-
Notifications
You must be signed in to change notification settings - Fork 21
/
math3dfunc.cpp
1804 lines (1544 loc) · 44.4 KB
/
math3dfunc.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#define LUA_LIB
#include <cmath>
#include <cassert>
#include <cstring>
#include <utility>
extern "C" {
#include "mathid.h"
#include "math3dfunc.h"
}
#ifndef M_PI
#define M_PI 3.1415926536
#endif
#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>
#include <glm/gtc/quaternion.hpp>
#include <glm/gtx/quaternion.hpp>
#include <glm/ext/scalar_relational.hpp>
#include <glm/ext/vector_relational.hpp>
#include <glm/gtx/euler_angles.hpp>
#include <glm/ext/vector_common.hpp>
#include <glm/gtx/matrix_decompose.hpp>
static const glm::vec4 XAXIS(1, 0, 0, 0);
static const glm::vec4 YAXIS(0, 1, 0, 0);
static const glm::vec4 ZAXIS(0, 0, 1, 0);
static const glm::vec4 WAXIS(0, 0, 0, 1);
static const glm::vec4 NXAXIS = -XAXIS;
static const glm::vec4 NYAXIS = -YAXIS;
static const glm::vec4 NZAXIS = -ZAXIS;
template<typename T>
inline bool
is_zero(const T& a, const T& e = T(glm::epsilon<float>())) {
return glm::all(glm::equal(a, glm::zero<T>(), e));
}
inline bool
is_zero(const float& a, float e = glm::epsilon<float>()) {
return glm::equal(a, glm::zero<float>(), e);
}
template<typename T>
inline bool
is_equal(const T& a, const T& b, const T& e = T(glm::epsilon<float>())) {
return is_zero(a - b, e);
}
static inline void
check_type(struct math_context *M, math_t id, int type) {
assert(math_type(M, id) == type);
}
static inline glm::mat4x4 &
allocmat(struct math_context *M, math_t *id) {
*id = math_matrix(M, NULL);
float * buf = math_init(M, *id);
return *(glm::mat4x4 *)buf;
}
// static inline glm::mat4x4 &
// initmat(struct math_context *M, math_t id) {
// check_type(M, id, MATH_TYPE_MAT);
// float * buf = math_init(M, id);
// return *(glm::mat4x4 *)buf;
// }
static inline glm::quat &
allocquat(struct math_context *M, math_t *id) {
*id = math_quat(M, NULL);
float *buf = math_init(M, *id);
return *(glm::quat *)buf;
}
static inline glm::vec4 &
allocvec4(struct math_context *M, math_t *id) {
*id = math_vec4(M, NULL);
float * buf = math_init(M, *id);
return *(glm::vec4 *)buf;
}
static inline glm::vec4 &
initvec4(struct math_context *M, math_t id) {
check_type(M, id, MATH_TYPE_VEC4);
float * buf = math_init(M, id);
return *(glm::vec4 *)buf;
}
static inline const glm::quat &
QUAT(struct math_context *M, math_t quat) {
check_type(M, quat, MATH_TYPE_QUAT);
const float * v = math_value(M, quat);
return *(const glm::quat *)(v);
}
static inline const glm::mat4x4 &
MAT(struct math_context *M, math_t mat) {
check_type(M, mat, MATH_TYPE_MAT);
const float *v = math_value(M, mat);
return *(const glm::mat4x4 *)(v);
}
static inline const glm::vec4 &
VEC(struct math_context *M, math_t v4) {
check_type(M, v4, MATH_TYPE_VEC4);
const float *v = math_value(M, v4);
