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 inline f64
vg_fractf64( f64 a
){
101 return a
- floor( a
);
104 static f32
vg_cfrictf( f32 velocity
, f32 F
)
106 return -vg_signf(velocity
) * vg_minf( F
, fabsf(velocity
) );
109 static inline f32
vg_rad( f32 deg
)
111 return deg
* VG_PIf
/ 180.0f
;
114 /* angle to reach b from a */
115 static f32
vg_angle_diff( f32 a
, f32 b
){
116 f32 d
= fmod(b
,VG_TAUf
)-fmodf(a
,VG_TAUf
);
117 if( fabsf(d
) > VG_PIf
)
118 d
= -vg_signf(d
) * (VG_TAUf
- fabsf(d
));
124 * quantize float to bit count
126 static u32
vg_quantf( f32 a
, u32 bits
, f32 min
, f32 max
){
127 u32 mask
= (0x1 << bits
) - 1;
128 return vg_clampf((a
- min
) * ((f32
)mask
/(max
-min
)), 0.0f
, mask
);
132 * un-quantize discreet to float
134 static f32
vg_dequantf( u32 q
, u32 bits
, f32 min
, f32 max
){
135 u32 mask
= (0x1 << bits
) - 1;
136 return min
+ (f32
)q
* ((max
-min
) / (f32
)mask
);
139 /* https://iquilezles.org/articles/functions/
141 * Use k to control the stretching of the function. Its maximum, which is 1,
142 * happens at exactly x = 1/k.
144 static f32
vg_exp_impulse( f32 x
, f32 k
){
146 return h
*expf(1.0f
-h
);
150 * -----------------------------------------------------------------------------
151 * Section 2.a 2D Vectors
152 * -----------------------------------------------------------------------------
155 static inline void v2_copy( v2f a
, v2f d
)
157 d
[0] = a
[0]; d
[1] = a
[1];
160 static inline void v2_zero( v2f a
)
162 a
[0] = 0.f
; a
[1] = 0.f
;
165 static inline void v2_add( v2f a
, v2f b
, v2f d
)
167 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
170 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
172 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
175 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
177 dest
[0] = vg_minf(a
[0], b
[0]);
178 dest
[1] = vg_minf(a
[1], b
[1]);
181 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
183 dest
[0] = vg_maxf(a
[0], b
[0]);
184 dest
[1] = vg_maxf(a
[1], b
[1]);
187 static inline f32
v2_dot( v2f a
, v2f b
)
189 return a
[0] * b
[0] + a
[1] * b
[1];
192 static inline f32
v2_cross( v2f a
, v2f b
)
194 return a
[0]*b
[1] - a
[1]*b
[0];
197 static inline void v2_abs( v2f a
, v2f d
)
199 d
[0] = fabsf( a
[0] );
200 d
[1] = fabsf( a
[1] );
203 static inline void v2_muls( v2f a
, f32 s
, v2f d
)
205 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
208 static inline void v2_divs( v2f a
, f32 s
, v2f d
)
210 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
213 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
219 static inline void v2_div( v2f a
, v2f b
, v2f d
)
221 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
224 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
226 d
[0] = a
[0]+b
[0]*s
[0];
227 d
[1] = a
[1]+b
[1]*s
[1];
230 static inline void v2_muladds( v2f a
, v2f b
, f32 s
, v2f d
)
236 static inline f32
v2_length2( v2f a
)
238 return a
[0]*a
[0] + a
[1]*a
[1];
241 static inline f32
v2_length( v2f a
)
243 return sqrtf( v2_length2( a
) );
246 static inline f32
v2_dist2( v2f a
, v2f b
)
249 v2_sub( a
, b
, delta
);
250 return v2_length2( delta
);
253 static inline f32
v2_dist( v2f a
, v2f b
)
255 return sqrtf( v2_dist2( a
, b
) );
258 static inline void v2_lerp( v2f a
, v2f b
, f32 t
, v2f d
)
260 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
261 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
264 static inline void v2_normalize( v2f a
)
266 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
269 static void v2_normalize_clamp( v2f a
)
271 f32 l2
= v2_length2( a
);
273 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
276 static inline void v2_floor( v2f a
, v2f b
)
278 b
[0] = floorf( a
[0] );
279 b
[1] = floorf( a
[1] );
282 static inline void v2_fill( v2f a
, f32 v
)
288 static inline void v2_copysign( v2f a
, v2f b
)
290 a
[0] = copysignf( a
[0], b
[0] );
291 a
[1] = copysignf( a
[1], b
[1] );
295 * ---------------- */
297 static inline void v2i_copy( v2i a
, v2i b
)
299 b
[0] = a
[0]; b
[1] = a
[1];
302 static inline int v2i_eq( v2i a
, v2i b
)
304 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
307 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
309 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
312 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
314 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
318 * -----------------------------------------------------------------------------
319 * Section 2.b 3D Vectors
320 * -----------------------------------------------------------------------------
323 static inline void v3_copy( v3f a
, v3f b
)
325 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
328 static inline void v3_zero( v3f a
)
330 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
333 static inline void v3_add( v3f a
, v3f b
, v3f d
)
335 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
338 static inline void v3i_add( v3i a
, v3i b
, v3i d
)
340 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
343 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
345 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
348 static inline void v3i_sub( v3i a
, v3i b
, v3i d
)
350 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
353 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
355 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
358 static inline void v3_div( v3f a
, v3f b
, v3f d
)
360 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
361 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
362 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
365 static inline void v3_muls( v3f a
, f32 s
, v3f d
)
367 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
370 static inline void v3_fill( v3f a
, f32 v
)
377 static inline void v3_divs( v3f a
, f32 s
, v3f d
)
380 v3_fill( d
, INFINITY
);
389 static inline void v3_muladds( v3f a
, v3f b
, f32 s
, v3f d
)
391 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
394 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
396 d
[0] = a
[0]+b
[0]*s
[0];
397 d
[1] = a
[1]+b
[1]*s
[1];
398 d
[2] = a
[2]+b
[2]*s
[2];
401 static inline f32
v3_dot( v3f a
, v3f b
)
403 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
406 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
409 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
410 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
411 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
