OpenVDB 3.2.0

Mat4.h
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30
31 #ifndef OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
33
34 #include <openvdb/Exceptions.h>
35 #include <openvdb/Platform.h>
36 #include <iomanip>
37 #include <assert.h>
38 #include <math.h>
39 #include <algorithm>
40 #include "Math.h"
41 #include "Mat3.h"
42 #include "Vec3.h"
43 #include "Vec4.h"
44
45
46 namespace openvdb {
47 OPENVDB_USE_VERSION_NAMESPACE
48 namespace OPENVDB_VERSION_NAME {
49 namespace math {
50
51 template<typename T> class Vec4;
52
53
56 template<typename T>
57 class Mat4: public Mat<4, T>
58 {
59 public:
61 typedef T value_type;
62 typedef T ValueType;
63 typedef Mat<4, T> MyBase;
64
66 Mat4() {}
67
69
75 template<typename Source>
76 Mat4(Source *a)
77 {
78 for (int i = 0; i < 16; i++) {
79 MyBase::mm[i] = a[i];
80 }
81 }
82
84
90 template<typename Source>
91 Mat4(Source a, Source b, Source c, Source d,
92 Source e, Source f, Source g, Source h,
93 Source i, Source j, Source k, Source l,
94 Source m, Source n, Source o, Source p)
95 {
96 MyBase::mm[ 0] = T(a);
97 MyBase::mm[ 1] = T(b);
98 MyBase::mm[ 2] = T(c);
99 MyBase::mm[ 3] = T(d);
100
101 MyBase::mm[ 4] = T(e);
102 MyBase::mm[ 5] = T(f);
103 MyBase::mm[ 6] = T(g);
104 MyBase::mm[ 7] = T(h);
105
106 MyBase::mm[ 8] = T(i);
107 MyBase::mm[ 9] = T(j);
108 MyBase::mm[10] = T(k);
109 MyBase::mm[11] = T(l);
110
111 MyBase::mm[12] = T(m);
112 MyBase::mm[13] = T(n);
113 MyBase::mm[14] = T(o);
114 MyBase::mm[15] = T(p);
115 }
116
119 template<typename Source>
120 Mat4(const Vec4<Source> &v1, const Vec4<Source> &v2,
121 const Vec4<Source> &v3, const Vec4<Source> &v4, bool rows = true)
122 {
123 if (rows) {
124 this->setRows(v1, v2, v3, v4);
125 } else {
126 this->setColumns(v1, v2, v3, v4);
127 }
128 }
129
131 Mat4(const Mat<4, T> &m)
132 {
133 for (int i = 0; i < 4; ++i) {
134 for (int j = 0; j < 4; ++j) {
135 MyBase::mm[i*4 + j] = m[i][j];
136 }
137 }
138 }
139
141 template<typename Source>
142 explicit Mat4(const Mat4<Source> &m)
143 {
144 const Source *src = m.asPointer();
145
146 for (int i=0; i<16; ++i) {
147 MyBase::mm[i] = static_cast<T>(src[i]);
148 }
149 }
150
152 static const Mat4<T>& identity() {
153 return sIdentity;
154 }
155
157 static const Mat4<T>& zero() {
158 return sZero;
159 }
160
162 void setRow(int i, const Vec4<T> &v)
163 {
164 // assert(i>=0 && i<4);
165 int i4 = i * 4;
166 MyBase::mm[i4+0] = v[0];
167 MyBase::mm[i4+1] = v[1];
168 MyBase::mm[i4+2] = v[2];
169 MyBase::mm[i4+3] = v[3];
170 }
171
173 Vec4<T> row(int i) const
174 {
175 // assert(i>=0 && i<3);
176 return Vec4<T>((*this)(i,0), (*this)(i,1), (*this)(i,2), (*this)(i,3));
177 }
178
180 void setCol(int j, const Vec4<T>& v)
181 {
182 // assert(j>=0 && j<4);
183 MyBase::mm[ 0+j] = v[0];
184 MyBase::mm[ 4+j] = v[1];
185 MyBase::mm[ 8+j] = v[2];
186 MyBase::mm[12+j] = v[3];
187 }
188
190 Vec4<T> col(int j) const
191 {
192 // assert(j>=0 && j<4);
193 return Vec4<T>((*this)(0,j), (*this)(1,j), (*this)(2,j), (*this)(3,j));
194 }
195
197 T* operator[](int i) { return &(MyBase::mm[i<<2]); }
200 const T* operator[](int i) const { return &(MyBase::mm[i<<2]); }
202
204 T* asPointer() {return MyBase::mm;}
205 const T* asPointer() const {return MyBase::mm;}
