4fe4590f944cae4d614e8577ea532998d49e82fa
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
;
111 * quantize float to bit count
113 static u32
vg_quantf( f32 a
, u32 bits
, f32 min
, f32 max
){
114 u32 mask
= (0x1 << bits
) - 1;
115 return vg_clampf((a
- min
) * ((f32
)mask
/(max
-min
)), 0.0f
, mask
);
119 * un-quantize discreet to float
121 static f32
vg_dequantf( u32 q
, u32 bits
, f32 min
, f32 max
){
122 u32 mask
= (0x1 << bits
) - 1;
123 return min
+ (f32
)q
* ((max
-min
) / (f32
)mask
);
127 * -----------------------------------------------------------------------------
128 * Section 2.a 2D Vectors
129 * -----------------------------------------------------------------------------
132 static inline void v2_copy( v2f a
, v2f d
)
134 d
[0] = a
[0]; d
[1] = a
[1];
137 static inline void v2_zero( v2f a
)
139 a
[0] = 0.f
; a
[1] = 0.f
;
142 static inline void v2_add( v2f a
, v2f b
, v2f d
)
144 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
147 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
149 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
152 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
154 dest
[0] = vg_minf(a
[0], b
[0]);
155 dest
[1] = vg_minf(a
[1], b
[1]);
158 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
160 dest
[0] = vg_maxf(a
[0], b
[0]);
161 dest
[1] = vg_maxf(a
[1], b
[1]);
164 static inline f32
v2_dot( v2f a
, v2f b
)
166 return a
[0] * b
[0] + a
[1] * b
[1];
169 static inline f32
v2_cross( v2f a
, v2f b
)
171 return a
[0]*b
[1] - a
[1]*b
[0];
174 static inline void v2_abs( v2f a
, v2f d
)
176 d
[0] = fabsf( a
[0] );
177 d
[1] = fabsf( a
[1] );
180 static inline void v2_muls( v2f a
, f32 s
, v2f d
)
182 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
185 static inline void v2_divs( v2f a
, f32 s
, v2f d
)
187 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
190 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
196 static inline void v2_div( v2f a
, v2f b
, v2f d
)
198 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
201 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
203 d
[0] = a
[0]+b
[0]*s
[0];
204 d
[1] = a
[1]+b
[1]*s
[1];
207 static inline void v2_muladds( v2f a
, v2f b
, f32 s
, v2f d
)
213 static inline f32
v2_length2( v2f a
)
215 return a
[0]*a
[0] + a
[1]*a
[1];
218 static inline f32
v2_length( v2f a
)
220 return sqrtf( v2_length2( a
) );
223 static inline f32
v2_dist2( v2f a
, v2f b
)
226 v2_sub( a
, b
, delta
);
227 return v2_length2( delta
);
230 static inline f32
v2_dist( v2f a
, v2f b
)
232 return sqrtf( v2_dist2( a
, b
) );
235 static inline void v2_lerp( v2f a
, v2f b
, f32 t
, v2f d
)
237 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
238 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
241 static inline void v2_normalize( v2f a
)
243 v2_muls( a
, 1.0f
/ v2_length( a
), a
);
246 static void v2_normalize_clamp( v2f a
)
248 f32 l2
= v2_length2( a
);
250 v2_muls( a
, 1.0f
/sqrtf(l2
), a
);
253 static inline void v2_floor( v2f a
, v2f b
)
255 b
[0] = floorf( a
[0] );
256 b
[1] = floorf( a
[1] );
259 static inline void v2_fill( v2f a
, f32 v
)
265 static inline void v2_copysign( v2f a
, v2f b
)
267 a
[0] = copysignf( a
[0], b
[0] );
268 a
[1] = copysignf( a
[1], b
[1] );
272 * ---------------- */
274 static inline void v2i_copy( v2i a
, v2i b
)
276 b
[0] = a
[0]; b
[1] = a
[1];
279 static inline int v2i_eq( v2i a
, v2i b
)
281 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
284 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
286 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
289 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
291 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
295 * -----------------------------------------------------------------------------
296 * Section 2.b 3D Vectors
297 * -----------------------------------------------------------------------------
300 static inline void v3_copy( v3f a
, v3f b
)
302 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
305 static inline void v3_zero( v3f a
)
307 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
310 static inline void v3_add( v3f a
, v3f b
, v3f d
)
312 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
315 static inline void v3i_add( v3i a
, v3i b
, v3i d
)
317 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
320 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
322 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
325 static inline void v3i_sub( v3i a
, v3i b
, v3i d
)
327 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
330 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
332 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
335 static inline void v3_div( v3f a
, v3f b
, v3f d
)
337 d
[0] = b
[0]!=0.0f
? a
[0]/b
[0]: INFINITY
;
338 d
[1] = b
[1]!=0.0f
? a
[1]/b
[1]: INFINITY
;
339 d
[2] = b
[2]!=0.0f
? a
[2]/b
[2]: INFINITY
;
342 static inline void v3_muls( v3f a
, f32 s
, v3f d
)
344 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
347 static inline void v3_fill( v3f a
, f32 v
)
354 static inline void v3_divs( v3f a
, f32 s
, v3f d
)
357 v3_fill( d
, INFINITY
);
366 static inline void v3_muladds( v3f a
, v3f b
, f32 s
, v3f d
)
368 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
371 static inline void v3_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
373 d
[0] = a
[0]+b
[0]*s
[0];
374 d
[1] = a
[1]+b
[1]*s
[1];
375 d
[2] = a
[2]+b
[2]*s
[2];
378 static inline f32
v3_dot( v3f a
, v3f b
)
380 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
383 static inline void v3_cross( v3f a
, v3f b
, v3f dest
)
386 d
[0] = a
[1]*b
[2] - a
[2]*b
[1];
387 d
[1] = a
[2]*b
[0] - a
[0]*b
[2];
388 d
[2] = a
[0]*b
[1] - a
[1]*b
[0];
392 static inline f32
v3_length2( v3f a
)
394 return v3_dot( a
, a
);
397 static inline f32
v3_length( v3f a
)
399 return sqrtf( v3_length2( a
) );
402 static inline f32
v3_dist2( v3f a
, v3f b
)
405 v3_sub( a
, b
, delta
);
406 return v3_length2( delta
);
