1 /* Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved */
3 #define VG_PIf 3.14159265358979323846264338327950288f
4 #define VG_TAUf 6.28318530717958647692528676655900576f
6 static inline float vg_minf( float a
, float b
)
11 static inline float vg_maxf( float a
, float b
)
16 static inline float vg_clampf( float a
, float min
, float max
)
18 return vg_minf( max
, vg_maxf( a
, min
) );
21 static inline float vg_signf( float a
)
23 return a
< 0.0f
? -1.0f
: 1.0f
;
26 #define VG_MIN( A, B ) ((A)<(B)?(A):(B))
27 #define VG_MAX( A, B ) ((A)>(B)?(A):(B))
29 static inline int vg_min( int a
, int b
)
34 static inline int vg_max( int a
, int b
)
39 static inline float vg_rad( float deg
)
41 return deg
* VG_PIf
/ 180.0f
;
47 static inline void v2_copy( v2f a
, v2f b
)
49 b
[0] = a
[0]; b
[1] = a
[1];
52 static inline void v2i_copy( v2i a
, v2i b
)
54 b
[0] = a
[0]; b
[1] = a
[1];
57 static inline int v2i_eq( v2i a
, v2i b
)
59 return ((a
[0] == b
[0]) && (a
[1] == b
[1]));
62 static inline void v2i_add( v2i a
, v2i b
, v2i d
)
64 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
67 static inline void v2i_sub( v2i a
, v2i b
, v2i d
)
69 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
72 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
74 dest
[0] = vg_minf(a
[0], b
[0]);
75 dest
[1] = vg_minf(a
[1], b
[1]);
78 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
80 dest
[0] = vg_maxf(a
[0], b
[0]);
81 dest
[1] = vg_maxf(a
[1], b
[1]);
84 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
86 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
89 static inline float v2_cross( v2f a
, v2f b
)
91 return a
[0] * b
[1] - a
[1] * b
[0];
94 static inline void v2_add( v2f a
, v2f b
, v2f d
)
96 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
99 static inline void v2_muls( v2f a
, float s
, v2f d
)
101 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
104 static inline void v2_divs( v2f a
, float s
, v2f d
)
106 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
;
109 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
115 static inline void v2_div( v2f a
, v2f b
, v2f d
)
117 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
120 static inline void v2_muladd( v2f a
, v2f b
, v2f s
, v2f d
)
122 d
[0] = a
[0]+b
[0]*s
[0];
123 d
[1] = a
[1]+b
[1]*s
[1];
126 static inline void v2_muladds( v2f a
, v2f b
, float s
, v2f d
)
132 static inline float v2_length2( v2f a
)
134 return a
[0]*a
[0] + a
[1]*a
[1];
137 static inline float v2_length( v2f a
)
139 return sqrtf( v2_length2( a
) );
142 static inline float v2_dist2( v2f a
, v2f b
)
145 v2_sub( a
, b
, delta
);
146 return v2_length2( delta
);
149 static inline float v2_dist( v2f a
, v2f b
)
151 return sqrtf( v2_dist2( a
, b
) );
154 static inline void v2_lerp( v2f a
, v2f b
, float t
, v2f d
)
156 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
157 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
163 static inline void v3_zero( v3f a
)
165 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
168 static inline void v3_copy( v3f a
, v3f b
)
170 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
173 static inline void v3_add( v3f a
, v3f b
, v3f d
)
175 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
178 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
180 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
183 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
185 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
188 static inline void v3_div( v3f a
, v3f b
, v3f d
)
190 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1]; d
[2] = a
[2]/b
[2];
193 static inline void v3_muls( v3f a
, float s
, v3f d
)
195 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
198 static inline void v3_divs( v3f a
, float s
, v3f d
)
200 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
; d
[2] = a
[2]/s
;
203 static inline void v3_muladds( v3f a
, v3f b
, float s
, v3f d
)
205 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
208 static inline float v3_dot( v3f a
, v3f b
)
210 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
213 static inline void v3_cross( v3f a
, v3f b
, v3f d
)
215 d
[0] = a
[1] * b
[2] - a
[2] * b
[1];
216 d
[1] = a
[2] * b
[0] - a
[0] * b
[2];
217 d
[2] = a
[0] * b
[1] - a
[1] * b
[0];
220 static inline float v3_length2( v3f a
)
222 return v3_dot( a
, a
);
225 static inline float v3_length( v3f a
)
227 return sqrtf( v3_length2( a
) );
230 static inline float v3_dist2( v3f a
, v3f b
)
233 v3_sub( a
, b
, delta
);
234 return v3_length2( delta
);
237 static inline float v3_dist( v3f a