206
210 T& operator()(int i, int j)
211 {
212 // assert(i>=0 && i<4);
213 // assert(j>=0 && j<4);
214 return MyBase::mm[4*i+j];
215 }
216
220 T operator()(int i, int j) const
221 {
222 // assert(i>=0 && i<4);
223 // assert(j>=0 && j<4);
224 return MyBase::mm[4*i+j];
225 }
226
228 void setRows(const Vec4<T> &v1, const Vec4<T> &v2,
229 const Vec4<T> &v3, const Vec4<T> &v4)
230 {
231 MyBase::mm[ 0] = v1[0];
232 MyBase::mm[ 1] = v1[1];
233 MyBase::mm[ 2] = v1[2];
234 MyBase::mm[ 3] = v1[3];
235
236 MyBase::mm[ 4] = v2[0];
237 MyBase::mm[ 5] = v2[1];
238 MyBase::mm[ 6] = v2[2];
239 MyBase::mm[ 7] = v2[3];
240
241 MyBase::mm[ 8] = v3[0];
242 MyBase::mm[ 9] = v3[1];
243 MyBase::mm[10] = v3[2];
244 MyBase::mm[11] = v3[3];
245
246 MyBase::mm[12] = v4[0];
247 MyBase::mm[13] = v4[1];
248 MyBase::mm[14] = v4[2];
249 MyBase::mm[15] = v4[3];
250 }
251
253 void setColumns(const Vec4<T> &v1, const Vec4<T> &v2,
254 const Vec4<T> &v3, const Vec4<T> &v4)
255 {
256 MyBase::mm[ 0] = v1[0];
257 MyBase::mm[ 1] = v2[0];
258 MyBase::mm[ 2] = v3[0];
259 MyBase::mm[ 3] = v4[0];
260
261 MyBase::mm[ 4] = v1[1];
262 MyBase::mm[ 5] = v2[1];
263 MyBase::mm[ 6] = v3[1];
264 MyBase::mm[ 7] = v4[1];
265
266 MyBase::mm[ 8] = v1[2];
267 MyBase::mm[ 9] = v2[2];
268 MyBase::mm[10] = v3[2];
269 MyBase::mm[11] = v4[2];
270
271 MyBase::mm[12] = v1[3];
272 MyBase::mm[13] = v2[3];
273 MyBase::mm[14] = v3[3];
274 MyBase::mm[15] = v4[3];
275 }
276
278 OPENVDB_DEPRECATED void setBasis(const Vec4<T> &v1, const Vec4<T> &v2,
279 const Vec4<T> &v3, const Vec4<T> &v4)
280 {
281 this->setRows(v1, v2, v3, v4);
282 }
283
284
285 // Set "this" matrix to zero
286 void setZero()
287 {
288 MyBase::mm[ 0] = 0;
289 MyBase::mm[ 1] = 0;
290 MyBase::mm[ 2] = 0;
291 MyBase::mm[ 3] = 0;
292 MyBase::mm[ 4] = 0;
293 MyBase::mm[ 5] = 0;
294 MyBase::mm[ 6] = 0;
295 MyBase::mm[ 7] = 0;
296 MyBase::mm[ 8] = 0;
297 MyBase::mm[ 9] = 0;
298 MyBase::mm[10] = 0;
299 MyBase::mm[11] = 0;
300 MyBase::mm[12] = 0;
301 MyBase::mm[13] = 0;
302 MyBase::mm[14] = 0;
303 MyBase::mm[15] = 0;
304 }
305
307 void setIdentity()
308 {
309 MyBase::mm[ 0] = 1;
310 MyBase::mm[ 1] = 0;
311 MyBase::mm[ 2] = 0;
312 MyBase::mm[ 3] = 0;
313
314 MyBase::mm[ 4] = 0;
315 MyBase::mm[ 5] = 1;
316 MyBase::mm[ 6] = 0;
317 MyBase::mm[ 7] = 0;
318
319 MyBase::mm[ 8] = 0;
320 MyBase::mm[ 9] = 0;
321 MyBase::mm[10] = 1;
322 MyBase::mm[11] = 0;
323
324 MyBase::mm[12] = 0;
325 MyBase::mm[13] = 0;
326 MyBase::mm[14] = 0;
327 MyBase::mm[15] = 1;
328 }
329
330
332 void setMat3(const Mat3<T> &m)
333 {
334 for (int i = 0; i < 3; i++)
335 for (int j=0; j < 3; j++)
336 MyBase::mm[i*4+j] = m[i][j];
337 }
338
339 Mat3<T> getMat3() const
340 {
341 Mat3<T> m;
342
343 for (int i = 0; i < 3; i++)
344 for (int j = 0; j < 3; j++)
345 m[i][j] = MyBase::mm[i*4+j];
346
347 return m;
348 }
349
351 Vec3<T> getTranslation() const
352 {
353 return Vec3<T>(MyBase::mm[12], MyBase::mm[13], MyBase::mm[14]);
354 }
355
356 void setTranslation(const Vec3<T> &t)
357 {
358 MyBase::mm[12] = t[0];
359 MyBase::mm[13] = t[1];
360 MyBase::mm[14] = t[2];
361 }
362
364 template<typename Source>
365 const Mat4& operator=(const Mat4<Source> &m)
366 {
367 const Source *src = m.asPointer();
368