415 static inline f32
v3_length2( v3f a
)
417 return v3_dot( a
, a
);
420 static inline f32
v3_length( v3f a
)
422 return sqrtf( v3_length2( a
) );
425 static inline f32
v3_dist2( v3f a
, v3f b
)
428 v3_sub( a
, b
, delta
);
429 return v3_length2( delta
);
432 static inline f32
v3_dist( v3f a
, v3f b
)
434 return sqrtf( v3_dist2( a
, b
) );
437 static inline void v3_normalize( v3f a
)
439 v3_muls( a
, 1.f
/ v3_length( a
), a
);
442 static inline f32
vg_lerpf( f32 a
, f32 b
, f32 t
){
446 static inline f64
vg_lerp( f64 a
, f64 b
, f64 t
)
451 static inline void vg_slewf( f32
*a
, f32 b
, f32 speed
){
452 f32 d
= vg_signf( b
-*a
),
454 *a
= vg_minf( b
*d
, c
*d
) * d
;
457 static inline f32
vg_smoothstepf( f32 x
){
458 return x
*x
*(3.0f
- 2.0f
*x
);
462 /* correctly lerp around circular period -pi -> pi */
463 static f32
vg_alerpf( f32 a
, f32 b
, f32 t
)
465 f32 d
= fmodf( b
-a
, VG_TAUf
),
466 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
470 static inline void v3_lerp( v3f a
, v3f b
, f32 t
, v3f d
)
472 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
473 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
474 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
477 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
479 dest
[0] = vg_minf(a
[0], b
[0]);
480 dest
[1] = vg_minf(a
[1], b
[1]);
481 dest
[2] = vg_minf(a
[2], b
[2]);
484 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
486 dest
[0] = vg_maxf(a
[0], b
[0]);
487 dest
[1] = vg_maxf(a
[1], b
[1]);
488 dest
[2] = vg_maxf(a
[2], b
[2]);
491 static inline f32
v3_minf( v3f a
)
493 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
496 static inline f32
v3_maxf( v3f a
)
498 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
501 static inline void v3_floor( v3f a
, v3f b
)
503 b
[0] = floorf( a
[0] );
504 b
[1] = floorf( a
[1] );
505 b
[2] = floorf( a
[2] );
508 static inline void v3_ceil( v3f a
, v3f b
)
510 b
[0] = ceilf( a
[0] );
511 b
[1] = ceilf( a
[1] );
512 b
[2] = ceilf( a
[2] );
515 static inline void v3_negate( v3f a
, v3f b
)
522 static inline void v3_rotate( v3f v
, f32 angle
, v3f axis
, v3f d
)
533 v3_cross( k
, v
, v2
);
534 v3_muls( v2
, s
, v2
);
535 v3_add( v1
, v2
, v1
);
536 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
540 static void v3_tangent_basis( v3f n
, v3f tx
, v3f ty
){
541 /* Compute tangent basis (box2d) */
542 if( fabsf( n
[0] ) >= 0.57735027f
){
554 v3_cross( n
, tx
, ty
);
558 * Compute yaw and pitch based of a normalized vector representing forward
560 * result -> (YAW,PITCH,0.0)
562 static void v3_angles( v3f v
, v3f out_angles
){
563 float yaw
= atan2f( v
[0], -v
[2] ),
567 v
[0]*v
[0] + v
[2]*v
[2]
572 out_angles
[1] = pitch
;
573 out_angles
[2] = 0.0f
;
577 * Compute the forward vector from (YAW,PITCH,ROLL)
580 static void v3_angles_vector( v3f angles
, v3f out_v
){
581 out_v
[0] = sinf( angles
[0] ) * cosf( angles
[1] );
582 out_v
[1] = -sinf( angles
[1] );
583 out_v
[2] = -cosf( angles
[0] ) * cosf( angles
[1] );
587 * -----------------------------------------------------------------------------
588 * Section 2.c 4D Vectors
589 * -----------------------------------------------------------------------------
592 static inline void v4_copy( v4f a
, v4f b
)
594 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
597 static inline void v4_add( v4f a
, v4f b
, v4f d
)
605 static inline void v4_zero( v4f a
)
607 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
610 static inline void v4_muls( v4f a
, f32 s
, v4f d
)
618 static inline void v4_muladds( v4f a
, v4f b
, f32 s
, v4f d
)
626 static inline void v4_lerp( v4f a
, v4f b
, f32 t
, v4f d
)
628 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
629 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
630 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
631 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
634 static inline f32
v4_dot( v4f a
, v4f b
)
636 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
639 static inline f32
v4_length( v4f a
)
641 return sqrtf( v4_dot(a
,a
) );
645 * -----------------------------------------------------------------------------
646 * Section 3 Quaternions
647 * -----------------------------------------------------------------------------
650 static inline void q_identity( v4f q
)
652 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
655 static inline void q_axis_angle( v4f q
, v3f axis
, f32 angle
)
667 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
670 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
671 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
672 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
673 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
677 static inline void q_normalize( v4f q
)
679 f32 l2
= v4_dot(q
,q
);
680 if( l2
< 0.00001f
) q_identity( q
);
682 f32 s
= 1.0f
/sqrtf(l2
);
690 static inline void q_inv( v4f q
, v4f d
)
692 f32 s
= 1.0f
/ v4_dot(q
,q
);
699 static inline void q_nlerp( v4f a
, v4f b
, f32 t
, v4f d
){
700 if( v4_dot(a
,b
) < 0.0f
){
702 v4_muls( b
, -1.0f
, c
);
703 v4_lerp( a
, c
, t
, d
);
706 v4_lerp( a
, b
, t
, d
);
711 static inline void q_m3x3( v4f q
, m3x3f d
)
715 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
717 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
718 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
719 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
721 d
[0][0] = 1.0f
- yy
- zz
;
722 d
[1][1] = 1.0f
- xx
- zz
;
723 d
[2][2] = 1.0f
- xx
- yy
;
732 static void q_mulv( v4f q
, v3f v
, v3f d
)
736 v3_muls( q
, 2.0f
*v3_dot(q
,v
), v1
);
737 v3_muls( v
, q
[3]*q
[3] - v3_dot(q
,q
), v2
);
738 v3_add( v1
, v2
, v1
);
739 v3_cross( q
, v
, v2
);
740 v3_muls( v2
, 2.0f
*q
[3], v2
);
744 static f32
q_dist( v4f q0
, v4f q1
){
745 return acosf( 2.0f
* v4_dot(q0
,q1
) -1.0f
);
749 * -----------------------------------------------------------------------------
750 * Section 4.a 2x2 matrices
751 * -----------------------------------------------------------------------------
754 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
757 #define M2X2_ZERO {{0.0f, 0.0f, }, \
760 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
762 v2_copy( a
[0], b
[0] );
763 v2_copy( a
[1], b
[1] );
766 static inline void m2x2_identity( m2x2f a
)
768 m2x2f id
= M2X2_INDENTIY
;
772 static inline void m2x2_create_rotation( m2x2f a
, f32 theta
)
785 static inline void m2x2_mulv( m2x2f m