409 static inline f32
v3_dist( v3f a
, v3f b
)
411 return sqrtf( v3_dist2( a
, b
) );
414 static inline void v3_normalize( v3f a
)
416 v3_muls( a
, 1.f
/ v3_length( a
), a
);
419 static inline f32
vg_lerpf( f32 a
, f32 b
, f32 t
){
423 static inline f64
vg_lerp( f64 a
, f64 b
, f64 t
)
428 static inline void vg_slewf( f32
*a
, f32 b
, f32 speed
){
429 f32 d
= vg_signf( b
-*a
),
431 *a
= vg_minf( b
*d
, c
*d
) * d
;
434 static inline f32
vg_smoothstepf( f32 x
){
435 return x
*x
*(3.0f
- 2.0f
*x
);
439 /* correctly lerp around circular period -pi -> pi */
440 static f32
vg_alerpf( f32 a
, f32 b
, f32 t
)
442 f32 d
= fmodf( b
-a
, VG_TAUf
),
443 s
= fmodf( 2.0f
*d
, VG_TAUf
) - d
;
447 static inline void v3_lerp( v3f a
, v3f b
, f32 t
, v3f d
)
449 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
450 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
451 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
454 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
456 dest
[0] = vg_minf(a
[0], b
[0]);
457 dest
[1] = vg_minf(a
[1], b
[1]);
458 dest
[2] = vg_minf(a
[2], b
[2]);
461 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
463 dest
[0] = vg_maxf(a
[0], b
[0]);
464 dest
[1] = vg_maxf(a
[1], b
[1]);
465 dest
[2] = vg_maxf(a
[2], b
[2]);
468 static inline f32
v3_minf( v3f a
)
470 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
473 static inline f32
v3_maxf( v3f a
)
475 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
478 static inline void v3_floor( v3f a
, v3f b
)
480 b
[0] = floorf( a
[0] );
481 b
[1] = floorf( a
[1] );
482 b
[2] = floorf( a
[2] );
485 static inline void v3_ceil( v3f a
, v3f b
)
487 b
[0] = ceilf( a
[0] );
488 b
[1] = ceilf( a
[1] );
489 b
[2] = ceilf( a
[2] );
492 static inline void v3_negate( v3f a
, v3f b
)
499 static inline void v3_rotate( v3f v
, f32 angle
, v3f axis
, v3f d
)
510 v3_cross( k
, v
, v2
);
511 v3_muls( v2
, s
, v2
);
512 v3_add( v1
, v2
, v1
);
513 v3_muls( k
, v3_dot(k
, v
) * (1.0f
- c
), v2
);
517 static void v3_tangent_basis( v3f n
, v3f tx
, v3f ty
){
518 /* Compute tangent basis (box2d) */
519 if( fabsf( n
[0] ) >= 0.57735027f
){
531 v3_cross( n
, tx
, ty
);
536 * -----------------------------------------------------------------------------
537 * Section 2.c 4D Vectors
538 * -----------------------------------------------------------------------------
541 static inline void v4_copy( v4f a
, v4f b
)
543 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
546 static inline void v4_add( v4f a
, v4f b
, v4f d
)
554 static inline void v4_zero( v4f a
)
556 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
559 static inline void v4_muls( v4f a
, f32 s
, v4f d
)
567 static inline void v4_muladds( v4f a
, v4f b
, f32 s
, v4f d
)
575 static inline void v4_lerp( v4f a
, v4f b
, f32 t
, v4f d
)
577 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
578 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
579 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
580 d
[3] = a
[3] + t
*(b
[3]-a
[3]);
583 static inline f32
v4_dot( v4f a
, v4f b
)
585 return a
[0]*b
[0] + a
[1]*b
[1] + a
[2]*b
[2] + a
[3]*b
[3];
588 static inline f32
v4_length( v4f a
)
590 return sqrtf( v4_dot(a
,a
) );
594 * -----------------------------------------------------------------------------
595 * Section 3 Quaternions
596 * -----------------------------------------------------------------------------
599 static inline void q_identity( v4f q
)
601 q
[0] = 0.0f
; q
[1] = 0.0f
; q
[2] = 0.0f
; q
[3] = 1.0f
;
604 static inline void q_axis_angle( v4f q
, v3f axis
, f32 angle
)
616 static inline void q_mul( v4f q
, v4f q1
, v4f d
)
619 t
[0] = q
[3]*q1
[0] + q
[0]*q1
[3] + q
[1]*q1
[2] - q
[2]*q1
[1];
620 t
[1] = q
[3]*q1
[1] - q
[0]*q1
[2] + q
[1]*q1
[3] + q
[2]*q1
[0];
621 t
[2] = q
[3]*q1
[2] + q
[0]*q1
[1] - q
[1]*q1
[0] + q
[2]*q1
[3];
622 t
[3] = q
[3]*q1
[3] - q
[0]*q1
[0] - q
[1]*q1
[1] - q
[2]*q1
[2];
626 static inline void q_normalize( v4f q
)
628 f32 l2
= v4_dot(q
,q
);
629 if( l2
< 0.00001f
) q_identity( q
);
631 f32 s
= 1.0f
/sqrtf(l2
);
639 static inline void q_inv( v4f q
, v4f d
)
641 f32 s
= 1.0f
/ v4_dot(q
,q
);
648 static inline void q_nlerp( v4f a
, v4f b
, f32 t
, v4f d
){
649 if( v4_dot(a
,b
) < 0.0f
){
651 v4_muls( b
, -1.0f
, c
);
652 v4_lerp( a
, c
, t
, d
);
655 v4_lerp( a
, b
, t
, d
);
660 static inline void q_m3x3( v4f q
, m3x3f d
)
664 s
= l
> 0.0f
? 2.0f
/l
: 0.0f
,
666 xx
= s
*q
[0]*q
[0], xy
= s
*q
[0]*q
[1], wx
= s
*q
[3]*q
[0],
667 yy
= s
*q
[1]*q
[1], yz
= s
*q
[1]*q
[2], wy
= s
*q
[3]*q
[1],
668 zz
= s
*q
[2]*q
[2], xz
= s
*q
[0]*q
[2], wz
= s
*q
[3]*q
[2];
670 d
[0][0] = 1.0f
- yy
- zz
;
671 d
[1][1] = 1.0f
- xx
- zz
;
672 d
[2][2] = 1.0f
- xx
- yy
;
681 static void q_mulv( v4f q
, v3f v
, v3f d
)
685 v3_muls( q
, 2.0f
*v3_dot(q
,v
), v1
);
686 v3_muls( v
, q
[3]*q
[3] - v3_dot(q
,q
), v2
);
687 v3_add( v1
, v2
, v1
);
688 v3_cross( q
, v
, v2
);
689 v3_muls( v2
, 2.0f
*q
[3], v2
);
694 * -----------------------------------------------------------------------------
695 * Section 4.a 2x2 matrices
696 * -----------------------------------------------------------------------------
699 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
702 #define M2X2_ZERO {{0.0f, 0.0f, }, \
705 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
707 v2_copy( a
[0], b
[0] );
708 v2_copy( a
[1], b
[1] );
711 static inline void m2x2_identity( m2x2f a
)
713 m2x2f id
= M2X2_INDENTIY
;
717 static inline void m2x2_create_rotation( m2x2f a
, f32 theta
)
730 static inline void m2x2_mulv( m2x2f m
, v2f v
, v2f d
)
734 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1];
735 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1];
741 * -----------------------------------------------------------------------------
742 * Section 4.b 3x3 matrices
743 * -----------------------------------------------------------------------------
746 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
