1 // Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved
4 // ==================================================================================================================
6 #define VG_PIf 3.14159265358979323846264338327950288f
7 #define VG_TAUf 6.28318530717958647692528676655900576f
9 // Simple min/max replacements
10 static inline float vg_minf( float a
, float b
)
15 static inline float vg_maxf( float a
, float b
)
20 static inline int vg_min( int a
, int b
)
25 static inline int vg_max( int a
, int b
)
30 // Convert degrees to radians
31 static inline float vg_rad( float deg
)
33 return deg
* VG_PIf
/ 180.0f
;
37 // ==================================================================================================================
39 static inline void v2_copy( v2f a
, v2f b
)
41 b
[0] = a
[0]; b
[1] = a
[1];
44 static inline void v2_minv( v2f a
, v2f b
, v2f dest
)
46 dest
[0] = vg_minf(a
[0], b
[0]);
47 dest
[1] = vg_minf(a
[1], b
[1]);
50 static inline void v2_maxv( v2f a
, v2f b
, v2f dest
)
52 dest
[0] = vg_maxf(a
[0], b
[0]);
53 dest
[1] = vg_maxf(a
[1], b
[1]);
56 static inline void v2_sub( v2f a
, v2f b
, v2f d
)
58 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
61 static inline float v2_cross( v2f a
, v2f b
)
63 return a
[0] * b
[1] - a
[1] * b
[0];
66 static inline void v2_add( v2f a
, v2f b
, v2f d
)
68 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
71 static inline void v2_muls( v2f a
, float s
, v2f d
)
73 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
76 static inline void v2_mul( v2f a
, v2f b
, v2f d
)
78 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1];
81 static inline void v2_div( v2f a
, v2f b
, v2f d
)
83 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
87 // ==================================================================================================================
89 static inline void v3_zero( v3f a
)
91 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
94 static inline void v3_copy( v3f a
, v3f b
)
96 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
99 static inline void v3_add( v3f a
, v3f b
, v3f d
)
101 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
104 static inline void v3_sub( v3f a
, v3f b
, v3f d
)
106 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
109 static inline void v3_mul( v3f a
, v3f b
, v3f d
)
111 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
114 static inline void v3_div( v3f a
, v3f b
, v3f d
)
116 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1]; d
[2] = a
[2]/b
[2];
119 static inline void v3_muls( v3f a
, float s
, v3f d
)
121 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
124 static inline void v3_divs( v3f a
, float s
, v3f d
)
126 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
; d
[2] = a
[2]/s
;
129 static inline void v3_muladds( v3f a
, v3f b
, float s
, v3f d
)
131 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
134 static inline float v3_dot( v3f a
, v3f b
)
136 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
139 static inline void v3_cross( v3f a
, v3f b
, v3f d
)
141 d
[0] = a
[1] * b
[2] - a
[2] * b
[1];
142 d
[1] = a
[2] * b
[0] - a
[0] * b
[2];
143 d
[2] = a
[0] * b
[1] - a
[1] * b
[0];
146 static inline float v3_length2( v3f a
)
148 return v3_dot( a
, a
);
151 static inline float v3_length( v3f a
)
153 return sqrtf( v3_length2( a
) );
156 static inline float v3_dist2( v3f a
, v3f b
)
159 v3_sub( a
, b
, delta
);
160 return v3_length2( delta
);
163 static inline float v3_dist( v3f a
, v3f b
)
165 return sqrtf( v3_dist2( a
, b
) );
168 static inline void v3_normalize( v3f a
)
170 v3_muls( a
, 1.f
/ v3_length( a
), a
);
173 static inline float csr_lerpf( float a
, float b
, float t
)
178 static inline void v3_lerp( v3f a
, v3f b
, float t
, v3f d
)
180 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
181 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
182 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
185 static inline void v3_minv( v3f a
, v3f b
, v3f dest
)
187 dest
[0] = vg_minf(a
[0], b
[0]);
188 dest
[1] = vg_minf(a
[1], b
[1]);
189 dest
[2] = vg_minf(a
[2], b
[2]);
192 static inline void v3_maxv( v3f a
, v3f b
, v3f dest
)
194 dest
[0] = vg_maxf(a
[0], b
[0]);
195 dest
[1] = vg_maxf(a
[1], b
[1]);
196 dest
[2] = vg_maxf(a
[2], b
[2]);
199 static inline float v3_minf( v3f a
)
201 return vg_minf( vg_minf( a
[0], a
[1] ), a
[2] );
204 static inline float v3_maxf( v3f a
)
206 return vg_maxf( vg_maxf( a
[0], a
[1] ), a
[2] );
209 static inline void v3_fill( v3f a
, float v
)
217 // ==================================================================================================================
219 static inline void v4_copy( v4f a
, v4f b
)
221 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
224 static inline void v4_zero( v4f a
)
226 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
230 //======================================================================================================
232 #define M3X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
233 { 0.0f, 1.0f, 0.0f, },\
234 { 0.0f, 0.0f, 1.0f, }}
236 #define M3X3_ZERO {{0.0f, 0.0f, 0.0f, },\
237 { 0.0f, 0.0f, 0.0f, },\
238 { 0.0f, 0.0f, 0.0f, }}
241 static inline void m3x3_copy( m3x3f a
, m3x3f b
)
243 v3_copy( a
[0], b
[0] );
244 v3_copy( a
[1], b
[1] );
245 v3_copy( a
[2], b
[2] );
248 static inline void m3x3_identity( m3x3f a
)
250 m3x3f id
= M3X3_IDENTITY
;
254 static inline void m3x3_zero( m3x3f a
)
260 static inline void m3x3_inv( m3x3f src
, m3x3f dest
)
262 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
263 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
264 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
271 dest
[0][0] = (e
*i
-h
*f
)*det
;
272 dest
[0][1] = -(b
*i
-c
*h
)*det
;
273 dest
[0][2] = (b
