1 /* Copyright (C) 2021-2023 Harry Godden (hgn) - All Rights Reserved
19 * 5.d Raycast & Spherecasts
28 #include "vg_platform.h"
32 #define VG_PIf 3.14159265358979323846264338327950288f
33 #define VG_TAUf 6.28318530717958647692528676655900576f
35 * -----------------------------------------------------------------------------
36 * Section 0. Misc Operations
37 * -----------------------------------------------------------------------------
40 /* get the f32 as the raw bits in a u32 without converting */
41 static u32
vg_ftu32( f32 a
)
43 u32
*ptr
= (u32
*)(&a
);
47 /* check if f32 is infinite */
48 static int vg_isinff( f32 a
)
50 return ((vg_ftu32(a
)) & 0x7FFFFFFFU
) == 0x7F800000U
;
53 /* check if f32 is not a number */
54 static int vg_isnanf( f32 a
)
56 return !vg_isinff(a
) && ((vg_ftu32(a
)) & 0x7F800000U
) == 0x7F800000U
;
59 /* check if f32 is a number and is not infinite */
60 static int vg_validf( f32 a
)
62 return ((vg_ftu32(a
)) & 0x7F800000U
) != 0x7F800000U
;
66 * -----------------------------------------------------------------------------
67 * Section 1. Scalar Operations
68 * -----------------------------------------------------------------------------
71 static inline f32
vg_minf( f32 a
, f32 b
){ return a
< b
? a
: b
; }
72 static inline f32
vg_maxf( f32 a
, f32 b
){ return a
> b
? a
: b
; }
74 static inline int vg_min( int a
, int b
){ return a
< b
? a
: b
; }
75 static inline int vg_max( int a
, int b
){ return a
> b
? a
: b
; }
77 static inline f32
vg_clampf( f32 a
, f32 min
, f32 max
)
79 return vg_minf( max
, vg_maxf( a
, min
) );
82 static inline f32
vg_signf( f32 a
)
84 return a
< 0.0f
? -1.0f
: 1.0f
;
87 static inline f32
vg_fractf( f32 a
)
89 return a
- floorf( a
);
92 static f32
vg_cfrictf( f32 velocity
, f32 F
)
94 return -vg_signf(velocity
) * vg_minf( F
, fabsf(velocity
) );
97 static inline f32
vg_rad( f32 deg
)
99 return deg
* VG_PIf
/ 180.0f
;
103 * -----------------------------------------------------------------------------
104 * Section 2.a 2D Vectors
105 * -----------------------------------------------------------------------------
108 static inline void v2_copy( v2f a
, v2f d
)
110 d
[0] = a
[0]; d
[1] = a
[1];
113 static inline void v2_zero( v2f a
)
115 a
[0] = 0.f
; a
[1] = 0.f
;
118 static inline void v2_add( v2f a
, v2f b
, v2f d
)
120 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
123 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
125 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
128 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
130 dest
[0] = vg_minf(a
[0], b
[0]);
131 dest
[1] = vg_minf(a
[1], b
[1]);
134 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
136 dest
[0] = vg_maxf(a
[0], b
[0]);
137 dest
[1] = vg_maxf(a
[1], b
[1]);
140 static inline f32
v2_dot( v2f a
, v2f b
)
142 return a
[0] * b
[0] + a
[1] * b
[1];
145 static inline f32
v2_cross( v2f a
, v2f b
)
147 return a
[0]*b
[1] - a
[1]*b
[0];
150 static inline void v2_abs( v2f a
, v2f d
)
152 d
[0] = fabsf( a
[0] );
153 d
[1] = fabsf( a
[1] );
156 static inline void v2_muls( v2f a
, f32 s
, v2f d
)
158 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
161 static inline void v2_divs( v2f a
, f32 s
, v2f d
)
163 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
166 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
172 static inline void v2_div( v2f a
, v2f b
, v2f d
)
174 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
177 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
179 d
[0] = a
[0]+b
[0]*s
[0];
180 d
[1] = a
[1]+b
[1]*s
[1];
183 static inline void v2_muladds( v2f a
, v2f b
, f32 s
, v2f d
)
189 static inline f32
v2_length2( v2f a
)
191 return a
[0]*a
[0] + a
[1]*a
[1];
194 static inline f32
v2_length( v2f a
)
196 return sqrtf( v2_length2( a
) );
199 static inline f32
v2_dist2( v2f a
, v2f b
)
202 v2_sub( a
, b
, delta
);
203 return v2_length2( delta
);
206 static inline f32
v2_dist( v2f a
, v2f b
)
208 return sqrtf( v2_dist2( a
, b
) );
211 static inline void v2_lerp( v2f a
, v2f b
, f32 t
, v2f d
)
213 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
214 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
217 static inline void v2_normalize( v2f a
)
219 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
222 static void v2_normalize_clamp( v2f a
)
224 f32 l2
= v2_length2( a
);
226 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
229 static inline void v2_floor( v2f a
, v2f b
)
231 b
[0] = floorf( a
[0] );
232 b
[1] = floorf( a
[1] );
235 static inline void v2_fill( v2f a
, f32 v
)
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] );
248 * ---------------- */
250 static inline void v2i_copy( v2i a
, v2i b
)
252 b
[0] = a
[0]; b
[1] = a
[1];
255 static inline int v2i_eq( v2i a
, v2i b
)
257 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
260 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
262 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
265 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
267 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
271 * -----------------------------------------------------------------------------
272 * Section 2.b 3D Vectors
273 * -----------------------------------------------------------------------------
276 static inline void v3_copy( v3f a
, v3f b
)
278 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
281 static inline void v3_zero( v3f a
)
283 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
286 static inline void v3_add( v3f a
, v3f b
, v3f d
)
288 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
291 static inline void v3i_add( v3i a
, v3i b
, v3i d
)
293 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
296 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
298 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
301 static inline void v3i_sub( v3i a
, v3i b
, v3i d
)
303 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
306 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