, v2f v
, v2f d
)
789 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1];
790 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1];
796 * -----------------------------------------------------------------------------
797 * Section 4.b 3x3 matrices
798 * -----------------------------------------------------------------------------
801 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
802 { 0.0f, 1.0f, 0.0f, },\
803 { 0.0f, 0.0f, 1.0f, }}
805 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
806 { 0.0f, 0.0f, 0.0f, },\
807 { 0.0f, 0.0f, 0.0f, }}
810 static void euler_m3x3( v3f angles
, m3x3f d
)
812 f32 cosY
= cosf( angles
[0] ),
813 sinY
= sinf( angles
[0] ),
814 cosP
= cosf( angles
[1] ),
815 sinP
= sinf( angles
[1] ),
816 cosR
= cosf( angles
[2] ),
817 sinR
= sinf( angles
[2] );
819 d
[2][0] = -sinY
* cosP
;
821 d
[2][2] = cosY
* cosP
;
823 d
[0][0] = cosY
* cosR
;
825 d
[0][2] = sinY
* cosR
;
827 v3_cross( d
[0], d
[2], d
[1] );
830 static void m3x3_q( m3x3f m
, v4f q
)
834 diag
= m
[0][0] + m
[1][1] + m
[2][2];
837 r
= sqrtf( 1.0f
+ diag
);
839 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
840 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
841 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
844 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
846 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
849 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
850 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
851 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
853 else if( m
[1][1] >= m
[2][2] )
855 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
857 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
859 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
860 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
864 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
866 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
867 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
869 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
873 /* a X b == [b]T a == ...*/
874 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
887 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
889 v3_add( a
[0], b
[0], d
[0] );
890 v3_add( a
[1], b
[1], d
[1] );
891 v3_add( a
[2], b
[2], d
[2] );
894 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
896 v3_copy( a
[0], b
[0] );
897 v3_copy( a
[1], b
[1] );
898 v3_copy( a
[2], b
[2] );
901 static inline void m3x3_identity( m3x3f a
)
903 m3x3f id
= M3X3_IDENTITY
;
907 static void m3x3_diagonal( m3x3f a
, f32 v
)
915 static void m3x3_setdiagonalv3( m3x3f a
, v3f v
)
922 static inline void m3x3_zero( m3x3f a
)
928 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
930 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
931 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
932 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
939 dest
[0][0] = (e
*i
-h
*f
)*det
;
940 dest
[0][1] = -(b
*i
-c
*h
)*det
;
941 dest
[0][2] = (b
*f
-c
*e
)*det
;
942 dest
[1][0] = -(d
*i
-f
*g
)*det
;
943 dest
[1][1] = (a
*i
-c
*g
)*det
;
944 dest
[1][2] = -(a
*f
-d
*c
)*det
;
945 dest
[2][0] = (d
*h
-g
*e
)*det
;
946 dest
[2][1] = -(a
*h
-g
*b
)*det
;
947 dest
[2][2] = (a
*e
-d
*b
)*det
;
950 static f32
m3x3_det( m3x3f m
)
952 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
953 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
954 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
957 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
959 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
960 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
961 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
974 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
976 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
977 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
978 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
980 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
981 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
982 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
984 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
985 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
986 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
987 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
988 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
989 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
990 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
991 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
992 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
995 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
999 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
1000 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
1001 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
1006 static inline void m3x3_projection( m3x3f dst
,
1007 f32
const left
, f32
const right
, f32
const bottom
, f32
const top
)
1013 rl
= 1.0f
/ (right
- left
);
1014 tb
= 1.0f
/ (top
- bottom
);
1016 dst
[0][0] = 2.0f
* rl
;
1017 dst
[1][1] = 2.0f
* tb
;
1021 static inline void m3x3_translate( m3x3f m
, v3f v
)
1023 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
1024 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
1025 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
1028 static inline void m3x3_scale( m3x3f m
, v3f v
)
1030 v3_muls( m
[0], v
[0], m
[0] );
1031 v3_muls( m
[1], v
[1], m
[1] );
1032 v3_muls( m
[2], v
[2], m
[2] );
1035 static inline void m3x3_scalef( m3x3f m
, f32 f
)
1042 static inline void m3x3_rotate( m3x3f m
, f32 angle
)
1044 f32 m00
= m
[0][0], m10
= m
[1][0],
1045 m01
= m
[0][1], m11
= m
[1][1],
1046 m02
= m
[0][2], m12
= m
[1][2];
1052 m
[0][0] = m00
* c
+ m10
* s
;
1053 m
[0][1] = m01
* c
+ m11
* s
;
1054 m
[0][2] = m02
* c
+ m12
* s
;
1056 m
[1][0] = m00
* -s
+ m10
* c
;
1057 m
[1][1] = m01
* -s
+ m11
* c
;
1058 m
[1][2] = m02
* -s
+ m12
* c
;
1062 * -----------------------------------------------------------------------------
1063 * Section 4.c 4x3 matrices
1064 * -----------------------------------------------------------------------------
1067 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
1068 { 0.0f, 1.0f, 0.0f, },\
1069 { 0.0f, 0.0f, 1.0f, },\
1070 { 0.0f, 0.0f, 0.0f }}
1072 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
1074 v3_copy( a
[0], b
[0] );
1075 v3_copy( a
[1], b
[1] );
1076 v3_copy( a