*f
-c
*e
)*det
;
274 dest
[1][0] = -(d
*i
-f
*g
)*det
;
275 dest
[1][1] = (a
*i
-c
*g
)*det
;
276 dest
[1][2] = -(a
*f
-d
*c
)*det
;
277 dest
[2][0] = (d
*h
-g
*e
)*det
;
278 dest
[2][1] = -(a
*h
-g
*b
)*det
;
279 dest
[2][2] = (a
*e
-d
*b
)*det
;
282 static inline void m3x3_transpose( m3x3f src
, m3x3f dest
)
284 float a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
285 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
286 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
299 static inline void m3x3_mul( m3x3f a
, m3x3f b
, m3x3f d
)
301 float a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
302 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
303 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
305 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
306 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
307 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2];
309 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
310 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
311 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
312 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
313 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
314 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
315 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
316 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
317 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
320 static inline void m3x3_mulv( m3x3f m
, v3f v
, v3f d
)
324 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2];
325 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2];
326 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2];
331 static inline void m3x3_projection( m3x3f dst
, float const left
, float const right
, float const bottom
, float const top
)
337 rl
= 1.0f
/ (right
- left
);
338 tb
= 1.0f
/ (top
- bottom
);
340 dst
[0][0] = 2.0f
* rl
;
341 dst
[1][1] = 2.0f
* tb
;
345 static inline void m3x3_translate( m3x3f m
, v3f v
)
347 m
[2][0] = m
[0][0] * v
[0] + m
[1][0] * v
[1] + m
[2][0];
348 m
[2][1] = m
[0][1] * v
[0] + m
[1][1] * v
[1] + m
[2][1];
349 m
[2][2] = m
[0][2] * v
[0] + m
[1][2] * v
[1] + m
[2][2];
352 static inline void m3x3_scale( m3x3f m
, v3f v
)
354 m
[0][0] = m
[0][0] * v
[0];
355 m
[0][1] = m
[0][1] * v
[0];
356 m
[0][2] = m
[0][2] * v
[0];
358 m
[1][0] = m
[1][0] * v
[1];
359 m
[1][1] = m
[1][1] * v
[1];
360 m
[1][2] = m
[1][2] * v
[1];
363 static inline void m3x3_rotate( m3x3f m
, float angle
)
365 float m00
= m
[0][0], m10
= m
[1][0],
366 m01
= m
[0][1], m11
= m
[1][1],
367 m02
= m
[0][2], m12
= m
[1][2];
373 m
[0][0] = m00
* c
+ m10
* s
;
374 m
[0][1] = m01
* c
+ m11
* s
;
375 m
[0][2] = m02
* c
+ m12
* s
;
377 m
[1][0] = m00
* -s
+ m10
* c
;
378 m
[1][1] = m01
* -s
+ m11
* c
;
379 m
[1][2] = m02
* -s
+ m12
* c
;
383 // ==================================================================================================================
385 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
386 { 0.0f, 1.0f, 0.0f, },\
387 { 0.0f, 0.0f, 1.0f, },\
388 { 0.0f, 0.0f, 0.0f }}
390 static inline void m4x3_to_3x3( m4x3f a
, m3x3f b
)
392 v3_copy( a
[0], b
[0] );
393 v3_copy( a
[1], b
[1] );
394 v3_copy( a
[2], b
[2] );
397 static inline void m4x3_copy( m4x3f a
, m4x3f b
)
399 v3_copy( a
[0], b
[0] );
400 v3_copy( a
[1], b
[1] );
401 v3_copy( a
[2], b
[2] );
402 v3_copy( a
[3], b
[3] );
405 static inline void m4x3_identity( m4x3f a
)
407 m4x3f id
= M4X3_IDENTITY
;
411 static inline void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
414 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
415 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
416 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
417 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
418 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
419 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
420 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
421 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
423 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
424 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
425 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
426 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
427 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
428 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
429 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
430 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
431 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
432 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
433 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
434 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
437 static inline void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
441 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
442 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
443 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
449 // ====================================================================================================================
451 static inline void m4x3_translate( m4x3f m
, v3f v
)
453 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
454 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
455 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
458 static inline void m4x3_scale( m4x3f m
, float s
)
460 v3_muls( m
[0], s
, m
[0] );
461 v3_muls( m
[1], s
, m
[1] );
462 v3_muls( m
[2], s
, m
[2] );
465 static inline void m4x3_rotate_x( m4x3f m
, float angle
)
467 m4x3f t
= M4X3_IDENTITY
;
481 static inline void m4x3_rotate_y( m4x3f m
, float angle
)
483 m4x3f t
= M4X3_IDENTITY
;
497 static inline void m4x3_rotate_z( m4x3f m
, float angle
)
499 m4x3f t
= M4X3_IDENTITY
;
513 // Warning: These functions are unoptimized..
