1 /* Copyright (C) 2021-2023 Harry Godden (hgn) - All Rights Reserved
19 * 5.d Raycast & Spherecasts
29 #include "vg_platform.h"
33 #define VG_PIf 3.14159265358979323846264338327950288f
34 #define VG_TAUf 6.28318530717958647692528676655900576f
37 * -----------------------------------------------------------------------------
38 * Section 0. Misc Operations
39 * -----------------------------------------------------------------------------
42 /* get the f32 as the raw bits in a u32 without converting */
43 static u32
vg_ftu32( f32 a
)
45 u32
*ptr
= (u32
*)(&a
);
49 /* check if f32 is infinite */
50 static int vg_isinff( f32 a
)
52 return ((vg_ftu32(a
)) & 0x7FFFFFFFU
) == 0x7F800000U
;
55 /* check if f32 is not a number */
56 static int vg_isnanf( f32 a
)
58 return !vg_isinff(a
) && ((vg_ftu32(a
)) & 0x7F800000U
) == 0x7F800000U
;
61 /* check if f32 is a number and is not infinite */
62 static int vg_validf( f32 a
)
64 return ((vg_ftu32(a
)) & 0x7F800000U
) != 0x7F800000U
;
67 static int v3_valid( v3f a
){
68 for( u32 i
=0; i
<3; i
++ )
69 if( !vg_validf(a
[i
]) ) return 0;
74 * -----------------------------------------------------------------------------
75 * Section 1. Scalar Operations
76 * -----------------------------------------------------------------------------
79 static inline f32
vg_minf( f32 a
, f32 b
){ return a
< b
? a
: b
; }
80 static inline f32
vg_maxf( f32 a
, f32 b
){ return a
> b
? a
: b
; }
82 static inline int vg_min( int a
, int b
){ return a
< b
? a
: b
; }
83 static inline int vg_max( int a
, int b
){ return a
> b
? a
: b
; }
85 static inline f32
vg_clampf( f32 a
, f32 min
, f32 max
)
87 return vg_minf( max
, vg_maxf( a
, min
) );
90 static inline f32
vg_signf( f32 a
)
92 return a
< 0.0f
? -1.0f
: 1.0f
;
95 static inline f32
vg_fractf( f32 a
)
97 return a
- floorf( a
);
100 static f32
vg_cfrictf( f32 velocity
, f32 F
)
102 return -vg_signf(velocity
) * vg_minf( F
, fabsf(velocity
) );
105 static inline f32
vg_rad( f32 deg
)
107 return deg
* VG_PIf
/ 180.0f
;
110 /* angle to reach b from a */
111 static f32
vg_angle_diff( f32 a
, f32 b
){
112 f32 d
= fmod(b
,VG_TAUf
)-fmodf(a
,VG_TAUf
);
113 if( fabsf(d
) > VG_PIf
)
114 d
= -vg_signf(d
) * (VG_TAUf
- fabsf(d
));
120 * quantize float to bit count
122 static u32
vg_quantf( f32 a
, u32 bits
, f32 min
, f32 max
){
123 u32 mask
= (0x1 << bits
) - 1;
124 return vg_clampf((a
- min
) * ((f32
)mask
/(max
-min
)), 0.0f
, mask
);
128 * un-quantize discreet to float
130 static f32
vg_dequantf( u32 q
, u32 bits
, f32 min
, f32 max
){
131 u32 mask
= (0x1 << bits
) - 1;
132 return min
+ (f32
)q
* ((max
-min
) / (f32
)mask
);
136 * -----------------------------------------------------------------------------
137 * Section 2.a 2D Vectors
138 * -----------------------------------------------------------------------------
141 static inline void v2_copy( v2f a
, v2f d
)
143 d
[0] = a
[0]; d
[1] = a
[1];
146 static inline void v2_zero( v2f a
)
148 a
[0] = 0.f
; a
[1] = 0.f
;
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_sub( v2f a
, v2f b
, v2f d
)
158 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
161 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
163 dest
[0] = vg_minf(a
[0], b
[0]);
164 dest
[1] = vg_minf(a
[1], b
[1]);
167 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
169 dest
[0] = vg_maxf(a
[0], b
[0]);
170 dest
[1] = vg_maxf(a
[1], b
[1]);
173 static inline f32
v2_dot( v2f a
, v2f b
)
175 return a
[0] * b
[0] + a
[1] * b
[1];
178 static inline f32
v2_cross( v2f a
, v2f b
)
180 return a
[0]*b
[1] - a
[1]*b
[0];
183 static inline void v2_abs( v2f a
, v2f d
)
185 d
[0] = fabsf( a
[0] );
186 d
[1] = fabsf( a
[1] );
189 static inline void v2_muls( v2f a
, f32 s
, v2f d
)
191 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
194 static inline void v2_divs( v2f a
, f32 s
, v2f d
)
196 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
199 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
205 static inline void v2_div( v2f a
, v2f b
, v2f d
)
207 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
210 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
212 d
[0] = a
[0]+b
[0]*s
[0];
213 d
[1] = a
[1]+b
[1]*s
[1];
216 static inline void v2_muladds( v2f a
, v2f b
, f32 s
, v2f d
)
222 static inline f32
v2_length2( v2f a
)
224 return a
[0]*a
[0] + a
[1]*a
[1];
227 static inline f32
v2_length( v2f a
)
229 return sqrtf( v2_length2( a
) );
232 static inline f32
v2_dist2( v2f a
, v2f b
)
235 v2_sub( a
, b
, delta
);
236 return v2_length2( delta
);
239 static inline f32
v2_dist( v2f a
, v2f b
)
241 return sqrtf( v2_dist2( a
, b
) );
244 static inline void v2_lerp( v2f a
, v2f b
, f32 t
, v2f d
)
246 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
247 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
250 static inline void v2_normalize( v2f a
)
252 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
255 static void v2_normalize_clamp( v2f a
)
257 f32 l2
= v2_length2( a
);
259 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
262 static inline void v2_floor( v2f a
, v2f b
)
264 b
[0] = floorf( a
[0] );
265 b
[1] = floorf( a
[1] );
268 static inline void v2_fill( v2f a
, f32 v
)
274 static inline void v2_copysign( v2f a
, v2f b
)
276 a
[0] = copysignf( a
[0], b
[0] );
277 a
[1] = copysignf( a
[1], b
[1] );
281 * ---------------- */
283 static inline void v2i_copy( v2i a
, v2i b
)
285 b
[0] = a
[0]; b
[1] = a
[1];
288 static inline int v2i_eq( v2i a
, v2i b
)
290 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
293 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
295 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
298 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
300 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
304 * -----------------------------------------------------------------------------
305 * Section 2.b 3D Vectors
306 * -----------------------------------------------------------------------------
309 static inline void v3_copy( v3f a
, v3f b
)
311 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
314 static inline void v3_zero( v3f a
)
316 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
319 static inline void v3_add( v3f a
, v3f b
, v3f d
)