308 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
311 static inline void v3_div( v3f a
, v3f b
, v3f d
)
313 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
314 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
315 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
318 static inline void v3_muls( v3f a
, f32 s
, v3f d
)
320 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
323 static inline void v3_fill( v3f a
, f32 v
)
330 static inline void v3_divs( v3f a
, f32 s
, v3f d
)
333 v3_fill( d
, INFINITY
);
342 static inline void v3_muladds( v3f a
, v3f b
, f32 s
, v3f d
)
344 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
347 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
349 d
[0] = a
[0]+b
[0]*s
[0];
350 d
[1] = a
[1]+b
[1]*s
[1];
351 d
[2] = a
[2]+b
[2]*s
[2];
354 static inline f32
v3_dot( v3f a
, v3f b
)
356 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
359 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
362 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
363 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
364 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
368 static inline f32
v3_length2( v3f a
)
370 return v3_dot( a
, a
);
373 static inline f32
v3_length( v3f a
)
375 return sqrtf( v3_length2( a
) );
378 static inline f32
v3_dist2( v3f a
, v3f b
)
381 v3_sub( a
, b
, delta
);
382 return v3_length2( delta
);
385 static inline f32
v3_dist( v3f a
, v3f b
)
387 return sqrtf( v3_dist2( a
, b
) );
390 static inline void v3_normalize( v3f a
)
392 v3_muls( a
, 1.f
/ v3_length( a
), a
);
395 static inline f32
vg_lerpf( f32 a
, f32 b
, f32 t
)
400 static inline f64
vg_lerp( f64 a
, f64 b
, f64 t
)
405 /* correctly lerp around circular period -pi -> pi */
406 static f32
vg_alerpf( f32 a
, f32 b
, f32 t
)
408 f32 d
= fmodf( b
-a
, VG_TAUf
),
409 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
413 static inline void v3_lerp( v3f a
, v3f b
, f32 t
, v3f d
)
415 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
416 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
417 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
420 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
422 dest
[0] = vg_minf(a
[0], b
[0]);
423 dest
[1] = vg_minf(a
[1], b
[1]);
424 dest
[2] = vg_minf(a
[2], b
[2]);
427 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
429 dest
[0] = vg_maxf(a
[0], b
[0]);
430 dest
[1] = vg_maxf(a
[1], b
[1]);
431 dest
[2] = vg_maxf(a
[2], b
[2]);
434 static inline f32
v3_minf( v3f a
)
436 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
439 static inline f32
v3_maxf( v3f a
)
441 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
444 static inline void v3_floor( v3f a
, v3f b
)
446 b
[0] = floorf( a
[0] );
447 b
[1] = floorf( a
[1] );
448 b
[2] = floorf( a
[2] );
451 static inline void v3_ceil( v3f a
, v3f b
)
453 b
[0] = ceilf( a
[0] );
454 b
[1] = ceilf( a
[1] );
455 b
[2] = ceilf( a
[2] );
458 static inline void v3_negate( v3f a
, v3f b
)
465 static inline void v3_rotate( v3f v
, f32 angle
, v3f axis
, v3f d
)
476 v3_cross( k
, v
, v2
);
477 v3_muls( v2
, s
, v2
);
478 v3_add( v1
, v2
, v1
);
479 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
484 * -----------------------------------------------------------------------------
485 * Section 2.c 4D Vectors
486 * -----------------------------------------------------------------------------
489 static inline void v4_copy( v4f a
, v4f b
)
491 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
494 static inline void v4_add( v4f a
, v4f b
, v4f d
)
502 static inline void v4_zero( v4f a
)
504 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
507 static inline void v4_muls( v4f a
, f32 s
, v4f d
)
515 static inline void v4_muladds( v4f a
, v4f b
, f32 s
, v4f d
)
523 static inline void v4_lerp( v4f a
, v4f b
, f32 t
, v4f d
)
525 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
526 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
527 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
528 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
531 static inline f32
v4_dot( v4f a
, v4f b
)
533 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
536 static inline f32
v4_length( v4f a
)
538 return sqrtf( v4_dot(a
,a
) );
542 * -----------------------------------------------------------------------------
543 * Section 3 Quaternions
544 * -----------------------------------------------------------------------------
547 static inline void q_identity( v4f q
)
549 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
552 static inline void q_axis_angle( v4f q
, v3f axis
, f32 angle
)
564 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
567 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
568 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
569 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
570 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
574 static inline void q_normalize( v4f q
)
576 f32 s
= 1.0f
/ sqrtf(v4_dot(q
,q
));
583 static inline void q_inv( v4f q
, v4f d
)
585 f32 s
= 1.0f
/ v4_dot(q
,q
);
592 static inline void q_nlerp( v4f a
, v4f b
, f32 t
, v4f d
)
594 if( v4_dot(a
,b
) < 0.0f
){
595 v4_muls( b
, -1.0f
, d
);
596 v4_lerp( a
, d
, t
, d
);
599 v4_lerp( a
, b
, t
, d
);
604 static inline void q_m3x3( v4f q
, m3x3f d
)
608 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
610 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
611 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
612 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
614 d
[0][0] = 1.0f
- yy
- zz
;
615 d
[1][1] = 1.0f
- xx
- zz
;
616 d
[2][2] = 1.0f
- xx
- yy
;
625 static void q_mulv( v4f q
, v3f v
, v3f d
)
629 v3_muls( q
, 2.0f
*v3_dot(q
,v
), v1
);
630 v3_muls( v
, q
[3]*q
[3] - v3_dot(q
,q
), v2
);
631 v3_add( v1
, v2
, v1
);
632 v3_cross( q
, v
, v2
);
633 v3_muls( v2
, 2.0f
*q
[3], v2
);
638 * -----------------------------------------------------------------------------
639 * Section 4.a 2x2 matrices