369 // don't suppress warnings when assigning from different numerical types
370 std::copy(src, (src + this->numElements()), MyBase::mm);
371 return *this;
372 }
373
375 bool eq(const Mat4 &m, T eps=1.0e-8) const
376 {
377 for (int i = 0; i < 16; i++) {
378 if (!isApproxEqual(MyBase::mm[i], m.mm[i], eps))
379 return false;
380 }
381 return true;
382 }
383
385 Mat4<T> operator-() const
386 {
387 return Mat4<T>(
388 -MyBase::mm[ 0], -MyBase::mm[ 1], -MyBase::mm[ 2], -MyBase::mm[ 3],
389 -MyBase::mm[ 4], -MyBase::mm[ 5], -MyBase::mm[ 6], -MyBase::mm[ 7],
390 -MyBase::mm[ 8], -MyBase::mm[ 9], -MyBase::mm[10], -MyBase::mm[11],
391 -MyBase::mm[12], -MyBase::mm[13], -MyBase::mm[14], -MyBase::mm[15]
392 );
393 } // trivial
394
396 template <typename S>
397 const Mat4<T>& operator*=(S scalar)
398 {
399 MyBase::mm[ 0] *= scalar;
400 MyBase::mm[ 1] *= scalar;
401 MyBase::mm[ 2] *= scalar;
402 MyBase::mm[ 3] *= scalar;
403
404 MyBase::mm[ 4] *= scalar;
405 MyBase::mm[ 5] *= scalar;
406 MyBase::mm[ 6] *= scalar;
407 MyBase::mm[ 7] *= scalar;
408
409 MyBase::mm[ 8] *= scalar;
410 MyBase::mm[ 9] *= scalar;
411 MyBase::mm[10] *= scalar;
412 MyBase::mm[11] *= scalar;
413
414 MyBase::mm[12] *= scalar;
415 MyBase::mm[13] *= scalar;
416 MyBase::mm[14] *= scalar;
417 MyBase::mm[15] *= scalar;
418 return *this;
419 }
420
422 template <typename S>
423 const Mat4<T> &operator+=(const Mat4<S> &m1)
424 {
425 const S* s = m1.asPointer();
426
427 MyBase::mm[ 0] += s[ 0];
428 MyBase::mm[ 1] += s[ 1];
429 MyBase::mm[ 2] += s[ 2];
430 MyBase::mm[ 3] += s[ 3];
431
432 MyBase::mm[ 4] += s[ 4];
433 MyBase::mm[ 5] += s[ 5];
434 MyBase::mm[ 6] += s[ 6];
435 MyBase::mm[ 7] += s[ 7];
436
437 MyBase::mm[ 8] += s[ 8];
438 MyBase::mm[ 9] += s[ 9];
439 MyBase::mm[10] += s[10];
440 MyBase::mm[11] += s[11];
441
442 MyBase::mm[12] += s[12];
443 MyBase::mm[13] += s[13];
444 MyBase::mm[14] += s[14];
445 MyBase::mm[15] += s[15];
446
447 return *this;
448 }
449
451 template <typename S>
452 const Mat4<T> &operator-=(const Mat4<S> &m1)
453 {
454 const S* s = m1.asPointer();
455
456 MyBase::mm[ 0] -= s[ 0];
457 MyBase::mm[ 1] -= s[ 1];
458 MyBase::mm[ 2] -= s[ 2];
459 MyBase::mm[ 3] -= s[ 3];
460
461 MyBase::mm[ 4] -= s[ 4];
462 MyBase::mm[ 5] -= s[ 5];
463 MyBase::mm[ 6] -= s[ 6];
464 MyBase::mm[ 7] -= s[ 7];
465
466 MyBase::mm[ 8] -= s[ 8];
467 MyBase::mm[ 9] -= s[ 9];
468 MyBase::mm[10] -= s[10];
469 MyBase::mm[11] -= s[11];
470
471 MyBase::mm[12] -= s[12];
472 MyBase::mm[13] -= s[13];
473 MyBase::mm[14] -= s[14];
474 MyBase::mm[15] -= s[15];
475
476 return *this;
477 }
478
480 template <typename S>
481 const Mat4<T> &operator*=(const Mat4<S> &m1)
482 {
483 Mat4<T> m0(*this);
484
485 const T* s0 = m0.asPointer();
486 const S* s1 = m1.asPointer();
487
488 for (int i = 0; i < 4; i++) {
489 int i4 = 4 * i;
490 MyBase::mm[i4+0] = static_cast<T>(s0[i4+0] * s1[ 0] +
491 s0[i4+1] * s1[ 4] +
492 s0[i4+2] * s1[ 8] +
493 s0[i4+3] * s1[12]);
494
495 MyBase::mm[i4+1] = static_cast<T>(s0[i4+0] * s1[ 1] +
496 s0[i4+1] * s1[ 5] +
497 s0[i4+2] * s1[ 9] +
498 s0[i4+3] * s1[13]);
499
500 MyBase::mm[i4+2] = static_cast<T>(s0[i4+0] * s1[ 2] +
501 s0[i4+1] * s1[ 6] +
502 s0[i4+2] * s1[10] +
503 s0[i4+3] * s1[14]);
504
505 MyBase::mm[i4+3] = static_cast<T>(s0[i4+0] * s1[ 3] +
