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
);
135 /* https://iquilezles.org/articles/functions/
137 * Use k to control the stretching of the function. Its maximum, which is 1,
138 * happens at exactly x = 1/k.
140 static f32
vg_exp_impulse( f32 x
, f32 k
){
142 return h
*expf(1.0f
-h
);
146 * -----------------------------------------------------------------------------
147 * Section 2.a 2D Vectors
148 * -----------------------------------------------------------------------------
151 static inline void v2_copy( v2f a
, v2f d
)
153 d
[0] = a
[0]; d
[1] = a
[1];
156 static inline void v2_zero( v2f a
)
158 a
[0] = 0.f
; a
[1] = 0.f
;
161 static inline void v2_add( v2f a
, v2f b
, v2f d
)
163 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
166 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
168 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
171 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
173 dest
[0] = vg_minf(a
[0], b
[0]);
174 dest
[1] = vg_minf(a
[1], b
[1]);
177 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
179 dest
[0] = vg_maxf(a
[0], b
[0]);
180 dest
[1] = vg_maxf(a
[1], b
[1]);
183 static inline f32
v2_dot( v2f a
, v2f b
)
185 return a
[0] * b
[0] + a
[1] * b
[1];
188 static inline f32
v2_cross( v2f a
, v2f b
)
190 return a
[0]*b
[1] - a
[1]*b
[0];
193 static inline void v2_abs( v2f a
, v2f d
)
195 d
[0] = fabsf( a
[0] );
196 d
[1] = fabsf( a
[1] );
199 static inline void v2_muls( v2f a
, f32 s
, v2f d
)
201 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
204 static inline void v2_divs( v2f a
, f32 s
, v2f d
)
206 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
209 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
215 static inline void v2_div( v2f a
, v2f b
, v2f d
)
217 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
220 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
222 d
[0] = a
[0]+b
[0]*s
[0];
223 d
[1] = a
[1]+b
[1]*s
[1];
226 static inline void v2_muladds( v2f a
, v2f b
, f32 s
, v2f d
)
232 static inline f32
v2_length2( v2f a
)
234 return a
[0]*a
[0] + a
[1]*a
[1];
237 static inline f32
v2_length( v2f a
)
239 return sqrtf( v2_length2( a
) );
242 static inline f32
v2_dist2( v2f a
, v2f b
)
245 v2_sub( a
, b
, delta
);
246 return v2_length2( delta
);
249 static inline f32
v2_dist( v2f a
, v2f b
)
251 return sqrtf( v2_dist2( a
, b
) );
254 static inline void v2_lerp( v2f a
, v2f b
, f32 t
, v2f d
)
256 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
257 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
260 static inline void v2_normalize( v2f a
)
262 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
265 static void v2_normalize_clamp( v2f a
)
267 f32 l2
= v2_length2( a
);
269 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
272 static inline void v2_floor( v2f a
, v2f b
)
274 b
[0] = floorf( a
[0] );
275 b
[1] = floorf( a
[1] );
278 static inline void v2_fill( v2f a
, f32 v
)
284 static inline void v2_copysign( v2f a
, v2f b
)
286 a
[0] = copysignf( a
[0], b
[0] );
287 a
[1] = copysignf( a
[1], b
[1] );
291 * ---------------- */
293 static inline void v2i_copy( v2i a
, v2i b
)
295 b
[0] = a
[0]; b
[1] = a
[1];
298 static inline int v2i_eq( v2i a
, v2i b
)
300 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
303 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
305 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
308 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
310 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
314 * -----------------------------------------------------------------------------
315 * Section 2.b 3D Vectors
316 * -----------------------------------------------------------------------------
319 static inline void v3_copy( v3f a
, v3f b
)
321 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
324 static inline void v3_zero( v3f a
)
326 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
329 static inline void v3_add( 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_add( 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_sub( 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 v3i_sub( v3i a
, v3i b
, v3i d
)
346 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
349 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
351 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
354 static inline void v3_div( v3f a
, v3f b
, v3f d
)
356 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
357 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
358 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
361 static inline void v3_muls( v3f a
, f32 s
, v3f d
)
363 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
366 static inline void v3_fill( v3f a
, f32 v
)
373 static inline void v3_divs( v3f a
, f32 s
, v3f d
)
376 v3_fill( d
, INFINITY
);
385 static inline void v3_muladds( v3f a
, v3f b
, f32 s
, v3f d
)
387 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
390 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
392 d
[0] = a
[0]+b
[0]*s
[0];
393 d
[1] = a
[1]+b
[1]*s
[1];
394 d
[2] = a
[2]+b
[2]*s
[2];
397 static inline f32
v3_dot( v3f a
, v3f b
)
399 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
402 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
405 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
406 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
407 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
411 static inline f32
v3_length2( v3f a
)
413 return v3_dot( a
, a
);
416 static inline f32
v3_length( v3f a
)
418 return sqrtf( v3_length2( a
) );
421 static inline f32
v3_dist2( v3f a
, v3f b
)
424 v3_sub( a
, b
, delta
);
425 return v3_length2( delta
);
428 static inline f32
v3_dist( v3f a
, v3f b
)
430 return sqrtf( v3_dist2( a
, b
) );
433 static inline void v3_normalize( v3f a
)
435 v3_muls( a
, 1.f
/ v3_length( a
), a
);
438 static inline f32
vg_lerpf( f32 a
, f32 b
, f32 t
){
442 static inline f64
vg_lerp( f64 a
, f64 b
, f64 t
)
447 static inline void vg_slewf( f32
*a
, f32 b
, f32 speed
){
448 f32 d
= vg_signf( b
-*a
),
450 *a
= vg_minf( b
*d
, c
*d
) * d
;
453 static inline f32
vg_smoothstepf( f32 x
){
454 return x
*x
*(3.0f
- 2.0f
*x
);
458 /* correctly lerp around circular period -pi -> pi */
459 static f32
vg_alerpf( f32 a
, f32 b
, f32 t
)
461 f32 d
= fmodf( b
-a
, VG_TAUf