return *(const glm::vec4 *)(v);
}
static inline const glm::vec4 &
VECPTR(const float *v) {
return *(const glm::vec4 *)(v);
}
static inline const glm::vec3 &
VEC3(struct math_context *M, math_t v3) {
check_type(M, v3, MATH_TYPE_VEC4);
const float *v = math_value(M, v3);
return *(const glm::vec3 *)(v);
}
static inline const glm::vec3* V3P(const glm::vec4 &v4) { return (const glm::vec3*)(&v4.x);}
static inline const glm::vec3& V3R(const glm::vec4 &v4) { return *V3P(v4);}
struct AABB {
const glm::vec4 &minv;
const glm::vec4 &maxv;
};
static inline struct AABB
AABB(struct math_context *M, math_t aabb) {
check_type(M, aabb, MATH_TYPE_VEC4);
const float *v = math_value(M, aabb);
return {
*(const glm::vec4 *)(v),
*(const glm::vec4 *)(v+4)
};
}
struct AABB_buffer {
glm::vec4 &minv;
glm::vec4 &maxv;
};
static inline struct AABB_buffer
initaabb(struct math_context *M, math_t id) {
check_type(M, id, MATH_TYPE_VEC4);
float * buf = math_init(M, id);
return {
*(glm::vec4 *)buf,
*(glm::vec4 *)(buf+4),
};
}
math_t
math3d_matrix_from_cols(struct math_context* M, math_t c1, math_t c2, math_t c3, math_t c4){
math_t r;
glm::mat4x4 &m = allocmat(M, &r);
m[0] = VEC(M, c1);
m[1] = VEC(M, c2);
m[2] = VEC(M, c3);
m[3] = VEC(M, c4);
return r;
}
math_t
math3d_quat_to_matrix(struct math_context *M, math_t quat) {
math_t r;
glm::mat4x4 &m = allocmat(M, &r);
m = glm::mat4x4(QUAT(M, quat));
return r;
}
math_t
math3d_matrix_to_quat(struct math_context *M, math_t mat) {
math_t r;
glm::quat &q = allocquat(M, &r);
q = glm::quat_cast(MAT(M, mat));
return r;
}
math_t
math3d_make_quat_from_axis(struct math_context *M, math_t axis_id, float radian) {
math_t r;
const float *axis = math_value(M, axis_id);
glm::vec3 a(axis[0],axis[1],axis[2]);
glm::quat &q = allocquat(M, &r);
q = glm::angleAxis(radian, a);
return r;
}
math_t
math3d_quat_between_2vectors(struct math_context *M, math_t a, math_t b) {
math_t r;
glm::quat &q = allocquat(M, &r);
q = glm::quat(VEC3(M, a), VEC3(M, b));
return r;
}
math_t
math3d_make_quat_from_euler(struct math_context *M, math_t euler) {
glm::quat q(VEC3(M, euler));
return math_quat(M, &q[0]);
}
static int
scale1(struct math_context *M, math_t s) {
const float * v = math_value(M, s);
return v[0] == 1 && v[1] == 1 && v[2] == 1;
}
static int
rot0(struct math_context *M, math_t r) {
const float * v = math_value(M, r);
return v[0] == 0 && v[1] == 0 && v[2] == 0 && v[3] == 1;
}
static int
trans0(struct math_context *M, math_t t) {
const float * v = math_value(M, t);
return v[0] == 0 && v[1] == 0 && v[2] == 0;
}
math_t
math3d_make_srt(struct math_context *M, math_t s, math_t r, math_t t) {
math_t id;
glm::mat4x4 &srt = allocmat(M, &id);
int ident = 1;
if (!math_isnull(s) && !scale1(M, s)) {
srt = glm::mat4x4(1);
const glm::vec3 &scale = VEC3(M, s);
srt[0][0] = scale[0];
srt[1][1] = scale[1];
srt[2][2] = scale[2];
ident = 0;
}
if (!math_isnull(r) && !rot0(M, r)) {