747 { 0.0f, 1.0f, 0.0f, },\
748 { 0.0f, 0.0f, 1.0f, }}
750 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
751 { 0.0f, 0.0f, 0.0f, },\
752 { 0.0f, 0.0f, 0.0f, }}
755 static void euler_m3x3( v3f angles
, m3x3f d
)
757 f32 cosY
= cosf( angles
[0] ),
758 sinY
= sinf( angles
[0] ),
759 cosP
= cosf( angles
[1] ),
760 sinP
= sinf( angles
[1] ),
761 cosR
= cosf( angles
[2] ),
762 sinR
= sinf( angles
[2] );
764 d
[2][0] = -sinY
* cosP
;
766 d
[2][2] = cosY
* cosP
;
768 d
[0][0] = cosY
* cosR
;
770 d
[0][2] = sinY
* cosR
;
772 v3_cross( d
[0], d
[2], d
[1] );
775 static void m3x3_q( m3x3f m
, v4f q
)
779 diag
= m
[0][0] + m
[1][1] + m
[2][2];
782 r
= sqrtf( 1.0f
+ diag
);
784 q
[0] = rinv
* (m
[1][2] - m
[2][1]);
785 q
[1] = rinv
* (m
[2][0] - m
[0][2]);
786 q
[2] = rinv
* (m
[0][1] - m
[1][0]);
789 else if( m
[0][0] >= m
[1][1] && m
[0][0] >= m
[2][2] )
791 r
= sqrtf( 1.0f
- m
[1][1] - m
[2][2] + m
[0][0] );
794 q
[1] = rinv
* (m
[0][1] + m
[1][0]);
795 q
[2] = rinv
* (m
[0][2] + m
[2][0]);
796 q
[3] = rinv
* (m
[1][2] - m
[2][1]);
798 else if( m
[1][1] >= m
[2][2] )
800 r
= sqrtf( 1.0f
- m
[0][0] - m
[2][2] + m
[1][1] );
802 q
[0] = rinv
* (m
[0][1] + m
[1][0]);
804 q
[2] = rinv
* (m
[1][2] + m
[2][1]);
805 q
[3] = rinv
* (m
[2][0] - m
[0][2]);
809 r
= sqrtf( 1.0f
- m
[0][0] - m
[1][1] + m
[2][2] );
811 q
[0] = rinv
* (m
[0][2] + m
[2][0]);
812 q
[1] = rinv
* (m
[1][2] + m
[2][1]);
814 q
[3] = rinv
* (m
[0][1] - m
[1][0]);
818 /* a X b == [b]T a == ...*/
819 static void m3x3_skew_symetric( m3x3f a
, v3f v
)
832 static void m3x3_add( m3x3f a
, m3x3f b
, m3x3f d
)
834 v3_add( a
[0], b
[0], d
[0] );
835 v3_add( a
[1], b
[1], d
[1] );
836 v3_add( a
[2], b
[2], d
[2] );
839 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
841 v3_copy( a
[0], b
[0] );
842 v3_copy( a
[1], b
[1] );
843 v3_copy( a
[2], b
[2] );
846 static inline void m3x3_identity( m3x3f a
)
848 m3x3f id
= M3X3_IDENTITY
;
852 static void m3x3_diagonal( m3x3f a
, f32 v
)
860 static void m3x3_setdiagonalv3( m3x3f a
, v3f v
)
867 static inline void m3x3_zero( m3x3f a
)
873 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
875 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
876 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
877 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
884 dest
[0][0] = (e
*i
-h
*f
)*det
;
885 dest
[0][1] = -(b
*i
-c
*h
)*det
;
886 dest
[0][2] = (b
*f
-c
*e
)*det
;
887 dest
[1][0] = -(d
*i
-f
*g
)*det
;
888 dest
[1][1] = (a
*i
-c
*g
)*det
;
889 dest
[1][2] = -(a
*f
-d
*c
)*det
;
890 dest
[2][0] = (d
*h
-g
*e
)*det
;
891 dest
[2][1] = -(a
*h
-g
*b
)*det
;
892 dest
[2][2] = (a
*e
-d
*b
)*det
;
895 static f32
m3x3_det( m3x3f m
)
897 return m
[0][0] * (m
[1][1] * m
[2][2] - m
[2][1] * m
[1][2])
898 - m
[0][1] * (m
[1][0] * m
[2][2] - m
[1][2] * m
[2][0])
899 + m
[0][2] * (m
[1][0] * m
[2][1] - m
[1][1] * m
[2][0]);
902 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
904 f32 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
905 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
906 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
919 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
921 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
922 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
923 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
925 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
926 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
927 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
929 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
930 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
931 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
932 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
933 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
934 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
935 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
936 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
937 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
940 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
944 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
945 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
946 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
951 static inline void m3x3_projection( m3x3f dst
,
952 f32
const left
, f32
const right
, f32
const bottom
, f32
const top
)
958 rl
= 1.0f
/ (right
- left
);
959 tb
= 1.0f
/ (top
- bottom
);
961 dst
[0][0] = 2.0f
* rl
;
962 dst
[1][1] = 2.0f
* tb
;
966 static inline void m3x3_translate( m3x3f m
, v3f v
)
968 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
969 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
970 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
973 static inline void m3x3_scale( m3x3f m
, v3f v
)
975 v3_muls( m
[0], v
[0], m
[0] );
976 v3_muls( m
[1], v
[1], m
[1] );
977 v3_muls( m
[2], v
[2], m
[2] );
980 static inline void m3x3_scalef( m3x3f m
, f32 f
)
987 static inline void m3x3_rotate( m3x3f m
, f32 angle
)
989 f32 m00
= m
[0][0], m10
= m
[1][0],
990 m01
= m
[0][1], m11
= m
[1][1],
991 m02
= m
[0][2], m12
= m
[1][2];
997 m
[0][0] = m00
* c
+ m10
* s
;
998 m
[0][1] = m01
* c
+ m11
* s
;
999 m
[0][2] = m02
* c
+ m12
* s
;
1001 m
[1][0] = m00
* -s
+ m10
* c
;
1002 m
[1][1] = m01
* -s
+ m11
* c
;
1003 m
[1][2] = m02
* -s
+ m12
* c
;
1007 * -----------------------------------------------------------------------------
1008 * Section 4.c 4x3 matrices
1009 * -----------------------------------------------------------------------------
1012 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
1013 { 0.0f, 1.0f, 0.0f, },\
1014 { 0.0f, 0.0f, 1.0f, },\
1015 { 0.0f, 0.0f, 0.0f }}
1017 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
1019 v3_copy( a
[0], b
[0] );
1020 v3_copy( a
[1], b
[1] );
1021 v3_copy( a
[2], b
[2] );
1024 static inline void m4x3_invert_affine( m4x3f a
, m4x3f b
)
1026 m3x3_transpose( a
, b
);
1027 m3x3_mulv( b