321 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
324 static inline void v3i_add( v3i a
, v3i b
, v3i d
)
326 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
329 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
331 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
334 static inline void v3i_sub( v3i a
, v3i b
, v3i d
)
336 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
339 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
341 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
344 static inline void v3_div( v3f a
, v3f b
, v3f d
)
346 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
347 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
348 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
351 static inline void v3_muls( v3f a
, f32 s
, v3f d
)
353 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
356 static inline void v3_fill( v3f a
, f32 v
)
363 static inline void v3_divs( v3f a
, f32 s
, v3f d
)
366 v3_fill( d
, INFINITY
);
375 static inline void v3_muladds( v3f a
, v3f b
, f32 s
, v3f d
)
377 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
380 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
382 d
[0] = a
[0]+b
[0]*s
[0];
383 d
[1] = a
[1]+b
[1]*s
[1];
384 d
[2] = a
[2]+b
[2]*s
[2];
387 static inline f32
v3_dot( v3f a
, v3f b
)
389 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
392 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
395 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
396 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
397 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
401 static inline f32
v3_length2( v3f a
)
403 return v3_dot( a
, a
);
406 static inline f32
v3_length( v3f a
)
408 return sqrtf( v3_length2( a
) );
411 static inline f32
v3_dist2( v3f a
, v3f b
)
414 v3_sub( a
, b
, delta
);
415 return v3_length2( delta
);
418 static inline f32
v3_dist( v3f a
, v3f b
)
420 return sqrtf( v3_dist2( a
, b
) );
423 static inline void v3_normalize( v3f a
)
425 v3_muls( a
, 1.f
/ v3_length( a
), a
);
428 static inline f32
vg_lerpf( f32 a
, f32 b
, f32 t
){
432 static inline f64
vg_lerp( f64 a
, f64 b
, f64 t
)
437 static inline void vg_slewf( f32
*a
, f32 b
, f32 speed
){
438 f32 d
= vg_signf( b
-*a
),
440 *a
= vg_minf( b
*d
, c
*d
) * d
;
443 static inline f32
vg_smoothstepf( f32 x
){
444 return x
*x
*(3.0f
- 2.0f
*x
);
448 /* correctly lerp around circular period -pi -> pi */
449 static f32
vg_alerpf( f32 a
, f32 b
, f32 t
)
451 f32 d
= fmodf( b
-a
, VG_TAUf
),
452 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
456 static inline void v3_lerp( v3f a
, v3f b
, f32 t
, v3f d
)
458 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
459 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
460 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
463 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
465 dest
[0] = vg_minf(a
[0], b
[0]);
466 dest
[1] = vg_minf(a
[1], b
[1]);
467 dest
[2] = vg_minf(a
[2], b
[2]);
470 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
472 dest
[0] = vg_maxf(a
[0], b
[0]);
473 dest
[1] = vg_maxf(a
[1], b
[1]);
474 dest
[2] = vg_maxf(a
[2], b
[2]);
477 static inline f32
v3_minf( v3f a
)
479 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
482 static inline f32
v3_maxf( v3f a
)
484 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
487 static inline void v3_floor( v3f a
, v3f b
)
489 b
[0] = floorf( a
[0] );
490 b
[1] = floorf( a
[1] );
491 b
[2] = floorf( a
[2] );
494 static inline void v3_ceil( v3f a
, v3f b
)
496 b
[0] = ceilf( a
[0] );
497 b
[1] = ceilf( a
[1] );
498 b
[2] = ceilf( a
[2] );
501 static inline void v3_negate( v3f a
, v3f b
)
508 static inline void v3_rotate( v3f v
, f32 angle
, v3f axis
, v3f d
)
519 v3_cross( k
, v
, v2
);
520 v3_muls( v2
, s
, v2
);
521 v3_add( v1
, v2
, v1
);
522 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
526 static void v3_tangent_basis( v3f n
, v3f tx
, v3f ty
){
527 /* Compute tangent basis (box2d) */
528 if( fabsf( n
[0] ) >= 0.57735027f
){
540 v3_cross( n
, tx
, ty
);
545 * -----------------------------------------------------------------------------
546 * Section 2.c 4D Vectors
547 * -----------------------------------------------------------------------------
550 static inline void v4_copy( v4f a
, v4f b
)
552 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
555 static inline void v4_add( v4f a
, v4f b
, v4f d
)
563 static inline void v4_zero( v4f a
)
565 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
568 static inline void v4_muls( v4f a
, f32 s
, v4f d
)
576 static inline void v4_muladds( v4f a
, v4f b
, f32 s
, v4f d
)
584 static inline void v4_lerp( v4f a
, v4f b
, f32 t
, v4f d
)
586 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
587 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
588 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
589 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
592 static inline f32
v4_dot( v4f a
, v4f b
)
594 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
597 static inline f32
v4_length( v4f a
)
599 return sqrtf( v4_dot(a
,a
) );
603 * -----------------------------------------------------------------------------
604 * Section 3 Quaternions
605 * -----------------------------------------------------------------------------
608 static inline void q_identity( v4f q
)
610 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
613 static inline void q_axis_angle( v4f q
, v3f axis
, f32 angle
)
625 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
628 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
629 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
630 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
631 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
635 static inline void q_normalize( v4f q
)
637 f32 l2
= v4_dot(q
,q
);
638 if( l2
< 0.00001f
) q_identity( q
);
640 f32 s
= 1.0f
/sqrtf(l2
);
648 static inline void q_inv( v4f q
, v4f d
)
650 f32 s
= 1.0f
/ v4_dot(q
,q
);
657 static inline void q_nlerp( v4f a
, v4f b
, f32 t
, v4f d
){
658 if( v4_dot(a
,b
) < 0.0f
){
660 v4_muls( b
, -1.0f
, c
);
661 v4_lerp( a
, c
, t
, d
);
664 v4_lerp( a
, b
, t
, d
);
669 static inline void q_m3x3( v4f q
, m3x3f d
)