640 * -----------------------------------------------------------------------------
643 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
646 #define M2X2_ZERO {{0.0f, 0.0f, }, \
649 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
651 v2_copy( a
[0], b
[0] );
652 v2_copy( a
[1], b
[1] );
655 static inline void m2x2_identity( m2x2f a
)
657 m2x2f id
= M2X2_INDENTIY
;
661 static inline void m2x2_create_rotation( m2x2f a
, f32 theta
)
675 * -----------------------------------------------------------------------------
676 * Section 4.b 3x3 matrices
677 * -----------------------------------------------------------------------------
680 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
681 { 0.0f, 1.0f, 0.0f, },\
682 { 0.0f, 0.0f, 1.0f, }}
684 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
685 { 0.0f, 0.0f, 0.0f, },\
686 { 0.0f, 0.0f, 0.0f, }}
689 static void euler_m3x3( v3f angles
, m3x3f d
)
691 f32 cosY
= cosf( angles
[0] ),
692 sinY
= sinf( angles
[0] ),
693 cosP
= cosf( angles
[1] ),
694 sinP
= sinf( angles
[1] ),
695 cosR
= cosf( angles
[2] ),
696 sinR
= sinf( angles
[2] );
698 d
[2][0] = -sinY
* cosP
;
700 d
[2][2] = cosY
* cosP
;
702 d
[0][0] = cosY
* cosR
;
704 d
[0][2] = sinY
* cosR
;
706 v3_cross( d
[0], d
[2], d
[1] );
709 static void m3x3_q( m3x3f m
, v4f q
)
713 diag
= m
[0][0] + m
[1][1] + m
[2][2];
716 r
= sqrtf( 1.0f
+ diag
);
718 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
719 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
720 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
723 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
725 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
728 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
729 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
730 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
732 else if( m
[1][1] >= m
[2][2] )
734 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
736 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
738 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
739 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
743 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
745 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
746 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
748 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
752 /* a X b == [b]T a == ...*/
753 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
766 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
768 v3_add( a
[0], b
[0], d
[0] );
769 v3_add( a
[1], b
[1], d
[1] );
770 v3_add( a
[2], b
[2], d
[2] );
773 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
775 v3_copy( a
[0], b
[0] );
776 v3_copy( a
[1], b
[1] );
777 v3_copy( a
[2], b
[2] );
780 static inline void m3x3_identity( m3x3f a
)
782 m3x3f id
= M3X3_IDENTITY
;
786 static void m3x3_diagonal( m3x3f a
, f32 v
)
794 static void m3x3_setdiagonalv3( m3x3f a
, v3f v
)
801 static inline void m3x3_zero( m3x3f a
)
807 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
809 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
810 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
811 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
818 dest
[0][0] = (e
*i
-h
*f
)*det
;
819 dest
[0][1] = -(b
*i
-c
*h
)*det
;
820 dest
[0][2] = (b
*f
-c
*e
)*det
;
821 dest
[1][0] = -(d
*i
-f
*g
)*det
;
822 dest
[1][1] = (a
*i
-c
*g
)*det
;
823 dest
[1][2] = -(a
*f
-d
*c
)*det
;
824 dest
[2][0] = (d
*h
-g
*e
)*det
;
825 dest
[2][1] = -(a
*h
-g
*b
)*det
;
826 dest
[2][2] = (a
*e
-d
*b
)*det
;
829 static f32
m3x3_det( m3x3f m
)
831 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
832 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
833 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
836 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
838 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
839 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
840 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
853 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
855 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
856 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
857 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
859 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
860 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
861 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
863 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
864 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
865 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
866 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
867 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
868 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
869 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
870 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
871 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
874 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
878 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
879 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
880 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
885 static inline void m3x3_projection( m3x3f dst
,
886 f32
const left
, f32
const right
, f32
const bottom
, f32
const top
)
892 rl
= 1.0f
/ (right
- left
);
893 tb
= 1.0f
/ (top
- bottom
);
895 dst
[0][0] = 2.0f
* rl
;
896 dst
[1][1] = 2.0f
* tb
;
900 static inline void m3x3_translate( m3x3f m
, v3f v
)
902 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
903 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
904 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
907 static inline void m3x3_scale( m3x3f m
, v3f v
)
909 v3_muls( m
[0], v
[0], m
[0] );
910 v3_muls( m
[1], v
[1], m
[1] );
911 v3_muls( m
[2], v
[2], m
[2] );
914 static inline void m3x3_scalef( m3x3f m
, f32 f
)
921 static inline void m3x3_rotate( m3x3f m
, f32 angle
)
923 f32 m00
= m
[0][0], m10
= m
[1][0],
924 m01
= m