, a
[3], b
[3] );
1028 v3_negate( b
[3], b
[3] );
1031 static void m4x3_invert_full( m4x3f src
, m4x3f dst
)
1035 a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
1036 e
= src
[1][0], f
= src
[1][1], g
= src
[1][2],
1037 i
= src
[2][0], j
= src
[2][1], k
= src
[2][2],
1038 m
= src
[3][0], n
= src
[3][1], o
= src
[3][2];
1044 dst
[0][0] = f
*k
- g
*j
;
1045 dst
[1][0] =-(e
*k
- g
*i
);
1046 dst
[2][0] = e
*j
- f
*i
;
1047 dst
[3][0] =-(e
*t2
- f
*t4
+ g
*t5
);
1049 dst
[0][1] =-(b
*k
- c
*j
);
1050 dst
[1][1] = a
*k
- c
*i
;
1051 dst
[2][1] =-(a
*j
- b
*i
);
1052 dst
[3][1] = a
*t2
- b
*t4
+ c
*t5
;
1058 dst
[0][2] = b
*g
- c
*f
;
1059 dst
[1][2] =-(a
*g
- c
*e
);
1060 dst
[2][2] = a
*f
- b
*e
;
1061 dst
[3][2] =-(a
*t2
- b
*t4
+ c
* t5
);
1063 det
= 1.0f
/ (a
* dst
[0][0] + b
* dst
[1][0] + c
* dst
[2][0]);
1064 v3_muls( dst
[0], det
, dst
[0] );
1065 v3_muls( dst
[1], det
, dst
[1] );
1066 v3_muls( dst
[2], det
, dst
[2] );
1067 v3_muls( dst
[3], det
, dst
[3] );
1070 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
1072 v3_copy( a
[0], b
[0] );
1073 v3_copy( a
[1], b
[1] );
1074 v3_copy( a
[2], b
[2] );
1075 v3_copy( a
[3], b
[3] );
1078 static inline void m4x3_identity( m4x3f a
)
1080 m4x3f id
= M4X3_IDENTITY
;
1084 static void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
1087 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
1088 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
1089 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
1090 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
1091 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
1092 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
1093 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
1094 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
1096 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
1097 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
1098 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
1099 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
1100 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
1101 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
1102 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
1103 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
1104 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
1105 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
1106 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
1107 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
1110 #if 0 /* shat appf mingw wstringop-overflow */
1113 static void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
1117 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
1118 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
1119 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
1125 * Transform plane ( xyz, distance )
1127 static void m4x3_mulp( m4x3f m
, v4f p
, v4f d
)
1131 v3_muls( p
, p
[3], o
);
1132 m4x3_mulv( m
, o
, o
);
1133 m3x3_mulv( m
, p
, d
);
1135 d
[3] = v3_dot( o
, d
);
1142 static void m4x3_translate( m4x3f m
, v3f v
)
1144 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
1145 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
1146 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
1149 static void m4x3_rotate_x( m4x3f m
, f32 angle
)
1151 m4x3f t
= M4X3_IDENTITY
;
1162 m4x3_mul( m
, t
, m
);
1165 static void m4x3_rotate_y( m4x3f m
, f32 angle
)
1167 m4x3f t
= M4X3_IDENTITY
;
1178 m4x3_mul( m
, t
, m
);
1181 static void m4x3_rotate_z( m4x3f m
, f32 angle
)
1183 m4x3f t
= M4X3_IDENTITY
;
1194 m4x3_mul( m
, t
, m
);
1197 static void m4x3_expand( m4x3f m
, m4x4f d
)
1199 v3_copy( m
[0], d
[0] );
1200 v3_copy( m
[1], d
[1] );
1201 v3_copy( m
[2], d
[2] );
1202 v3_copy( m
[3], d
[3] );
1209 static void m4x3_decompose( m4x3f m
, v3f co
, v4f q
, v3f s
)
1211 v3_copy( m
[3], co
);
1212 s
[0] = v3_length(m
[0]);
1213 s
[1] = v3_length(m
[1]);
1214 s
[2] = v3_length(m
[2]);
1217 v3_divs( m
[0], s
[0], rot
[0] );
1218 v3_divs( m
[1], s
[1], rot
[1] );
1219 v3_divs( m
[2], s
[2], rot
[2] );
1224 static void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
){
1226 m4x3_mulv( m
, point
, v
);
1228 v3_minv( box
[0], v
, box
[0] );
1229 v3_maxv( box
[1], v
, box
[1] );
1232 static void m4x3_expand_aabb_aabb( m4x3f m
, boxf boxa
, boxf boxb
){
1234 v3_copy( boxb
[0], a
);
1235 v3_copy( boxb
[1], b
);
1236 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], a
[2] } );
1237 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], a
[2] } );
1238 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], a
[2] } );
1239 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], a
[2] } );
1240 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], a
[1], b
[2] } );
1241 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ a
[0], b
[1], b
[2] } );
1242 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], b
[1], b
[2] } );
1243 m4x3_expand_aabb_point( m
, boxa
, (v3f
){ b
[0], a
[1], b
[2] } );
1245 static inline void m4x3_lookat( m4x3f m
, v3f pos
, v3f target
, v3f up
)
1248 v3_sub( target
, pos
, dir
);
1249 v3_normalize( dir
);
1251 v3_copy( dir
, m
[2] );
1253 v3_cross( up
, m
[2], m
[0] );
1254 v3_normalize( m
[0] );
1256 v3_cross( m
[2], m
[0], m
[1] );
1257 v3_copy( pos
, m
[3] );
1261 * -----------------------------------------------------------------------------
1262 * Section 4.d 4x4 matrices
1263 * -----------------------------------------------------------------------------
1266 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
1267 { 0.0f, 1.0f, 0.0f, 0.0f },\
1268 { 0.0f, 0.0f, 1.0f, 0.0f },\
1269 { 0.0f, 0.0f, 0.0f, 1.0f }}
1270 #define M4X4_ZERO {{0.0f, 0.0f, 0.0f, 0.0f },\
1271 { 0.0f, 0.0f, 0.0f, 0.0f },\
1272 { 0.0f, 0.0f, 0.0f, 0.0f },\
1273 { 0.0f, 0.0f, 0.0f, 0.0f }}
1275 static void m4x4_projection( m4x4f m
, f32 angle
,
1276 f32 ratio
, f32 fnear
, f32 ffar
)
1278 f32 scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * fnear
