1 /* Copyright (C) 2021 Harry Godden (hgn)
3 * Straightforward implementations for:
5 * Simple Matrices in 3x3 and 4x3
7 * Other useful geometric functions
10 #define CXR_INLINE static inline
11 #define CXR_PIf 3.14159265358979323846264338327950288f
13 CXR_INLINE
double cxr_minf( double a
, double b
)
18 CXR_INLINE
double cxr_maxf( double a
, double b
)
23 CXR_INLINE
int cxr_min( int a
, int b
)
28 CXR_INLINE
int cxr_max( int a
, int b
)
33 CXR_INLINE
double cxr_clampf( double v
, double a
, double b
)
35 return cxr_minf( b
, cxr_maxf( a
, v
) );
38 CXR_INLINE
double cxr_rad( double deg
)
40 return deg
* CXR_PIf
/ 180.0f
;
46 CXR_INLINE
void v2_zero( v2f a
)
48 a
[0] = 0.0; a
[1] = 0.0;
51 CXR_INLINE
void v2_fill( v2f a
, double v
)
56 CXR_INLINE
void v2_copy( v2f a
, v2f b
)
58 b
[0] = a
[0]; b
[1] = a
[1];
61 CXR_INLINE
void v2_minv( v2f a
, v2f b
, v2f dest
)
63 dest
[0] = cxr_minf(a
[0], b
[0]);
64 dest
[1] = cxr_minf(a
[1], b
[1]);
67 CXR_INLINE
void v2_maxv( v2f a
, v2f b
, v2f dest
)
69 dest
[0] = cxr_maxf(a
[0], b
[0]);
70 dest
[1] = cxr_maxf(a
[1], b
[1]);
73 CXR_INLINE
void v2_sub( v2f a
, v2f b
, v2f d
)
75 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1];
78 CXR_INLINE
double v2_cross( v2f a
, v2f b
)
80 return a
[0] * b
[1] - a
[1] * b
[0];
83 CXR_INLINE
void v2_add( v2f a
, v2f b
, v2f d
)
85 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1];
88 CXR_INLINE
void v2_muls( v2f a
, double s
, v2f d
)
90 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
;
93 CXR_INLINE
void v2_mul( v2f a
, v2f b
, v2f d
)
95 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1];
98 CXR_INLINE
void v2_muladds( v2f a
, v2f b
, double s
, v2f d
)
100 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
;
103 CXR_INLINE
double v2_dot( v2f a
, v2f b
)
105 return a
[0] * b
[0] + a
[1] * b
[1];
108 CXR_INLINE
void v2_div( v2f a
, v2f b
, v2f d
)
110 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1];
113 CXR_INLINE
double v2_length2( v2f a
)
115 return v2_dot( a
, a
);
118 CXR_INLINE
double v2_length( v2f a
)
120 return sqrt( v2_length2( a
) );
123 CXR_INLINE
double v2_dist2( v2f a
, v2f b
)
126 v2_sub( a
, b
, delta
);
127 return v2_length2( delta
);
130 CXR_INLINE
double v2_dist( v2f a
, v2f b
)
132 return sqrt( v2_dist2( a
, b
) );
135 CXR_INLINE
void v2_normalize( v2f a
)
137 v2_muls( a
, 1.0 / v2_length( a
), a
);
144 CXR_INLINE
void v3_zero( v3f a
)
146 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
;
149 CXR_INLINE
void v3_copy( v3f a
, v3f b
)
151 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2];
154 CXR_INLINE
void v3_add( v3f a
, v3f b
, v3f d
)
156 d
[0] = a
[0]+b
[0]; d
[1] = a
[1]+b
[1]; d
[2] = a
[2]+b
[2];
159 CXR_INLINE
void v3_sub( v3f a
, v3f b
, v3f d
)
161 d
[0] = a
[0]-b
[0]; d
[1] = a
[1]-b
[1]; d
[2] = a
[2]-b
[2];
164 CXR_INLINE
void v3_mul( v3f a
, v3f b
, v3f d
)
166 d