506 s0[i4+1] * s1[ 7] +
507 s0[i4+2] * s1[11] +
508 s0[i4+3] * s1[15]);
509 }
510 return *this;
511 }
512
514 Mat4 transpose() const
515 {
516 return Mat4<T>(
517 MyBase::mm[ 0], MyBase::mm[ 4], MyBase::mm[ 8], MyBase::mm[12],
518 MyBase::mm[ 1], MyBase::mm[ 5], MyBase::mm[ 9], MyBase::mm[13],
519 MyBase::mm[ 2], MyBase::mm[ 6], MyBase::mm[10], MyBase::mm[14],
520 MyBase::mm[ 3], MyBase::mm[ 7], MyBase::mm[11], MyBase::mm[15]
521 );
522 }
523
524
527 Mat4 inverse(T tolerance = 0) const
528 {
529 //
530 // inv [ A | b ] = [ E | f ] A: 3x3, b: 3x1, c': 1x3 d: 1x1
531 // [ c' | d ] [ g' | h ]
532 //
533 // If A is invertible use
534 //
535 // E = A^-1 + p*h*r
536 // p = A^-1 * b
537 // f = -p * h
538 // g' = -h * c'
539 // h = 1 / (d - c'*p)
540 // r' = c'*A^-1
541 //
542 // Otherwise use gauss-jordan elimination
543 //
544
545 //
546 // We create this alias to ourself so we can easily use own subscript
547 // operator.
548 const Mat4<T>& m(*this);
549
550 T m0011 = m[0][0] * m[1][1];
551 T m0012 = m[0][0] * m[1][2];
552 T m0110 = m[0][1] * m[1][0];
553 T m0210 = m[0][2] * m[1][0];
554 T m0120 = m[0][1] * m[2][0];
555 T m0220 = m[0][2] * m[2][0];
556
557 T detA = m0011 * m[2][2] - m0012 * m[2][1] - m0110 * m[2][2]
558 + m0210 * m[2][1] + m0120 * m[1][2] - m0220 * m[1][1];
559
560 bool hasPerspective =
561 (!isExactlyEqual(m[0][3], T(0.0)) ||
562 !isExactlyEqual(m[1][3], T(0.0)) ||
563 !isExactlyEqual(m[2][3], T(0.0)) ||
564 !isExactlyEqual(m[3][3], T(1.0)));
565
566 T det;
567 if (hasPerspective) {
568 det = m[0][3] * det3(m, 1,2,3, 0,2,1)
569 + m[1][3] * det3(m, 2,0,3, 0,2,1)
570 + m[2][3] * det3(m, 3,0,1, 0,2,1)
571 + m[3][3] * detA;
572 } else {
573 det = detA * m[3][3];
574 }
575
576 Mat4<T> inv;
577 bool invertible;
578
579 if (isApproxEqual(det,T(0.0),tolerance)) {
580 invertible = false;
581
582 } else if (isApproxEqual(detA,T(0.0),T(1e-8))) {
583 // det is too small to rely on inversion by subblocks
584 invertible = m.invert(inv, tolerance);
585
586 } else {
587 invertible = true;
588 detA = 1.0 / detA;
589
590 //
591 // Calculate A^-1
592 //
593 inv[0][0] = detA * ( m[1][1] * m[2][2] - m[1][2] * m[2][1]);
594 inv[0][1] = detA * (-m[0][1] * m[2][2] + m[0][2] * m[2][1]);
595 inv[0][2] = detA * ( m[0][1] * m[1][2] - m[0][2] * m[1][1]);
596
597 inv[1][0] = detA * (-m[1][0] * m[2][2] + m[1][2] * m[2][0]);
598 inv[1][1] = detA * ( m[0][0] * m[2][2] - m0220);
599 inv[1][2] = detA * ( m0210 - m0012);
600
601 inv[2][0] = detA * ( m[1][0] * m[2][1] - m[1][1] * m[2][0]);
602 inv[2][1] = detA * ( m0120 - m[0][0] * m[2][1]);
603 inv[2][2] = detA * ( m0011 - m0110);
604
605 if (hasPerspective) {
606 //
607 // Calculate r, p, and h
608 //
609 Vec3<T> r;
610 r[0] = m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
611 + m[3][2] * inv[2][0];
612 r[1] = m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
613 + m[3][2] * inv[2][1];
614 r[2] = m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
615 + m[3][2] * inv[2][2];
616
617 Vec3<T> p;
618 p[0] = inv[0][0] * m[0][3] + inv[0][1] * m[1][3]
619 + inv[0][2] * m[2][3];
620 p[1] = inv[1][0] * m[0][3] + inv[1][1] * m[1][3]
621 + inv[1][2] * m[2][3];
622 p[2] = inv[2][0] * m[0][3] + inv[2][1] * m[1][3]
623 + inv[2][2] * m[2][3];