[2], b
[2] );
1079 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
1081 m3x3_transpose( a
, b
);
1082 m3x3_mulv( b
, a
[3], b
[3] );
1083 v3_negate( b
[3], b
[3] );
1086 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
1090 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
1091 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
1092 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
1093 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
1099 dst
[0][0] = f
*k
- g
*j
;
1100 dst
[1][0] =-(e
*k
- g
*i
);
1101 dst
[2][0] = e
*j
- f
*i
;
1102 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
1104 dst
[0][1] =-(b
*k
- c
*j
);
1105 dst
[1][1] = a
*k
- c
*i
;
1106 dst
[2][1] =-(a
*j
- b
*i
);
1107 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
1113 dst
[0][2] = b
*g
- c
*f
;
1114 dst
[1][2] =-(a
*g
- c
*e
);
1115 dst
[2][2] = a
*f
- b
*e
;
1116 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
1118 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
1119 v3_muls( dst
[0], det
, dst
[0] );
1120 v3_muls( dst
[1], det
, dst
[1] );
1121 v3_muls( dst
[2], det
, dst
[2] );
1122 v3_muls( dst
[3], det
, dst
[3] );
1125 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
1127 v3_copy( a
[0], b
[0] );
1128 v3_copy( a
[1], b
[1] );
1129 v3_copy( a
[2], b
[2] );
1130 v3_copy( a
[3], b
[3] );
1133 static inline void m4x3_identity( m4x3f a
)
1135 m4x3f id
= M4X3_IDENTITY
;
1139 static void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
1142 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
1143 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
1144 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
1145 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
1146 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
1147 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
1148 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
1149 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
1151 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
1152 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
1153 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
1154 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
1155 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
1156 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
1157 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
1158 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
1159 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
1160 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
1161 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
1162 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
1165 #if 0 /* shat appf mingw wstringop-overflow */
1168 static void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
1172 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
1173 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
1174 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
1180 * Transform plane ( xyz, distance )
1182 static void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
1186 v3_muls( p
, p
[3], o
);
1187 m4x3_mulv( m
, o
, o
);
1188 m3x3_mulv( m
, p
, d
);
1190 d
[3] = v3_dot( o
, d
);
1197 static void m4x3_translate( m4x3f m
, v3f v
)
1199 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
1200 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
1201 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
1204 static void m4x3_rotate_x( m4x3f m
, f32 angle
)
1206 m4x3f t
= M4X3_IDENTITY
;
1217 m4x3_mul( m
, t
, m
);
1220 static void m4x3_rotate_y( m4x3f m
, f32 angle
)
1222 m4x3f t
= M4X3_IDENTITY
;
1233 m4x3_mul( m
, t
, m
);
1236 static void m4x3_rotate_z( m4x3f m
, f32 angle
)
1238 m4x3f t
= M4X3_IDENTITY
;
1249 m4x3_mul( m
, t
, m
);
1252 static void m4x3_expand( m4x3f m
, m4x4f d
)
1254 v3_copy( m
[0], d
[0] );
1255 v3_copy( m
[1], d
[1] );
1256 v3_copy( m
[2], d
[2] );
1257 v3_copy( m
[3], d
[3] );
1264 static void m4x3_decompose( m4x3f m
, v3f co
, v4f q
, v3f s
)
1266 v3_copy( m
[3], co
);
1267 s
[0] = v3_length(m
[0]);
1268 s
[1] = v3_length(m
[1]);
1269 s
[2] = v3_length(m
[2]);
1272 v3_divs( m
[0], s
[0], rot
[0] );
1273 v3_divs( m
[1], s
[1], rot
[1] );
1274 v3_divs( m
[2], s
[2], rot
[2] );
1279 static void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
){
1281 m4x3_mulv( m
, point
, v
);
1283 v3_minv( box
[0], v
, box
[0] );
1284 v3_maxv( box
[1], v
, box
[1] );
1287 static void m4x3_expand_aabb_aabb( m4x3f m
, boxf boxa
, boxf boxb
){
1289 v3_copy( boxb
[0], a
);
1290 v3_copy( boxb
[1], b
);
1291 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], a
[2] } );
1292 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], a
[2] } );
1293 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], a
[2] } );
1294 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], a
[2] } );
1295 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], b
[2] } );
1296 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], b
[2] } );
1297 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], b
[2] } );
1298 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], b
[2] } );
1300 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1303 v3_sub( target
, pos
, dir
);
1304 v3_normalize( dir
);
1306 v3_copy( dir
, m
[2] );
1308 v3_cross( up
, m
[2], m
[0] );
1309 v3_normalize( m
[0] );
1311 v3_cross( m
[2], m
[0], m
[1] );
1312 v3_copy( pos
, m
[3] );
1316 * -----------------------------------------------------------------------------
1317 * Section 4.d 4x4 matrices
1318 * -----------------------------------------------------------------------------
1321 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1322 { 0.0f, 1.0f, 0.0f, 0.0f },\
1323 { 0.0f, 0.0f, 1.0f, 0.0f },\
1324 { 0.0f, 0.0f, 0.0f, 1.0f }}
1325 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1326 { 0.0f, 0.0f, 0.0f, 0.0f },\
1327 { 0.0f, 0.0f, 0.0f, 0.0f },\
1328 { 0.0f, 0.0f, 0.0f, 0.0f }}
1330 static void m4x4_projection( m4x4f m
, f32 angle
,
1331 f32 ratio
, f32 fnear
, f32 ffar
)
1333 f32 scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1339 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1345 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1349 m
[2][0] = (r
+ l
) / (r
- l
);
1350 m
[2][1] = (t
+ b
) / (t
- b
);
1351 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1356 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1360 static void m4x4_translate( m4x4f m