),
462 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
466 static inline void v3_lerp( v3f a
, v3f b
, f32 t
, v3f d
)
468 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
469 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
470 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
473 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
475 dest
[0] = vg_minf(a
[0], b
[0]);
476 dest
[1] = vg_minf(a
[1], b
[1]);
477 dest
[2] = vg_minf(a
[2], b
[2]);
480 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
482 dest
[0] = vg_maxf(a
[0], b
[0]);
483 dest
[1] = vg_maxf(a
[1], b
[1]);
484 dest
[2] = vg_maxf(a
[2], b
[2]);
487 static inline f32
v3_minf( v3f a
)
489 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
492 static inline f32
v3_maxf( v3f a
)
494 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
497 static inline void v3_floor( v3f a
, v3f b
)
499 b
[0] = floorf( a
[0] );
500 b
[1] = floorf( a
[1] );
501 b
[2] = floorf( a
[2] );
504 static inline void v3_ceil( v3f a
, v3f b
)
506 b
[0] = ceilf( a
[0] );
507 b
[1] = ceilf( a
[1] );
508 b
[2] = ceilf( a
[2] );
511 static inline void v3_negate( v3f a
, v3f b
)
518 static inline void v3_rotate( v3f v
, f32 angle
, v3f axis
, v3f d
)
529 v3_cross( k
, v
, v2
);
530 v3_muls( v2
, s
, v2
);
531 v3_add( v1
, v2
, v1
);
532 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
536 static void v3_tangent_basis( v3f n
, v3f tx
, v3f ty
){
537 /* Compute tangent basis (box2d) */
538 if( fabsf( n
[0] ) >= 0.57735027f
){
550 v3_cross( n
, tx
, ty
);
554 * Compute yaw and pitch based of a normalized vector representing forward
556 * result -> (YAW,PITCH,0.0)
558 static void v3_angles( v3f v
, v3f out_angles
){
559 float yaw
= atan2f( v
[0], -v
[2] ),
563 v
[0]*v
[0] + v
[2]*v
[2]
568 out_angles
[1] = pitch
;
569 out_angles
[2] = 0.0f
;
573 * Compute the forward vector from (YAW,PITCH,ROLL)
576 static void v3_angles_vector( v3f angles
, v3f out_v
){
577 out_v
[0] = sinf( angles
[0] ) * cosf( angles
[1] );
578 out_v
[1] = -sinf( angles
[1] );
579 out_v
[2] = -cosf( angles
[0] ) * cosf( angles
[1] );
583 * -----------------------------------------------------------------------------
584 * Section 2.c 4D Vectors
585 * -----------------------------------------------------------------------------
588 static inline void v4_copy( v4f a
, v4f b
)
590 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
593 static inline void v4_add( v4f a
, v4f b
, v4f d
)
601 static inline void v4_zero( v4f a
)
603 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
606 static inline void v4_muls( v4f a
, f32 s
, v4f d
)
614 static inline void v4_muladds( v4f a
, v4f b
, f32 s
, v4f d
)
622 static inline void v4_lerp( v4f a
, v4f b
, f32 t
, v4f d
)
624 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
625 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
626 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
627 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
630 static inline f32
v4_dot( v4f a
, v4f b
)
632 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
635 static inline f32
v4_length( v4f a
)
637 return sqrtf( v4_dot(a
,a
) );
641 * -----------------------------------------------------------------------------
642 * Section 3 Quaternions
643 * -----------------------------------------------------------------------------
646 static inline void q_identity( v4f q
)
648 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
651 static inline void q_axis_angle( v4f q
, v3f axis
, f32 angle
)
663 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
666 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
667 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
668 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
669 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
673 static inline void q_normalize( v4f q
)
675 f32 l2
= v4_dot(q
,q
);
676 if( l2
< 0.00001f
) q_identity( q
);
678 f32 s
= 1.0f
/sqrtf(l2
);
686 static inline void q_inv( v4f q
, v4f d
)
688 f32 s
= 1.0f
/ v4_dot(q
,q
);
695 static inline void q_nlerp( v4f a
, v4f b
, f32 t
, v4f d
){
696 if( v4_dot(a
,b
) < 0.0f
){
698 v4_muls( b
, -1.0f
, c
);
699 v4_lerp( a
, c
, t
, d
);
702 v4_lerp( a
, b
, t
, d
);
707 static inline void q_m3x3( v4f q
, m3x3f d
)
711 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
713 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
714 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
715 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
717 d
[0][0] = 1.0f
- yy
- zz
;
718 d
[1][1] = 1.0f
- xx
- zz
;
719 d
[2][2] = 1.0f
- xx
- yy
;
728 static void q_mulv( v4f q
, v3f v
, v3f d
)
732 v3_muls( q
, 2.0f
*v3_dot(q
,v
), v1
);
733 v3_muls( v
, q
[3]*q
[3] - v3_dot(q
,q
), v2
);
734 v3_add( v1
, v2
, v1
);
735 v3_cross( q
, v
, v2
);
736 v3_muls( v2
, 2.0f
*q
[3], v2
);
740 static f32
q_dist( v4f q0
, v4f q1
){
741 return acosf( 2.0f
* v4_dot(q0
,q1
) -1.0f
);
745 * -----------------------------------------------------------------------------
746 * Section 4.a 2x2 matrices
747 * -----------------------------------------------------------------------------
750 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
753 #define M2X2_ZERO {{0.0f, 0.0f, }, \
756 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
758 v2_copy( a
[0], b
[0] );
759 v2_copy( a
[1], b
[1] );
762 static inline void m2x2_identity( m2x2f a
)
764 m2x2f id
= M2X2_INDENTIY
;
768 static inline void m2x2_create_rotation( m2x2f a
, f32 theta
)
781 static inline void m2x2_mulv( m2x2f m
, v2f v
, v2f d
)
785 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1];
786 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1];
792 * -----------------------------------------------------------------------------
793 * Section 4.b 3x3 matrices
794 * -----------------------------------------------------------------------------
797 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
798 { 0.0f, 1.0f, 0.0f, },\
799 { 0.0f, 0.0f, 1.0f, }}
801 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
802 { 0.0f, 0.0f, 0.0f, },\
803 { 0.0f, 0.0f, 0.0f, }}
806 static void euler_m3x3( v3f angles
, m3x3f d
)
808 f32 cosY
= cosf( angles
[0] ),
809 sinY
= sinf( angles
[0] ),
810 cosP
= cosf( angles
[1] ),
811 sinP
= sinf( angles
[1] ),
812 cosR
= cosf( angles
[2] ),
813 sinR