[0] = a
[0]*b
[0]; d
[1] = a
[1]*b
[1]; d
[2] = a
[2]*b
[2];
169 CXR_INLINE
void v3_div( v3f a
, v3f b
, v3f d
)
171 d
[0] = a
[0]/b
[0]; d
[1] = a
[1]/b
[1]; d
[2] = a
[2]/b
[2];
174 CXR_INLINE
void v3_muls( v3f a
, double s
, v3f d
)
176 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
;
179 CXR_INLINE
void v3_divs( v3f a
, double s
, v3f d
)
181 d
[0] = a
[0]/s
; d
[1] = a
[1]/s
; d
[2] = a
[2]/s
;
184 CXR_INLINE
void v3_muladds( v3f a
, v3f b
, double s
, v3f d
)
186 d
[0] = a
[0]+b
[0]*s
; d
[1] = a
[1]+b
[1]*s
; d
[2] = a
[2]+b
[2]*s
;
189 CXR_INLINE
double v3_dot( v3f a
, v3f b
)
191 return a
[0] * b
[0] + a
[1] * b
[1] + a
[2] * b
[2];
194 CXR_INLINE
void v3_cross( v3f a
, v3f b
, v3f d
)
196 d
[0] = a
[1] * b
[2] - a
[2] * b
[1];
197 d
[1] = a
[2] * b
[0] - a
[0] * b
[2];
198 d
[2] = a
[0] * b
[1] - a
[1] * b
[0];
201 CXR_INLINE
double v3_length2( v3f a
)
203 return v3_dot( a
, a
);
206 CXR_INLINE
double v3_length( v3f a
)
208 return sqrt( v3_length2( a
) );
211 CXR_INLINE
double v3_dist2( v3f a
, v3f b
)
214 v3_sub( a
, b
, delta
);
215 return v3_length2( delta
);
218 CXR_INLINE
double v3_dist( v3f a
, v3f b
)
220 return sqrt( v3_dist2( a
, b
) );
223 CXR_INLINE
void v3_normalize( v3f a
)
225 v3_muls( a
, 1.0 / v3_length( a
), a
);
228 CXR_INLINE
void v3_negate( v3f a
, v3f dest
)
230 v3_muls( a
, -1.0, dest
);
233 CXR_INLINE
double cxr_lerpf( double a
, double b
, double t
)
238 CXR_INLINE
void v3_lerp( v3f a
, v3f b
, double t
, v3f d
)
240 d
[0] = a
[0] + t
*(b
[0]-a
[0]);
241 d
[1] = a
[1] + t
*(b
[1]-a
[1]);
242 d
[2] = a
[2] + t
*(b
[2]-a
[2]);
245 CXR_INLINE
void v3_minv( v3f a
, v3f b
, v3f dest
)
247 dest
[0] = cxr_minf(a
[0], b
[0]);
248 dest
[1] = cxr_minf(a
[1], b
[1]);
249 dest
[2] = cxr_minf(a
[2], b
[2]);
252 CXR_INLINE
void v3_maxv( v3f a
, v3f b
, v3f dest
)
254 dest
[0] = cxr_maxf(a
[0], b
[0]);
255 dest
[1] = cxr_maxf(a
[1], b
[1]);
256 dest
[2] = cxr_maxf(a
[2], b
[2]);
259 CXR_INLINE
double v3_minf( v3f a
)
261 return cxr_minf( cxr_minf( a
[0], a
[1] ), a
[2] );
264 CXR_INLINE
double v3_maxf( v3f a
)
266 return cxr_maxf( cxr_maxf( a
[0], a
[1] ), a
[2] );
269 CXR_INLINE
void v3_fill( v3f a
, double v
)
279 CXR_INLINE
void v4_copy( v4f a
, v4f b
)
281 b
[0] = a
[0]; b
[1] = a
[1]; b
[2] = a
[2]; b
[3] = a
[3];
284 CXR_INLINE
void v4_zero( v4f a
)
286 a
[0] = 0.f
; a
[1] = 0.f
; a
[2] = 0.f
; a
[3] = 0.f
;
289 CXR_INLINE
void v4_muls( v4f a
, double s
, v4f d
)
291 d
[0] = a
[0]*s
; d
[1] = a
[1]*s
; d
[2] = a
[2]*s
; d
[3] = a
[3]*s
;
298 CXR_INLINE
void m3x3_inv_transpose( m3x3f src
, m3x3f dest
)
300 double a
= src
[0][0], b
= src
[0][1], c
= src
[0][2],
301 d
= src
[1][0], e
= src
[1][1], f
= src
[1][2],
302 g
= src
[2][0], h
= src
[2][1], i
= src
[2][2];
309 dest
[0][0] = (e
*i
-h
*f
)*det
;
310 dest
[1][0] = -(b
*i
-c
*h
)*det
;
311 dest
[2][0] = (b
*f
-c
*e
)*det
;
312 dest