624
625 T h = m[3][3] - p.dot(Vec3<T>(m[3][0],m[3][1],m[3][2]));
626 if (isApproxEqual(h,T(0.0),tolerance)) {
627 invertible = false;
628
629 } else {
630 h = 1.0 / h;
631
632 //
633 // Calculate h, g, and f
634 //
635 inv[3][3] = h;
636 inv[3][0] = -h * r[0];
637 inv[3][1] = -h * r[1];
638 inv[3][2] = -h * r[2];
639
640 inv[0][3] = -h * p[0];
641 inv[1][3] = -h * p[1];
642 inv[2][3] = -h * p[2];
643
644 //
645 // Calculate E
646 //
647 p *= h;
648 inv[0][0] += p[0] * r[0];
649 inv[0][1] += p[0] * r[1];
650 inv[0][2] += p[0] * r[2];
651 inv[1][0] += p[1] * r[0];
652 inv[1][1] += p[1] * r[1];
653 inv[1][2] += p[1] * r[2];
654 inv[2][0] += p[2] * r[0];
655 inv[2][1] += p[2] * r[1];
656 inv[2][2] += p[2] * r[2];
657 }
658 } else {
659 // Equations are much simpler in the non-perspective case
660 inv[3][0] = - (m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
661 + m[3][2] * inv[2][0]);
662 inv[3][1] = - (m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
663 + m[3][2] * inv[2][1]);
664 inv[3][2] = - (m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
665 + m[3][2] * inv[2][2]);
666 inv[0][3] = 0.0;
667 inv[1][3] = 0.0;
668 inv[2][3] = 0.0;
669 inv[3][3] = 1.0;
670 }
671 }
672
673 if (!invertible) OPENVDB_THROW(ArithmeticError, "Inversion of singular 4x4 matrix");
674 return inv;
675 }
676
677
679 T det() const
680 {
681 const T *ap;
682 Mat3<T> submat;
683 T det;
684 T *sp;
685 int i, j, k, sign;
686
687 det = 0;
688 sign = 1;
689 for (i = 0; i < 4; i++) {
690 ap = &MyBase::mm[ 0];
691 sp = submat.asPointer();
692 for (j = 0; j < 4; j++) {
693 for (k = 0; k < 4; k++) {
694 if ((k != i) && (j != 0)) {
695 *sp++ = *ap;
696 }
697 ap++;
698 }
699 }
700
701 det += sign * MyBase::mm[i] * submat.det();
702 sign = -sign;
703 }
704
705 return det;
706 }
707
709 static Mat4 translation(const Vec3d& v)
710 {
711 return Mat4(
712 T(1), T(0), T(0), T(0),
713 T(0), T(1), T(0), T(0),
714 T(0), T(0), T(1), T(0),
715 T(v.x()), T(v.y()),T(v.z()), T(1));
716 }
717
719 template <typename T0>
720 void setToTranslation(const Vec3<T0>& v)
721 {
722 MyBase::mm[ 0] = 1;
723 MyBase::mm[ 1] = 0;
724 MyBase::mm[ 2] = 0;
725 MyBase::mm[ 3] = 0;
726
727 MyBase::mm[ 4] = 0;
728 MyBase::mm[ 5] = 1;
729 MyBase::mm[ 6] = 0;
730 MyBase::mm[ 7] = 0;
731
732 MyBase::mm[ 8] = 0;
733 MyBase::mm[ 9] = 0;
734 MyBase::mm[10] = 1;
735 MyBase::mm[11] = 0;
736
737 MyBase::mm[12] = v.x();
738 MyBase::mm[13] = v.y();
739 MyBase::mm[14] = v.z();
740 MyBase::mm[15] = 1;
741 }
742
744 template <typename T0>
745 void preTranslate(const Vec3<T0>& tr)
746 {
747 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
748 Mat4<T> Tr = Mat4<T>::translation(tmp);
749
750 *this = Tr * (*this);
751
752 }
753
755 template <typename T0>
756 void postTranslate(const Vec3<T0>& tr)
757 {
758 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
759 Mat4<T> Tr = Mat4<T>::translation(tmp);
760
761 *this = (*this) * Tr;
762
763 }
764
765
767 template <typename T0>
768 void setToScale(const Vec3<T0>& v)
769 {
770 this->setIdentity();
771 MyBase::mm[ 0] = v.x();
772 MyBase::mm[ 5] = v.y();
773 MyBase::mm[10] = v.z();
774 }
775
776 // Left multiples by the specified scale matrix, i.e. Sc * (*this)
777 template <typename T0>