const glm::quat &q = QUAT(M, r);
if (!ident) {
srt = glm::mat4x4(q) * srt;
} else {
srt = glm::mat4x4(q);
}
ident = 0;
} else if (ident) {
srt = glm::mat4x4(1);
}
if (!math_isnull(t) && !trans0(M, t)) {
const glm::vec3 &translate = VEC3(M, t);
srt[3][0] = translate[0];
srt[3][1] = translate[1];
srt[3][2] = translate[2];
srt[3][3] = 1;
ident = 0;
}
if (ident) {
return math_identity(MATH_TYPE_MAT);
}
return id;
}
void
math3d_decompose_matrix(struct math_context *M, math_t mat, math_t v[3]) {
const glm::mat4x4 &m = MAT(M, mat);
v[0] = math_vec4(M, NULL);
v[1] = math_quat(M, NULL);
v[2] = math_vec4(M, NULL);
float *scale = math_init(M, v[0]);
float *quat = math_init(M, v[1]);
float *trans = math_init(M, v[2]);
glm::vec3 skew;
glm::vec4 perspective;
glm::decompose(m, *(glm::vec3*)scale, *(glm::quat *)quat, *(glm::vec3*)trans, skew, perspective);
}
// epsilon for pow2
//#define EPSILON 0.00001f
// glm::equal(dot , 1.0f, EPSILON)
static inline int
equal_one(float f) {
union {
float f;
uint32_t n;
} u;
u.f = f;
return ((u.n + 0x1f) & ~0x3f) == 0x3f800000; // float 1
}
math_t
math3d_decompose_scale(struct math_context *M, math_t mat) {
math_t id = math_vec4(M, NULL);
float * scale = math_init(M, id);
const glm::mat4& m = MAT(M, mat);
int ii;
scale[3] = 0;
for (ii = 0; ii < 3; ++ii) {
const float* v = &m[ii].x;
float dot = glm::dot(*(const glm::vec3 *)v, *(const glm::vec3 *)v);
if (equal_one(dot)) {
scale[ii] = 1.0f;
} else {
scale[ii] = sqrtf(dot);
if (scale[ii] == 0) {
// invalid scale, use 1 instead
scale[0] = scale[1] = scale[2] = 1.0f;
return id;
}
}
if (glm::determinant(m) < 0){
scale[ii] *= -1;
}
}
return id;
}
math_t
math3d_decompose_rot(struct math_context *M, math_t mat) {
math_t id;
glm::quat &q = allocquat(M, &id);
glm::mat4 rotMat(MAT(M, mat));
math_t s = math3d_decompose_scale(M, mat);
const float *scale = math_value(M, s);
int ii;
for (ii = 0; ii < 3; ++ii) {
rotMat[ii] /= scale[ii];
}
q = glm::quat_cast(rotMat);
return id;
}
math_t
math3d_add_vec(struct math_context *M, math_t v1, math_t v2) {
math_t id;
glm::vec4 &r = allocvec4(M, &id);
r = VEC(M, v1) + VEC(M, v2);
return id;
}
math_t
math3d_sub_vec(struct math_context *M, math_t v1, math_t v2) {
math_t id;
glm::vec4 &r = allocvec4(M, &id);
r = VEC(M, v1) - VEC(M, v2);
return id;
}
math_t
math3d_mul_vec(struct math_context *M, math_t v1, math_t v2) {
math_t id;
glm::vec4 &r = allocvec4(M, &id);
r = VEC(M, v1) * VEC(M, v2);
return id;
}
math_t
math3d_mul_quat(struct math_context *M, math_t v1, math_t v2) {
if (math_isidentity(v1)) {
return v2;
}
if (math_isidentity(v2)) {
return v1;
}
math_t id;
glm::quat &quat = allocquat(M, &id);
quat = QUAT(M, v1) * QUAT(M, v2);
return id;
}
math_t
math3d_mul_matrix(struct math_context *M, math_t v1, math_t v2) {
if (math_isidentity(v1)) {
return v2;
}
if (math_isidentity(v2)) {
return v1;
}
math_t id;
glm::mat4x4 &mat = allocmat(M, &id);