,
1284 m
[0][0] = 2.0f
* fnear
/ (r
- l
);
1290 m
[1][1] = 2.0f
* fnear
/ (t
- b
);
1294 m
[2][0] = (r
+ l
) / (r
- l
);
1295 m
[2][1] = (t
+ b
) / (t
- b
);
1296 m
[2][2] = -(ffar
+ fnear
) / (ffar
- fnear
);
1301 m
[3][2] = -2.0f
* ffar
* fnear
/ (ffar
- fnear
);
1305 static void m4x4_translate( m4x4f m
, v3f v
)
1307 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
1308 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
1309 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
1312 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
1314 v4_copy( a
[0], b
[0] );
1315 v4_copy( a
[1], b
[1] );
1316 v4_copy( a
[2], b
[2] );
1317 v4_copy( a
[3], b
[3] );
1320 static inline void m4x4_identity( m4x4f a
)
1322 m4x4f id
= M4X4_IDENTITY
;
1326 static inline void m4x4_zero( m4x4f a
)
1328 m4x4f zero
= M4X4_ZERO
;
1329 m4x4_copy( zero
, a
);
1332 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
1334 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1335 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1336 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1337 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1339 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
1340 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
1341 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
1342 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
1344 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
1345 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
1346 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
1347 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
1348 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
1349 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
1350 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
1351 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
1352 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
1353 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
1354 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
1355 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
1356 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
1357 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
1358 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
1359 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
1362 static inline void m4x4_mulv( m4x4f m
, v4f v
, v4f d
)
1366 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0]*v
[3];
1367 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1]*v
[3];
1368 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2]*v
[3];
1369 res
[3] = m
[0][3]*v
[0] + m
[1][3]*v
[1] + m
[2][3]*v
[2] + m
[3][3]*v
[3];
1374 static inline void m4x4_inv( m4x4f a
, m4x4f d
)
1376 f32 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
1377 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
1378 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
1379 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
1383 t
[0] = a22
*a33
- a32
*a23
;
1384 t
[1] = a21
*a33
- a31
*a23
;
1385 t
[2] = a21
*a32
- a31
*a22
;
1386 t
[3] = a20
*a33
- a30
*a23
;
1387 t
[4] = a20
*a32
- a30
*a22
;
1388 t
[5] = a20
*a31
- a30
*a21
;
1390 d
[0][0] = a11
*t
[0] - a12
*t
[1] + a13
*t
[2];
1391 d
[1][0] =-(a10
*t
[0] - a12
*t
[3] + a13
*t
[4]);
1392 d
[2][0] = a10
*t
[1] - a11
*t
[3] + a13
*t
[5];
1393 d
[3][0] =-(a10
*t
[2] - a11
*t
[4] + a12
*t
[5]);
1395 d
[0][1] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1396 d
[1][1] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1397 d
[2][1] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1398 d
[3][1] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1400 t
[0] = a12
*a33
- a32
*a13
;
1401 t
[1] = a11
*a33
- a31
*a13
;
1402 t
[2] = a11
*a32
- a31
*a12
;
1403 t
[3] = a10
*a33
- a30
*a13
;
1404 t
[4] = a10
*a32
- a30
*a12
;
1405 t
[5] = a10
*a31
- a30
*a11
;
1407 d
[0][2] = a01
*t
[0] - a02
*t
[1] + a03
*t
[2];
1408 d
[1][2] =-(a00
*t
[0] - a02
*t
[3] + a03
*t
[4]);
1409 d
[2][2] = a00
*t
[1] - a01
*t
[3] + a03
*t
[5];
1410 d
[3][2] =-(a00
*t
[2] - a01
*t
[4] + a02
*t
[5]);
1412 t
[0] = a12
*a23
- a22
*a13
;
1413 t
[1] = a11
*a23
- a21
*a13
;
1414 t
[2] = a11
*a22
- a21
*a12
;
1415 t
[3] = a10
*a23
- a20
*a13
;
1416 t
[4] = a10
*a22
- a20
*a12
;
1417 t
[5] = a10
*a21
- a20
*a11
;
1419 d
[0][3] =-(a01
*t
[0] - a02
*t
[1] + a03
*t
[2]);
1420 d
[1][3] = a00
*t
[0] - a02
*t
[3] + a03
*t
[4];
1421 d
[2][3] =-(a00
*t
[1] - a01
*t
[3] + a03
*t
[5]);
1422 d
[3][3] = a00
*t
[2] - a01
*t
[4] + a02
*t
[5];
1424 det
= 1.0f
/ (a00
*d
[0][0] + a01
*d
[1][0] + a02
*d
[2][0] + a03
*d
[3][0]);
1425 v4_muls( d
[0], det
, d
[0] );
1426 v4_muls( d
[1], det
, d
[1] );
1427 v4_muls( d
[2], det
, d
[2] );
1428 v4_muls( d
[3], det
, d
[3] );
1432 * -----------------------------------------------------------------------------
1434 * -----------------------------------------------------------------------------
1437 static inline void box_addpt( boxf a
, v3f pt
)
1439 v3_minv( a
[0], pt
, a
[0] );
1440 v3_maxv( a
[1], pt
, a
[1] );
1443 static inline void box_concat( boxf a
, boxf b
)
1445 v3_minv( a
[0], b
[0], a
[0] );
1446 v3_maxv( a
[1], b
[1], a
[1] );
1449 static inline void box_copy( boxf a
, boxf b
)
1451 v3_copy( a
[0], b
[0] );
1452 v3_copy( a
[1], b
[1] );
1455 static inline int box_overlap( boxf a
, boxf b
)
1458 ( a
[0][0] <= b
[1][0] && a
[1][0] >= b
[0][0] ) &&
1459 ( a
[0][1] <= b
[1][1] && a
[1][1] >= b
[0][1] ) &&
1460 ( a
[0][2] <= b
[1][2] && a
[1][2] >= b
[0][2] )
1464 static int box_within( boxf greater
, boxf lesser
)
1467 v3_sub( lesser
[0], greater
[0], a
);
1468 v3_sub( lesser
[1], greater
[1], b
);
1470 if( (a
[0] >= 0.0f
) && (a
[1] >= 0.0f
) && (a
[2] >= 0.0f
) &&
1471 (b
[0] <= 0.0f
) && (b
[1] <= 0.0f
) && (b
[2] <= 0.0f
) )
1479 static inline void box_init_inf( boxf box
){
1480 v3_fill( box
[0], INFINITY
);
1481 v3_fill( box
[1], -INFINITY
);