, v3f v
)
1362 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1363 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1364 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1367 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1369 v4_copy( a
[0], b
[0] );
1370 v4_copy( a
[1], b
[1] );
1371 v4_copy( a
[2], b
[2] );
1372 v4_copy( a
[3], b
[3] );
1375 static inline void m4x4_identity( m4x4f a
)
1377 m4x4f id
= M4X4_IDENTITY
;
1381 static inline void m4x4_zero( m4x4f a
)
1383 m4x4f zero
= M4X4_ZERO
;
1384 m4x4_copy( zero
, a
);
1387 static inline void m4x4_mul( m4x4f a
, m4x4f b
, 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],
1394 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1395 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1396 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1397 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1399 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1400 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1401 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1402 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1403 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1404 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1405 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1406 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1407 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1408 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1409 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1410 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1411 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1412 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1413 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1414 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1417 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1421 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1422 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1423 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1424 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1429 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1431 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1432 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1433 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1434 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1438 t
[0] = a22
*a33
- a32
*a23
;
1439 t
[1] = a21
*a33
- a31
*a23
;
1440 t
[2] = a21
*a32
- a31
*a22
;
1441 t
[3] = a20
*a33
- a30
*a23
;
1442 t
[4] = a20
*a32
- a30
*a22
;
1443 t
[5] = a20
*a31
- a30
*a21
;
1445 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1446 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1447 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1448 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1450 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1451 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1452 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1453 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1455 t
[0] = a12
*a33
- a32
*a13
;
1456 t
[1] = a11
*a33
- a31
*a13
;
1457 t
[2] = a11
*a32
- a31
*a12
;
1458 t
[3] = a10
*a33
- a30
*a13
;
1459 t
[4] = a10
*a32
- a30
*a12
;
1460 t
[5] = a10
*a31
- a30
*a11
;
1462 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1463 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1464 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1465 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1467 t
[0] = a12
*a23
- a22
*a13
;
1468 t
[1] = a11
*a23
- a21
*a13
;
1469 t
[2] = a11
*a22
- a21
*a12
;
1470 t
[3] = a10
*a23
- a20
*a13
;
1471 t
[4] = a10
*a22
- a20
*a12
;
1472 t
[5] = a10
*a21
- a20
*a11
;
1474 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1475 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1476 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1477 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1479 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1480 v4_muls( d
[0], det
, d
[0] );
1481 v4_muls( d
[1], det
, d
[1] );
1482 v4_muls( d
[2], det
, d
[2] );
1483 v4_muls( d
[3], det
, d
[3] );
1487 * -----------------------------------------------------------------------------
1489 * -----------------------------------------------------------------------------
1492 static inline void box_addpt( boxf a
, v3f pt
)
1494 v3_minv( a
[0], pt
, a
[0] );
1495 v3_maxv( a
[1], pt
, a
[1] );
1498 static inline void box_concat( boxf a
, boxf b
)
1500 v3_minv( a
[0], b
[0], a
[0] );
1501 v3_maxv( a
[1], b
[1], a
[1] );
1504 static inline void box_copy( boxf a
, boxf b
)
1506 v3_copy( a
[0], b
[0] );
1507 v3_copy( a
[1], b
[1] );
1510 static inline int box_overlap( boxf a
, boxf b
)
1513 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
1514 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
1515 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
1519 static int box_within( boxf greater
, boxf lesser
)
1522 v3_sub( lesser
[0], greater
[0], a
);
1523 v3_sub( lesser
[1], greater
[1], b
);
1525 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
1526 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
1534 static inline void box_init_inf( boxf box
){
1535 v3_fill( box
[0], INFINITY
);
1536 v3_fill( box
[1], -INFINITY
);
1540 * -----------------------------------------------------------------------------
1541 * Section 5.b Planes
1542 * -----------------------------------------------------------------------------
1545 static inline void tri_to_plane( f64 a
[3], f64 b
[3],
1546 f64 c
[3], f64 p
[4] )
1552 edge0
[0] = b
[0] - a
[0];
1553 edge0
[1] = b
[1] - a
[1];
1554 edge0
[2] = b
[2] - a
[2];
1556 edge1
[0] = c
[0] - a
[0];
1557 edge1
[1] = c
[1] - a
[1];
1558 edge1
[2] = c
[2] - a
[2];
1560 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1561 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1562 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1564 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1565 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1572 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1574 f32
const epsilon
= 1e-6f
;
1577 v3_cross( a
, b
, x
);
1578 f32 d
= v3_dot( x
, c
);
1580 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1583 v3_cross( b
, c
, v0
);
1584 v3_cross( c
, a
, v1
);
1585 v3_cross( a
, b
, v2
);
1587 v3_muls( v0
, a
[3], p
);
1588 v3_muladds( p
, v1
, b