673 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
675 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
676 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
677 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
679 d
[0][0] = 1.0f
- yy
- zz
;
680 d
[1][1] = 1.0f
- xx
- zz
;
681 d
[2][2] = 1.0f
- xx
- yy
;
690 static void q_mulv( v4f q
, v3f v
, v3f d
)
694 v3_muls( q
, 2.0f
*v3_dot(q
,v
), v1
);
695 v3_muls( v
, q
[3]*q
[3] - v3_dot(q
,q
), v2
);
696 v3_add( v1
, v2
, v1
);
697 v3_cross( q
, v
, v2
);
698 v3_muls( v2
, 2.0f
*q
[3], v2
);
702 static f32
q_dist( v4f q0
, v4f q1
){
703 return acosf( 2.0f
* v4_dot(q0
,q1
) -1.0f
);
707 * -----------------------------------------------------------------------------
708 * Section 4.a 2x2 matrices
709 * -----------------------------------------------------------------------------
712 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
715 #define M2X2_ZERO {{0.0f, 0.0f, }, \
718 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
720 v2_copy( a
[0], b
[0] );
721 v2_copy( a
[1], b
[1] );
724 static inline void m2x2_identity( m2x2f a
)
726 m2x2f id
= M2X2_INDENTIY
;
730 static inline void m2x2_create_rotation( m2x2f a
, f32 theta
)
743 static inline void m2x2_mulv( m2x2f m
, v2f v
, v2f d
)
747 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1];
748 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1];
754 * -----------------------------------------------------------------------------
755 * Section 4.b 3x3 matrices
756 * -----------------------------------------------------------------------------
759 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
760 { 0.0f, 1.0f, 0.0f, },\
761 { 0.0f, 0.0f, 1.0f, }}
763 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
764 { 0.0f, 0.0f, 0.0f, },\
765 { 0.0f, 0.0f, 0.0f, }}
768 static void euler_m3x3( v3f angles
, m3x3f d
)
770 f32 cosY
= cosf( angles
[0] ),
771 sinY
= sinf( angles
[0] ),
772 cosP
= cosf( angles
[1] ),
773 sinP
= sinf( angles
[1] ),
774 cosR
= cosf( angles
[2] ),
775 sinR
= sinf( angles
[2] );
777 d
[2][0] = -sinY
* cosP
;
779 d
[2][2] = cosY
* cosP
;
781 d
[0][0] = cosY
* cosR
;
783 d
[0][2] = sinY
* cosR
;
785 v3_cross( d
[0], d
[2], d
[1] );
788 static void m3x3_q( m3x3f m
, v4f q
)
792 diag
= m
[0][0] + m
[1][1] + m
[2][2];
795 r
= sqrtf( 1.0f
+ diag
);
797 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
798 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
799 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
802 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
804 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
807 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
808 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
809 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
811 else if( m
[1][1] >= m
[2][2] )
813 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
815 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
817 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
818 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
822 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
824 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
825 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
827 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
831 /* a X b == [b]T a == ...*/
832 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
845 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
847 v3_add( a
[0], b
[0], d
[0] );
848 v3_add( a
[1], b
[1], d
[1] );
849 v3_add( a
[2], b
[2], d
[2] );
852 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
854 v3_copy( a
[0], b
[0] );
855 v3_copy( a
[1], b
[1] );
856 v3_copy( a
[2], b
[2] );
859 static inline void m3x3_identity( m3x3f a
)
861 m3x3f id
= M3X3_IDENTITY
;
865 static void m3x3_diagonal( m3x3f a
, f32 v
)
873 static void m3x3_setdiagonalv3( m3x3f a
, v3f v
)
880 static inline void m3x3_zero( m3x3f a
)
886 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
888 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
889 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
890 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
897 dest
[0][0] = (e
*i
-h
*f
)*det
;
898 dest
[0][1] = -(b
*i
-c
*h
)*det
;
899 dest
[0][2] = (b
*f
-c
*e
)*det
;
900 dest
[1][0] = -(d
*i
-f
*g
)*det
;
901 dest
[1][1] = (a
*i
-c
*g
)*det
;
902 dest
[1][2] = -(a
*f
-d
*c
)*det
;
903 dest
[2][0] = (d
*h
-g
*e
)*det
;
904 dest
[2][1] = -(a
*h
-g
*b
)*det
;
905 dest
[2][2] = (a
*e
-d
*b
)*det
;
908 static f32
m3x3_det( m3x3f m
)
910 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
911 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
912 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
915 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
917 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
918 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
919 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
932 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
934 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
935 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
936 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
938 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
939 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
940 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
942 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
943 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
944 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
945 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
946 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
947 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
948 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
949 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
950 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
953 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
957 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
958 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
959 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
964 static inline void m3x3_projection( m3x3f dst
,
965 f32
const left
, f32
const right
, f32
const bottom
, f32
const top
)
