 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1088 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1092 m
[2][0] = (r
+ l
) / (r
- l
);
1093 m
[2][1] = (t
+ b
) / (t
- b
);
1094 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1099 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1103 static void m4x4_translate( m4x4f m
, v3f v
)
1105 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1106 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1107 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1110 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1112 v4_copy( a
[0], b
[0] );
1113 v4_copy( a
[1], b
[1] );
1114 v4_copy( a
[2], b
[2] );
1115 v4_copy( a
[3], b
[3] );
1118 static inline void m4x4_identity( m4x4f a
)
1120 m4x4f id
= M4X4_IDENTITY
;
1124 static inline void m4x4_zero( m4x4f a
)
1126 m4x4f zero
= M4X4_ZERO
;
1127 m4x4_copy( zero
, a
);
1130 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1132 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1133 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1134 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1135 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1137 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1138 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1139 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1140 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1142 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1143 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1144 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1145 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1146 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1147 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1148 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1149 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1150 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1151 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1152 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1153 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1154 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1155 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1156 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1157 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1160 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1164 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1165 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1166 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1167 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1172 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1174 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1175 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1176 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1177 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1181 t
[0] = a22
*a33
- a32
*a23
;
1182 t
[1] = a21
*a33
- a31
*a23
;
1183 t
[2] = a21
*a32
- a31
*a22
;
1184 t
[3] = a20
*a33
- a30
*a23
;
1185 t
[4] = a20
*a32
- a30
*a22
;
1186 t
[5] = a20
*a31
- a30
*a21
;
1188 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1189 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1190 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1191 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1193 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1194 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1195 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1196 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1198 t
[0] = a12
*a33
- a32
*a13
;
1199 t
[1] = a11
*a33
- a31
*a13
;
1200 t
[2] = a11
*a32
- a31
*a12
;
1201 t
[3] = a10
*a33
- a30
*a13
;
1202 t
[4] = a10
*a32
- a30
*a12
;
1203 t
[5] = a10
*a31
- a30
*a11
;
1205 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1206 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1207 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1208 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1210 t
[0] = a12
*a23
- a22
*a13
;
1211 t
[1] = a11
*a23
- a21
*a13
;
1212 t
[2] = a11
*a22
- a21
*a12
;
1213 t
[3] = a10
*a23
- a20
*a13
;
1214 t
[4] = a10
*a22
- a20
*a12
;
1215 t
[5] = a10
*a21
- a20
*a11
;
1217 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1218 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1219 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1220 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1222 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1223 v4_muls( d
[0], det
, d
[0] );
1224 v4_muls( d
[1], det
, d
[1] );
1225 v4_muls( d
[2], det
, d
[2] );
1226 v4_muls( d
[3], det
, d
[3] );
1230 * Planes (double precision)
1232 static inline void tri_to_plane( double a