[3], p
);
1589 v3_muladds( p
, v2
, c
[3], p
);
1595 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1597 f32
const epsilon
= 1e-6f
;
1600 v3_cross( a
, b
, c
);
1601 f32 d
= v3_length2( c
);
1603 if( (d
< epsilon
) && (d
> -epsilon
) )
1607 v3_cross( c
, b
, v0
);
1608 v3_cross( a
, c
, v1
);
1610 v3_muls( v0
, a
[3], vx
);
1611 v3_muladds( vx
, v1
, b
[3], vx
);
1612 v3_divs( vx
, d
, p
);
1618 static int plane_segment( v4f plane
, v3f a
, v3f b
, v3f co
)
1620 f32 d0
= v3_dot( a
, plane
) - plane
[3],
1621 d1
= v3_dot( b
, plane
) - plane
[3];
1625 f32 tot
= 1.0f
/( fabsf(d0
)+fabsf(d1
) );
1627 v3_muls( a
, fabsf(d1
) * tot
, co
);
1628 v3_muladds( co
, b
, fabsf(d0
) * tot
, co
);
1635 static inline f64
plane_polarity( f64 p
[4], f64 a
[3] )
1638 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1639 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1643 static f32
ray_plane( v4f plane
, v3f co
, v3f dir
){
1644 f32 d
= v3_dot( plane
, dir
);
1645 if( fabsf(d
) > 1e-6f
){
1647 v3_muls( plane
, plane
[3], v0
);
1648 v3_sub( v0
, co
, v0
);
1649 return v3_dot( v0
, plane
) / d
;
1651 else return INFINITY
;
1655 * -----------------------------------------------------------------------------
1656 * Section 5.c Closest point functions
1657 * -----------------------------------------------------------------------------
1661 * These closest point tests were learned from Real-Time Collision Detection by
1664 static f32
closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1665 f32
*s
, f32
*t
, v3f c1
, v3f c2
)
1668 v3_sub( q1
, p1
, d1
);
1669 v3_sub( q2
, p2
, d2
);
1670 v3_sub( p1
, p2
, r
);
1672 f32 a
= v3_length2( d1
),
1673 e
= v3_length2( d2
),
1674 f
= v3_dot( d2
, r
);
1676 const f32 kEpsilon
= 0.0001f
;
1678 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1686 v3_sub( c1
, c2
, v0
);
1688 return v3_length2( v0
);
1694 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1698 f32 c
= v3_dot( d1
, r
);
1702 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1706 f32 b
= v3_dot(d1
,d2
),
1711 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1718 *t
= (b
*(*s
)+f
) / e
;
1723 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1725 else if( *t
> 1.0f
)
1728 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1733 v3_muladds( p1
, d1
, *s
, c1
);
1734 v3_muladds( p2
, d2
, *t
, c2
);
1737 v3_sub( c1
, c2
, v0
);
1738 return v3_length2( v0
);
1741 static int point_inside_aabb( boxf box
, v3f point
)
1743 if((point
[0]<=box
[1][0]) && (point
[1]<=box
[1][1]) && (point
[2]<=box
[1][2]) &&
1744 (point
[0]>=box
[0][0]) && (point
[1]>=box
[0][1]) && (point
[2]>=box
[0][2]) )
1750 static void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1752 v3_maxv( p
, box
[0], dest
);
1753 v3_minv( dest
, box
[1], dest
);
1756 static void closest_point_obb( v3f p
, boxf box
,
1757 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1760 m4x3_mulv( inv_mtx
, p
, local
);
1761 closest_point_aabb( local
, box
, local
);
1762 m4x3_mulv( mtx
, local
, dest
);
1765 static f32
closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1769 v3_sub( point
, a
, v1
);
1771 f32 t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1772 t
= vg_clampf(t
,0.0f
,1.0f
);
1773 v3_muladds( a
, v0
, t
, dest
);
1777 static void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1782 /* Region outside A */
1783 v3_sub( tri
[1], tri
[0], ab
);
1784 v3_sub( tri
[2], tri
[0], ac
);
1785 v3_sub( p
, tri
[0], ap
);
1789 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1791 v3_copy( tri
[0], dest
);
1792 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1796 /* Region outside B */
1800 v3_sub( p
, tri
[1], bp
);
1801 d3
= v3_dot( ab
, bp
);
1802 d4
= v3_dot( ac
, bp
);
1804 if( d3
>= 0.0f
&& d4
<= d3
)
1806 v3_copy( tri
[1], dest
);
1807 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1811 /* Edge region of AB */
1812 f32 vc
= d1
*d4
- d3
*d2
;
1813 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1815 f32 v
= d1
/ (d1
-d3
);
1816 v3_muladds( tri
[0], ab
, v
, dest
);
1817 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1821 /* Region outside C */
1824 v3_sub( p
, tri
[2], cp
);
1825 d5
= v3_dot(ab
, cp
);
1826 d6
= v3_dot(ac
, cp
);
1828 if( d6
>= 0.0f
&& d5
<= d6
)
1830 v3_copy( tri
[2], dest
);
1831 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1836 f32 vb
= d5
*d2
- d1
*d6
;
1837 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1839 f32 w
= d2
/ (d2
-d6
);
1840 v3_muladds( tri
[0], ac
, w
, dest
);
1841 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1846 f32 va
= d3
*d6
- d5
*d4
;
1847 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1849 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1851 v3_sub( tri
[2], tri
[1], bc
);
1852 v3_muladds( tri
[1], bc
, w
, dest
);
1853 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1857 /* P inside region, Q via barycentric coordinates uvw */
1858 f32 d
= 1.0f
/(va
+vb
+vc
),
1862 v3_muladds( tri
[0], ab
, v
, dest
);
1863 v3_muladds( dest
, ac
, w
, dest
);
1868 k_contact_type_default
,
1869 k_contact_type_disabled
,
1873 static enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1878 /* Region outside A */
1879 v3_sub( tri
[1], tri
[0], ab
);
1880 v3_sub( tri
[2], tri
[0], ac
);
1881 v3_sub( p
, tri
[0], ap
);
1885 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1887 v3_copy( tri
[0], dest
);
1888 return k_contact_type_default
;
1891 /* Region outside B */
1895 v3_sub( p
, tri
[1], bp
);
1896 d3
= v3_dot( ab
, bp
);
1897 d4
= v3_dot( ac
, bp
);
1899 if( d3
>= 0.0f
&& d4
<= d3
)
1901 v3_copy( tri
[1], dest
);
1902 return k_contact_type_edge
;
1905 /* Edge region of AB */
1906 f32 vc
= d1
*d4
- d3
*d2
;
1907 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1909 f32 v
= d1
/ (d1
-d3
);
1910 v3_muladds( tri
[0], ab
, v
, dest
);
1911 return k_contact_type_edge
;
1914 /* Region outside C */
1917 v3_sub( p
, tri
[2], cp
);
1918 d5
= v3_dot(ab
, cp
);
1919 d6
= v3_dot(ac
, cp
);
1921 if( d6
>= 0.0f
&& d5
<= d6
)
1923 v3_copy( tri
[2], dest
);
1924 return k_contact_type_edge
;
1928 f32 vb
= d5
*d2
- d1
*d6
;
1929 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1931 f32 w
= d2
/ (d2
-d6
);
1932 v3_muladds( tri
[0], ac
, w
, dest
);
1933 return k_contact_type_edge
;
1937 f32 va
= d3
*d6
- d5
*d4
;
1938 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1940 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1942 v3_sub( tri