514 static inline void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
517 m4x3_mulv( m
, point
, v
);
519 v3_minv( box
[0], v
, box
[0] );
520 v3_maxv( box
[1], v
, box
[1] );
523 static inline void box_concat( boxf a
, boxf b
)
525 v3_minv( a
[0], b
[0], a
[0] );
526 v3_maxv( a
[1], b
[1], a
[1] );
529 static inline void box_copy( boxf a
, boxf b
)
531 v3_copy( a
[0], b
[0] );
532 v3_copy( a
[1], b
[1] );
535 static inline void m4x3_transform_aabb( m4x3f m
, boxf box
)
539 v3_copy( box
[0], a
);
540 v3_copy( box
[1], b
);
541 v3_fill( box
[0], INFINITY
);
542 v3_fill( box
[1], -INFINITY
);
544 m4x3_expand_aabb_point( m
, box
, a
);
545 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
546 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
547 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
548 m4x3_expand_aabb_point( m
, box
, b
);
549 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
550 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
551 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
554 // Planes (double precision)
555 // ==================================================================================================================
557 static inline void tri_to_plane( double a
[3], double b
[3], double c
[3], double p
[4] )
563 edge0
[0] = b
[0] - a
[0];
564 edge0
[1] = b
[1] - a
[1];
565 edge0
[2] = b
[2] - a
[2];
567 edge1
[0] = c
[0] - a
[0];
568 edge1
[1] = c
[1] - a
[1];
569 edge1
[2] = c
[2] - a
[2];
571 p
[0] = edge0
[1] * edge1
[2] - edge0
[2] * edge1
[1];
572 p
[1] = edge0
[2] * edge1
[0] - edge0
[0] * edge1
[2];
573 p
[2] = edge0
[0] * edge1
[1] - edge0
[1] * edge1
[0];
575 l
= sqrt(p
[0] * p
[0] + p
[1] * p
[1] + p
[2] * p
[2]);
576 p
[3] = (p
[0] * a
[0] + p
[1] * a
[1] + p
[2] * a
[2]) / l
;
583 static inline int plane_intersect( double a
[4], double b
[4], double c
[4], double p
[4] )
585 double const epsilon
= 1e-8f
;
590 x
[0] = a
[1] * b
[2] - a
[2] * b
[1];
591 x
[1] = a
[2] * b
[0] - a
[0] * b
[2];
592 x
[2] = a
[0] * b
[1] - a
[1] * b
[0];
594 d
= x
[0] * c
[0] + x
[1] * c
[1] + x
[2] * c
[2];
596 if( d
< epsilon
&& d
> -epsilon
) return 0;
598 p
[0] = (b
[1] * c
[2] - b
[2] * c
[1]) * -a
[3];
599 p
[1] = (b
[2] * c
[0] - b
[0] * c
[2]) * -a
[3];
600 p
[2] = (b
[0] * c
[1] - b
[1] * c
[0]) * -a
[3];
602 p
[0] += (c
[1] * a
[2] - c
[2] * a
[1]) * -b
[3];
603 p
[1] += (c
[2] * a
[0] - c
[0] * a
[2]) * -b
[3];
604 p
[2] += (c
[0] * a
[1] - c
[1] * a
[0]) * -b
[3];
606 p
[0] += (a
[1] * b
[2] - a
[2] * b
[1]) * -c
[3];
607 p
[1] += (a
[2] * b
[0] - a
[0] * b
[2]) * -c
[3];
608 p
[2] += (a
[0] * b
[1] - a
[1] * b
[0]) * -c
[3];
617 static inline double plane_polarity( double p
[4], double a
[3] )
620 (a
[0] * p
[0] + a
[1] * p
[1] + a
[2] * p
[2])
621 -(p
[0]*p
[3] * p
[0] + p
[1]*p
[3] * p
[1] + p
[2]*p
[3] * p
[2])