mat = MAT(M, v1) * MAT(M, v2);
return id;
}
static inline void
matrix_mul(float * output, const float *m1, const float *m2) {
glm::mat4x4 & omat = *(glm::mat4x4 *)(output);
const glm::mat4x4 & mat1 = *(const glm::mat4x4 *)(m1);
const glm::mat4x4 & mat2 = *(const glm::mat4x4 *)(m2);
omat = mat1 * mat2;
}
math_t
math3d_mul_matrix_array(struct math_context *M, math_t mat, math_t array_mat, math_t output_ref) {
int reverse = 0;
int sz = math_size(M, array_mat);
if (sz == 1) {
sz = math_size(M, mat);
reverse = 1;
math_t tmp = mat;
mat = array_mat;
array_mat = tmp;
} else {
int matsz = math_size(M, mat);
if (matsz > 1) {
// array(mat) * array(array_mat)
if (matsz < sz)
sz = matsz;
if (math_isnull(output_ref)) {
output_ref = math_import(M, NULL, MATH_TYPE_MAT, sz);
} else {
int output_sz = math_size(M, output_ref);
if (output_sz < sz)
sz = output_sz;
}
int i;
const float * lm = math_value(M, mat);
const float * rm = math_value(M, array_mat);
float * out_buf = math_init(M, output_ref);
for (i=0;i<sz;i++) {
matrix_mul(out_buf + i * 16, lm + i * 16, rm + i * 16);
}
return output_ref;
}
}
// matrix * array
if (math_isidentity(mat)) {
// mul identity, copy array
if (math_isnull(output_ref)) {
return array_mat;
} else {
float * result = math_init(M, output_ref);
const float * source = math_value(M, array_mat);
int sz_output = math_size(M, output_ref);
if (sz_output < sz)
sz = sz_output;
memcpy(result, source, sz * 16 * sizeof(float));
return output_ref;
}
}
if (math_isnull(output_ref)) {
output_ref = math_import(M, NULL, MATH_TYPE_MAT, sz);
} else {
int output_sz = math_size(M, output_ref);
if (output_sz < sz)
sz = output_sz;
}
int i;
const float * m = math_value(M, mat);
float * out_buf = math_init(M, output_ref);
const float * in_buf = math_value(M, array_mat);
if (reverse) {
for (i=0;i<sz;i++) {
matrix_mul(out_buf + i * 16, in_buf + i * 16, m);
}
} else {
for (i=0;i<sz;i++) {
matrix_mul(out_buf + i * 16, m, in_buf + i * 16);
}
}
return output_ref;
}
float
math3d_length(struct math_context *M, math_t v) {
return glm::length(VEC3(M, v));
}
math_t
math3d_floor(struct math_context *M, math_t v) {
math_t id = math_vec4(M, NULL);
float *vv = math_init(M, id);
check_type(M, v, MATH_TYPE_VEC4);
const float *value = math_value(M, v);
vv[0] = floor(value[0]);
vv[1] = floor(value[1]);
vv[2] = floor(value[2]);
vv[3] = floor(value[3]);
return id;
}
math_t
math3d_ceil(struct math_context *M, math_t v) {
math_t id = math_vec4(M, NULL);
float *vv = math_init(M, id);
check_type(M, v, MATH_TYPE_VEC4);
const float *value = math_value(M, v);
vv[0] = ceil(value[0]);
vv[1] = ceil(value[1]);
vv[2] = ceil(value[2]);
vv[3] = ceil(value[3]);
return id;
}
float
math3d_dot(struct math_context *M, math_t v1, math_t v2) {
return glm::dot(VEC3(M, v1), VEC3(M, v2));
}
math_t
math3d_cross(struct math_context *M, math_t v1, math_t v2) {
glm::vec3 c = glm::cross(VEC3(M, v1), VEC3(M, v2));