[3], double b
[3],
1233 double c
[3], double p
[4] )
1239 edge0
[0] = b
[0] - a
[0];
1240 edge0
[1] = b
[1] - a
[1];
1241 edge0
[2] = b
[2] - a
[2];
1243 edge1
[0] = c
[0] - a
[0];
1244 edge1
[1] = c
[1] - a
[1];
1245 edge1
[2] = c
[2] - a
[2];
1247 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1248 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1249 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1251 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1252 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1259 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1261 float const epsilon
= 1e-6f
;
1264 v3_cross( a
, b
, x
);
1265 float d
= v3_dot( x
, c
);
1267 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1270 v3_cross( b
, c
, v0
);
1271 v3_cross( c
, a
, v1
);
1272 v3_cross( a
, b
, v2
);
1274 v3_muls( v0
, a
[3], p
);
1275 v3_muladds( p
, v1
, b
[3], p
);
1276 v3_muladds( p
, v2
, c
[3], p
);
1282 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1284 float const epsilon
= 1e-6f
;
1287 v3_cross( a
, b
, c
);
1288 float d
= v3_length2( c
);
1290 if( (d
< epsilon
) && (d
> -epsilon
) )
1294 v3_cross( c
, b
, v0
);
1295 v3_cross( a
, c
, v1
);
1297 v3_muls( v0
, a
[3], vx
);
1298 v3_muladds( vx
, v1
, b
[3], vx
);
1299 v3_divs( vx
, d
, p
);
1306 static inline double plane_polarity( double p
[4], double a
[3] )
1309 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1310 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1316 static inline void q_identity( v4f q
)
1318 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
1321 static inline void q_axis_angle( v4f q
, v3f axis
, float angle
)
1323 float a
= angle
*0.5f
,
1333 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
1336 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
1337 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
1338 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
1339 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
1343 static inline void q_normalize( v4f q
)
1345 float s
= 1.0f
/ sqrtf(v4_dot(q
,q
));
1352 static inline void q_inv( v4f q
, v4f d
)
1354 float s
= 1.0f
/ v4_dot(q
,q
);
1361 static inline void q_nlerp( v4f a
, v4f b
, float t
, v4f d
)
1363 if( v4_dot(a
,b
) < 0.0f
)
1365 v4_muls( b
, -1.0f
, d
);
1366 v4_lerp( a
, d
, t
, d
);
1369 v4_lerp( a
, b
, t
, d
);
1374 static void euler_m3x3( v3f angles
, m3x3f d
)
1376 float cosY
= cosf( angles
[0] ),
1377 sinY
= sinf( angles
[0] ),
1378 cosP
= cosf( angles
[1] ),
1379 sinP
= sinf( angles
[1] ),
1380 cosR
= cosf( angles
[2] ),
1381 sinR
= sinf( angles
[2] );
1383 d
[2][0] = -sinY
* cosP
;
1385 d
[2][2] = cosY
* cosP
;
1387 d
[0][0] = cosY
* cosR
;
1389 d
[0][2] = sinY
* cosR
;
1391 v3_cross( d
[0], d
[2], d
[1] );
1394 static inline void q_m3x3( v4f q
, m3x3f d
)
1398 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
1400 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
1401 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
1402 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
1404 d
[0][0] = 1.0f
- yy
- zz
;
1405 d
[1][1] = 1.0f
- xx
- zz
;
1406 d
[2][2] = 1.0f
- xx
- yy
;
1415 static void m3x3_q( m3x3f m
, v4f q
)
1417 float diag
, r
, rinv
;
1419 diag
= m
[0][0] + m
[1][1] + m
[2][2];
1422 r
= sqrtf( 1.0f
+ diag
);
1424 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
1425 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
1426 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
1429 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
1431 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
1434 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
1435 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
1436 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
1438 else if( m
[1][1] >= m
[2][2] )
1440 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
1442 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
1444 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
1445 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
1449 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
1451 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
1452 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
1454 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
1460 k_contact_type_default
,
1461 k_contact_type_disabled
,
1466 * -----------------------------------------------------------------------------
1467 * Closest point functions
1468 * -----------------------------------------------------------------------------
1472 * These closest point tests were learned from Real-Time Collision Detection by
1475 VG_STATIC
float closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1476 float *s
, float *t
, v3f c1