, v3f b
)
239 return sqrtf( v3_dist2( a
, b
) );
242 static inline void v3_normalize( v3f a
)
244 v3_muls( a
, 1.f
/ v3_length( a
), a
);
247 static inline float vg_lerpf( float a
, float b
, float t
)
252 static inline void v3_lerp( v3f a
, v3f b
, float t
, v3f d
)
254 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
255 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
256 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
259 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
261 dest
[0] = vg_minf(a
[0], b
[0]);
262 dest
[1] = vg_minf(a
[1], b
[1]);
263 dest
[2] = vg_minf(a
[2], b
[2]);
266 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
268 dest
[0] = vg_maxf(a
[0], b
[0]);
269 dest
[1] = vg_maxf(a
[1], b
[1]);
270 dest
[2] = vg_maxf(a
[2], b
[2]);
273 static inline float v3_minf( v3f a
)
275 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
278 static inline float v3_maxf( v3f a
)
280 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
283 static inline void v3_fill( v3f a
, float v
)
290 static inline void v3_floor( v3f a
, v3f b
)
292 b
[0] = floorf( a
[0] );
293 b
[1] = floorf( a
[1] );
294 b
[2] = floorf( a
[2] );
297 static inline void v3_negate( v3f a
, v3f b
)
307 static inline void v4_copy( v4f a
, v4f b
)
309 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
312 static inline void v4_zero( v4f a
)
314 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
317 static inline void v4_muladds( v3f a
, v3f b
, float s
, v3f d
)
329 #define M2X2_INDENTIY {{1.0f, 0.0f, }, \
332 #define M2X2_ZERO {{0.0f, 0.0f, }, \
335 static inline void m2x2_copy( m2x2f a
, m2x2f b
)
337 v2_copy( a
[0], b
[0] );
338 v2_copy( a
[1], b
[1] );
341 static inline void m2x2_identity( m2x2f a
)
343 m2x2f id
= M2X2_INDENTIY
;
347 static inline void m2x2_create_rotation( m2x2f a
, float theta
)
364 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
365 { 0.0f, 1.0f, 0.0f, },\
366 { 0.0f, 0.0f, 1.0f, }}
368 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
369 { 0.0f, 0.0f, 0.0f, },\
370 { 0.0f, 0.0f, 0.0f, }}
373 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
375 v3_copy( a
[0], b
[0] );
376 v3_copy( a
[1], b
[1] );
377 v3_copy( a
[2], b
[2] );
380 static inline void m3x3_identity( m3x3f a
)
382 m3x3f id
= M3X3_IDENTITY
;
386 static inline void m3x3_zero( m3x3f a
)
392 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
394 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
395 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
396 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
403 dest
[0][0] = (e
*i
-h
*f
)*det
;
404 dest
[0][1] = -(b
*i
-c
*h
)*det
;
405 dest
[0][2] = (b
*f
-c
*e
)*det
;
406 dest
[1][0] = -(d
*i
-f
*g
)*det
;
407 dest
[1][1] = (a
*i
-c
*g
)*det
;
408 dest
[1][2] = -(a
*f
-d
*c
)*det
;
409 dest
[2][0] = (d
*h
-g
*e
)*det
;
410 dest
[2][1] = -(a
*h
-g
*b
)*det
;
411 dest
[2][2] = (a
*e
-d
*b
)*det
;
414 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
416 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
417 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
418 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
431 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
433 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
434 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
435 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
437 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
438 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
439 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
441 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
442 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
443 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
444 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
445 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
446 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
447 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
448 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
449 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
452 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
456 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
457 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
458 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
463 static inline void m3x3_projection( m3x3f dst
,
464 float const left
, float const right
, float const bottom
, float const top
)
470 rl
= 1.0f
/ (right
- left
);
471 tb
= 1.0f
/ (top
- bottom
);
473 dst
[0][0] = 2.0f
* rl
;
474 dst
[1][1] = 2.0f
* tb
;