971 rl
= 1.0f
/ (right
- left
);
972 tb
= 1.0f
/ (top
- bottom
);
974 dst
[0][0] = 2.0f
* rl
;
975 dst
[1][1] = 2.0f
* tb
;
979 static inline void m3x3_translate( m3x3f m
, v3f v
)
981 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
982 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
983 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
986 static inline void m3x3_scale( m3x3f m
, v3f v
)
988 v3_muls( m
[0], v
[0], m
[0] );
989 v3_muls( m
[1], v
[1], m
[1] );
990 v3_muls( m
[2], v
[2], m
[2] );
993 static inline void m3x3_scalef( m3x3f m
, f32 f
)
1000 static inline void m3x3_rotate( m3x3f m
, f32 angle
)
1002 f32 m00
= m
[0][0], m10
= m
[1][0],
1003 m01
= m
[0][1], m11
= m
[1][1],
1004 m02
= m
[0][2], m12
= m
[1][2];
1010 m
[0][0] = m00
* c
+ m10
* s
;
1011 m
[0][1] = m01
* c
+ m11
* s
;
1012 m
[0][2] = m02
* c
+ m12
* s
;
1014 m
[1][0] = m00
* -s
+ m10
* c
;
1015 m
[1][1] = m01
* -s
+ m11
* c
;
1016 m
[1][2] = m02
* -s
+ m12
* c
;
1020 * -----------------------------------------------------------------------------
1021 * Section 4.c 4x3 matrices
1022 * -----------------------------------------------------------------------------
1025 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
1026 { 0.0f, 1.0f, 0.0f, },\
1027 { 0.0f, 0.0f, 1.0f, },\
1028 { 0.0f, 0.0f, 0.0f }}
1030 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
1032 v3_copy( a
[0], b
[0] );
1033 v3_copy( a
[1], b
[1] );
1034 v3_copy( a
[2], b
[2] );
1037 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
1039 m3x3_transpose( a
, b
);
1040 m3x3_mulv( b
, a
[3], b
[3] );
1041 v3_negate( b
[3], b
[3] );
1044 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
1048 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
1049 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
1050 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
1051 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
1057 dst
[0][0] = f
*k
- g
*j
;
1058 dst
[1][0] =-(e
*k
- g
*i
);
1059 dst
[2][0] = e
*j
- f
*i
;
1060 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
1062 dst
[0][1] =-(b
*k
- c
*j
);
1063 dst
[1][1] = a
*k
- c
*i
;
1064 dst
[2][1] =-(a
*j
- b
*i
);
1065 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
1071 dst
[0][2] = b
*g
- c
*f
;
1072 dst
[1][2] =-(a
*g
- c
*e
);
1073 dst
[2][2] = a
*f
- b
*e
;
1074 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
1076 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
1077 v3_muls( dst
[0], det
, dst
[0] );
1078 v3_muls( dst
[1], det
, dst
[1] );
1079 v3_muls( dst
[2], det
, dst
[2] );
1080 v3_muls( dst
[3], det
, dst
[3] );
1083 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
1085 v3_copy( a
[0], b
[0] );
1086 v3_copy( a
[1], b
[1] );
1087 v3_copy( a
[2], b
[2] );
1088 v3_copy( a
[3], b
[3] );
1091 static inline void m4x3_identity( m4x3f a
)
1093 m4x3f id
= M4X3_IDENTITY
;
1097 static void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
1100 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
1101 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
1102 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
1103 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
1104 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
1105 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
1106 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
1107 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
1109 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
1110 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
1111 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
1112 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
1113 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
1114 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
1115 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
1116 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
1117 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
1118 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
1119 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
1120 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
1123 #if 0 /* shat appf mingw wstringop-overflow */
1126 static void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
1130 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
1131 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
1132 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
1138 * Transform plane ( xyz, distance )
1140 static void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
1144 v3_muls( p
, p
[3], o
);
1145 m4x3_mulv( m
, o
, o
);
1146 m3x3_mulv( m
, p
, d
);
1148 d
[3] = v3_dot( o
, d
);
1155 static void m4x3_translate( m4x3f m
, v3f v
)
1157 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
1158 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
1159 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
1162 static void m4x3_rotate_x( m4x3f m
, f32 angle
)
1164 m4x3f t
= M4X3_IDENTITY
;
1175 m4x3_mul( m
, t
, m
);
1178 static void m4x3_rotate_y( m4x3f m
, f32 angle
)
1180 m4x3f t
= M4X3_IDENTITY
;
1191 m4x3_mul( m
, t
, m
);
1194 static void m4x3_rotate_z( m4x3f m
, f32 angle
)
1196 m4x3f t
= M4X3_IDENTITY
;
1207 m4x3_mul( m
, t
, m
);
1210 static void m4x3_expand( m4x3f m
, m4x4f d
)
1212 v3_copy( m
[0], d
[0] );
1213 v3_copy( m
[1], d
[1] );
1214 v3_copy( m
[2], d
[2] );
1215 v3_copy( m
[3], d
[3] );
1222 static void m4x3_decompose( m4x3f m
, v3f co
, v4f q
, v3f s
)
1224 v3_copy( m
[3], co
);
1225 s
[0] = v3_length(m
[0]);
1226 s
[1] = v3_length(m
[1]);
1227 s
[2] = v3_length(m
[2]);
1230 v3_divs( m
[0], s
[0], rot
[0] );
1231 v3_divs( m
[1], s
[1], rot
[1] );
1232 v3_divs( m
[2], s
[2], rot
[2] );
1237 static void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
){
1239 m4x3_mulv( m
, point
, v
);
1241 v3_minv( box
[0], v
, box
[0] );
1242 v3_maxv( box
[1], v
, box
[1] );
1245 static void m4x3_expand_aabb_aabb( m4x3f m
, boxf boxa
, boxf boxb
){
1247 v3_copy( boxb
[0], a
);
1248 v3_copy( boxb
[1], b
);
1249 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], a
[2] } );
1250 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], a
[2] } );
1251 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], a
[2] } );