[2], tri
[1], bc
);
1943 v3_muladds( tri
[1], bc
, w
, dest
);
1944 return k_contact_type_edge
;
1947 /* P inside region, Q via barycentric coordinates uvw */
1948 f32 d
= 1.0f
/(va
+vb
+vc
),
1952 v3_muladds( tri
[0], ab
, v
, dest
);
1953 v3_muladds( dest
, ac
, w
, dest
);
1955 return k_contact_type_default
;
1958 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1960 v2f pabs
, ei
, e2
, ve
, t
;
1963 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1965 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1967 v2_fill( t
, 0.70710678118654752f
);
1969 for( int i
=0; i
<3; i
++ ){
1972 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1976 v2_sub( pabs
, v
, u
);
1980 v2_sub( ud
, v
, ud
);
1982 v2_muls( u
, v2_length( ud
), u
);
1987 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1992 v2_copysign( o
, p
);
1996 * -----------------------------------------------------------------------------
1997 * Section 5.d Raycasts & Spherecasts
1998 * -----------------------------------------------------------------------------
2001 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, f32 dist
)
2006 v3_sub( box
[0], co
, v0
);
2007 v3_sub( box
[1], co
, v1
);
2009 v3_mul( v0
, dir_inv
, v0
);
2010 v3_mul( v1
, dir_inv
, v1
);
2012 tmin
= vg_minf( v0
[0], v1
[0] );
2013 tmax
= vg_maxf( v0
[0], v1
[0] );
2014 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
2015 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
2016 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
2017 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
2019 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
2022 /* Time of intersection with ray vs triangle */
2023 static int ray_tri( v3f tri
[3], v3f co
,
2024 v3f dir
, f32
*dist
, int backfaces
)
2026 f32
const kEpsilon
= 0.00001f
;
2028 v3f v0
, v1
, h
, s
, q
, n
;
2035 v3_sub( pb
, pa
, v0
);
2036 v3_sub( pc
, pa
, v1
);
2037 v3_cross( dir
, v1
, h
);
2038 v3_cross( v0
, v1
, n
);
2040 if( (v3_dot( n
, dir
) > 0.0f
) && !backfaces
) /* Backface culling */
2044 a
= v3_dot( v0
, h
);
2046 if( a
> -kEpsilon
&& a
< kEpsilon
)
2050 v3_sub( co
, pa
, s
);
2052 u
= f
* v3_dot(s
, h
);
2053 if( u
< 0.0f
|| u
> 1.0f
)
2056 v3_cross( s
, v0
, q
);
2057 v
= f
* v3_dot( dir
, q
);
2058 if( v
< 0.0f
|| u
+v
> 1.0f
)
2061 t
= f
* v3_dot(v1
, q
);
2070 /* time of intersection with ray vs sphere */
2071 static int ray_sphere( v3f c
, f32 r
,
2072 v3f co
, v3f dir
, f32
*t
)
2077 f32 b
= v3_dot( m
, dir
),
2078 c1
= v3_dot( m
, m
) - r
*r
;
2080 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
2081 if( c1
> 0.0f
&& b
> 0.0f
)
2084 f32 discr
= b
*b
- c1
;
2086 /* A negative discriminant corresponds to ray missing sphere */
2091 * Ray now found to intersect sphere, compute smallest t value of
2094 *t
= -b
- sqrtf( discr
);
2096 /* If t is negative, ray started inside sphere so clamp t to zero */
2104 * time of intersection of ray vs cylinder
2105 * The cylinder does not have caps but is finite
2107 * Heavily adapted from regular segment vs cylinder from:
2108 * Real-Time Collision Detection
2110 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, f32 r
,
2111 v3f co
, v3f dir
, f32
*t
)
2114 v3_muladds( co
, dir
, 1.0f
, sb
);
2118 v3_sub( sb
, co
, n
);
2120 f32 md
= v3_dot( m
, d
),
2121 nd
= v3_dot( n
, d
),
2122 dd
= v3_dot( d
, d
),
2123 nn
= v3_dot( n
, n
),
2124 mn
= v3_dot( m
, n
),
2126 k
= v3_dot( m
, m
) - r
*r
,
2129 if( fabsf(a
) < 0.00001f
)
2131 /* Segment runs parallel to cylinder axis */
2135 f32 b
= dd
*mn
- nd
*md
,
2139 return 0; /* No real roots; no intersection */
2141 *t
= (-b
- sqrtf(discr
)) / a
;
2143 return 0; /* Intersection behind ray */
2145 /* Check within cylinder segment */
2146 if( md
+ (*t
)*nd
< 0.0f
)
2149 if( md
+ (*t
)*nd
> dd
)
2152 /* Segment intersects cylinder between the endcaps; t is correct */
2157 * Time of intersection of sphere and triangle. Origin must be outside the
2158 * colliding area. This is a fairly long procedure.
2160 static int spherecast_triangle( v3f tri
[3],
2161 v3f co
, v3f dir
, f32 r
, f32
*t
, v3f n
)
2166 v3_sub( tri
[1], tri
[0], v0
);
2167 v3_sub( tri
[2], tri
[0], v1
);
2168 v3_cross( v0
, v1
, n
);
2170 v3_muladds( tri
[0], n
, r
, sum
[0] );
2171 v3_muladds( tri
[1], n
, r
, sum
[1] );
2172 v3_muladds( tri
[2], n
, r
, sum
[2] );
2175 f32 t_min
= INFINITY
,
2178 if( ray_tri( sum
, co
, dir
, &t1
, 0 ) ){
2179 t_min
= vg_minf( t_min
, t1
);
2184 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2187 for( int i
=0; i
<3; i
++ ){
2188 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) ){
2189 t_min
= vg_minf( t_min
, t1
);
2195 for( int i
=0; i
<3; i
++ ){
2199 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) ){
2204 v3_add( dir
, co
, co1
);
2205 v3_lerp( co
, co1
, t_min
, ct
);
2207 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
2208 v3_sub( ct
, cx
, n
);
2221 * -----------------------------------------------------------------------------
2222 * Section 5.e Curves
2223 * -----------------------------------------------------------------------------
2226 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, f32 t
, v3f p
)
2231 v3_muls( p1
, ttt
, p
);
2232 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2233 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2234 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);
2237 static void eval_bezier3( v3f p0
, v3f p1
, v3f p2
, f32 t
, v3f p
)
2241 v3_muls( p0
, u
*u
, p
);
2242 v3_muladds( p
, p1
, 2.0f
*u
*t
, p
);
2243 v3_muladds( p
, p2
, t
*t
, p
);
2247 * -----------------------------------------------------------------------------
2248 * Section 5.f Volumes
2249 * -----------------------------------------------------------------------------
2252 static float vg_sphere_volume( float radius
){
2253 float r3
= radius
*radius
*radius
;
2254 return (4.0f
/3.0f
) * VG_PIf
* r3
;
2258 * -----------------------------------------------------------------------------
2259 * Section 6.a PSRNG and some distributions
2260 * -----------------------------------------------------------------------------
2263 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2264 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2265 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2266 * equidistributed uniform pseudorandom number generator," ACM
2267 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2268 * January pp.3-30 1998.