math_t id = math_vec4(M, NULL);
float *r = math_init(M, id);
r[0] = c[0];
r[1] = c[1];
r[2] = c[2];
r[3] = 0;
return id;
}
math_t
math3d_normalize_vector(struct math_context *M, math_t id) {
const float *v = math_value(M, id);
glm::vec3 v3 = glm::normalize(*(const glm::vec3 *)(v));
math_t result = math_vec4(M, NULL);
float *r = math_init(M, result);
r[0] = v3[0];
r[1] = v3[1];
r[2] = v3[2];
r[3] = v[3];
return result;
}
math_t
math3d_normalize_quat(struct math_context *M, math_t quat) {
math_t id;
glm::quat &q = allocquat(M, &id);
q = glm::normalize(QUAT(M, quat));
return id;
}
math_t
math3d_transpose_matrix(struct math_context *M, math_t mat) {
math_t id;
glm::mat4x4 &r = allocmat(M, &id);
r = glm::transpose(MAT(M, mat));
return id;
}
math_t
math3d_inverse_quat(struct math_context *M, math_t quat) {
math_t id;
glm::quat &q = allocquat(M, &id);
q = glm::inverse(QUAT(M, quat));
return id;
}
math_t
math3d_inverse_matrix(struct math_context *M, math_t mat) {
math_t id;
glm::mat4x4 &r = allocmat(M, &id);
r = glm::inverse(MAT(M, mat));
return id;
}
math_t
math3d_inverse_matrix_fast(struct math_context *M, math_t mat) {
math_t id;
const auto &m = MAT(M, mat);
glm::mat4x4 &r = allocmat(M, &id);
r = m;
assert( is_zero(glm::dot(V3R(m[0]), V3R(m[1])), 1e-6f) &&
is_zero(glm::dot(V3R(m[1]), V3R(m[2])), 1e-6f) &&
is_zero(glm::dot(V3R(m[2]), V3R(m[0])), 1e-6f));
// DO NOT write: auto m3 = (glm::mat3*)(&m);
// transpose 3x3
std::swap(r[0][1], r[1][0]);
std::swap(r[0][2], r[2][0]);
std::swap(r[1][2], r[2][1]);
glm::vec3& c3 = *(glm::vec3*)(&r[3]);
// rotate t -> T = r * t ==> glm::vec3(dot(row0(r), t), dot(row1(r), t), dot(row2(r), t), here row0(r) = col0(m)
c3 = -glm::vec3(glm::dot(V3R(m[0]), c3), glm::dot(V3R(m[1]), c3), glm::dot(V3R(m[2]), c3));
return id;
}
math_t
math3d_quat_transform(struct math_context *M, math_t quat, math_t v) {
math_t id;
glm::vec4 &vv = allocvec4(M, &id);
vv = glm::rotate(QUAT(M, quat), VEC(M, v));
return id;
}
math_t
math3d_rotmat_transform(struct math_context *M, math_t mat, math_t v) {
math_t id;
glm::vec4 &vv = allocvec4(M, &id);
vv = MAT(M, mat) * VEC(M, v);
return id;
}
math_t
math3d_mulH(struct math_context *M, math_t mat, math_t v) {
math_t id;
glm::vec4 &r = allocvec4(M, &id);
check_type(M, v, MATH_TYPE_VEC4);
const float *vec = math_value(M, v);
if (vec[3] != 1.f){
glm::vec4 tmp ( vec[0], vec[1], vec[2], 1 );
r = MAT(M, mat) * tmp;
} else {
r = MAT(M, mat) * (*(const glm::vec4 *)(vec));
}
if (r.w != 0) {
r /= fabs(r.w);
r.w = 1.f;
}
return id;
}
math_t
math3d_reciprocal(struct math_context *M, math_t v) {
math_t id;
glm::vec4 &vv = allocvec4(M, &id);
check_type(M, v, MATH_TYPE_VEC4);
const float *value = math_value(M, v);
const glm::vec4 & vec = *(const glm::vec4 *)(value);
vv = 1.f / vec;
vv[3] = value[3];
return id;
}
math_t
math3d_lookat_matrix(struct math_context *M, int direction, math_t eye, math_t at, math_t up_id) {