1252 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], a
[2] } );
1253 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], b
[2] } );
1254 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], b
[2] } );
1255 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], b
[2] } );
1256 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], b
[2] } );
1258 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1261 v3_sub( target
, pos
, dir
);
1262 v3_normalize( dir
);
1264 v3_copy( dir
, m
[2] );
1266 v3_cross( up
, m
[2], m
[0] );
1267 v3_normalize( m
[0] );
1269 v3_cross( m
[2], m
[0], m
[1] );
1270 v3_copy( pos
, m
[3] );
1274 * -----------------------------------------------------------------------------
1275 * Section 4.d 4x4 matrices
1276 * -----------------------------------------------------------------------------
1279 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1280 { 0.0f, 1.0f, 0.0f, 0.0f },\
1281 { 0.0f, 0.0f, 1.0f, 0.0f },\
1282 { 0.0f, 0.0f, 0.0f, 1.0f }}
1283 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1284 { 0.0f, 0.0f, 0.0f, 0.0f },\
1285 { 0.0f, 0.0f, 0.0f, 0.0f },\
1286 { 0.0f, 0.0f, 0.0f, 0.0f }}
1288 static void m4x4_projection( m4x4f m
, f32 angle
,
1289 f32 ratio
, f32 fnear
, f32 ffar
)
1291 f32 scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1297 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1303 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1307 m
[2][0] = (r
+ l
) / (r
- l
);
1308 m
[2][1] = (t
+ b
) / (t
- b
);
1309 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1314 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1318 static void m4x4_translate( m4x4f m
, v3f v
)
1320 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1321 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1322 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1325 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1327 v4_copy( a
[0], b
[0] );
1328 v4_copy( a
[1], b
[1] );
1329 v4_copy( a
[2], b
[2] );
1330 v4_copy( a
[3], b
[3] );
1333 static inline void m4x4_identity( m4x4f a
)
1335 m4x4f id
= M4X4_IDENTITY
;
1339 static inline void m4x4_zero( m4x4f a
)
1341 m4x4f zero
= M4X4_ZERO
;
1342 m4x4_copy( zero
, a
);
1345 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1347 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1348 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1349 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1350 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1352 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1353 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1354 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1355 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1357 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1358 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1359 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1360 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1361 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1362 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1363 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1364 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1365 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1366 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1367 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1368 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1369 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1370 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1371 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1372 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1375 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1379 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1380 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1381 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1382 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1387 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1389 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1390 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1391 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1392 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1396 t
[0] = a22
*a33
- a32
*a23
;
1397 t
[1] = a21
*a33
- a31
*a23
;
1398 t
[2] = a21
*a32
- a31
*a22
;
1399 t
[3] = a20
*a33
- a30
*a23
;
1400 t
[4] = a20
*a32
- a30
*a22
;
1401 t
[5] = a20
*a31
- a30
*a21
;
1403 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1404 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1405 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1406 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1408 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1409 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1410 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1411 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1413 t
[0] = a12
*a33
- a32
*a13
;
1414 t
[1] = a11
*a33
- a31
*a13
;
1415 t
[2] = a11
*a32
- a31
*a12
;
1416 t
[3] = a10
*a33
- a30
*a13
;
1417 t
[4] = a10
*a32
- a30
*a12
;
1418 t
[5] = a10
*a31
- a30
*a11
;
1420 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1421 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1422 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1423 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1425 t
[0] = a12
*a23
- a22
*a13
;
1426 t
[1] = a11
*a23
- a21
*a13
;
1427 t
[2] = a11
*a22
- a21
*a12
;
1428 t
[3] = a10
*a23
- a20
*a13
;
1429 t
[4] = a10
*a22
- a20
*a12
;
1430 t
[5] = a10
*a21
- a20
*a11
;
1432 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1433 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1434 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1435 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1437 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1438 v4_muls( d
[0], det
, d
[0] );
1439 v4_muls( d
[1], det
, d
[1] );
1440 v4_muls( d
[2], det
, d
[2] );
1441 v4_muls( d
[3], det
, d
[3] );
1445 * -----------------------------------------------------------------------------
1447 * -----------------------------------------------------------------------------
1450 static inline void box_addpt( boxf a
, v3f pt