, v3f c2
)
1479 v3_sub( q1
, p1
, d1
);
1480 v3_sub( q2
, p2
, d2
);
1481 v3_sub( p1
, p2
, r
);
1483 float a
= v3_length2( d1
),
1484 e
= v3_length2( d2
),
1485 f
= v3_dot( d2
, r
);
1487 const float kEpsilon
= 0.0001f
;
1489 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1497 v3_sub( c1
, c2
, v0
);
1499 return v3_length2( v0
);
1505 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1509 float c
= v3_dot( d1
, r
);
1513 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1517 float b
= v3_dot(d1
,d2
),
1522 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1529 *t
= (b
*(*s
)+f
) / e
;
1534 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1536 else if( *t
> 1.0f
)
1539 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1544 v3_muladds( p1
, d1
, *s
, c1
);
1545 v3_muladds( p2
, d2
, *t
, c2
);
1548 v3_sub( c1
, c2
, v0
);
1549 return v3_length2( v0
);
1552 VG_STATIC
void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1554 v3_maxv( p
, box
[0], dest
);
1555 v3_minv( dest
, box
[1], dest
);
1558 VG_STATIC
void closest_point_obb( v3f p
, boxf box
,
1559 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1562 m4x3_mulv( inv_mtx
, p
, local
);
1563 closest_point_aabb( local
, box
, local
);
1564 m4x3_mulv( mtx
, local
, dest
);
1567 VG_STATIC
float closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1571 v3_sub( point
, a
, v1
);
1573 float t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1574 t
= vg_clampf(t
,0.0f
,1.0f
);
1575 v3_muladds( a
, v0
, t
, dest
);
1579 VG_STATIC
void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1584 /* Region outside A */
1585 v3_sub( tri
[1], tri
[0], ab
);
1586 v3_sub( tri
[2], tri
[0], ac
);
1587 v3_sub( p
, tri
[0], ap
);
1591 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1593 v3_copy( tri
[0], dest
);
1594 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1598 /* Region outside B */
1602 v3_sub( p
, tri
[1], bp
);
1603 d3
= v3_dot( ab
, bp
);
1604 d4
= v3_dot( ac
, bp
);
1606 if( d3
>= 0.0f
&& d4
<= d3
)
1608 v3_copy( tri
[1], dest
);
1609 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1613 /* Edge region of AB */
1614 float vc
= d1
*d4
- d3
*d2
;
1615 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1617 float v
= d1
/ (d1
-d3
);
1618 v3_muladds( tri
[0], ab
, v
, dest
);
1619 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1623 /* Region outside C */
1626 v3_sub( p
, tri
[2], cp
);
1627 d5
= v3_dot(ab
, cp
);
1628 d6
= v3_dot(ac
, cp
);
1630 if( d6
>= 0.0f
&& d5
<= d6
)
1632 v3_copy( tri
[2], dest
);
1633 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1638 float vb
= d5
*d2
- d1
*d6
;
1639 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1641 float w
= d2
/ (d2
-d6
);
1642 v3_muladds( tri
[0], ac
, w
, dest
);
1643 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1648 float va
= d3
*d6
- d5
*d4
;
1649 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1651 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1653 v3_sub( tri
[2], tri
[1], bc
);
1654 v3_muladds( tri
[1], bc
, w
, dest
);
1655 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1659 /* P inside region, Q via barycentric coordinates uvw */
1660 float d
= 1.0f
/(va
+vb
+vc
),
1664 v3_muladds( tri
[0], ab
, v
, dest
);
1665 v3_muladds( dest
, ac
, w
, dest
);
1668 VG_STATIC
enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1673 /* Region outside A */
1674 v3_sub( tri
[1], tri
[0], ab
);
1675 v3_sub( tri
[2], tri
[0], ac
);
1676 v3_sub( p
, tri
[0], ap
);
1680 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1682 v3_copy( tri
[0], dest
);
1683 return k_contact_type_default
;
1686 /* Region outside B */
1690 v3_sub( p
, tri
[1], bp
);
1691 d3
= v3_dot( ab
, bp
);
1692 d4
= v3_dot( ac
, bp
);
1694 if( d3
>= 0.0f
&& d4
<= d3
)
1696 v3_copy( tri
[1], dest
);
1697 return k_contact_type_edge
;
1700 /* Edge region of AB */
1701 float vc
= d1
*d4
- d3
*d2
;
1702 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1704 float v
= d1
/ (d1
-d3
);
1705 v3_muladds( tri
[0], ab
, v
, dest
);
1706 return k_contact_type_edge
;
1709 /* Region outside C */
1712 v3_sub( p
, tri
[2], cp
);
1713 d5
= v3_dot(ab
, cp
);
1714 d6
= v3_dot(ac
, cp
);
1716 if( d6
>= 0.0f
&& d5
<= d6
)
1718 v3_copy( tri
[2], dest
);
1719 return k_contact_type_edge
;
1723 float vb
= d5
*d2
- d1
*d6
;
1724 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1726 float w
= d2
/ (d2
-d6
);
1727 v3_muladds( tri
[0], ac
, w
, dest
);
1728 return k_contact_type_edge
;
1732 float va
= d3
*d6
- d5
*d4
;
1733 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1735 float w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1737 v3_sub( tri
[2], tri
[1], bc
);
1738 v3_muladds( tri
[1], bc
, w
, dest
);
1739 return k_contact_type_edge