1485 * -----------------------------------------------------------------------------
1486 * Section 5.b Planes
1487 * -----------------------------------------------------------------------------
1490 static inline void tri_to_plane( f64 a
[3], f64 b
[3],
1491 f64 c
[3], f64 p
[4] )
1497 edge0
[0] = b
[0] - a
[0];
1498 edge0
[1] = b
[1] - a
[1];
1499 edge0
[2] = b
[2] - a
[2];
1501 edge1
[0] = c
[0] - a
[0];
1502 edge1
[1] = c
[1] - a
[1];
1503 edge1
[2] = c
[2] - a
[2];
1505 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
1506 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
1507 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
1509 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
1510 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
1517 static int plane_intersect3( v4f a
, v4f b
, v4f c
, v3f p
)
1519 f32
const epsilon
= 1e-6f
;
1522 v3_cross( a
, b
, x
);
1523 f32 d
= v3_dot( x
, c
);
1525 if( (d
< epsilon
) && (d
> -epsilon
) ) return 0;
1528 v3_cross( b
, c
, v0
);
1529 v3_cross( c
, a
, v1
);
1530 v3_cross( a
, b
, v2
);
1532 v3_muls( v0
, a
[3], p
);
1533 v3_muladds( p
, v1
, b
[3], p
);
1534 v3_muladds( p
, v2
, c
[3], p
);
1540 int plane_intersect2( v4f a
, v4f b
, v3f p
, v3f n
)
1542 f32
const epsilon
= 1e-6f
;
1545 v3_cross( a
, b
, c
);
1546 f32 d
= v3_length2( c
);
1548 if( (d
< epsilon
) && (d
> -epsilon
) )
1552 v3_cross( c
, b
, v0
);
1553 v3_cross( a
, c
, v1
);
1555 v3_muls( v0
, a
[3], vx
);
1556 v3_muladds( vx
, v1
, b
[3], vx
);
1557 v3_divs( vx
, d
, p
);
1563 static int plane_segment( v4f plane
, v3f a
, v3f b
, v3f co
)
1565 f32 d0
= v3_dot( a
, plane
) - plane
[3],
1566 d1
= v3_dot( b
, plane
) - plane
[3];
1570 f32 tot
= 1.0f
/( fabsf(d0
)+fabsf(d1
) );
1572 v3_muls( a
, fabsf(d1
) * tot
, co
);
1573 v3_muladds( co
, b
, fabsf(d0
) * tot
, co
);
1580 static inline f64
plane_polarity( f64 p
[4], f64 a
[3] )
1583 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
1584 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])
1588 static f32
ray_plane( v4f plane
, v3f co
, v3f dir
){
1589 f32 d
= v3_dot( plane
, dir
);
1590 if( fabsf(d
) > 1e-6f
){
1592 v3_muls( plane
, plane
[3], v0
);
1593 v3_sub( v0
, co
, v0
);
1594 return v3_dot( v0
, plane
) / d
;
1596 else return INFINITY
;
1600 * -----------------------------------------------------------------------------
1601 * Section 5.c Closest point functions
1602 * -----------------------------------------------------------------------------
1606 * These closest point tests were learned from Real-Time Collision Detection by
1609 static f32
closest_segment_segment( v3f p1
, v3f q1
, v3f p2
, v3f q2
,
1610 f32
*s
, f32
*t
, v3f c1
, v3f c2
)
1613 v3_sub( q1
, p1
, d1
);
1614 v3_sub( q2
, p2
, d2
);
1615 v3_sub( p1
, p2
, r
);
1617 f32 a
= v3_length2( d1
),
1618 e
= v3_length2( d2
),
1619 f
= v3_dot( d2
, r
);
1621 const f32 kEpsilon
= 0.0001f
;
1623 if( a
<= kEpsilon
&& e
<= kEpsilon
)
1631 v3_sub( c1
, c2
, v0
);
1633 return v3_length2( v0
);
1639 *t
= vg_clampf( f
/ e
, 0.0f
, 1.0f
);
1643 f32 c
= v3_dot( d1
, r
);
1647 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1651 f32 b
= v3_dot(d1
,d2
),
1656 *s
= vg_clampf((b
*f
- c
*e
)/d
, 0.0f
, 1.0f
);
1663 *t
= (b
*(*s
)+f
) / e
;
1668 *s
= vg_clampf( -c
/ a
, 0.0f
, 1.0f
);
1670 else if( *t
> 1.0f
)
1673 *s
= vg_clampf((b
-c
)/a
,0.0f
,1.0f
);
1678 v3_muladds( p1
, d1
, *s
, c1
);
1679 v3_muladds( p2
, d2
, *t
, c2
);
1682 v3_sub( c1
, c2
, v0
);
1683 return v3_length2( v0
);
1686 static int point_inside_aabb( boxf box
, v3f point
)
1688 if((point
[0]<=box
[1][0]) && (point
[1]<=box
[1][1]) && (point
[2]<=box
[1][2]) &&
1689 (point
[0]>=box
[0][0]) && (point
[1]>=box
[0][1]) && (point
[2]>=box
[0][2]) )
1695 static void closest_point_aabb( v3f p
, boxf box
, v3f dest
)
1697 v3_maxv( p
, box
[0], dest
);
1698 v3_minv( dest
, box
[1], dest
);
1701 static void closest_point_obb( v3f p
, boxf box
,
1702 m4x3f mtx
, m4x3f inv_mtx
, v3f dest
)
1705 m4x3_mulv( inv_mtx
, p
, local
);
1706 closest_point_aabb( local
, box
, local
);
1707 m4x3_mulv( mtx
, local
, dest
);
1710 static f32
closest_point_segment( v3f a
, v3f b
, v3f point
, v3f dest
)
1714 v3_sub( point
, a
, v1
);
1716 f32 t
= v3_dot( v1
, v0
) / v3_length2(v0
);
1717 t
= vg_clampf(t
,0.0f
,1.0f
);
1718 v3_muladds( a
, v0
, t
, dest
);
1722 static void closest_on_triangle( v3f p
, v3f tri
[3], v3f dest
)
1727 /* Region outside A */
1728 v3_sub( tri
[1], tri
[0], ab
);
1729 v3_sub( tri
[2], tri
[0], ac
);
1730 v3_sub( p
, tri
[0], ap
);
1734 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1736 v3_copy( tri
[0], dest
);
1737 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1741 /* Region outside B */
1745 v3_sub( p
, tri
[1], bp
);
1746 d3
= v3_dot( ab
, bp
);
1747 d4
= v3_dot( ac
, bp
);
1749 if( d3
>= 0.0f
&& d4
<= d3
)
1751 v3_copy( tri
[1], dest
);
1752 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1756 /* Edge region of AB */
1757 f32 vc
= d1
*d4
- d3
*d2
;
1758 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1760 f32 v
= d1
/ (d1
-d3
);
1761 v3_muladds( tri
[0], ab
, v
, dest
);
1762 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1766 /* Region outside C */
1769 v3_sub( p
, tri
[2], cp
);
1770 d5
= v3_dot(ab
, cp
);
1771 d6
= v3_dot(ac
, cp
);
1773 if( d6
>= 0.0f
&& d5
<= d6
)
1775 v3_copy( tri
[2], dest
);
1776 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1781 f32 vb
= d5
*d2
- d1
*d6
;
1782 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1784 f32 w
= d2
/ (d2
-d6
);
1785 v3_muladds( tri
[0], ac
, w
, dest
);
1786 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1791 f32 va
= d3
*d6
- d5
*d4
;
1792 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1794 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1796 v3_sub( tri
[2], tri
[1], bc
);
1797 v3_muladds( tri
[1], bc
, w
, dest
);
1798 v3_copy( (v3f
){INFINITY
,INFINITY
,INFINITY
}, dest
);
1802 /* P inside region, Q via barycentric coordinates uvw */