)
1452 v3_minv( a
[0], pt
, a
[0] );
1453 v3_maxv( a
[1], pt
, a
[1] );
1456 static inline void box_concat( boxf a
, boxf b
)
1458 v3_minv( a
[0], b
[0], a
[0] );
1459 v3_maxv( a
[1], b
[1], a
[1] );
1462 static inline void box_copy( boxf a
, boxf b
)
1464 v3_copy( a
[0], b
[0] );
1465 v3_copy( a
[1], b
[1] );
1468 static inline int box_overlap( boxf a
, boxf b
)
1471 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
1472 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
1473 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
1477 static int box_within( boxf greater
, boxf lesser
)
1480 v3_sub( lesser
[0], greater
[0], a
);
1481 v3_sub( lesser
[1], greater
[1], b
);
1483 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
1484 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
1492 static inline void box_init_inf( boxf box
){
1493 v3_fill( box
[0], INFINITY
);
1494 v3_fill( box
[1], -INFINITY
);
1498 * -----------------------------------------------------------------------------
1499 * Section 5.b Planes
1500 * -----------------------------------------------------------------------------
1503 static inline void tri_to_plane( f64 a
[3], f64 b
[3],
1504 f64 c
[3], f64 p
[4] )
1510 edge0
[0] = b
[0] - a
[0];
1511 edge0
[1] = b
[1] - a
[1];
1512 edge0
[2] = b
[2] - a
[2];
1514 edge1
[0] = c
[0] - a
[0];
1515 edge1
[1] = c
[1] - a
[1];
1516 edge1
[2] = c
[2] - a
[2];
1518 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1519 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1520 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1522 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1523 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1530 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1532 f32
const epsilon
= 1e-6f
;
1535 v3_cross( a
, b
, x
);
1536 f32 d
= v3_dot( x
, c
);
1538 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1541 v3_cross( b
, c
, v0
);
1542 v3_cross( c
, a
, v1
);
1543 v3_cross( a
, b
, v2
);
1545 v3_muls( v0
, a
[3], p
);
1546 v3_muladds( p
, v1
, b
[3], p
);
1547 v3_muladds( p
, v2
, c
[3], p
);
1553 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1555 f32
const epsilon
= 1e-6f
;
1558 v3_cross( a
, b
, c
);
1559 f32 d
= v3_length2( c
);
1561 if( (d
< epsilon
) && (d
> -epsilon
) )
1565 v3_cross( c
, b
, v0
);
1566 v3_cross( a
, c
, v1
);
1568 v3_muls( v0
, a
[3], vx
);
1569 v3_muladds( vx
, v1
, b
[3], vx
);
1570 v3_divs( vx
, d
, p
);
1576 static int plane_segment( v4f plane
, v3f a
, v3f b
, v3f co
)
1578 f32 d0
= v3_dot( a
, plane
) - plane
[3],
1579 d1
= v3_dot( b
, plane
) - plane
[3];
1583 f32 tot
= 1.0f
/( fabsf(d0
)+fabsf(d1
) );
1585 v3_muls( a
, fabsf(d1
) * tot
, co
);
1586 v3_muladds( co
, b
, fabsf(d0
) * tot
, co
);
1593 static inline f64
plane_polarity( f64 p
[4], f64 a
[3] )
1596 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1597 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1601 static f32
ray_plane( v4f plane
, v3f co
, v3f dir
){
1602 f32 d
= v3_dot( plane
, dir
);
1603 if( fabsf(d
) > 1e-6f
){
1605 v3_muls( plane
, plane
[3], v0
);
1606 v3_sub( v0
, co
, v0
);
1607 return v3_dot( v0
, plane
) / d
;
1609 else return INFINITY
;
1613 * -----------------------------------------------------------------------------
1614 * Section 5.c Closest point functions
1615 * -----------------------------------------------------------------------------
1619 * These closest point tests were learned from Real-Time Collision Detection by
1622 static f32
closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1623 f32
*s
, f32
*t
, v3f c1
, v3f c2
)
1626 v3_sub( q1
, p1
, d1
);
1627 v3_sub( q2
, p2
, d2
);
1628 v3_sub( p1
, p2
, r
);
1630 f32 a
= v3_length2( d1
),
1631 e
= v3_length2( d2
),
1632 f
= v3_dot( d2
, r
);
1634 const f32 kEpsilon
= 0.0001f
;
1636 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1644 v3_sub( c1
, c2
, v0
);
1646 return v3_length2( v0
);
1652 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1656 f32 c
= v3_dot( d1
, r
);
1660 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1664 f32 b
= v3_dot(d1
,d2
),
1669 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1676 *t
= (b
*(*s
)+f
) / e
;
1681 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1683 else if( *t
> 1.0f
)
1686 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1691 v3_muladds( p1
, d1
, *s
, c1
);
1692 v3_muladds( p2
, d2
, *t
, c2
);
1695 v3_sub( c1
, c2
, v0
);
1696 return v3_length2( v0
);
1699 static int point_inside_aabb( boxf box
, v3f point
)
1701 if((point
[0]<=box
[1][0]) && (point
[1]<=box
[1][1]) && (point
[2]<=box
[1][2]) &&
1702 (point
[0]>=box
[0][0]) && (point
[1]>=box
[0][1]) && (point
[2]>=box
[0][2]) )
1708 static void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1710 v3_maxv( p
, box
[0], dest
);
1711 v3_minv( dest
, box
[1], dest
);
1714 static void closest_point_obb( v3f p
, boxf box
,
1715 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1718 m4x3_mulv( inv_mtx
, p
, local
);
1719 closest_point_aabb( local
, box
, local
);
1720 m4x3_mulv( mtx
, local
, dest
);
1723 static f32
closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1727 v3_sub( point
, a
, v1
);
1729 f32 t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1730 t
= vg_clampf(t
,0.0f
,1.0f
);
1731 v3_muladds( a
, v0
, t
, dest
);
1735 static void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1740 /* Region outside A */
1741 v3_sub( tri
[1], tri
[0], ab
);
1742 v3_sub( tri
[2], tri
[0], ac
);
1743 v3_sub( p
, tri
[0], ap
);
1747 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1749 v3_copy( tri
[0], dest
);
1750 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1754 /* Region outside B */
1758 v3_sub( p
, tri
[1], bp
);
1759 d3
= v3_dot( ab
, bp
);
1760 d4
= v3_dot( ac
, bp
);
1762 if( d3
>= 0.0f
&& d4
<= d3
)
1764 v3_copy( tri
[1], dest
);
1765 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1769 /* Edge region of AB */
1770 f32 vc
= d1
*d4
- d3
*d2
;
1771 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1773 f32 v
= d1
/ (d1
-d3
);
1774 v3_muladds( tri
[0], ab
, v
, dest
);
1775 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1779 /* Region outside C */
1782 v3_sub( p
, tri
[2], cp
);