[0][1], m11
= m
[1][1],
925 m02
= m
[0][2], m12
= m
[1][2];
931 m
[0][0] = m00
* c
+ m10
* s
;
932 m
[0][1] = m01
* c
+ m11
* s
;
933 m
[0][2] = m02
* c
+ m12
* s
;
935 m
[1][0] = m00
* -s
+ m10
* c
;
936 m
[1][1] = m01
* -s
+ m11
* c
;
937 m
[1][2] = m02
* -s
+ m12
* c
;
941 * -----------------------------------------------------------------------------
942 * Section 4.c 4x3 matrices
943 * -----------------------------------------------------------------------------
946 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
947 { 0.0f, 1.0f, 0.0f, },\
948 { 0.0f, 0.0f, 1.0f, },\
949 { 0.0f, 0.0f, 0.0f }}
951 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
953 v3_copy( a
[0], b
[0] );
954 v3_copy( a
[1], b
[1] );
955 v3_copy( a
[2], b
[2] );
958 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
960 m3x3_transpose( a
, b
);
961 m3x3_mulv( b
, a
[3], b
[3] );
962 v3_negate( b
[3], b
[3] );
965 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
969 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
970 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
971 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
972 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
978 dst
[0][0] = f
*k
- g
*j
;
979 dst
[1][0] =-(e
*k
- g
*i
);
980 dst
[2][0] = e
*j
- f
*i
;
981 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
983 dst
[0][1] =-(b
*k
- c
*j
);
984 dst
[1][1] = a
*k
- c
*i
;
985 dst
[2][1] =-(a
*j
- b
*i
);
986 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
992 dst
[0][2] = b
*g
- c
*f
;
993 dst
[1][2] =-(a
*g
- c
*e
);
994 dst
[2][2] = a
*f
- b
*e
;
995 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
997 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
998 v3_muls( dst
[0], det
, dst
[0] );
999 v3_muls( dst
[1], det
, dst
[1] );
1000 v3_muls( dst
[2], det
, dst
[2] );
1001 v3_muls( dst
[3], det
, dst
[3] );
1004 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
1006 v3_copy( a
[0], b
[0] );
1007 v3_copy( a
[1], b
[1] );
1008 v3_copy( a
[2], b
[2] );
1009 v3_copy( a
[3], b
[3] );
1012 static inline void m4x3_identity( m4x3f a
)
1014 m4x3f id
= M4X3_IDENTITY
;
1018 static void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
1021 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
1022 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
1023 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
1024 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
1025 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
1026 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
1027 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
1028 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
1030 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
1031 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
1032 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
1033 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
1034 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
1035 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
1036 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
1037 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
1038 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
1039 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
1040 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
1041 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
1044 #if 0 /* shat appf mingw wstringop-overflow */
1047 static void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
1051 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
1052 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
1053 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
1059 * Transform plane ( xyz, distance )
1061 static void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
1065 v3_muls( p
, p
[3], o
);
1066 m4x3_mulv( m
, o
, o
);
1067 m3x3_mulv( m
, p
, d
);
1069 d
[3] = v3_dot( o
, d
);
1076 static void m4x3_translate( m4x3f m
, v3f v
)
1078 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
1079 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
1080 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
1083 static void m4x3_rotate_x( m4x3f m
, f32 angle
)
1085 m4x3f t
= M4X3_IDENTITY
;
1096 m4x3_mul( m
, t
, m
);
1099 static void m4x3_rotate_y( m4x3f m
, f32 angle
)
1101 m4x3f t
= M4X3_IDENTITY
;
1112 m4x3_mul( m
, t
, m
);
1115 static void m4x3_rotate_z( m4x3f m
, f32 angle
)
1117 m4x3f t
= M4X3_IDENTITY
;
1128 m4x3_mul( m
, t
, m
);
1131 static void m4x3_expand( m4x3f m
, m4x4f d
)
1133 v3_copy( m
[0], d
[0] );
1134 v3_copy( m
[1], d
[1] );
1135 v3_copy( m
[2], d
[2] );
1136 v3_copy( m
[3], d
[3] );
1143 static void m4x3_decompose( m4x3f m
, v3f co
, v4f q
, v3f s
)
1145 v3_copy( m
[3], co
);
1146 s
[0] = v3_length(m
[0]);
1147 s
[1] = v3_length(m
[1]);
1148 s
[2] = v3_length(m
[2]);
1151 v3_divs( m
[0], s
[0], rot
[0] );
1152 v3_divs( m
[1], s
[1], rot
[1] );
1153 v3_divs( m
[2], s
[2], rot
[2] );
1158 static void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
1161 m4x3_mulv( m
, point
, v
);
1163 v3_minv( box
[0], v
, box
[0] );
1164 v3_maxv( box
[1], v
, box
[1] );
1167 static void m4x3_transform_aabb( m4x3f m
, boxf box
)
1171 v3_copy( box
[0], a
);
1172 v3_copy( box
[1], b
);
1173 v3_fill( box
[0], INFINITY
);
1174 v3_fill( box
[1], -INFINITY
);
1176 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], a
[2] } );
1177 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
1178 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
1179 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
1181 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], a
[1], b
[2] } );
1182 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
1183 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
1184 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
1187 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1190 v3_sub( target
, pos
, dir
);
1191 v3_normalize( dir
);
1193 v3_copy( dir
, m
[2] );