1803 f32 d
= 1.0f
/(va
+vb
+vc
),
1807 v3_muladds( tri
[0], ab
, v
, dest
);
1808 v3_muladds( dest
, ac
, w
, dest
);
1813 k_contact_type_default
,
1814 k_contact_type_disabled
,
1818 static enum contact_type
closest_on_triangle_1( v3f p
, v3f tri
[3], v3f dest
)
1823 /* Region outside A */
1824 v3_sub( tri
[1], tri
[0], ab
);
1825 v3_sub( tri
[2], tri
[0], ac
);
1826 v3_sub( p
, tri
[0], ap
);
1830 if( d1
<= 0.0f
&& d2
<= 0.0f
)
1832 v3_copy( tri
[0], dest
);
1833 return k_contact_type_default
;
1836 /* Region outside B */
1840 v3_sub( p
, tri
[1], bp
);
1841 d3
= v3_dot( ab
, bp
);
1842 d4
= v3_dot( ac
, bp
);
1844 if( d3
>= 0.0f
&& d4
<= d3
)
1846 v3_copy( tri
[1], dest
);
1847 return k_contact_type_edge
;
1850 /* Edge region of AB */
1851 f32 vc
= d1
*d4
- d3
*d2
;
1852 if( vc
<= 0.0f
&& d1
>= 0.0f
&& d3
<= 0.0f
)
1854 f32 v
= d1
/ (d1
-d3
);
1855 v3_muladds( tri
[0], ab
, v
, dest
);
1856 return k_contact_type_edge
;
1859 /* Region outside C */
1862 v3_sub( p
, tri
[2], cp
);
1863 d5
= v3_dot(ab
, cp
);
1864 d6
= v3_dot(ac
, cp
);
1866 if( d6
>= 0.0f
&& d5
<= d6
)
1868 v3_copy( tri
[2], dest
);
1869 return k_contact_type_edge
;
1873 f32 vb
= d5
*d2
- d1
*d6
;
1874 if( vb
<= 0.0f
&& d2
>= 0.0f
&& d6
<= 0.0f
)
1876 f32 w
= d2
/ (d2
-d6
);
1877 v3_muladds( tri
[0], ac
, w
, dest
);
1878 return k_contact_type_edge
;
1882 f32 va
= d3
*d6
- d5
*d4
;
1883 if( va
<= 0.0f
&& (d4
-d3
) >= 0.0f
&& (d5
-d6
) >= 0.0f
)
1885 f32 w
= (d4
-d3
) / ((d4
-d3
) + (d5
-d6
));
1887 v3_sub( tri
[2], tri
[1], bc
);
1888 v3_muladds( tri
[1], bc
, w
, dest
);
1889 return k_contact_type_edge
;
1892 /* P inside region, Q via barycentric coordinates uvw */
1893 f32 d
= 1.0f
/(va
+vb
+vc
),
1897 v3_muladds( tri
[0], ab
, v
, dest
);
1898 v3_muladds( dest
, ac
, w
, dest
);
1900 return k_contact_type_default
;
1903 static void closest_point_elipse( v2f p
, v2f e
, v2f o
)
1905 v2f pabs
, ei
, e2
, ve
, t
;
1908 v2_div( (v2f
){ 1.0f
, 1.0f
}, e
, ei
);
1910 v2_mul( ei
, (v2f
){ e2
[0]-e2
[1], e2
[1]-e2
[0] }, ve
);
1912 v2_fill( t
, 0.70710678118654752f
);
1914 for( int i
=0; i
<3; i
++ ){
1917 v2_mul( ve
, t
, v
); /* ve*t*t*t */
1921 v2_sub( pabs
, v
, u
);
1925 v2_sub( ud
, v
, ud
);
1927 v2_muls( u
, v2_length( ud
), u
);
1932 v2_maxv( (v2f
){0.0f
,0.0f
}, w
, t
);
1937 v2_copysign( o
, p
);
1941 * -----------------------------------------------------------------------------
1942 * Section 5.d Raycasts & Spherecasts
1943 * -----------------------------------------------------------------------------
1946 int ray_aabb1( boxf box
, v3f co
, v3f dir_inv
, f32 dist
)
1951 v3_sub( box
[0], co
, v0
);
1952 v3_sub( box
[1], co
, v1
);
1954 v3_mul( v0
, dir_inv
, v0
);
1955 v3_mul( v1
, dir_inv
, v1
);
1957 tmin
= vg_minf( v0
[0], v1
[0] );
1958 tmax
= vg_maxf( v0
[0], v1
[0] );
1959 tmin
= vg_maxf( tmin
, vg_minf( v0
[1], v1
[1] ));
1960 tmax
= vg_minf( tmax
, vg_maxf( v0
[1], v1
[1] ));
1961 tmin
= vg_maxf( tmin
, vg_minf( v0
[2], v1
[2] ));
1962 tmax
= vg_minf( tmax
, vg_maxf( v0
[2], v1
[2] ));
1964 return (tmax
>= tmin
) && (tmin
<= dist
) && (tmax
>= 0.0f
);
1967 /* Time of intersection with ray vs triangle */
1968 static int ray_tri( v3f tri
[3], v3f co
,
1969 v3f dir
, f32
*dist
)
1971 f32
const kEpsilon
= 0.00001f
;
1973 v3f v0
, v1
, h
, s
, q
, n
;
1980 v3_sub( pb
, pa
, v0
);
1981 v3_sub( pc
, pa
, v1
);
1982 v3_cross( dir
, v1
, h
);
1983 v3_cross( v0
, v1
, n
);
1985 if( v3_dot( n
, dir
) > 0.0f
) /* Backface culling */
1989 a
= v3_dot( v0
, h
);
1991 if( a
> -kEpsilon
&& a
< kEpsilon
)
1995 v3_sub( co
, pa
, s
);
1997 u
= f
* v3_dot(s
, h
);
1998 if( u
< 0.0f
|| u
> 1.0f
)
2001 v3_cross( s
, v0
, q
);
2002 v
= f
* v3_dot( dir
, q
);
2003 if( v
< 0.0f
|| u
+v
> 1.0f
)
2006 t
= f
* v3_dot(v1
, q
);
2015 /* time of intersection with ray vs sphere */
2016 static int ray_sphere( v3f c
, f32 r
,
2017 v3f co
, v3f dir
, f32
*t
)
2022 f32 b
= v3_dot( m
, dir
),
2023 c1
= v3_dot( m
, m
) - r
*r
;
2025 /* Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0) */
2026 if( c1
> 0.0f
&& b
> 0.0f
)
2029 f32 discr
= b
*b
- c1
;
2031 /* A negative discriminant corresponds to ray missing sphere */
2036 * Ray now found to intersect sphere, compute smallest t value of
2039 *t
= -b
- sqrtf( discr
);
2041 /* If t is negative, ray started inside sphere so clamp t to zero */
2049 * time of intersection of ray vs cylinder
2050 * The cylinder does not have caps but is finite
2052 * Heavily adapted from regular segment vs cylinder from:
2053 * Real-Time Collision Detection
2055 static int ray_uncapped_finite_cylinder( v3f q
, v3f p
, f32 r
,
2056 v3f co
, v3f dir
, f32
*t
)
2059 v3_muladds( co
, dir
, 1.0f
, sb
);
2063 v3_sub( sb
, co
, n
);
2065 f32 md
= v3_dot( m
, d
),
2066 nd
= v3_dot( n
, d
),
2067 dd
= v3_dot( d
, d
),
2068 nn
= v3_dot( n
, n
),
2069 mn
= v3_dot( m
, n
),
2071 k
= v3_dot( m
, m
) - r
*r
,
2074 if( fabsf(a
) < 0.00001f
)
2076 /* Segment runs parallel to cylinder axis */
2080 f32 b
= dd
*mn
- nd
*md
,
2084 return 0; /* No real roots; no intersection */
2086 *t
= (-b
- sqrtf(discr
)) / a
;
2088 return 0; /* Intersection behind ray */
2090 /* Check within cylinder segment */
2091 if( md
+ (*t
)*nd
< 0.0f
)
2094 if( md
+ (*t
)*nd
> dd
)
2097 /* Segment intersects cylinder between the endcaps; t is correct */
2102 * Time of intersection of sphere and triangle. Origin must be outside the
2103 * colliding area. This is a fairly long procedure.
2105 static int spherecast_triangle( v3f tri
[3],
2106 v3f co
, v3f dir
, f32 r
, f32
*t
, v3f n
)
2111 v3_sub( tri
[1], tri
[0], v0
);
2112 v3_sub( tri
[2], tri
[0], v1
);
2113 v3_cross( v0
, v1
, n
);
2115 v3_muladds( tri
[0], n
, r
, sum
[0] );
2116 v3_muladds( tri
[1], n
, r
, sum
[1] );
2117 v3_muladds( tri
[2], n
, r
, sum
[2] );
2120 f32 t_min
= INFINITY
,
2123 if( ray_tri( sum
, co
, dir
, &t1
) ){
2124 t_min
= vg_minf( t_min
, t1
);
2129 * Currently disabled; ray_sphere requires |d| = 1. it is not very important.