= sinf( angles
[2] );
815 d
[2][0] = -sinY
* cosP
;
817 d
[2][2] = cosY
* cosP
;
819 d
[0][0] = cosY
* cosR
;
821 d
[0][2] = sinY
* cosR
;
823 v3_cross( d
[0], d
[2], d
[1] );
826 static void m3x3_q( m3x3f m
, v4f q
)
830 diag
= m
[0][0] + m
[1][1] + m
[2][2];
833 r
= sqrtf( 1.0f
+ diag
);
835 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
836 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
837 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
840 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
842 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
845 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
846 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
847 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
849 else if( m
[1][1] >= m
[2][2] )
851 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
853 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
855 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
856 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
860 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
862 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
863 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
865 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
869 /* a X b == [b]T a == ...*/
870 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
883 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
885 v3_add( a
[0], b
[0], d
[0] );
886 v3_add( a
[1], b
[1], d
[1] );
887 v3_add( a
[2], b
[2], d
[2] );
890 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
892 v3_copy( a
[0], b
[0] );
893 v3_copy( a
[1], b
[1] );
894 v3_copy( a
[2], b
[2] );
897 static inline void m3x3_identity( m3x3f a
)
899 m3x3f id
= M3X3_IDENTITY
;
903 static void m3x3_diagonal( m3x3f a
, f32 v
)
911 static void m3x3_setdiagonalv3( m3x3f a
, v3f v
)
918 static inline void m3x3_zero( m3x3f a
)
924 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
926 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
927 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
928 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
935 dest
[0][0] = (e
*i
-h
*f
)*det
;
936 dest
[0][1] = -(b
*i
-c
*h
)*det
;
937 dest
[0][2] = (b
*f
-c
*e
)*det
;
938 dest
[1][0] = -(d
*i
-f
*g
)*det
;
939 dest
[1][1] = (a
*i
-c
*g
)*det
;
940 dest
[1][2] = -(a
*f
-d
*c
)*det
;
941 dest
[2][0] = (d
*h
-g
*e
)*det
;
942 dest
[2][1] = -(a
*h
-g
*b
)*det
;
943 dest
[2][2] = (a
*e
-d
*b
)*det
;
946 static f32
m3x3_det( m3x3f m
)
948 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
949 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
950 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
953 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
955 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
956 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
957 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
970 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
972 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
973 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
974 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
976 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
977 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
978 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
980 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
981 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
982 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
983 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
984 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
985 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
986 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
987 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
988 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
991 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
995 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
996 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
997 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
1002 static inline void m3x3_projection( m3x3f dst
,
1003 f32
const left
, f32
const right
, f32
const bottom
, f32
const top
)
1009 rl
= 1.0f
/ (right
- left
);
1010 tb
= 1.0f
/ (top
- bottom
);
1012 dst
[0][0] = 2.0f
* rl
;
1013 dst
[1][1] = 2.0f
* tb
;
1017 static inline void m3x3_translate( m3x3f m
, v3f v
)
1019 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
1020 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
1021 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
1024 static inline void m3x3_scale( m3x3f m
, v3f v
)
1026 v3_muls( m
[0], v
[0], m
[0] );
1027 v3_muls( m
[1], v
[1], m
[1] );
1028 v3_muls( m
[2], v
[2], m
[2] );
1031 static inline void m3x3_scalef( m3x3f m
, f32 f
)
1038 static inline void m3x3_rotate( m3x3f m
, f32 angle
)
1040 f32 m00
= m
[0][0], m10
= m
[1][0],
1041 m01
= m
[0][1], m11
= m
[1][1],
1042 m02
= m
[0][2], m12
= m
[1][2];
1048 m
[0][0] = m00
* c
+ m10
* s
;
1049 m
[0][1] = m01
* c
+ m11
* s
;
1050 m
[0][2] = m02
* c
+ m12
* s
;
1052 m
[1][0] = m00
* -s
+ m10
* c
;
1053 m
[1][1] = m01
* -s
+ m11
* c
;
1054 m
[1][2] = m02
* -s
+ m12
* c
;
1058 * -----------------------------------------------------------------------------
1059 * Section 4.c 4x3 matrices
1060 * -----------------------------------------------------------------------------
1063 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
1064 { 0.0f, 1.0f, 0.0f, },\
1065 { 0.0f, 0.0f, 1.0f, },\
1066 { 0.0f, 0.0f, 0.0f }}
1068 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
1070 v3_copy( a
[0], b
[0] );
1071 v3_copy( a
[1], b
[1] );
1072 v3_copy( a
[2], b
[2] );
1075 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
1077 m3x3_transpose( a
, b
);
1078 m3x3_mulv( b
, a
[3], b
[3] );
1079 v3_negate( b
[3], b
[3] );
1082 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
1086 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
1087 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
1088 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
1089 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
1095 dst
[0][0] = f
*k
- g
*j
;
1096 dst
[1][0] =-(e
*k
- g
*i
);
1097 dst
[2][0] = e
*j
- f
*i
;
1098 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
1100 dst
[0][1] =-(b
*k
- c
*j
);
1101 dst