1195 v3_cross( up
, m
[2], m
[0] );
1196 v3_normalize( m
[0] );
1198 v3_cross( m
[2], m
[0], m
[1] );
1199 v3_copy( pos
, m
[3] );
1203 * -----------------------------------------------------------------------------
1204 * Section 4.d 4x4 matrices
1205 * -----------------------------------------------------------------------------
1208 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1209 { 0.0f, 1.0f, 0.0f, 0.0f },\
1210 { 0.0f, 0.0f, 1.0f, 0.0f },\
1211 { 0.0f, 0.0f, 0.0f, 1.0f }}
1212 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1213 { 0.0f, 0.0f, 0.0f, 0.0f },\
1214 { 0.0f, 0.0f, 0.0f, 0.0f },\
1215 { 0.0f, 0.0f, 0.0f, 0.0f }}
1217 static void m4x4_projection( m4x4f m
, f32 angle
,
1218 f32 ratio
, f32 fnear
, f32 ffar
)
1220 f32 scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1226 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1232 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1236 m
[2][0] = (r
+ l
) / (r
- l
);
1237 m
[2][1] = (t
+ b
) / (t
- b
);
1238 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1243 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1247 static void m4x4_translate( m4x4f m
, v3f v
)
1249 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1250 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1251 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1254 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1256 v4_copy( a
[0], b
[0] );
1257 v4_copy( a
[1], b
[1] );
1258 v4_copy( a
[2], b
[2] );
1259 v4_copy( a
[3], b
[3] );
1262 static inline void m4x4_identity( m4x4f a
)
1264 m4x4f id
= M4X4_IDENTITY
;
1268 static inline void m4x4_zero( m4x4f a
)
1270 m4x4f zero
= M4X4_ZERO
;
1271 m4x4_copy( zero
, a
);
1274 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1276 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1277 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1278 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1279 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1281 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1282 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1283 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1284 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1286 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1287 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1288 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1289 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1290 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1291 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1292 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1293 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1294 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1295 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1296 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1297 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1298 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1299 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1300 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1301 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1304 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1308 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1309 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1310 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1311 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1316 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1318 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1319 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1320 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1321 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1325 t
[0] = a22
*a33
- a32
*a23
;
1326 t
[1] = a21
*a33
- a31
*a23
;
1327 t
[2] = a21
*a32
- a31
*a22
;
1328 t
[3] = a20
*a33
- a30
*a23
;
1329 t
[4] = a20
*a32
- a30
*a22
;
1330 t
[5] = a20
*a31
- a30
*a21
;
1332 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1333 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1334 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1335 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1337 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1338 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1339 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1340 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1342 t
[0] = a12
*a33
- a32
*a13
;
1343 t
[1] = a11
*a33
- a31
*a13
;
1344 t
[2] = a11
*a32
- a31
*a12
;
1345 t
[3] = a10
*a33
- a30
*a13
;
1346 t
[4] = a10
*a32
- a30
*a12
;
1347 t
[5] = a10
*a31
- a30
*a11
;
1349 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1350 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1351 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1352 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1354 t
[0] = a12
*a23
- a22
*a13
;
1355 t
[1] = a11
*a23
- a21
*a13
;
1356 t
[2] = a11
*a22
- a21
*a12
;
1357 t
[3] = a10
*a23
- a20
*a13
;
1358 t
[4] = a10
*a22
- a20
*a12
;
1359 t
[5] = a10
*a21
- a20
*a11
;
1361 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1362 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1363 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1364 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1366 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1367 v4_muls( d
[0], det
, d
[0] );
1368 v4_muls( d
[1], det
, d
[1] );
1369 v4_muls( d
[2], det
, d
[2] );
1370 v4_muls( d
[3], det
, d
[3] );
1374 * -----------------------------------------------------------------------------
1376 * -----------------------------------------------------------------------------
1379 static inline void box_addpt( boxf a
, v3f pt
)
1381 v3_minv( a
[0], pt
, a
[0] );
1382 v3_maxv( a
[1], pt
, a
[1] );
1385 static inline void box_concat( boxf a
, boxf b
)
1387 v3_minv( a
[0], b
[0], a
[0] );
1388 v3_maxv( a
[1], b
[1], a
[1] );
1391 static inline void box_copy( boxf a
, boxf b
)