2132 for( int i
=0; i
<3; i
++ ){
2133 if( ray_sphere( tri
[i
], r
, co
, dir
, &t1
) ){
2134 t_min
= vg_minf( t_min
, t1
);
2140 for( int i
=0; i
<3; i
++ ){
2144 if( ray_uncapped_finite_cylinder( tri
[i0
], tri
[i1
], r
, co
, dir
, &t1
) ){
2149 v3_add( dir
, co
, co1
);
2150 v3_lerp( co
, co1
, t_min
, ct
);
2152 closest_point_segment( tri
[i0
], tri
[i1
], ct
, cx
);
2153 v3_sub( ct
, cx
, n
);
2166 * -----------------------------------------------------------------------------
2167 * Section 5.e Curves
2168 * -----------------------------------------------------------------------------
2171 static void eval_bezier_time( v3f p0
, v3f p1
, v3f h0
, v3f h1
, f32 t
, v3f p
)
2176 v3_muls( p1
, ttt
, p
);
2177 v3_muladds( p
, h1
, 3.0f
*tt
-3.0f
*ttt
, p
);
2178 v3_muladds( p
, h0
, 3.0f
*ttt
-6.0f
*tt
+3.0f
*t
, p
);
2179 v3_muladds( p
, p0
, 3.0f
*tt
-ttt
-3.0f
*t
+1.0f
, p
);
2182 static void eval_bezier3( v3f p0
, v3f p1
, v3f p2
, f32 t
, v3f p
)
2186 v3_muls( p0
, u
*u
, p
);
2187 v3_muladds( p
, p1
, 2.0f
*u
*t
, p
);
2188 v3_muladds( p
, p2
, t
*t
, p
);
2192 * -----------------------------------------------------------------------------
2193 * Section 5.f Volumes
2194 * -----------------------------------------------------------------------------
2197 static float vg_sphere_volume( float radius
){
2198 float r3
= radius
*radius
*radius
;
2199 return (4.0f
/3.0f
) * VG_PIf
* r3
;
2203 * -----------------------------------------------------------------------------
2204 * Section 6.a PSRNG and some distributions
2205 * -----------------------------------------------------------------------------
2208 /* An implementation of the MT19937 Algorithm for the Mersenne Twister
2209 * by Evan Sultanik. Based upon the pseudocode in: M. Matsumoto and
2210 * T. Nishimura, "Mersenne Twister: A 623-dimensionally
2211 * equidistributed uniform pseudorandom number generator," ACM
2212 * Transactions on Modeling and Computer Simulation Vol. 8, No. 1,
2213 * January pp.3-30 1998.
2215 * http://www.sultanik.com/Mersenne_twister
2216 * https://github.com/ESultanik/mtwister/blob/master/mtwister.c
2219 #define MT_UPPER_MASK 0x80000000
2220 #define MT_LOWER_MASK 0x7fffffff
2221 #define MT_TEMPERING_MASK_B 0x9d2c5680
2222 #define MT_TEMPERING_MASK_C 0xefc60000
2224 #define MT_STATE_VECTOR_LENGTH 624
2226 /* changes to STATE_VECTOR_LENGTH also require changes to this */
2227 #define MT_STATE_VECTOR_M 397
2230 u32 mt
[MT_STATE_VECTOR_LENGTH
];
2235 static void vg_rand_seed( unsigned long seed
)
2237 /* set initial seeds to mt[STATE_VECTOR_LENGTH] using the generator
2238 * from Line 25 of Table 1 in: Donald Knuth, "The Art of Computer
2239 * Programming," Vol. 2 (2nd Ed.) pp.102.
2241 vg_rand
.mt
[0] = seed
& 0xffffffff;
2242 for( vg_rand
.index
=1; vg_rand
.index
<MT_STATE_VECTOR_LENGTH
; vg_rand
.index
++){
2243 vg_rand
.mt
[vg_rand
.index
] =
2244 (6069 * vg_rand
.mt
[vg_rand
.index
-1]) & 0xffffffff;
2249 * Generates a pseudo-randomly generated long.
2251 static u32
vg_randu32(void)
2254 /* mag[x] = x * 0x9908b0df for x = 0,1 */
2255 static u32 mag
[2] = {0x0, 0x9908b0df};
2256 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
|| vg_rand
.index
< 0 ){
2257 /* generate STATE_VECTOR_LENGTH words at a time */
2259 if( vg_rand
.index
>= MT_STATE_VECTOR_LENGTH
+1 || vg_rand
.index
< 0 ){
2260 vg_rand_seed( 4357 );
2262 for( kk
=0; kk
<MT_STATE_VECTOR_LENGTH
-MT_STATE_VECTOR_M
; kk
++ ){
2263 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2264 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2265 vg_rand
.mt
[kk
] = vg_rand
.mt
[kk
+MT_STATE_VECTOR_M
] ^
2266 (y
>> 1) ^ mag
[y
& 0x1];
2268 for( ; kk
<MT_STATE_VECTOR_LENGTH
-1; kk
++ ){
2269 y
= (vg_rand
.mt
[kk
] & MT_UPPER_MASK
) |
2270 (vg_rand
.mt
[kk
+1] & MT_LOWER_MASK
);
2272 vg_rand
.mt
[ kk
+(MT_STATE_VECTOR_M
-MT_STATE_VECTOR_LENGTH
)] ^
2273 (y
>> 1) ^ mag
[y
& 0x1];
2275 y
= (vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] & MT_UPPER_MASK
) |
2276 (vg_rand
.mt
[0] & MT_LOWER_MASK
);
2277 vg_rand
.mt
[MT_STATE_VECTOR_LENGTH
-1] =
2278 vg_rand
.mt
[MT_STATE_VECTOR_M
-1] ^ (y
>> 1) ^ mag
[y
& 0x1];
2281 y
= vg_rand
.mt
[vg_rand
.index
++];
2283 y
^= (y
<< 7) & MT_TEMPERING_MASK_B
;
2284 y
^= (y
<< 15) & MT_TEMPERING_MASK_C
;
2290 * Generates a pseudo-randomly generated f64 in the range [0..1].
2292 static inline f64
vg_randf64(void)
2294 return (f64
)vg_randu32()/(f64
)0xffffffff;
2297 static inline f64
vg_randf64_range( f64 min
, f64 max
)
2299 return vg_lerp( min
, max
, (f64
)vg_randf64() );
2302 static inline void vg_rand_dir( v3f dir
)
2304 dir
[0] = vg_randf64();
2305 dir
[1] = vg_randf64();
2306 dir
[2] = vg_randf64();
2308 v3_muls( dir
, 2.0f
, dir
);
2309 v3_sub( dir
, (v3f
){1.0f
,1.0f
,1.0f
}, dir
);
2311 v3_normalize( dir
);
2314 static inline void vg_rand_sphere( v3f co
)
2317 v3_muls( co
, cbrtf( vg_randf64() ), co
);