;
1742 /* P inside region, Q via barycentric coordinates uvw */
1743 float d
= 1.0f
/(va
+vb
+vc
),
1747 v3_muladds( tri
[0], ab
, v
, dest
);
1748 v3_muladds( dest
, ac
, w
, dest
);
1750 return k_contact_type_default
;
1754 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1756 v2f pabs
, ei
, e2
, ve
, t
;
1759 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1761 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1763 v2_fill( t
, 0.70710678118654752f
);
1765 for( int i
=0; i
<3; i
++ )
1769 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1773 v2_sub( pabs
, v
, u
);
1777 v2_sub( ud
, v
, ud
);
1779 v2_muls( u
, v2_length( ud
), u
);
1784 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1789 v2_copysign( o
, p
);
1796 /* Time of intersection with ray vs triangle */
1797 static int ray_tri( v3f tri
[3], v3f co
,
1798 v3f dir
, float *dist
)
1800 float const kEpsilon
= 0.00001f
;
1802 v3f v0
, v1
, h
, s
, q
, n
;
1809 v3_sub( pb
, pa
, v0
);
1810 v3_sub( pc
, pa
, v1
);
1811 v3_cross( dir
, v1
, h
);
1812 v3_cross( v0
, v1
, n
);
1814 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
1818 a
= v3_dot( v0
, h
);
1820 if( a
> -kEpsilon
&& a
< kEpsilon
)
1824 v3_sub( co
, pa
, s
);
1826 u
= f
* v3_dot(s
, h
);
1827 if( u
< 0.0f
|| u
> 1.0f
)
1830 v3_cross( s
, v0
, q
);
1831 v
= f
* v3_dot( dir
, q
);
1832 if( v
< 0.0f
|| u
+v
> 1.0f
)
1835 t
= f
* v3_dot(v1
, q
);
1844 /* time of intersection with ray vs sphere */
1845 static int ray_sphere( v3f c
, float r
,
1846 v3f co
, v3f dir
, float *t
)
1851 float b
= v3_dot( m
, dir
),
1852 c1
= v3_dot( m
, m
) - r
*r
;
1854 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
1855 if( c1
> 0.0f
&& b
> 0.0f
)
1858 float discr
= b
*b
- c1
;
1860 /* A negative discriminant corresponds to ray missing sphere */
1865 * Ray now found to intersect sphere, compute smallest t value of
1868 *t
= -b
- sqrtf( discr
);
1870 /* If t is negative, ray started inside sphere so clamp t to zero */
1878 * time of intersection of ray vs cylinder
1879 * The cylinder does not have caps but is finite
1881 * Heavily adapted from regular segment vs cylinder from:
1882 * Real-Time Collision Detection
1884 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, float r
,
1885 v3f co
, v3f dir
, float *t
)
1888 v3_muladds( co
, dir
, 1.0f
, sb
);
1892 v3_sub( sb
, co
, n
);
1894 float md
= v3_dot( m
, d
),
1895 nd
= v3_dot( n
, d
),
1896 dd
= v3_dot( d
, d
),
1897 nn
= v3_dot( n
, n
),
1898 mn
= v3_dot( m
, n
),
1900 k
= v3_dot( m
, m
) - r
*r
,
1903 if( fabsf(a
) < 0.00001f
)
1905 /* Segment runs parallel to cylinder axis */
1909 float b
= dd
*mn
- nd
*md
,
1913 return 0; /* No real roots; no intersection */
1915 *t
= (-b
- sqrtf(discr
)) / a
;
1917 return 0; /* Intersection behind ray */
1919 /* Check within cylinder segment */
1920 if( md
+ (*t
)*nd
< 0.0f
)
1923 if( md
+ (*t
)*nd
> dd
)
1926 /* Segment intersects cylinder between the endcaps; t is correct */
1931 * Time of intersection of sphere and triangle. Origin must be outside the
1932 * colliding area. This is a fairly long procedure.
1934 static int spherecast_triangle( v3f tri
[3],
1935 v3f co
, v3f dir
, float r
, float *t
, v3f n
)
1940 v3_sub( tri
[1], tri
[0], v0
);
1941 v3_sub( tri
[2], tri
[0], v1
);
1942 v3_cross( v0
, v1
, n
);
1944 v3_muladds( tri
[0], n
, r
, sum
[0] );
1945 v3_muladds( tri
[1], n
, r
, sum
[1] );
1946 v3_muladds( tri
[2], n
, r
, sum
[2] );
1949 float t_min
= INFINITY
,
1952 if( ray_tri( sum
, co
, dir
, &t1
) )
1954 t_min
= vg_minf( t_min
, t1
);
1959 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
1962 for( int i
=0; i
<3; i
++ )
1964 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) )
1966 t_min
= vg_minf( t_min
, t1
);
1972 for( int i
=0; i
<3; i
++ )
1977 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) )
1984 v3_add( dir
, co
, co1
);
1985 v3_lerp( co
, co1
, t_min
, ct
);
1987 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
1988 v3_sub( ct
, cx
, n
);
2000 static inline float vg_randf(void)
2002 return (float)rand()/(float)(RAND_MAX
);
2005 static inline void vg_rand_dir(v3f dir
)
2007 dir
[0] = vg_randf();
2008 dir
[1] = vg_randf();
2009 dir
[2] = vg_randf();
2011 v3_muls( dir
, 2.0f
, dir
);
2012 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2014 v3_normalize( dir
);
2017 static inline void vg_rand_sphere( v3f co
)
2020 v3_muls( co
, cbrtf( vg_randf() ), co
);
2023 static inline int vg_randint(int max
)
2028 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, float t
, v3f p
)
2033 v3_muls( p1
, ttt
, p
);
2034 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2035 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2036 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);