1393 v3_copy( a
[0], b
[0] );
1394 v3_copy( a
[1], b
[1] );
1397 static inline int box_overlap( boxf a
, boxf b
)
1400 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
1401 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
1402 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
1406 static int box_within( boxf greater
, boxf lesser
)
1409 v3_sub( lesser
[0], greater
[0], a
);
1410 v3_sub( lesser
[1], greater
[1], b
);
1412 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
1413 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
1421 static inline void box_init_inf( boxf box
)
1423 v3_fill( box
[0], INFINITY
);
1424 v3_fill( box
[1], -INFINITY
);
1428 * -----------------------------------------------------------------------------
1429 * Section 5.b Planes
1430 * -----------------------------------------------------------------------------
1433 static inline void tri_to_plane( f64 a
[3], f64 b
[3],
1434 f64 c
[3], f64 p
[4] )
1440 edge0
[0] = b
[0] - a
[0];
1441 edge0
[1] = b
[1] - a
[1];
1442 edge0
[2] = b
[2] - a
[2];
1444 edge1
[0] = c
[0] - a
[0];
1445 edge1
[1] = c
[1] - a
[1];
1446 edge1
[2] = c
[2] - a
[2];
1448 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1449 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1450 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1452 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1453 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1460 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1462 f32
const epsilon
= 1e-6f
;
1465 v3_cross( a
, b
, x
);
1466 f32 d
= v3_dot( x
, c
);
1468 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1471 v3_cross( b
, c
, v0
);
1472 v3_cross( c
, a
, v1
);
1473 v3_cross( a
, b
, v2
);
1475 v3_muls( v0
, a
[3], p
);
1476 v3_muladds( p
, v1
, b
[3], p
);
1477 v3_muladds( p
, v2
, c
[3], p
);
1483 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1485 f32
const epsilon
= 1e-6f
;
1488 v3_cross( a
, b
, c
);
1489 f32 d
= v3_length2( c
);
1491 if( (d
< epsilon
) && (d
> -epsilon
) )
1495 v3_cross( c
, b
, v0
);
1496 v3_cross( a
, c
, v1
);
1498 v3_muls( v0
, a
[3], vx
);
1499 v3_muladds( vx
, v1
, b
[3], vx
);
1500 v3_divs( vx
, d
, p
);
1506 static int plane_segment( v4f plane
, v3f a
, v3f b
, v3f co
)
1508 f32 d0
= v3_dot( a
, plane
) - plane
[3],
1509 d1
= v3_dot( b
, plane
) - plane
[3];
1513 f32 tot
= 1.0f
/( fabsf(d0
)+fabsf(d1
) );
1515 v3_muls( a
, fabsf(d1
) * tot
, co
);
1516 v3_muladds( co
, b
, fabsf(d0
) * tot
, co
);
1523 static inline f64
plane_polarity( f64 p
[4], f64 a
[3] )
1526 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1527 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1532 * -----------------------------------------------------------------------------
1533 * Section 5.c Closest point functions
1534 * -----------------------------------------------------------------------------
1538 * These closest point tests were learned from Real-Time Collision Detection by
1541 VG_STATIC f32
closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1542 f32
*s
, f32
*t
, v3f c1
, v3f c2
)
1545 v3_sub( q1
, p1
, d1
);
1546 v3_sub( q2
, p2
, d2
);
1547 v3_sub( p1
, p2
, r
);
1549 f32 a
= v3_length2( d1
),
1550 e
= v3_length2( d2
),
1551 f
= v3_dot( d2
, r
);
1553 const f32 kEpsilon
= 0.0001f
;
1555 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1563 v3_sub( c1
, c2
, v0
);
1565 return v3_length2( v0
);
1571 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1575 f32 c
= v3_dot( d1
, r
);
1579 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1583 f32 b
= v3_dot(d1
,d2
),
1588 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1595 *t
= (b
*(*s
)+f
) / e
;
1600 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1602 else if( *t
> 1.0f
)
1605 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1610 v3_muladds( p1
, d1
, *s
, c1
);
1611 v3_muladds( p2
, d2
, *t
, c2
);
1614 v3_sub( c1
, c2
, v0
);
1615 return v3_length2( v0
);
1618 VG_STATIC
int point_inside_aabb( boxf box
, v3f point
)
1620 if((point
[0]<=box
[1][0]) && (point
[1]<=box
[1][1]) && (point
[2]<=box
[1][2]) &&
1621 (point
[0]>=box
[0][0]) && (point
[1]>=box
[0][1]) && (point
[2]>=box
[0][2]) )
1627 VG_STATIC
void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1629 v3_maxv( p
, box
[0], dest
);
1630 v3_minv( dest
, box
[1], dest
);
1633 VG_STATIC
void closest_point_obb( v3f p
, boxf box
,
1634 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1637 m4x3_mulv( inv_mtx
, p
, local
);
1638 closest_point_aabb( local
, box
, local
);
1639 m4x3_mulv( mtx
, local
, dest
);
1642 VG_STATIC f32
closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1646 v3_sub( point
, a
, v1
);
1648 f32 t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1649 t
= vg_clampf(t
,0.0f
,1.0f
);
1650 v3_muladds( a
, v0
, t
, dest
);
1654 VG_STATIC
void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1659 /* Region outside A */
1660 v3_sub( tri
[1], tri
[0], ab
);
1661 v3_sub( tri
[2], tri
[0], ac
);
1662 v3_sub( p
, tri
[0], ap
);
1666 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1668 v3_copy( tri
[0], dest
);
1669 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1673 /* Region outside B */
1677 v3_sub( p
, tri
[1], bp
);
1678 d3
= v3_dot( ab
, bp
);
1679 d4
= v3_dot( ac
, bp
);
1681 if( d3
>= 0.0f
&& d4
<= d3
)
1683 v3_copy( tri
[1], dest
);
1684 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1688 /* Edge region of AB */
1689 f32 vc
= d1
*d4
- d3
*d2
;
1690 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1692 f32 v
= d1
/ (d1
-d3
);
1693 v3_muladds( tri
[0], ab
, v
, dest
);
1694 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1698 /* Region outside C */
1701 v3_sub( p
, tri
[2], cp
);
1702 d5
= v3_dot(ab
, cp
);
1703 d6
= v3_dot(ac
, cp
);
1705 if( d6
>= 0.0f
&& d5
<= d6
)
1707 v3_copy( tri
[2], dest
);
1708 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1713 f32 vb
= d5
*d2
- d1
*d6
;
1714 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1716 f32 w