1783 d5
= v3_dot(ab
, cp
);
1784 d6
= v3_dot(ac
, cp
);
1786 if( d6
>= 0.0f
&& d5
<= d6
)
1788 v3_copy( tri
[2], dest
);
1789 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1794 f32 vb
= d5
*d2
- d1
*d6
;
1795 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1797 f32 w
= d2
/ (d2
-d6
);
1798 v3_muladds( tri
[0], ac
, w
, dest
);
1799 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1804 f32 va
= d3
*d6
- d5
*d4
;
1805 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1807 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1809 v3_sub( tri
[2], tri
[1], bc
);
1810 v3_muladds( tri
[1], bc
, w
, dest
);
1811 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1815 /* P inside region, Q via barycentric coordinates uvw */
1816 f32 d
= 1.0f
/(va
+vb
+vc
),
1820 v3_muladds( tri
[0], ab
, v
, dest
);
1821 v3_muladds( dest
, ac
, w
, dest
);
1826 k_contact_type_default
,
1827 k_contact_type_disabled
,
1831 static enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1836 /* Region outside A */
1837 v3_sub( tri
[1], tri
[0], ab
);
1838 v3_sub( tri
[2], tri
[0], ac
);
1839 v3_sub( p
, tri
[0], ap
);
1843 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1845 v3_copy( tri
[0], dest
);
1846 return k_contact_type_default
;
1849 /* Region outside B */
1853 v3_sub( p
, tri
[1], bp
);
1854 d3
= v3_dot( ab
, bp
);
1855 d4
= v3_dot( ac
, bp
);
1857 if( d3
>= 0.0f
&& d4
<= d3
)
1859 v3_copy( tri
[1], dest
);
1860 return k_contact_type_edge
;
1863 /* Edge region of AB */
1864 f32 vc
= d1
*d4
- d3
*d2
;
1865 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1867 f32 v
= d1
/ (d1
-d3
);
1868 v3_muladds( tri
[0], ab
, v
, dest
);
1869 return k_contact_type_edge
;
1872 /* Region outside C */
1875 v3_sub( p
, tri
[2], cp
);
1876 d5
= v3_dot(ab
, cp
);
1877 d6
= v3_dot(ac
, cp
);
1879 if( d6
>= 0.0f
&& d5
<= d6
)
1881 v3_copy( tri
[2], dest
);
1882 return k_contact_type_edge
;
1886 f32 vb
= d5
*d2
- d1
*d6
;
1887 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1889 f32 w
= d2
/ (d2
-d6
);
1890 v3_muladds( tri
[0], ac
, w
, dest
);
1891 return k_contact_type_edge
;
1895 f32 va
= d3
*d6
- d5
*d4
;
1896 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1898 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1900 v3_sub( tri
[2], tri
[1], bc
);
1901 v3_muladds( tri
[1], bc
, w
, dest
);
1902 return k_contact_type_edge
;
1905 /* P inside region, Q via barycentric coordinates uvw */
1906 f32 d
= 1.0f
/(va
+vb
+vc
),
1910 v3_muladds( tri
[0], ab
, v
, dest
);
1911 v3_muladds( dest
, ac
, w
, dest
);
1913 return k_contact_type_default
;
1916 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1918 v2f pabs
, ei
, e2
, ve
, t
;
1921 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1923 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1925 v2_fill( t
, 0.70710678118654752f
);
1927 for( int i
=0; i
<3; i
++ ){
1930 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1934 v2_sub( pabs
, v
, u
);
1938 v2_sub( ud
, v
, ud
);
1940 v2_muls( u
, v2_length( ud
), u
);
1945 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1950 v2_copysign( o
, p
);
1954 * -----------------------------------------------------------------------------
1955 * Section 5.d Raycasts & Spherecasts
1956 * -----------------------------------------------------------------------------
1959 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, f32 dist
)
1964 v3_sub( box
[0], co
, v0
);
1965 v3_sub( box
[1], co
, v1
);
1967 v3_mul( v0
, dir_inv
, v0
);
1968 v3_mul( v1
, dir_inv
, v1
);
1970 tmin
= vg_minf( v0
[0], v1
[0] );
1971 tmax
= vg_maxf( v0
[0], v1
[0] );
1972 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
1973 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
1974 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
1975 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
1977 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
1980 /* Time of intersection with ray vs triangle */
1981 static int ray_tri( v3f tri
[3], v3f co
,
1982 v3f dir
, f32
*dist
)
1984 f32
const kEpsilon
= 0.00001f
;
1986 v3f v0
, v1
, h
, s
, q
, n
;
1993 v3_sub( pb
, pa
, v0
);
1994 v3_sub( pc
, pa
, v1
);
1995 v3_cross( dir
, v1
, h
);
1996 v3_cross( v0
, v1
, n
);
1998 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
2002 a
= v3_dot( v0
, h
);
2004 if( a
> -kEpsilon
&& a
< kEpsilon
)
2008 v3_sub( co
, pa
, s
);
2010 u
= f
* v3_dot(s
, h
);
2011 if( u
< 0.0f
|| u
> 1.0f
)
2014 v3_cross( s
, v0
, q
);
2015 v
= f
* v3_dot( dir
, q
);
2016 if( v
< 0.0f
|| u
+v
> 1.0f
)
2019 t
= f
* v3_dot(v1
, q
);
2028 /* time of intersection with ray vs sphere */
2029 static int ray_sphere( v3f c
, f32 r
,
2030 v3f co
, v3f dir
, f32
*t
)
2035 f32 b
= v3_dot( m
, dir
),
2036 c1
= v3_dot( m
, m
) - r
*r
;
2038 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
2039 if( c1
> 0.0f
&& b
> 0.0f
)
2042 f32 discr
= b
*b
- c1
;
2044 /* A negative discriminant corresponds to ray missing sphere */
2049 * Ray now found to intersect sphere, compute smallest t value of
2052 *t
= -b
- sqrtf( discr
);
2054 /* If t is negative, ray started inside sphere so clamp t to zero */
2062 * time of intersection of ray vs cylinder
2063 * The cylinder does not have caps but is finite
2065 * Heavily adapted from regular segment vs cylinder from:
2066 * Real-Time Collision Detection
2068 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, f32 r
,
2069 v3f co
, v3f dir
, f32
*t
)
2072 v3_muladds( co
, dir
, 1.0f
, sb
);
2076 v3_sub( sb
, co
, n
);
2078 f32 md
= v3_dot( m
, d
),
2079 nd
= v3_dot( n
, d
),
2080 dd
= v3_dot( d
, d
),
2081 nn
= v3_dot( n
, n
),
2082 mn
= v3_dot( m
, n
),
2084 k
= v3_dot( m
, m
) - r
*r
,
2087 if( fabsf(a
) < 0.00001f
)
2089 /* Segment runs parallel to cylinder axis */
2093 f32 b
= dd
*mn
- nd
*md
,
2097 return 0; /* No real roots; no intersection */
2099 *t
= (-b
- sqrtf(discr
)) / a
;
2101 return 0; /* Intersection behind ray */
2103 /* Check within cylinder segment */
2104 if( md
+ (*t
)*nd
< 0.0f
)
2107 if( md
+ (*t
)*nd
> dd
)
2110 /* Segment intersects cylinder between the endcaps; t is correct */
2115 * Time of intersection of sphere and triangle. Origin must be outside the
2116 * colliding area. This is a fairly long procedure.