778 void preScale(const Vec3<T0>& v)
779 {
780 MyBase::mm[ 0] *= v.x();
781 MyBase::mm[ 1] *= v.x();
782 MyBase::mm[ 2] *= v.x();
783 MyBase::mm[ 3] *= v.x();
784
785 MyBase::mm[ 4] *= v.y();
786 MyBase::mm[ 5] *= v.y();
787 MyBase::mm[ 6] *= v.y();
788 MyBase::mm[ 7] *= v.y();
789
790 MyBase::mm[ 8] *= v.z();
791 MyBase::mm[ 9] *= v.z();
792 MyBase::mm[10] *= v.z();
793 MyBase::mm[11] *= v.z();
794 }
795
796
797
798 // Right multiples by the specified scale matrix, i.e. (*this) * Sc
799 template <typename T0>
800 void postScale(const Vec3<T0>& v)
801 {
802
803 MyBase::mm[ 0] *= v.x();
804 MyBase::mm[ 1] *= v.y();
805 MyBase::mm[ 2] *= v.z();
806
807 MyBase::mm[ 4] *= v.x();
808 MyBase::mm[ 5] *= v.y();
809 MyBase::mm[ 6] *= v.z();
810
811 MyBase::mm[ 8] *= v.x();
812 MyBase::mm[ 9] *= v.y();
813 MyBase::mm[10] *= v.z();
814
815 MyBase::mm[12] *= v.x();
816 MyBase::mm[13] *= v.y();
817 MyBase::mm[14] *= v.z();
818
819 }
820
821
825 void setToRotation(Axis axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
826
830 void setToRotation(const Vec3<T>& axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
831
834 void setToRotation(const Vec3<T>& v1, const Vec3<T>& v2) {*this = rotation<Mat4<T> >(v1, v2);}
835
836
840 void preRotate(Axis axis, T angle)
841 {
842 T c = static_cast<T>(cos(angle));
843 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
844
845 switch (axis) {
846 case X_AXIS:
847 {
848 T a4, a5, a6, a7;
849
850 a4 = c * MyBase::mm[ 4] - s * MyBase::mm[ 8];
851 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 9];
852 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[10];
853 a7 = c * MyBase::mm[ 7] - s * MyBase::mm[11];
854
855
856 MyBase::mm[ 8] = s * MyBase::mm[ 4] + c * MyBase::mm[ 8];
857 MyBase::mm[ 9] = s * MyBase::mm[ 5] + c * MyBase::mm[ 9];
858 MyBase::mm[10] = s * MyBase::mm[ 6] + c * MyBase::mm[10];
859 MyBase::mm[11] = s * MyBase::mm[ 7] + c * MyBase::mm[11];
860
861 MyBase::mm[ 4] = a4;
862 MyBase::mm[ 5] = a5;
863 MyBase::mm[ 6] = a6;
864 MyBase::mm[ 7] = a7;
865 }
866 break;
867
868 case Y_AXIS:
869 {
870 T a0, a1, a2, a3;
871
872 a0 = c * MyBase::mm[ 0] + s * MyBase::mm[ 8];
873 a1 = c * MyBase::mm[ 1] + s * MyBase::mm[ 9];
874 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[10];
875 a3 = c * MyBase::mm[ 3] + s * MyBase::mm[11];
876
877 MyBase::mm[ 8] = -s * MyBase::mm[ 0] + c * MyBase::mm[ 8];
878 MyBase::mm[ 9] = -s * MyBase::mm[ 1] + c * MyBase::mm[ 9];
879 MyBase::mm[10] = -s * MyBase::mm[ 2] + c * MyBase::mm[10];
880 MyBase::mm[11] = -s * MyBase::mm[ 3] + c * MyBase::mm[11];
881
882
883 MyBase::mm[ 0] = a0;
884 MyBase::mm[ 1] = a1;
885 MyBase::mm[ 2] = a2;
886 MyBase::mm[ 3] = a3;
887 }
888 break;
889
890 case Z_AXIS:
891 {
892 T a0, a1, a2, a3;
893
894 a0 = c * MyBase::mm[ 0] - s * MyBase::mm[ 4];
895 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 5];
896 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 6];
897 a3 = c * MyBase::mm[ 3] - s * MyBase::mm[ 7];
898
899 MyBase::mm[ 4] = s * MyBase::mm[ 0] + c * MyBase::mm[ 4];
900 MyBase::mm[ 5] = s * MyBase::mm[ 1] + c * MyBase::mm[ 5];
901 MyBase::mm[ 6] = s * MyBase::mm[ 2] + c * MyBase::mm[ 6];
902 MyBase::mm[ 7] = s * MyBase::mm[ 3] + c * MyBase::mm[ 7];