[1][1] = a
*k
- c
*i
;
1102 dst
[2][1] =-(a
*j
- b
*i
);
1103 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
1109 dst
[0][2] = b
*g
- c
*f
;
1110 dst
[1][2] =-(a
*g
- c
*e
);
1111 dst
[2][2] = a
*f
- b
*e
;
1112 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
1114 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
1115 v3_muls( dst
[0], det
, dst
[0] );
1116 v3_muls( dst
[1], det
, dst
[1] );
1117 v3_muls( dst
[2], det
, dst
[2] );
1118 v3_muls( dst
[3], det
, dst
[3] );
1121 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
1123 v3_copy( a
[0], b
[0] );
1124 v3_copy( a
[1], b
[1] );
1125 v3_copy( a
[2], b
[2] );
1126 v3_copy( a
[3], b
[3] );
1129 static inline void m4x3_identity( m4x3f a
)
1131 m4x3f id
= M4X3_IDENTITY
;
1135 static void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
1138 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
1139 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
1140 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
1141 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
1142 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
1143 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
1144 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
1145 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
1147 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
1148 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
1149 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
1150 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
1151 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
1152 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
1153 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
1154 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
1155 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
1156 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
1157 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
1158 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
1161 #if 0 /* shat appf mingw wstringop-overflow */
1164 static void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
1168 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
1169 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
1170 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
1176 * Transform plane ( xyz, distance )
1178 static void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
1182 v3_muls( p
, p
[3], o
);
1183 m4x3_mulv( m
, o
, o
);
1184 m3x3_mulv( m
, p
, d
);
1186 d
[3] = v3_dot( o
, d
);
1193 static void m4x3_translate( m4x3f m
, v3f v
)
1195 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
1196 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
1197 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
1200 static void m4x3_rotate_x( m4x3f m
, f32 angle
)
1202 m4x3f t
= M4X3_IDENTITY
;
1213 m4x3_mul( m
, t
, m
);
1216 static void m4x3_rotate_y( m4x3f m
, f32 angle
)
1218 m4x3f t
= M4X3_IDENTITY
;
1229 m4x3_mul( m
, t
, m
);
1232 static void m4x3_rotate_z( m4x3f m
, f32 angle
)
1234 m4x3f t
= M4X3_IDENTITY
;
1245 m4x3_mul( m
, t
, m
);
1248 static void m4x3_expand( m4x3f m
, m4x4f d
)
1250 v3_copy( m
[0], d
[0] );
1251 v3_copy( m
[1], d
[1] );
1252 v3_copy( m
[2], d
[2] );
1253 v3_copy( m
[3], d
[3] );
1260 static void m4x3_decompose( m4x3f m
, v3f co
, v4f q
, v3f s
)
1262 v3_copy( m
[3], co
);
1263 s
[0] = v3_length(m
[0]);
1264 s
[1] = v3_length(m
[1]);
1265 s
[2] = v3_length(m
[2]);
1268 v3_divs( m
[0], s
[0], rot
[0] );
1269 v3_divs( m
[1], s
[1], rot
[1] );
1270 v3_divs( m
[2], s
[2], rot
[2] );
1275 static void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
){
1277 m4x3_mulv( m
, point
, v
);
1279 v3_minv( box
[0], v
, box
[0] );
1280 v3_maxv( box
[1], v
, box
[1] );
1283 static void m4x3_expand_aabb_aabb( m4x3f m
, boxf boxa
, boxf boxb
){
1285 v3_copy( boxb
[0], a
);
1286 v3_copy( boxb
[1], b
);
1287 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], a
[2] } );
1288 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], a
[2] } );
1289 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], a
[2] } );
1290 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], a
[2] } );
1291 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], b
[2] } );
1292 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], b
[2] } );
1293 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], b
[2] } );
1294 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], b
[2] } );
1296 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1299 v3_sub( target
, pos
, dir
);
1300 v3_normalize( dir
);
1302 v3_copy( dir
, m
[2] );
1304 v3_cross( up
, m
[2], m
[0] );
1305 v3_normalize( m
[0] );
1307 v3_cross( m
[2], m
[0], m
[1] );
1308 v3_copy( pos
, m
[3] );
1312 * -----------------------------------------------------------------------------
1313 * Section 4.d 4x4 matrices
1314 * -----------------------------------------------------------------------------
1317 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1318 { 0.0f, 1.0f, 0.0f, 0.0f },\
1319 { 0.0f, 0.0f, 1.0f, 0.0f },\
1320 { 0.0f, 0.0f, 0.0f, 1.0f }}
1321 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1322 { 0.0f, 0.0f, 0.0f, 0.0f },\
1323 { 0.0f, 0.0f, 0.0f, 0.0f },\
1324 { 0.0f, 0.0f, 0.0f, 0.0f }}
1326 static void m4x4_projection( m4x4f m
, f32 angle
,
1327 f32 ratio
, f32 fnear
, f32 ffar
)
1329 f32 scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1335 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1341 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1345 m
[2][0] = (r
+ l
) / (r
- l
);
1346 m
[2][1] = (t
+ b
) / (t
- b
);
1347 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1352 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1356 static void m4x4_translate( m4x4f m
, v3f v
)
1358 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1359 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1360 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1363 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1365 v4_copy( a
[0], b
[0] );
1366 v4_copy( a
[1], b
[1] );
1367 v4_copy( a
[2], b
[2] );
1368 v4_copy( a
[3], b
[3] );
1371 static inline void m4x4_identity( m4x4f a
)
1373 m4x4f id
= M4X4_IDENTITY
;
1377 static inline void m4x4_zero( m4x4f a
)
1379 m4x4f zero
= M4X4_ZERO
;
1380 m4x4_copy( zero