2118 static int spherecast_triangle( v3f tri
[3],
2119 v3f co
, v3f dir
, f32 r
, f32
*t
, v3f n
)
2124 v3_sub( tri
[1], tri
[0], v0
);
2125 v3_sub( tri
[2], tri
[0], v1
);
2126 v3_cross( v0
, v1
, n
);
2128 v3_muladds( tri
[0], n
, r
, sum
[0] );
2129 v3_muladds( tri
[1], n
, r
, sum
[1] );
2130 v3_muladds( tri
[2], n
, r
, sum
[2] );
2133 f32 t_min
= INFINITY
,
2136 if( ray_tri( sum
, co
, dir
, &t1
) ){
2137 t_min
= vg_minf( t_min
, t1
);
2142 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2145 for( int i
=0; i
<3; i
++ ){
2146 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) ){
2147 t_min
= vg_minf( t_min
, t1
);
2153 for( int i
=0; i
<3; i
++ ){
2157 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) ){
2162 v3_add( dir
, co
, co1
);
2163 v3_lerp( co
, co1
, t_min
, ct
);
2165 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
2166 v3_sub( ct
, cx
, n
);
2179 * -----------------------------------------------------------------------------
2180 * Section 5.e Curves
2181 * -----------------------------------------------------------------------------
2184 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, f32 t
, v3f p
)
2189 v3_muls( p1
, ttt
, p
);
2190 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2191 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2192 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);
2195 static void eval_bezier3( v3f p0
, v3f p1
, v3f p2
, f32 t
, v3f p
)
2199 v3_muls( p0
, u
*u
, p
);
2200 v3_muladds( p
, p1
, 2.0f
*u
*t
, p
);
2201 v3_muladds( p
, p2
, t
*t
, p
);
2205 * -----------------------------------------------------------------------------
2206 * Section 5.f Volumes
2207 * -----------------------------------------------------------------------------
2210 static float vg_sphere_volume( float radius
){
2211 float r3
= radius
*radius
*radius
;
2212 return (4.0f
/3.0f
) * VG_PIf
* r3
;
2216 * -----------------------------------------------------------------------------
2217 * Section 6.a PSRNG and some distributions
2218 * -----------------------------------------------------------------------------
2221 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2222 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2223 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2224 * equidistributed uniform pseudorandom number generator," ACM
2225 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2226 * January pp.3-30 1998.
2228 * http://www.sultanik.com/Mersenne_twister
2229 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2232 #define MT_UPPER_MASK 0x80000000
2233 #define MT_LOWER_MASK 0x7fffffff
2234 #define MT_TEMPERING_MASK_B 0x9d2c5680
2235 #define MT_TEMPERING_MASK_C 0xefc60000
2237 #define MT_STATE_VECTOR_LENGTH 624
2239 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2240 #define MT_STATE_VECTOR_M 397
2243 u32 mt
[MT_STATE_VECTOR_LENGTH
];
2248 static void vg_rand_seed( unsigned long seed
)
2250 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2251 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2252 * Programming," Vol. 2 (2nd Ed.) pp.102.
2254 vg_rand
.mt
[0] = seed
& 0xffffffff;
2255 for( vg_rand
.index
=1; vg_rand
.index
<MT_STATE_VECTOR_LENGTH
; vg_rand
.index
++){
2256 vg_rand
.mt
[vg_rand
.index
] =
2257 (6069 * vg_rand
.mt
[vg_rand
.index
-1]) & 0xffffffff;
2262 * Generates a pseudo-randomly generated long.
2264 static u32
vg_randu32(void)
2267 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2268 static u32 mag
[2] = {0x0, 0x9908b0df};
2269 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
|| vg_rand
.index
< 0 ){
2270 /* generate STATE_VECTOR_LENGTH words at a time */
2272 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
+1 || vg_rand
.index
< 0 ){
2273 vg_rand_seed( 4357 );
2275 for( kk
=0; kk
<MT_STATE_VECTOR_LENGTH
-MT_STATE_VECTOR_M
; kk
++ ){
2276 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2277 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2278 vg_rand
.mt
[kk
] = vg_rand
.mt
[kk
+MT_STATE_VECTOR_M
] ^
2279 (y
>> 1) ^ mag
[y
& 0x1];
2281 for( ; kk
<MT_STATE_VECTOR_LENGTH
-1; kk
++ ){
2282 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2283 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2285 vg_rand
.mt
[ kk
+(MT_STATE_VECTOR_M
-MT_STATE_VECTOR_LENGTH
)] ^
2286 (y
>> 1) ^ mag
[y
& 0x1];
2288 y
= (vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] & MT_UPPER_MASK
) |
2289 (vg_rand
.mt
[0] & MT_LOWER_MASK
);
2290 vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] =
2291 vg_rand
.mt
[MT_STATE_VECTOR_M
-1] ^ (y
>> 1) ^ mag
[y
& 0x1];
2294 y
= vg_rand
.mt
[vg_rand
.index
++];
2296 y
^= (y
<< 7) & MT_TEMPERING_MASK_B
;
2297 y
^= (y
<< 15) & MT_TEMPERING_MASK_C
;
2303 * Generates a pseudo-randomly generated f64 in the range [0..1].
2305 static inline f64
vg_randf64(void)
2307 return (f64
)vg_randu32()/(f64
)0xffffffff;
2310 static inline f64
vg_randf64_range( f64 min
, f64 max
)
2312 return vg_lerp( min
, max
, (f64
)vg_randf64() );
2315 static inline void vg_rand_dir( v3f dir
)
2317 dir
[0] = vg_randf64();
2318 dir
[1] = vg_randf64();
2319 dir
[2] = vg_randf64();
2321 v3_muls( dir
, 2.0f
, dir
);
2322 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2324 v3_normalize( dir
);
2327 static inline void vg_rand_sphere( v3f co
)
2330 v3_muls( co
, cbrtf( vg_randf64() ), co
);