[0][1] = -(d
*i
-f
*g
)*det
;
313 dest
[1][1] = (a
*i
-c
*g
)*det
;
314 dest
[2][1] = -(a
*f
-d
*c
)*det
;
315 dest
[0][2] = (d
*h
-g
*e
)*det
;
316 dest
[1][2] = -(a
*h
-g
*b
)*det
;
317 dest
[2][2] = (a
*e
-d
*b
)*det
;
320 CXR_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];
335 #define M4X3_IDENTITY {{1.0f, 0.0f, 0.0f, },\
336 { 0.0f, 1.0f, 0.0f, },\
337 { 0.0f, 0.0f, 1.0f, },\
338 { 0.0f, 0.0f, 0.0f }}
340 CXR_INLINE
void m4x3_to_3x3( m4x3f a
, m3x3f b
)
342 v3_copy( a
[0], b
[0] );
343 v3_copy( a
[1], b
[1] );
344 v3_copy( a
[2], b
[2] );
347 CXR_INLINE
void m4x3_copy( m4x3f a
, m4x3f b
)
349 v3_copy( a
[0], b
[0] );
350 v3_copy( a
[1], b
[1] );
351 v3_copy( a
[2], b
[2] );
352 v3_copy( a
[3], b
[3] );
355 CXR_INLINE
void m4x3_identity( m4x3f a
)
357 m4x3f id
= M4X3_IDENTITY
;
361 CXR_INLINE
void m4x3_mul( m4x3f a
, m4x3f b
, m4x3f d
)
364 a00
= a
[0][0], a01
= a
[0][1], a02
= a
[0][2],
365 a10
= a
[1][0], a11
= a
[1][1], a12
= a
[1][2],
366 a20
= a
[2][0], a21
= a
[2][1], a22
= a
[2][2],
367 a30
= a
[3][0], a31
= a
[3][1], a32
= a
[3][2],
368 b00
= b
[0][0], b01
= b
[0][1], b02
= b
[0][2],
369 b10
= b
[1][0], b11
= b
[1][1], b12
= b
[1][2],
370 b20
= b
[2][0], b21
= b
[2][1], b22
= b
[2][2],
371 b30
= b
[3][0], b31
= b
[3][1], b32
= b
[3][2];
373 d
[0][0] = a00
*b00
+ a10
*b01
+ a20
*b02
;
374 d
[0][1] = a01
*b00
+ a11
*b01
+ a21
*b02
;
375 d
[0][2] = a02
*b00
+ a12
*b01
+ a22
*b02
;
376 d
[1][0] = a00
*b10
+ a10
*b11
+ a20
*b12
;
377 d
[1][1] = a01
*b10
+ a11
*b11
+ a21
*b12
;
378 d
[1][2] = a02
*b10
+ a12
*b11
+ a22
*b12
;
379 d
[2][0] = a00
*b20
+ a10
*b21
+ a20
*b22
;
380 d
[2][1] = a01
*b20
+ a11
*b21
+ a21
*b22
;
381 d
[2][2] = a02
*b20
+ a12
*b21
+ a22
*b22
;
382 d
[3][0] = a00
*b30
+ a10
*b31
+ a20
*b32
+ a30
;
383 d
[3][1] = a01
*b30
+ a11
*b31
+ a21
*b32
+ a31
;
384 d
[3][2] = a02
*b30
+ a12
*b31
+ a22
*b32
+ a32
;
387 CXR_INLINE
void m4x3_mulv( m4x3f m
, v3f v
, v3f d
)
391 res
[0] = m
[0][0]*v
[0] + m
[1][0]*v
[1] + m
[2][0]*v
[2] + m
[3][0];
392 res
[1] = m
[0][1]*v
[0] + m
[1][1]*v
[1] + m
[2][1]*v
[2] + m
[3][1];
393 res
[2] = m
[0][2]*v
[0] + m
[1][2]*v
[1] + m
[2][2]*v
[2] + m
[3][2];
399 * Affine transformations
401 CXR_INLINE
void m4x3_translate( m4x3f m
, v3f v
)
403 v3_muladds( m
[3], m
[0], v
[0], m
[3] );
404 v3_muladds( m
[3], m
[1], v
[1], m
[3] );
405 v3_muladds( m
[3], m
[2], v
[2], m
[3] );
408 CXR_INLINE
void m4x3_scale( m4x3f m
, double s
)
410 v3_muls( m
[0], s
, m
[0] );
411 v3_muls( m
[1], s
, m
[1] );
412 v3_muls( m
[2], s
, m
[2] );
415 CXR_INLINE
void m4x3_rotate_x( m4x3f m
, double angle
)
417 m4x3f t
= M4X3_IDENTITY
;
431 CXR_INLINE
void m4x3_rotate_y( m4x3f m
, double angle
)
433 m4x3f t
= M4X3_IDENTITY
;
447 CXR_INLINE
void m4x3_rotate_z( m4x3f m
, double angle
)
449 m4x3f t
= M4X3_IDENTITY
;
463 CXR_INLINE
void m4x3_expand_aabb_point( m4x3f m
, boxf box
, v3f point