, a
);
1383 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1385 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1386 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1387 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1388 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1390 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1391 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1392 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1393 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1395 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1396 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1397 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1398 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1399 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1400 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1401 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1402 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1403 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1404 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1405 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1406 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1407 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1408 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1409 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1410 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1413 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1417 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1418 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1419 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1420 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1425 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1427 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1428 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1429 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1430 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1434 t
[0] = a22
*a33
- a32
*a23
;
1435 t
[1] = a21
*a33
- a31
*a23
;
1436 t
[2] = a21
*a32
- a31
*a22
;
1437 t
[3] = a20
*a33
- a30
*a23
;
1438 t
[4] = a20
*a32
- a30
*a22
;
1439 t
[5] = a20
*a31
- a30
*a21
;
1441 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1442 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1443 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1444 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1446 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1447 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1448 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1449 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1451 t
[0] = a12
*a33
- a32
*a13
;
1452 t
[1] = a11
*a33
- a31
*a13
;
1453 t
[2] = a11
*a32
- a31
*a12
;
1454 t
[3] = a10
*a33
- a30
*a13
;
1455 t
[4] = a10
*a32
- a30
*a12
;
1456 t
[5] = a10
*a31
- a30
*a11
;
1458 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1459 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1460 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1461 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1463 t
[0] = a12
*a23
- a22
*a13
;
1464 t
[1] = a11
*a23
- a21
*a13
;
1465 t
[2] = a11
*a22
- a21
*a12
;
1466 t
[3] = a10
*a23
- a20
*a13
;
1467 t
[4] = a10
*a22
- a20
*a12
;
1468 t
[5] = a10
*a21
- a20
*a11
;
1470 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1471 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1472 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1473 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1475 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1476 v4_muls( d
[0], det
, d
[0] );
1477 v4_muls( d
[1], det
, d
[1] );
1478 v4_muls( d
[2], det
, d
[2] );
1479 v4_muls( d
[3], det
, d
[3] );
1483 * -----------------------------------------------------------------------------
1485 * -----------------------------------------------------------------------------
1488 static inline void box_addpt( boxf a
, v3f pt
)
1490 v3_minv( a
[0], pt
, a
[0] );
1491 v3_maxv( a
[1], pt
, a
[1] );
1494 static inline void box_concat( boxf a
, boxf b
)
1496 v3_minv( a
[0], b
[0], a
[0] );
1497 v3_maxv( a
[1], b
[1], a
[1] );
1500 static inline void box_copy( boxf a
, boxf b
)
1502 v3_copy( a
[0], b
[0] );
1503 v3_copy( a
[1], b
[1] );
1506 static inline int box_overlap( boxf a
, boxf b
)
1509 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
1510 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
1511 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
1515 static int box_within( boxf greater
, boxf lesser
)
1518 v3_sub( lesser
[0], greater
[0], a
);
1519 v3_sub( lesser
[1], greater
[1], b
);
1521 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
1522 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
1530 static inline void box_init_inf( boxf box
){
1531 v3_fill( box
[0], INFINITY
);
1532 v3_fill( box
[1], -INFINITY
);
1536 * -----------------------------------------------------------------------------
1537 * Section 5.b Planes
1538 * -----------------------------------------------------------------------------
1541 static inline void tri_to_plane( f64 a
[3], f64 b
[3],
1542 f64 c
[3], f64 p
[4] )
1548 edge0
[0] = b
[0] - a
[0];
1549 edge0
[1] = b
[1] - a
[1];
1550 edge0
[2] = b
[2] - a
[2];
1552 edge1
[0] = c
[0] - a
[0];
1553 edge1
[1] = c
[1] - a
[1];
1554 edge1
[2] = c
[2] - a
[2];
1556 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1557 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1558 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1560 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1561 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1568 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1570 f32
const epsilon
= 1e-6f
;
1573 v3_cross( a
, b
, x
);
1574 f32 d
= v3_dot( x
, c
);
1576 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1579 v3_cross( b
, c
, v0
);
1580 v3_cross( c
, a
, v1
);
1581 v3_cross( a
, b
, v2
);
1583 v3_muls( v0
, a
[3], p
);
1584 v3_muladds( p
, v1
, b
[3], p
);
1585 v3_muladds( p
, v2
, c
[3], p
);
1591 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1593 f32
const epsilon
= 1e-6f
;
1596 v3_cross( a
, b
, c
);
1597 f32 d
= v3_length2( c
);
1599 if( (d
< epsilon
) && (d
> -epsilon
) )