= d2
/ (d2
-d6
);
1717 v3_muladds( tri
[0], ac
, w
, dest
);
1718 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1723 f32 va
= d3
*d6
- d5
*d4
;
1724 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1726 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1728 v3_sub( tri
[2], tri
[1], bc
);
1729 v3_muladds( tri
[1], bc
, w
, dest
);
1730 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1734 /* P inside region, Q via barycentric coordinates uvw */
1735 f32 d
= 1.0f
/(va
+vb
+vc
),
1739 v3_muladds( tri
[0], ab
, v
, dest
);
1740 v3_muladds( dest
, ac
, w
, dest
);
1745 k_contact_type_default
,
1746 k_contact_type_disabled
,
1750 VG_STATIC
enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1755 /* Region outside A */
1756 v3_sub( tri
[1], tri
[0], ab
);
1757 v3_sub( tri
[2], tri
[0], ac
);
1758 v3_sub( p
, tri
[0], ap
);
1762 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1764 v3_copy( tri
[0], dest
);
1765 return k_contact_type_default
;
1768 /* Region outside B */
1772 v3_sub( p
, tri
[1], bp
);
1773 d3
= v3_dot( ab
, bp
);
1774 d4
= v3_dot( ac
, bp
);
1776 if( d3
>= 0.0f
&& d4
<= d3
)
1778 v3_copy( tri
[1], dest
);
1779 return k_contact_type_edge
;
1782 /* Edge region of AB */
1783 f32 vc
= d1
*d4
- d3
*d2
;
1784 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1786 f32 v
= d1
/ (d1
-d3
);
1787 v3_muladds( tri
[0], ab
, v
, dest
);
1788 return k_contact_type_edge
;
1791 /* Region outside C */
1794 v3_sub( p
, tri
[2], cp
);
1795 d5
= v3_dot(ab
, cp
);
1796 d6
= v3_dot(ac
, cp
);
1798 if( d6
>= 0.0f
&& d5
<= d6
)
1800 v3_copy( tri
[2], dest
);
1801 return k_contact_type_edge
;
1805 f32 vb
= d5
*d2
- d1
*d6
;
1806 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1808 f32 w
= d2
/ (d2
-d6
);
1809 v3_muladds( tri
[0], ac
, w
, dest
);
1810 return k_contact_type_edge
;
1814 f32 va
= d3
*d6
- d5
*d4
;
1815 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1817 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1819 v3_sub( tri
[2], tri
[1], bc
);
1820 v3_muladds( tri
[1], bc
, w
, dest
);
1821 return k_contact_type_edge
;
1824 /* P inside region, Q via barycentric coordinates uvw */
1825 f32 d
= 1.0f
/(va
+vb
+vc
),
1829 v3_muladds( tri
[0], ab
, v
, dest
);
1830 v3_muladds( dest
, ac
, w
, dest
);
1832 return k_contact_type_default
;
1835 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1837 v2f pabs
, ei
, e2
, ve
, t
;
1840 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1842 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1844 v2_fill( t
, 0.70710678118654752f
);
1846 for( int i
=0; i
<3; i
++ ){
1849 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1853 v2_sub( pabs
, v
, u
);
1857 v2_sub( ud
, v
, ud
);
1859 v2_muls( u
, v2_length( ud
), u
);
1864 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1869 v2_copysign( o
, p
);
1873 * -----------------------------------------------------------------------------
1874 * Section 5.d Raycasts & Spherecasts
1875 * -----------------------------------------------------------------------------
1878 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, f32 dist
)
1883 v3_sub( box
[0], co
, v0
);
1884 v3_sub( box
[1], co
, v1
);
1886 v3_mul( v0
, dir_inv
, v0
);
1887 v3_mul( v1
, dir_inv
, v1
);
1889 tmin
= vg_minf( v0
[0], v1
[0] );
1890 tmax
= vg_maxf( v0
[0], v1
[0] );
1891 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
1892 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
1893 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
1894 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
1896 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
1899 /* Time of intersection with ray vs triangle */
1900 static int ray_tri( v3f tri
[3], v3f co
,
1901 v3f dir
, f32
*dist
)
1903 f32
const kEpsilon
= 0.00001f
;
1905 v3f v0
, v1
, h
, s
, q
, n
;
1912 v3_sub( pb
, pa
, v0
);
1913 v3_sub( pc
, pa
, v1
);
1914 v3_cross( dir
, v1
, h
);
1915 v3_cross( v0
, v1
, n
);
1917 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
1921 a
= v3_dot( v0
, h
);
1923 if( a
> -kEpsilon
&& a
< kEpsilon
)
1927 v3_sub( co
, pa
, s
);
1929 u
= f
* v3_dot(s
, h
);
1930 if( u
< 0.0f
|| u
> 1.0f
)
1933 v3_cross( s
, v0
, q
);
1934 v
= f
* v3_dot( dir
, q
);
1935 if( v
< 0.0f
|| u
+v
> 1.0f
)
1938 t
= f
* v3_dot(v1
, q
);
1947 /* time of intersection with ray vs sphere */
1948 static int ray_sphere( v3f c
, f32 r
,
1949 v3f co
, v3f dir
, f32
*t
)
1954 f32 b
= v3_dot( m
, dir
),
1955 c1
= v3_dot( m
, m
) - r
*r
;
1957 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
1958 if( c1
> 0.0f
&& b
> 0.0f
)
1961 f32 discr
= b
*b
- c1
;
1963 /* A negative discriminant corresponds to ray missing sphere */
1968 * Ray now found to intersect sphere, compute smallest t value of
1971 *t
= -b
- sqrtf( discr
);
1973 /* If t is negative, ray started inside sphere so clamp t to zero */
1981 * time of intersection of ray vs cylinder
1982 * The cylinder does not have caps but is finite
1984 * Heavily adapted from regular segment vs cylinder from:
1985 * Real-Time Collision Detection
1987 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, f32 r
,
1988 v3f co
, v3f dir
, f32
*t
)
1991 v3_muladds( co
, dir
, 1.0f
, sb
);
1995 v3_sub( sb
, co
, n
);
1997 f32 md
= v3_dot( m
, d
),
1998 nd
= v3_dot( n
, d
),
1999 dd
= v3_dot( d
, d
),
2000 nn
= v3_dot( n
, n
),
2001 mn
= v3_dot( m
, n
),
2003 k
= v3_dot( m
, m
) - r
*r
,
2006 if( fabsf(a
) < 0.00001f
)
2008 /* Segment runs parallel to cylinder axis */
2012 f32 b
= dd
*mn
- nd
*md
,
2016 return 0; /* No real roots; no intersection */
2018 *t
= (-b
- sqrtf(discr
)) / a
;
2020 return 0; /* Intersection behind ray */
2022 /* Check within cylinder segment */
2023 if( md
+ (*t
)*nd
< 0.0f
)
2026 if( md
+ (*t
)*nd
> dd
)
2029 /* Segment intersects cylinder between the endcaps; t is correct */
2034 * Time of intersection of sphere and triangle. Origin must be outside the
2035 * colliding area. This is a fairly long procedure.