)
466 m4x3_mulv( m
, point
, v
);
468 v3_minv( box
[0], v
, box
[0] );
469 v3_maxv( box
[1], v
, box
[1] );
472 CXR_INLINE
void box_concat( boxf a
, boxf b
)
474 v3_minv( a
[0], b
[0], a
[0] );
475 v3_maxv( a
[1], b
[1], a
[1] );
478 CXR_INLINE
void box_copy( boxf a
, boxf b
)
480 v3_copy( a
[0], b
[0] );
481 v3_copy( a
[1], b
[1] );
484 CXR_INLINE
void m4x3_transform_aabb( m4x3f m
, boxf box
)
488 v3_copy( box
[0], a
);
489 v3_copy( box
[1], b
);
490 v3_fill( box
[0], INFINITY
);
491 v3_fill( box
[1], -INFINITY
);
493 m4x3_expand_aabb_point( m
, box
, a
);
494 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], a
[2] } );
495 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], a
[2] } );
496 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], a
[2] } );
497 m4x3_expand_aabb_point( m
, box
, b
);
498 m4x3_expand_aabb_point( m
, box
, (v3f
){ a
[0], b
[1], b
[2] } );
499 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], a
[1], b
[2] } );
500 m4x3_expand_aabb_point( m
, box
, (v3f
){ b
[0], b
[1], b
[2] } );
503 CXR_INLINE
void tri_normal( v3f p0
, v3f p1
, v3f p2
, v3f normal
)
506 v3_sub( p1
, p0
, v0
);
507 v3_sub( p2
, p0
, v1
);
508 v3_cross( v0
, v1
, normal
);
509 v3_normalize( normal
);
512 CXR_INLINE
void tri_to_plane( v3f a
, v3f b
, v3f c
, v4f plane
)
514 tri_normal( a
,b
,c
, plane
);
515 plane
[3] = v3_dot( plane
, a
);
518 CXR_INLINE
int plane_intersect( v4f a
, v4f b
, v4f c
, v3f p
)
520 double const epsilon
= 0.001;
528 if( d
< epsilon
&& d
> -epsilon
) return 0;
534 v3_muls( bc
, -a
[3], p
);
535 v3_muladds( p
, ca
, -b
[3], p
);
536 v3_muladds( p
, ab
, -c
[3], p
);
544 CXR_INLINE
void normal_to_plane( v3f normal
, v3f p
, v4f plane
)
546 v3_copy( normal
, plane
);
547 plane
[3] = v3_dot( normal
, p
);
550 CXR_INLINE
double plane_polarity( v4f p
, v3f a
)
554 - (p
[0]*p
[3]*p
[0] + p
[1]*p
[3]*p
[1] + p
[2]*p
[3]*p
[2]);
557 CXR_INLINE
void plane_project_point( v4f plane
, v3f a
, v3f d
)
560 v3_muls( plane
, plane
[3], ref
);
562 v3_sub( a
, ref
, delta
);
563 v3_muladds( a
, plane
, -v3_dot(delta
,plane
), d
);
566 CXR_INLINE
double line_line_dist( v3f pa0
, v3f pa1
, v3f pb0
, v3f pb1
)
568 v3f va
, vb
, n
, delta
;
569 v3_sub( pa1
, pa0
, va
);
570 v3_sub( pb1
, pb0
, vb
);
572 v3_cross( va
, vb
, n
);
575 v3_sub( pb0
, pa0
, delta
);
577 return fabs( v3_dot( n
, delta
) );
580 CXR_INLINE
double segment_segment_dist( v3f a0
, v3f a1
, v3f b0
, v3f b1
,
588 double ru
= v3_dot( r
,u
),
594 double det
= uu
*vv
- uv
*uv
,
598 if( det
< 1e-6 *uu
*vv
)
605 s
= (ru
*vv
- rv
*uv
)/det
;
606 t
= (ru
*uv
- rv
*uu
)/det
;
609 s
= cxr_clampf( s
, 0.0, 1.0 );
610 t
= cxr_clampf( t
, 0.0, 1.0 );
612 double S
= cxr_clampf((t
*uv
+ ru
)/uu
, 0.0, 1.0),
613 T
= cxr_clampf((s
*uv
- rv
)/vv
, 0.0, 1.0);
615 v3_muladds( a0
, u
, S
, a
);
616 v3_muladds( b0
, v
, T
, b
);
618 return v3_dist( a
, b
);