478 static inline void m3x3_translate( m3x3f m
, v3f v
)
480 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
481 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
482 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
485 static inline void m3x3_scale( m3x3f m
, v3f v
)
487 m
[0][0] = m
[0][0] * v
[0];
488 m
[0][1] = m
[0][1] * v
[0];
489 m
[0][2] = m
[0][2] * v
[0];
491 m
[1][0] = m
[1][0] * v
[1];
492 m
[1][1] = m
[1][1] * v
[1];
493 m
[1][2] = m
[1][2] * v
[1];
496 static inline void m3x3_rotate( m3x3f m
, float angle
)
498 float m00
= m
[0][0], m10
= m
[1][0],
499 m01
= m
[0][1], m11
= m
[1][1],
500 m02
= m
[0][2], m12
= m
[1][2];
506 m
[0][0] = m00
* c
+ m10
* s
;
507 m
[0][1] = m01
* c
+ m11
* s
;
508 m
[0][2] = m02
* c
+ m12
* s
;
510 m
[1][0] = m00
* -s
+ m10
* c
;
511 m
[1][1] = m01
* -s
+ m11
* c
;
512 m
[1][2] = m02
* -s
+ m12
* c
;
519 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
520 { 0.0f, 1.0f, 0.0f, },\
521 { 0.0f, 0.0f, 1.0f, },\
522 { 0.0f, 0.0f, 0.0f }}
524 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
526 v3_copy( a
[0], b
[0] );
527 v3_copy( a
[1], b
[1] );
528 v3_copy( a
[2], b
[2] );
531 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
533 v3_copy( a
[0], b
[0] );
534 v3_copy( a
[1], b
[1] );
535 v3_copy( a
[2], b
[2] );
536 v3_copy( a
[3], b
[3] );
539 static inline void m4x3_identity( m4x3f a
)
541 m4x3f id
= M4X3_IDENTITY
;
545 static inline void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
548 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
549 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
550 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
551 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
552 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
553 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
554 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
555 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
557 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
558 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
559 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
560 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
561 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
562 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
563 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
564 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
565 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
566 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
567 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
568 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
571 static inline void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
575 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
576 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
577 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
586 static inline void m4x3_translate( m4x3f m
, v3f v
)
588 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
589 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
590 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
593 static inline void m4x3_scale( m4x3f m
, float s
)
595 v3_muls( m
[0], s
, m
[0] );
596 v3_muls( m
[1], s
, m
[1] );
597 v3_muls( m
[2], s
, m
[2] );
600 static inline void m4x3_rotate_x( m4x3f m
, float angle
)
602 m4x3f t
= M4X3_IDENTITY
;
616 static inline void m4x3_rotate_y( m4x3f m
, float angle
)
618 m4x3f t
= M4X3_IDENTITY
;
632 static inline void m4x3_rotate_z( m4x3f m
, float angle
)
634 m4x3f t
= M4X3_IDENTITY
;
648 static inline void m4x3_expand( m4x3f m
, m4x4f d
)
650 v3_copy( m
[0], d
[0] );
651 v3_copy( m
[1], d
[1] );
652 v3_copy( m
[2], d
[2] );
653 v3_copy( m
[3], d
[3] );
660 static inline void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
663 m4x3_mulv( m
, point
, v
);
665 v3_minv( box
[0], v
, box
[0] );
666 v3_maxv( box
[1], v
, box
[1] );
669 static inline void box_concat( boxf a
, boxf b
)
671 v3_minv( a
[0], b
[0], a
[0] );
672 v3_maxv( a
[1], b
[1], a
[1] );
675 static inline void box_copy( boxf a
, boxf b
)
677 v3_copy( a
[0], b
[0] );
678 v3_copy( a
[1], b
[1] );
681 static inline void m4x3_transform_aabb( m4x3f m
, boxf box
)
685 v3_copy( box
[0], a
);
686 v3_copy( box
[1], b
);
687 v3_fill( box
[0], INFINITY
);
688 v3_fill( box
[1], -INFINITY
);
690 m4x3_expand_aabb_point( m
, box
, a
);
691 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
692 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
693 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
694 m4x3_expand_aabb_point( m
, box
, b
);