math_t id;
glm::mat4x4 &m = allocmat(M, &id);
const float *up;
if (math_isnull(up_id)) {
static const float default_up[3] = {0,1,0};
up = default_up;
} else {
check_type(M, up_id, MATH_TYPE_VEC4);
up = math_value(M, up_id);
}
const glm::vec3 &eyev = VEC3(M, eye);
if (direction) {
const glm::vec3 vat = eyev + VEC3(M, at);
m = glm::lookAtLH(eyev, vat, *(const glm::vec3 *)(up));
} else {
m = glm::lookAtLH(eyev, VEC3(M, at), *(const glm::vec3 *)(up));
}
return id;
}
static inline glm::vec2
perspective_AB(float near, float far, struct projection_flags flags){
float A, B;
if (flags.infinity_far){
if (flags.homogeneous_depth){
//(far+near) / (far-near);
// flags.invert_z ==> near/-near ==> -1
// far/far ==> 1
A = flags.invert_z ? -1.f : 1.f;
} else {
//far / (far-near);
//flags.invert_z ==> far/-near ==> -0 ==> -glm::epsilon<float>()
// ==> far/far ==> 1
A = flags.invert_z ? -glm::epsilon<float>() : 1.f;
}
// -(far*near) / (far-near)
//if invert_z ==> -far*near/-near = far
// ==> -far*near/far =-near
B = flags.invert_z ? far : -near;
} else {
const float zrange = far-near;
A = (flags.homogeneous_depth ? (far+near) : far) / zrange;
B =-(far*near) / zrange;
}
return glm::vec2(A, B);
}
static inline glm::mat4
perspectiveLH(float fovy, float aspect, float near, float far, struct projection_flags flags)
{
if (flags.invert_z){
std::swap(near, far);
}
assert(abs(aspect - glm::epsilon<float>()) > 0);
const float tanHalfFovy = tan(fovy / 2);
glm::mat4 r(0);
r[0][0] = 1 / (aspect * tanHalfFovy);
r[1][1] = 1 / (tanHalfFovy);
r[2][3] = 1;
const glm::vec2 AB = perspective_AB(near, far, flags);
r[2][2] = AB[0];
r[3][2] = AB[1];
return r;
}
static glm::mat4
frustumLH(float left, float right, float bottom, float top, float near, float far, struct projection_flags flags)
{
if (flags.invert_z){
std::swap(near, far);
}
const float xrange = (right - left);
const float yrange = (top - bottom);
glm::mat4 r(0);
r[0][0] = 2.f* near / xrange;
r[1][1] = 2.f* near / yrange;
r[2][0] = (right + left) / xrange;
r[2][1] = (top + bottom) / yrange;
r[2][3] = 1.f;
const glm::vec2 AB = perspective_AB(near, far, flags);
r[2][2] = AB[0];
r[3][2] = AB[1];
return r;
}
static glm::mat4
orthoLH(float left, float right, float bottom, float top, float near, float far, struct projection_flags flags)
{
if (flags.invert_z){
std::swap(near, far);
}
glm::mat4 r(1);
const float xrange = (right - left);
const float yrange = (top - bottom);
r[0][0] = 2.f / xrange;
r[1][1] = 2.f / yrange;
r[3][0] =-(right + left)/xrange;
r[3][1] =-(top + bottom)/yrange;
if (flags.infinity_far){
//(1.f/(far-near)) | (2.f/(far-near)) ==> c/(far-near)
//flags.invert_z ==> c/-near ==> -0 ==>-glm::epsilon<float>()
// c/far ==> 0
r[2][2] = flags.invert_z ? -glm::epsilon<float>() : glm::epsilon<float>();
if (flags.homogeneous_depth){
//-(far+near)/(far-near);
//flags.invert_z ==> -near/-near ==> 1