903
904 MyBase::mm[ 0] = a0;
905 MyBase::mm[ 1] = a1;
906 MyBase::mm[ 2] = a2;
907 MyBase::mm[ 3] = a3;
908 }
909 break;
910
911 default:
912 assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
913 }
914 }
915
916
920 void postRotate(Axis axis, T angle)
921 {
922 T c = static_cast<T>(cos(angle));
923 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
924
925
926
927 switch (axis) {
928 case X_AXIS:
929 {
930 T a2, a6, a10, a14;
931
932 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 1];
933 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[ 5];
934 a10 = c * MyBase::mm[10] - s * MyBase::mm[ 9];
935 a14 = c * MyBase::mm[14] - s * MyBase::mm[13];
936
937
938 MyBase::mm[ 1] = c * MyBase::mm[ 1] + s * MyBase::mm[ 2];
939 MyBase::mm[ 5] = c * MyBase::mm[ 5] + s * MyBase::mm[ 6];
940 MyBase::mm[ 9] = c * MyBase::mm[ 9] + s * MyBase::mm[10];
941 MyBase::mm[13] = c * MyBase::mm[13] + s * MyBase::mm[14];
942
943 MyBase::mm[ 2] = a2;
944 MyBase::mm[ 6] = a6;
945 MyBase::mm[10] = a10;
946 MyBase::mm[14] = a14;
947 }
948 break;
949
950 case Y_AXIS:
951 {
952 T a2, a6, a10, a14;
953
954 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[ 0];
955 a6 = c * MyBase::mm[ 6] + s * MyBase::mm[ 4];
956 a10 = c * MyBase::mm[10] + s * MyBase::mm[ 8];
957 a14 = c * MyBase::mm[14] + s * MyBase::mm[12];
958
959 MyBase::mm[ 0] = c * MyBase::mm[ 0] - s * MyBase::mm[ 2];
960 MyBase::mm[ 4] = c * MyBase::mm[ 4] - s * MyBase::mm[ 6];
961 MyBase::mm[ 8] = c * MyBase::mm[ 8] - s * MyBase::mm[10];
962 MyBase::mm[12] = c * MyBase::mm[12] - s * MyBase::mm[14];
963
964 MyBase::mm[ 2] = a2;
965 MyBase::mm[ 6] = a6;
966 MyBase::mm[10] = a10;
967 MyBase::mm[14] = a14;
968 }
969 break;
970
971 case Z_AXIS:
972 {
973 T a1, a5, a9, a13;
974
975 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 0];
976 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 4];
977 a9 = c * MyBase::mm[ 9] - s * MyBase::mm[ 8];
978 a13 = c * MyBase::mm[13] - s * MyBase::mm[12];
979
980 MyBase::mm[ 0] = c * MyBase::mm[ 0] + s * MyBase::mm[ 1];
981 MyBase::mm[ 4] = c * MyBase::mm[ 4] + s * MyBase::mm[ 5];
982 MyBase::mm[ 8] = c * MyBase::mm[ 8] + s * MyBase::mm[ 9];
983 MyBase::mm[12] = c * MyBase::mm[12] + s * MyBase::mm[13];
984
985 MyBase::mm[ 1] = a1;
986 MyBase::mm[ 5] = a5;
987 MyBase::mm[ 9] = a9;
988 MyBase::mm[13] = a13;
989
990 }
991 break;
992
993 default:
994 assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
995 }
996 }
997
1002 void setToShear(Axis axis0, Axis axis1, T shearby)
1003 {
1004 *this = shear<Mat4<T> >(axis0, axis1, shearby);
1005 }
1006
1007
1010 void preShear(Axis axis0, Axis axis1, T shear)
1011 {
1012 int index0 = static_cast<int>(axis0);
1013 int index1 = static_cast<int>(axis1);
1014
1015 // to row "index1" add a multiple of the index0 row
1016 MyBase::mm[index1 * 4 + 0] += shear * MyBase::mm[index0 * 4 + 0];
1017 MyBase::mm[index1 * 4 + 1] += shear * MyBase::mm[index0 * 4 + 1];
1018 MyBase::mm[index1 * 4 + 2] += shear * MyBase::mm[index0 * 4 + 2];
1019 MyBase::mm[index1 * 4 + 3] += shear * MyBase::mm[index0 * 4 + 3];
1020 }
1021
1022
1025 void postShear(Axis axis0, Axis axis1, T shear)
1026 {
1027 int index0 = static_cast<int>(axis0);
1028 int index1 = static_cast<int>(axis1);