2037 static int spherecast_triangle( v3f tri
[3],
2038 v3f co
, v3f dir
, f32 r
, f32
*t
, v3f n
)
2043 v3_sub( tri
[1], tri
[0], v0
);
2044 v3_sub( tri
[2], tri
[0], v1
);
2045 v3_cross( v0
, v1
, n
);
2047 v3_muladds( tri
[0], n
, r
, sum
[0] );
2048 v3_muladds( tri
[1], n
, r
, sum
[1] );
2049 v3_muladds( tri
[2], n
, r
, sum
[2] );
2052 f32 t_min
= INFINITY
,
2055 if( ray_tri( sum
, co
, dir
, &t1
) ){
2056 t_min
= vg_minf( t_min
, t1
);
2061 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2064 for( int i
=0; i
<3; i
++ ){
2065 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) ){
2066 t_min
= vg_minf( t_min
, t1
);
2072 for( int i
=0; i
<3; i
++ ){
2076 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) ){
2081 v3_add( dir
, co
, co1
);
2082 v3_lerp( co
, co1
, t_min
, ct
);
2084 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
2085 v3_sub( ct
, cx
, n
);
2098 * -----------------------------------------------------------------------------
2099 * Section 5.e Curves
2100 * -----------------------------------------------------------------------------
2103 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, f32 t
, v3f p
)
2108 v3_muls( p1
, ttt
, p
);
2109 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2110 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2111 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);
2114 static void eval_bezier3( v3f p0
, v3f p1
, v3f p2
, f32 t
, v3f p
)
2118 v3_muls( p0
, u
*u
, p
);
2119 v3_muladds( p
, p1
, 2.0f
*u
*t
, p
);
2120 v3_muladds( p
, p2
, t
*t
, p
);
2124 * -----------------------------------------------------------------------------
2125 * Section 6.a PSRNG and some distributions
2126 * -----------------------------------------------------------------------------
2129 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2130 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2131 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2132 * equidistributed uniform pseudorandom number generator," ACM
2133 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2134 * January pp.3-30 1998.
2136 * http://www.sultanik.com/Mersenne_twister
2137 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2140 #define MT_UPPER_MASK 0x80000000
2141 #define MT_LOWER_MASK 0x7fffffff
2142 #define MT_TEMPERING_MASK_B 0x9d2c5680
2143 #define MT_TEMPERING_MASK_C 0xefc60000
2145 #define MT_STATE_VECTOR_LENGTH 624
2147 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2148 #define MT_STATE_VECTOR_M 397
2151 u32 mt
[MT_STATE_VECTOR_LENGTH
];
2156 static void vg_rand_seed( unsigned long seed
)
2158 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2159 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2160 * Programming," Vol. 2 (2nd Ed.) pp.102.
2162 vg_rand
.mt
[0] = seed
& 0xffffffff;
2163 for( vg_rand
.index
=1; vg_rand
.index
<MT_STATE_VECTOR_LENGTH
; vg_rand
.index
++ ){
2164 vg_rand
.mt
[vg_rand
.index
] =
2165 (6069 * vg_rand
.mt
[vg_rand
.index
-1]) & 0xffffffff;
2170 * Generates a pseudo-randomly generated long.
2172 static u32
vg_randu32(void)
2175 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2176 static u32 mag
[2] = {0x0, 0x9908b0df};
2177 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
|| vg_rand
.index
< 0 ){
2178 /* generate STATE_VECTOR_LENGTH words at a time */
2180 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
+1 || vg_rand
.index
< 0 ){
2181 vg_rand_seed( 4357 );
2183 for( kk
=0; kk
<MT_STATE_VECTOR_LENGTH
-MT_STATE_VECTOR_M
; kk
++ ){
2184 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2185 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2186 vg_rand
.mt
[kk
] = vg_rand
.mt
[kk
+MT_STATE_VECTOR_M
] ^
2187 (y
>> 1) ^ mag
[y
& 0x1];
2189 for( ; kk
<MT_STATE_VECTOR_LENGTH
-1; kk
++ ){
2190 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2191 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2193 vg_rand
.mt
[ kk
+(MT_STATE_VECTOR_M
-MT_STATE_VECTOR_LENGTH
)] ^
2194 (y
>> 1) ^ mag
[y
& 0x1];
2196 y
= (vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] & MT_UPPER_MASK
) |
2197 (vg_rand
.mt
[0] & MT_LOWER_MASK
);
2198 vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] =
2199 vg_rand
.mt
[MT_STATE_VECTOR_M
-1] ^ (y
>> 1) ^ mag
[y
& 0x1];
2202 y
= vg_rand
.mt
[vg_rand
.index
++];
2204 y
^= (y
<< 7) & MT_TEMPERING_MASK_B
;
2205 y
^= (y
<< 15) & MT_TEMPERING_MASK_C
;
2211 * Generates a pseudo-randomly generated f64 in the range [0..1].
2213 static inline f64
vg_randf64(void)
2215 return (f64
)vg_randu32()/(f64
)0xffffffff;
2218 static inline f64
vg_randf64_range( f64 min
, f64 max
)
2220 return vg_lerp( min
, max
, (f64
)vg_randf64() );
2223 static inline void vg_rand_dir( v3f dir
)
2225 dir
[0] = vg_randf64();
2226 dir
[1] = vg_randf64();
2227 dir
[2] = vg_randf64();
2229 v3_muls( dir
, 2.0f
, dir
);
2230 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2232 v3_normalize( dir
);
2235 static inline void vg_rand_sphere( v3f co
)
2238 v3_muls( co
, cbrtf( vg_randf64() ), co
);