1603 v3_cross( c
, b
, v0
);
1604 v3_cross( a
, c
, v1
);
1606 v3_muls( v0
, a
[3], vx
);
1607 v3_muladds( vx
, v1
, b
[3], vx
);
1608 v3_divs( vx
, d
, p
);
1614 static int plane_segment( v4f plane
, v3f a
, v3f b
, v3f co
)
1616 f32 d0
= v3_dot( a
, plane
) - plane
[3],
1617 d1
= v3_dot( b
, plane
) - plane
[3];
1621 f32 tot
= 1.0f
/( fabsf(d0
)+fabsf(d1
) );
1623 v3_muls( a
, fabsf(d1
) * tot
, co
);
1624 v3_muladds( co
, b
, fabsf(d0
) * tot
, co
);
1631 static inline f64
plane_polarity( f64 p
[4], f64 a
[3] )
1634 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1635 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1639 static f32
ray_plane( v4f plane
, v3f co
, v3f dir
){
1640 f32 d
= v3_dot( plane
, dir
);
1641 if( fabsf(d
) > 1e-6f
){
1643 v3_muls( plane
, plane
[3], v0
);
1644 v3_sub( v0
, co
, v0
);
1645 return v3_dot( v0
, plane
) / d
;
1647 else return INFINITY
;
1651 * -----------------------------------------------------------------------------
1652 * Section 5.c Closest point functions
1653 * -----------------------------------------------------------------------------
1657 * These closest point tests were learned from Real-Time Collision Detection by
1660 static f32
closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1661 f32
*s
, f32
*t
, v3f c1
, v3f c2
)
1664 v3_sub( q1
, p1
, d1
);
1665 v3_sub( q2
, p2
, d2
);
1666 v3_sub( p1
, p2
, r
);
1668 f32 a
= v3_length2( d1
),
1669 e
= v3_length2( d2
),
1670 f
= v3_dot( d2
, r
);
1672 const f32 kEpsilon
= 0.0001f
;
1674 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1682 v3_sub( c1
, c2
, v0
);
1684 return v3_length2( v0
);
1690 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1694 f32 c
= v3_dot( d1
, r
);
1698 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1702 f32 b
= v3_dot(d1
,d2
),
1707 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1714 *t
= (b
*(*s
)+f
) / e
;
1719 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1721 else if( *t
> 1.0f
)
1724 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1729 v3_muladds( p1
, d1
, *s
, c1
);
1730 v3_muladds( p2
, d2
, *t
, c2
);
1733 v3_sub( c1
, c2
, v0
);
1734 return v3_length2( v0
);
1737 static int point_inside_aabb( boxf box
, v3f point
)
1739 if((point
[0]<=box
[1][0]) && (point
[1]<=box
[1][1]) && (point
[2]<=box
[1][2]) &&
1740 (point
[0]>=box
[0][0]) && (point
[1]>=box
[0][1]) && (point
[2]>=box
[0][2]) )
1746 static void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1748 v3_maxv( p
, box
[0], dest
);
1749 v3_minv( dest
, box
[1], dest
);
1752 static void closest_point_obb( v3f p
, boxf box
,
1753 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1756 m4x3_mulv( inv_mtx
, p
, local
);
1757 closest_point_aabb( local
, box
, local
);
1758 m4x3_mulv( mtx
, local
, dest
);
1761 static f32
closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1765 v3_sub( point
, a
, v1
);
1767 f32 t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1768 t
= vg_clampf(t
,0.0f
,1.0f
);
1769 v3_muladds( a
, v0
, t
, dest
);
1773 static void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1778 /* Region outside A */
1779 v3_sub( tri
[1], tri
[0], ab
);
1780 v3_sub( tri
[2], tri
[0], ac
);
1781 v3_sub( p
, tri
[0], ap
);
1785 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1787 v3_copy( tri
[0], dest
);
1788 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1792 /* Region outside B */
1796 v3_sub( p
, tri
[1], bp
);
1797 d3
= v3_dot( ab
, bp
);
1798 d4
= v3_dot( ac
, bp
);
1800 if( d3
>= 0.0f
&& d4
<= d3
)
1802 v3_copy( tri
[1], dest
);
1803 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1807 /* Edge region of AB */
1808 f32 vc
= d1
*d4
- d3
*d2
;
1809 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1811 f32 v
= d1
/ (d1
-d3
);
1812 v3_muladds( tri
[0], ab
, v
, dest
);
1813 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1817 /* Region outside C */
1820 v3_sub( p
, tri
[2], cp
);
1821 d5
= v3_dot(ab
, cp
);
1822 d6
= v3_dot(ac
, cp
);
1824 if( d6
>= 0.0f
&& d5
<= d6
)
1826 v3_copy( tri
[2], dest
);
1827 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1832 f32 vb
= d5
*d2
- d1
*d6
;
1833 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1835 f32 w
= d2
/ (d2
-d6
);
1836 v3_muladds( tri
[0], ac
, w
, dest
);
1837 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1842 f32 va
= d3
*d6
- d5
*d4
;
1843 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1845 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1847 v3_sub( tri
[2], tri
[1], bc
);
1848 v3_muladds( tri
[1], bc
, w
, dest
);
1849 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1853 /* P inside region, Q via barycentric coordinates uvw */
1854 f32 d
= 1.0f
/(va
+vb
+vc
),
1858 v3_muladds( tri
[0], ab
, v
, dest
);
1859 v3_muladds( dest
, ac
, w
, dest
);
1864 k_contact_type_default
,
1865 k_contact_type_disabled
,
1869 static enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1874 /* Region outside A */
1875 v3_sub( tri
[1], tri
[0], ab
);
1876 v3_sub( tri
[2], tri
[0], ac
);
1877 v3_sub( p
, tri
[0], ap
);
1881 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1883 v3_copy( tri
[0], dest
);
1884 return k_contact_type_default
;
1887 /* Region outside B */
1891 v3_sub( p
, tri
[1], bp
);
1892 d3
= v3_dot( ab
, bp
);
1893 d4
= v3_dot( ac
, bp
);
1895 if( d3
>= 0.0f
&& d4
<= d3
)
1897 v3_copy( tri
[1], dest
);
1898 return k_contact_type_edge
;
1901 /* Edge region of AB */
1902 f32 vc
= d1
*d4
- d3
*d2
;
1903 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1905 f32 v
= d1
/ (d1
-d3
);
1906 v3_muladds( tri
[0], ab
, v
, dest
);
1907 return k_contact_type_edge
;
1910 /* Region outside C */
1913 v3_sub( p
, tri
[2], cp
);
1914 d5
= v3_dot(ab
, cp
);
1915 d6
= v3_dot(ac
, cp
);
1917 if( d6
>= 0.0f
&& d5
<= d6
)
1919 v3_copy( tri
[2], dest
);
1920 return k_contact_type_edge
;
1924 f32 vb
= d5
*d2
- d1
*d6
;
1925 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1927 f32 w
= d2
/ (d2
-d6
);
1928 v3_muladds( tri
[0], ac
, w
, dest
);
1929 return k_contact_type_edge
;
1933 f32 va
= d3
*d6
- d5
*d4
;
1934 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1936 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1938 v3_sub( tri
[2], tri
[1], bc
);
1939 v3_muladds( tri
[1], bc
, w
, dest
);
1940 return k_contact_type_edge
;