// -far/far ==> -1
r[3][2] = flags.invert_z ? 1.f : -1.f;
} else {
//-near/(far-near);
//flags.invert_z ==> -near/-near ==> 1
// -0/far ==> -0 ==> -glm::epsilon<float>()
r[3][2] = flags.invert_z ? 1.f : -glm::epsilon<float>();
}
} else {
const float zrange = (far - near);
if (flags.homogeneous_depth){
r[2][2] = 2.f /zrange;
r[3][2] =-(far+near)/zrange;
} else {
r[2][2] = 1.f /zrange;
r[3][2] =-near/zrange;
}
}
return r;
}
math_t
math3d_perspectiveLH(struct math_context *M, float fov, float aspect, float near, float far, struct projection_flags flags) {
math_t id;
glm::mat4x4 &mat = allocmat(M, &id);
mat = perspectiveLH(fov, aspect, near, far, flags);
return id;
}
math_t
math3d_frustumLH(struct math_context *M, float left, float right, float bottom, float top, float near, float far, struct projection_flags flags) {
math_t id;
glm::mat4x4 &mat = allocmat(M, &id);
mat = frustumLH(left, right, bottom, top, near, far, flags);
return id;
}
math_t
math3d_orthoLH(struct math_context *M, float left, float right, float bottom, float top, float near, float far, struct projection_flags flags) {
math_t id;
glm::mat4x4 &mat = allocmat(M, &id);
mat = orthoLH(left, right, bottom, top, near, far, flags);
return id;
}
math_t
math3d_base_axes(struct math_context *M, math_t forward_id) {
math_t result = math_import(M, NULL, MATH_TYPE_VEC4, 2);
glm::vec4 &up = initvec4(M, math_index(M, result, 0));
glm::vec4 &right = initvec4(M, math_index(M, result, 1));
const glm::vec4 &forward = VEC(M, forward_id);
const glm::vec3 &forward3 = VEC3(M, forward_id);
if (is_equal(forward, ZAXIS)) {
up = YAXIS;
right = XAXIS;
} else {
if (is_equal(forward, YAXIS)) {
up = NZAXIS;
right = XAXIS;
} else if (is_equal(forward, NYAXIS)) {
up = ZAXIS;
right = XAXIS;
} else {
right = glm::vec4(glm::normalize(glm::cross(*(const glm::vec3 *)(&YAXIS.x), forward3)), 0);
up = glm::vec4(glm::normalize(glm::cross(forward3, *(const glm::vec3 *)(&right.x))), 0);
}
}
return result;
}
math_t
math3d_quat_to_viewdir(struct math_context *M, math_t quat) {
math_t id;
glm::vec4 &d = allocvec4(M, &id);
d = glm::rotate(QUAT(M, quat), glm::vec4(0, 0, 1, 0));
return id;
}
math_t
math3d_rotmat_to_viewdir(struct math_context *M, math_t mat) {
math_t id;
glm::vec4 &d = allocvec4(M, &id);
d = MAT(M, mat) * glm::vec4(0, 0, 1, 0);
return id;
}
math_t
math3d_viewdir_to_quat(struct math_context *M, math_t v) {
float tmp[4] = {0, 0, 1, 0};
math_t vv = math_vec4(M, tmp);
return math3d_quat_between_2vectors(M, vv, v);
}
static math_t
minv(struct math_context *M, math_t v0, math_t v1) {
const float * left = math_value(M, v0);
const float * right = math_value(M, v1);
float tmp[4];
int left_n = 0;
int right_n = 0;
int i;
for (i=0;i<3;i++) {
if (left[i] <= right[i]) {
if (left[i] == right[i])
++right_n;
++left_n;
tmp[i] = left[i];
} else {
// left[i] > right[i]
++right_n;
tmp[i] = right[i];