695 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
696 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
697 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
704 #define M4X4_IDENTITY {{1.0f, 0.0f, 0.0f, 0.0f },\
705 { 0.0f, 1.0f, 0.0f, 0.0f },\
706 { 0.0f, 0.0f, 1.0f, 0.0f },\
707 { 0.0f, 0.0f, 0.0f, 1.0f }}
709 static void m4x4_projection( m4x4f m
, float angle
,
710 float ratio
, float near
, float far
)
712 float scale
= tanf( angle
* 0.5f
* VG_PIf
/ 180.0f
) * near
,
718 m
[0][0] = 2.0f
* near
/ (r
- l
);
723 m
[1][1] = 2.0f
* near
/ (t
- b
);
726 m
[2][0] = (r
+ l
) / (r
- l
);
727 m
[2][1] = (t
+ b
) / (t
- b
);
728 m
[2][2] = -(far
+ near
) / (far
- near
);
732 m
[3][2] = -2.0f
* far
* near
/ (far
- near
);
736 static void m4x4_translate( m4x4f m
, v3f v
)
738 v4_muladds( m
[3], m
[0], v
[0], m
[3] );
739 v4_muladds( m
[3], m
[1], v
[1], m
[3] );
740 v4_muladds( m
[3], m
[2], v
[2], m
[3] );
743 static inline void m4x4_copy( m4x4f a
, m4x4f b
)
745 v4_copy( a
[0], b
[0] );
746 v4_copy( a
[1], b
[1] );
747 v4_copy( a
[2], b
[2] );
748 v4_copy( a
[3], b
[3] );
751 static inline void m4x4_identity( m4x4f a
)
753 m4x4f id
= M4X4_IDENTITY
;
757 static inline void m4x4_mul( m4x4f a
, m4x4f b
, m4x4f d
)
759 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2], a03
= a
[0][3],
760 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2], a13
= a
[1][3],
761 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2], a23
= a
[2][3],
762 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2], a33
= a
[3][3],
764 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2], b03
= b
[0][3],
765 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2], b13
= b
[1][3],
766 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2], b23
= b
[2][3],
767 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2], b33
= b
[3][3];
769 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
+ a30
*b03
;
770 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
+ a31
*b03
;
771 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
+ a32
*b03
;
772 d
[0][3] = a03
*b00
+ a13
*b01
+ a23
*b02
+ a33
*b03
;
773 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
+ a30
*b13
;
774 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
+ a31
*b13
;
775 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
+ a32
*b13
;
776 d
[1][3] = a03
*b10
+ a13
*b11
+ a23
*b12
+ a33
*b13
;
777 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
+ a30
*b23
;
778 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
+ a31
*b23
;
779 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
+ a32
*b23
;
780 d
[2][3] = a03
*b20
+ a13
*b21
+ a23
*b22
+ a33
*b23
;
781 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
*b33
;
782 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
*b33
;
783 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
*b33
;
784 d
[3][3] = a03
*b30
+ a13
*b31
+ a23
*b32
+ a33
*b33
;
788 * Planes (double precision)
790 static inline void tri_to_plane( double a
[3], double b
[3],
791 double c
[3], double p
[4] )
797 edge0
[0] = b
[0] - a
[0];
798 edge0
[1] = b
[1] - a
[1];
799 edge0
[2] = b
[2] - a
[2];
801 edge1
[0] = c
[0] - a
[0];
802 edge1
[1] = c
[1] - a
[1];
803 edge1
[2] = c
[2] - a
[2];
805 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
806 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
807 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
809 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
810 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
817 static inline int plane_intersect( double a
[4], double b
[4],
818 double c
[4], double p
[4] )
820 double const epsilon
= 1e-8f
;
825 x
[0] = a
[1] * b
[2] - a
[2] * b
[1];
826 x
[1] = a
[2] * b
[0] - a
[0] * b
[2];
827 x
[2] = a
[0] * b
[1] - a
[1] * b
[0];
829 d
= x
[0] * c
[0] + x
[1] * c
[1] + x
[2] * c
[2];
831 if( d
< epsilon
&& d
> -epsilon
) return 0;
833 p
[0] = (b
[1] * c
[2] - b
[2] * c
[1]) * -a
[3];
834 p
[1] = (b
[2] * c
[0] - b
[0] * c
[2]) * -a
[3];
835 p
[2] = (b
[0] * c
[1] - b
[1] * c
[0]) * -a
[3];
837 p
[0] += (c
[1] * a
[2] - c
[2] * a
[1]) * -b
[3];
838 p
[1] += (c
[2] * a
[0] - c
[0] * a
[2]) * -b
[3];
839 p
[2] += (c
[0] * a
[1] - c
[1] * a
[0]) * -b
[3];
841 p
[0] += (a
[1] * b
[2] - a
[2] * b
[1]) * -c
[3];
842 p
[1] += (a
[2] * b
[0] - a
[0] * b
[2]) * -c
[3];
843 p
[2] += (a
[0] * b
[1] - a
[1] * b
[0]) * -c
[3];
852 static inline double plane_polarity( double p
[4], double a
[3] )
855 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
856 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])