1943 /* P inside region, Q via barycentric coordinates uvw */
1944 f32 d
= 1.0f
/(va
+vb
+vc
),
1948 v3_muladds( tri
[0], ab
, v
, dest
);
1949 v3_muladds( dest
, ac
, w
, dest
);
1951 return k_contact_type_default
;
1954 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1956 v2f pabs
, ei
, e2
, ve
, t
;
1959 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1961 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1963 v2_fill( t
, 0.70710678118654752f
);
1965 for( int i
=0; i
<3; i
++ ){
1968 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1972 v2_sub( pabs
, v
, u
);
1976 v2_sub( ud
, v
, ud
);
1978 v2_muls( u
, v2_length( ud
), u
);
1983 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1988 v2_copysign( o
, p
);
1992 * -----------------------------------------------------------------------------
1993 * Section 5.d Raycasts & Spherecasts
1994 * -----------------------------------------------------------------------------
1997 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, f32 dist
)
2002 v3_sub( box
[0], co
, v0
);
2003 v3_sub( box
[1], co
, v1
);
2005 v3_mul( v0
, dir_inv
, v0
);
2006 v3_mul( v1
, dir_inv
, v1
);
2008 tmin
= vg_minf( v0
[0], v1
[0] );
2009 tmax
= vg_maxf( v0
[0], v1
[0] );
2010 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
2011 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
2012 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
2013 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
2015 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
2018 /* Time of intersection with ray vs triangle */
2019 static int ray_tri( v3f tri
[3], v3f co
,
2020 v3f dir
, f32
*dist
, int backfaces
)
2022 f32
const kEpsilon
= 0.00001f
;
2024 v3f v0
, v1
, h
, s
, q
, n
;
2031 v3_sub( pb
, pa
, v0
);
2032 v3_sub( pc
, pa
, v1
);
2033 v3_cross( dir
, v1
, h
);
2034 v3_cross( v0
, v1
, n
);
2036 if( (v3_dot( n
, dir
) > 0.0f
) && !backfaces
) /* Backface culling */
2040 a
= v3_dot( v0
, h
);
2042 if( a
> -kEpsilon
&& a
< kEpsilon
)
2046 v3_sub( co
, pa
, s
);
2048 u
= f
* v3_dot(s
, h
);
2049 if( u
< 0.0f
|| u
> 1.0f
)
2052 v3_cross( s
, v0
, q
);
2053 v
= f
* v3_dot( dir
, q
);
2054 if( v
< 0.0f
|| u
+v
> 1.0f
)
2057 t
= f
* v3_dot(v1
, q
);
2066 /* time of intersection with ray vs sphere */
2067 static int ray_sphere( v3f c
, f32 r
,
2068 v3f co
, v3f dir
, f32
*t
)
2073 f32 b
= v3_dot( m
, dir
),
2074 c1
= v3_dot( m
, m
) - r
*r
;
2076 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
2077 if( c1
> 0.0f
&& b
> 0.0f
)
2080 f32 discr
= b
*b
- c1
;
2082 /* A negative discriminant corresponds to ray missing sphere */
2087 * Ray now found to intersect sphere, compute smallest t value of
2090 *t
= -b
- sqrtf( discr
);
2092 /* If t is negative, ray started inside sphere so clamp t to zero */
2100 * time of intersection of ray vs cylinder
2101 * The cylinder does not have caps but is finite
2103 * Heavily adapted from regular segment vs cylinder from:
2104 * Real-Time Collision Detection
2106 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, f32 r
,
2107 v3f co
, v3f dir
, f32
*t
)
2110 v3_muladds( co
, dir
, 1.0f
, sb
);
2114 v3_sub( sb
, co
, n
);
2116 f32 md
= v3_dot( m
, d
),
2117 nd
= v3_dot( n
, d
),
2118 dd
= v3_dot( d
, d
),
2119 nn
= v3_dot( n
, n
),
2120 mn
= v3_dot( m
, n
),
2122 k
= v3_dot( m
, m
) - r
*r
,
2125 if( fabsf(a
) < 0.00001f
)
2127 /* Segment runs parallel to cylinder axis */
2131 f32 b
= dd
*mn
- nd
*md
,
2135 return 0; /* No real roots; no intersection */
2137 *t
= (-b
- sqrtf(discr
)) / a
;
2139 return 0; /* Intersection behind ray */
2141 /* Check within cylinder segment */
2142 if( md
+ (*t
)*nd
< 0.0f
)
2145 if( md
+ (*t
)*nd
> dd
)
2148 /* Segment intersects cylinder between the endcaps; t is correct */
2153 * Time of intersection of sphere and triangle. Origin must be outside the
2154 * colliding area. This is a fairly long procedure.
2156 static int spherecast_triangle( v3f tri
[3],
2157 v3f co
, v3f dir
, f32 r
, f32
*t
, v3f n
)
2162 v3_sub( tri
[1], tri
[0], v0
);
2163 v3_sub( tri
[2], tri
[0], v1
);
2164 v3_cross( v0
, v1
, n
);
2166 v3_muladds( tri
[0], n
, r
, sum
[0] );
2167 v3_muladds( tri
[1], n
, r
, sum
[1] );
2168 v3_muladds( tri
[2], n
, r
, sum
[2] );
2171 f32 t_min
= INFINITY
,
2174 if( ray_tri( sum
, co
, dir
, &t1
, 0 ) ){
2175 t_min
= vg_minf( t_min
, t1
);
2180 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2183 for( int i
=0; i
<3; i
++ ){
2184 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) ){
2185 t_min
= vg_minf( t_min
, t1
);
2191 for( int i
=0; i
<3; i
++ ){
2195 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) ){
2200 v3_add( dir
, co
, co1
);
2201 v3_lerp( co
, co1
, t_min
, ct
);
2203 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
2204 v3_sub( ct
, cx
, n
);
2217 * -----------------------------------------------------------------------------
2218 * Section 5.e Curves
2219 * -----------------------------------------------------------------------------
2222 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, f32 t
, v3f p
)
2227 v3_muls( p1
, ttt
, p
);
2228 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2229 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2230 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);
2233 static void eval_bezier3( v3f p0
, v3f p1
, v3f p2
, f32 t
, v3f p
)
2237 v3_muls( p0
, u
*u
, p
);
2238 v3_muladds( p
, p1
, 2.0f
*u
*t
, p
);
2239 v3_muladds( p
, p2
, t
*t
, p
);
2243 * -----------------------------------------------------------------------------
2244 * Section 5.f Volumes
2245 * -----------------------------------------------------------------------------
2248 static float vg_sphere_volume( float radius
){
2249 float r3
= radius
*radius
*radius
;
2250 return (4.0f
/3.0f
) * VG_PIf
* r3
;
2254 * -----------------------------------------------------------------------------
2255 * Section 6.a PSRNG and some distributions
2256 * -----------------------------------------------------------------------------
2259 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2260 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2261 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2262 * equidistributed uniform pseudorandom number generator," ACM
2263 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2264 * January pp.3-30 1998.