2270 * http://www.sultanik.com/Mersenne_twister
2271 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2274 #define MT_UPPER_MASK 0x80000000
2275 #define MT_LOWER_MASK 0x7fffffff
2276 #define MT_TEMPERING_MASK_B 0x9d2c5680
2277 #define MT_TEMPERING_MASK_C 0xefc60000
2279 #define MT_STATE_VECTOR_LENGTH 624
2281 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2282 #define MT_STATE_VECTOR_M 397
2284 typedef struct vg_rand vg_rand
;
2286 u32 mt
[MT_STATE_VECTOR_LENGTH
];
2290 static void vg_rand_seed( vg_rand
*rand
, unsigned long seed
) {
2291 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2292 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2293 * Programming," Vol. 2 (2nd Ed.) pp.102.
2295 rand
->mt
[0] = seed
& 0xffffffff;
2296 for( rand
->index
=1; rand
->index
<MT_STATE_VECTOR_LENGTH
; rand
->index
++){
2297 rand
->mt
[rand
->index
] = (6069 * rand
->mt
[rand
->index
-1]) & 0xffffffff;
2302 * Generates a pseudo-randomly generated long.
2304 static u32
vg_randu32( vg_rand
*rand
) {
2306 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2307 static u32 mag
[2] = {0x0, 0x9908b0df};
2308 if( rand
->index
>= MT_STATE_VECTOR_LENGTH
|| rand
->index
< 0 ){
2309 /* generate STATE_VECTOR_LENGTH words at a time */
2311 if( rand
->index
>= MT_STATE_VECTOR_LENGTH
+1 || rand
->index
< 0 ){
2312 vg_rand_seed( rand
, 4357 );
2314 for( kk
=0; kk
<MT_STATE_VECTOR_LENGTH
-MT_STATE_VECTOR_M
; kk
++ ){
2315 y
= (rand
->mt
[kk
] & MT_UPPER_MASK
) |
2316 (rand
->mt
[kk
+1] & MT_LOWER_MASK
);
2317 rand
->mt
[kk
] = rand
->mt
[kk
+MT_STATE_VECTOR_M
] ^ (y
>>1) ^ mag
[y
& 0x1];
2319 for( ; kk
<MT_STATE_VECTOR_LENGTH
-1; kk
++ ){
2320 y
= (rand
->mt
[kk
] & MT_UPPER_MASK
) |
2321 (rand
->mt
[kk
+1] & MT_LOWER_MASK
);
2323 rand
->mt
[ kk
+(MT_STATE_VECTOR_M
-MT_STATE_VECTOR_LENGTH
)] ^
2324 (y
>> 1) ^ mag
[y
& 0x1];
2326 y
= (rand
->mt
[MT_STATE_VECTOR_LENGTH
-1] & MT_UPPER_MASK
) |
2327 (rand
->mt
[0] & MT_LOWER_MASK
);
2328 rand
->mt
[MT_STATE_VECTOR_LENGTH
-1] =
2329 rand
->mt
[MT_STATE_VECTOR_M
-1] ^ (y
>> 1) ^ mag
[y
& 0x1];
2332 y
= rand
->mt
[rand
->index
++];
2334 y
^= (y
<< 7) & MT_TEMPERING_MASK_B
;
2335 y
^= (y
<< 15) & MT_TEMPERING_MASK_C
;
2341 * Generates a pseudo-randomly generated f64 in the range [0..1].
2343 static inline f64
vg_randf64( vg_rand
*rand
){
2344 return (f64
)vg_randu32(rand
)/(f64
)0xffffffff;
2347 static inline f64
vg_randf64_range( vg_rand
*rand
, f64 min
, f64 max
){
2348 return vg_lerp( min
, max
, (f64
)vg_randf64(rand
) );
2351 static inline void vg_rand_dir( vg_rand
*rand
, v3f dir
){
2352 dir
[0] = vg_randf64(rand
);
2353 dir
[1] = vg_randf64(rand
);
2354 dir
[2] = vg_randf64(rand
);
2356 /* warning: *could* be 0 length.
2357 * very unlikely.. 1 in (2^32)^3. but its mathematically wrong. */
2359 v3_muls( dir
, 2.0f
, dir
);
2360 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2362 v3_normalize( dir
);
2365 static inline void vg_rand_sphere( vg_rand
*rand
, v3f co
){
2366 vg_rand_dir(rand
,co
);
2367 v3_muls( co
, cbrtf( vg_randf64(rand
) ), co
);
2370 static void vg_rand_disc( vg_rand
*rand
, v2f co
){
2371 f32 a
= vg_randf64(rand
) * VG_TAUf
;
2374 v2_muls( co
, sqrtf( vg_randf64(rand
) ), co
);
2377 static void vg_rand_cone( vg_rand
*rand
, v3f out_dir
, f32 angle
){
2378 f32 r
= sqrtf(vg_randf64(rand
)) * angle
* 0.5f
,
2379 a
= vg_randf64(rand
) * VG_TAUf
;
2381 out_dir
[0] = sinf(a
) * sinf(r
);
2382 out_dir
[1] = cosf(a
) * sinf(r
);
2383 out_dir
[2] = cosf(r
);