}
}
if (left_n == 3) {
return v0;
} else if (right_n == 3) {
return v1;
}
tmp[3] = 0;
return math_vec4(M, tmp);
}
static math_t
maxv(struct math_context *M, math_t v0, math_t v1) {
const float * left = math_value(M, v0);
const float * right = math_value(M, v1);
float tmp[4];
int left_n = 0;
int right_n = 0;
int i;
for (i=0;i<3;i++) {
if (left[i] >= right[i]) {
if (left[i] == right[i])
++right_n;
++left_n;
tmp[i] = left[i];
} else {
// left[i] < right[i]
++right_n;
tmp[i] = right[i];
}
}
if (left_n == 3) {
return v0;
} else if (right_n == 3) {
return v1;
}
tmp[3] = 0;
return math_vec4(M, tmp);
}
static inline glm::vec4
transform_pt(struct math_context *M, const glm::mat4& m, math_t p){
glm::vec4 v = VEC(M, p);
v.w = 1.f;//we assue p must be a point
v = m * v;
return v / v.w;
}
math_t
math3d_minmax(struct math_context *M, math_t transform, math_t points) {
const size_t numpoints = math_size(M, points);
if (numpoints == 0)
return MATH_NULL;
const math_t p = math_index(M, points, 0);
glm::vec4 minmax[2];
if (math_isnull(transform)){
minmax[0] = minmax[1] = VEC(M, p);
for (int ii=1; ii<(int)numpoints; ++ii){
const auto& pp = VEC(M, math_index(M, points, ii));
minmax[0] = glm::min(minmax[0], pp);
minmax[1] = glm::max(minmax[1], pp);
}
} else {
const glm::mat4& m = MAT(M, transform);
minmax[0] = minmax[1] = transform_pt(M, m, p);
for (int ii=1; ii<(int)numpoints; ++ii){
const glm::vec4 tpp = transform_pt(M, m, math_index(M, points, ii));
minmax[0] = glm::min(minmax[0], tpp);
minmax[1] = glm::max(minmax[1], tpp);
}
}
return math_import(M, (const float*)minmax, MATH_TYPE_VEC4, 2);
}
math_t
math3d_aabb_merge(struct math_context *M, math_t aabblhs, math_t aabbrhs) {
check_type(M, aabblhs, MATH_TYPE_VEC4);
check_type(M, aabbrhs, MATH_TYPE_VEC4);
const math_t lhsmin = math_index(M, aabblhs, 0);
const math_t lhsmax = math_index(M, aabblhs, 1);
const math_t rhsmin = math_index(M, aabbrhs, 0);
const math_t rhsmax = math_index(M, aabbrhs, 1);
math_t min_id = minv(M, lhsmin, rhsmin);
math_t max_id = maxv(M, lhsmax, rhsmax);
if (math_issame(min_id, lhsmin) && math_issame(max_id, lhsmax)) {
return aabblhs;
}
if (math_issame(min_id, rhsmin) && math_issame(max_id, rhsmax)) {
return aabbrhs;
}
math_t r = math_import(M, NULL, MATH_TYPE_VEC4, 2);
float *value = math_init(M, r);
memcpy(value, math_value(M, min_id), 4 * sizeof(float));
memcpy(value+4, math_value(M, max_id), 4 * sizeof(float));
return r;
}
math_t
math3d_lerp(struct math_context *M, math_t v0, math_t v1, float ratio) {
math_t id;
glm::vec4 &r = allocvec4(M, &id);
r = glm::lerp(VEC(M, v0), VEC(M, v1), ratio);
return id;
}
math_t
math3d_quat_lerp(struct math_context *M, math_t v0, math_t v1, float ratio) {
math_t id;
glm::quat &r = allocquat(M, &id);
r = glm::lerp(QUAT(M, v0), QUAT(M, v1), ratio);
return id;
}
math_t
math3d_quat_slerp(struct math_context *M, math_t v0, math_t v1, float ratio) {