2266 * http://www.sultanik.com/Mersenne_twister
2267 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2270 #define MT_UPPER_MASK 0x80000000
2271 #define MT_LOWER_MASK 0x7fffffff
2272 #define MT_TEMPERING_MASK_B 0x9d2c5680
2273 #define MT_TEMPERING_MASK_C 0xefc60000
2275 #define MT_STATE_VECTOR_LENGTH 624
2277 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2278 #define MT_STATE_VECTOR_M 397
2280 typedef struct vg_rand vg_rand
;
2282 u32 mt
[MT_STATE_VECTOR_LENGTH
];
2286 static void vg_rand_seed( vg_rand
*rand
, unsigned long seed
) {
2287 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2288 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2289 * Programming," Vol. 2 (2nd Ed.) pp.102.
2291 rand
->mt
[0] = seed
& 0xffffffff;
2292 for( rand
->index
=1; rand
->index
<MT_STATE_VECTOR_LENGTH
; rand
->index
++){
2293 rand
->mt
[rand
->index
] = (6069 * rand
->mt
[rand
->index
-1]) & 0xffffffff;
2298 * Generates a pseudo-randomly generated long.
2300 static u32
vg_randu32( vg_rand
*rand
) {
2302 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2303 static u32 mag
[2] = {0x0, 0x9908b0df};
2304 if( rand
->index
>= MT_STATE_VECTOR_LENGTH
|| rand
->index
< 0 ){
2305 /* generate STATE_VECTOR_LENGTH words at a time */
2307 if( rand
->index
>= MT_STATE_VECTOR_LENGTH
+1 || rand
->index
< 0 ){
2308 vg_rand_seed( rand
, 4357 );
2310 for( kk
=0; kk
<MT_STATE_VECTOR_LENGTH
-MT_STATE_VECTOR_M
; kk
++ ){
2311 y
= (rand
->mt
[kk
] & MT_UPPER_MASK
) |
2312 (rand
->mt
[kk
+1] & MT_LOWER_MASK
);
2313 rand
->mt
[kk
] = rand
->mt
[kk
+MT_STATE_VECTOR_M
] ^ (y
>>1) ^ mag
[y
& 0x1];
2315 for( ; kk
<MT_STATE_VECTOR_LENGTH
-1; kk
++ ){
2316 y
= (rand
->mt
[kk
] & MT_UPPER_MASK
) |
2317 (rand
->mt
[kk
+1] & MT_LOWER_MASK
);
2319 rand
->mt
[ kk
+(MT_STATE_VECTOR_M
-MT_STATE_VECTOR_LENGTH
)] ^
2320 (y
>> 1) ^ mag
[y
& 0x1];
2322 y
= (rand
->mt
[MT_STATE_VECTOR_LENGTH
-1] & MT_UPPER_MASK
) |
2323 (rand
->mt
[0] & MT_LOWER_MASK
);
2324 rand
->mt
[MT_STATE_VECTOR_LENGTH
-1] =
2325 rand
->mt
[MT_STATE_VECTOR_M
-1] ^ (y
>> 1) ^ mag
[y
& 0x1];
2328 y
= rand
->mt
[rand
->index
++];
2330 y
^= (y
<< 7) & MT_TEMPERING_MASK_B
;
2331 y
^= (y
<< 15) & MT_TEMPERING_MASK_C
;
2337 * Generates a pseudo-randomly generated f64 in the range [0..1].
2339 static inline f64
vg_randf64( vg_rand
*rand
){
2340 return (f64
)vg_randu32(rand
)/(f64
)0xffffffff;
2343 static inline f64
vg_randf64_range( vg_rand
*rand
, f64 min
, f64 max
){
2344 return vg_lerp( min
, max
, (f64
)vg_randf64(rand
) );
2347 static inline void vg_rand_dir( vg_rand
*rand
, v3f dir
){
2348 dir
[0] = vg_randf64(rand
);
2349 dir
[1] = vg_randf64(rand
);
2350 dir
[2] = vg_randf64(rand
);
2352 /* warning: *could* be 0 length.
2353 * very unlikely.. 1 in (2^32)^3. but its mathematically wrong. */
2355 v3_muls( dir
, 2.0f
, dir
);
2356 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2358 v3_normalize( dir
);
2361 static inline void vg_rand_sphere( vg_rand
*rand
, v3f co
){
2362 vg_rand_dir(rand
,co
);
2363 v3_muls( co
, cbrtf( vg_randf64(rand
) ), co
);
2366 static void vg_rand_disc( vg_rand
*rand
, v2f co
){
2367 f32 a
= vg_randf64(rand
) * VG_TAUf
;
2370 v2_muls( co
, sqrtf( vg_randf64(rand
) ), co
);
2373 static void vg_rand_cone( vg_rand
*rand
, v3f out_dir
, f32 angle
){
2374 f32 r
= sqrtf(vg_randf64(rand
)) * angle
* 0.5f
,
2375 a
= vg_randf64(rand
) * VG_TAUf
;
2377 out_dir
[0] = sinf(a
) * sinf(r
);
2378 out_dir
[1] = cosf(a
) * sinf(r
);
2379 out_dir
[2] = cosf(r
);