1029
1030 // to collumn "index0" add a multiple of the index1 row
1031 MyBase::mm[index0 + 0] += shear * MyBase::mm[index1 + 0];
1032 MyBase::mm[index0 + 4] += shear * MyBase::mm[index1 + 4];
1033 MyBase::mm[index0 + 8] += shear * MyBase::mm[index1 + 8];
1034 MyBase::mm[index0 + 12] += shear * MyBase::mm[index1 + 12];
1035
1036 }
1037
1039 template<typename T0>
1040 Vec4<T0> transform(const Vec4<T0> &v) const
1041 {
1042 return static_cast< Vec4<T0> >(v * *this);
1043 }
1044
1046 template<typename T0>
1047 Vec3<T0> transform(const Vec3<T0> &v) const
1048 {
1049 return static_cast< Vec3<T0> >(v * *this);
1050 }
1051
1053 template<typename T0>
1054 Vec4<T0> pretransform(const Vec4<T0> &v) const
1055 {
1056 return static_cast< Vec4<T0> >(*this * v);
1057 }
1058
1060 template<typename T0>
1061 Vec3<T0> pretransform(const Vec3<T0> &v) const
1062 {
1063 return static_cast< Vec3<T0> >(*this * v);
1064 }
1065
1067 template<typename T0>
1068 Vec3<T0> transformH(const Vec3<T0> &p) const
1069 {
1070 T0 w;
1071
1072 // w = p * (*this).col(3);
1073 w = static_cast<T0>(p[0] * MyBase::mm[ 3] + p[1] * MyBase::mm[ 7]
1074 + p[2] * MyBase::mm[11] + MyBase::mm[15]);
1075
1076 if ( !isExactlyEqual(w , 0.0) ) {
1077 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 4] +
1078 p[2] * MyBase::mm[ 8] + MyBase::mm[12]) / w),
1079 static_cast<T0>((p[0] * MyBase::mm[ 1] + p[1] * MyBase::mm[ 5] +
1080 p[2] * MyBase::mm[ 9] + MyBase::mm[13]) / w),
1081 static_cast<T0>((p[0] * MyBase::mm[ 2] + p[1] * MyBase::mm[ 6] +
1082 p[2] * MyBase::mm[10] + MyBase::mm[14]) / w));
1083 }
1084
1085 return Vec3<T0>(0, 0, 0);
1086 }
1087
1089 template<typename T0>
1090 Vec3<T0> pretransformH(const Vec3<T0> &p) const
1091 {
1092 T0 w;
1093
1094 // w = p * (*this).col(3);
1095 w = p[0] * MyBase::mm[12] + p[1] * MyBase::mm[13] + p[2] * MyBase::mm[14] + MyBase::mm[15];
1096
1097 if ( !isExactlyEqual(w , 0.0) ) {
1098 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 1] +
1099 p[2] * MyBase::mm[ 2] + MyBase::mm[ 3]) / w),
1100 static_cast<T0>((p[0] * MyBase::mm[ 4] + p[1] * MyBase::mm[ 5] +
1101 p[2] * MyBase::mm[ 6] + MyBase::mm[ 7]) / w),
1102 static_cast<T0>((p[0] * MyBase::mm[ 8] + p[1] * MyBase::mm[ 9] +
1103 p[2] * MyBase::mm[10] + MyBase::mm[11]) / w));
1104 }
1105
1106 return Vec3<T0>(0, 0, 0);
1107 }
1108
1110 template<typename T0>
1111 Vec3<T0> transform3x3(const Vec3<T0> &v) const
1112 {
1113 return Vec3<T0>(
1114 static_cast<T0>(v[0] * MyBase::mm[ 0] + v[1] * MyBase::mm[ 4] + v[2] * MyBase::mm[ 8]),
1115 static_cast<T0>(v[0] * MyBase::mm[ 1] + v[1] * MyBase::mm[ 5] + v[2] * MyBase::mm[ 9]),
1116 static_cast<T0>(v[0] * MyBase::mm[ 2] + v[1] * MyBase::mm[ 6] + v[2] * MyBase::mm[10]));
1117 }
1118
1119
1120 private:
1121 bool invert(Mat4<T> &inverse, T tolerance) const;
1122
1123 T det2(const Mat4<T> &a, int i0, int i1, int j0, int j1) const {
1124 int i0row = i0 * 4;
1125 int i1row = i1 * 4;
1126 return a.mm[i0row+j0]*a.mm[i1row+j1] - a.mm[i0row+j1]*a.mm[i1row+j0];
1127 }
1128
1129 T det3(const Mat4<T> &a, int i0, int i1, int i2,
1130 int j0, int j1, int j2) const {
1131 int i0row = i0 * 4;
1132 return a.mm[i0row+j0]*det2(a, i1,i2, j1,j2) +
1133 a.mm[i0row+j1]*det2(a, i1,i2, j2,j0) +
1134 a.mm[i0row+j2]*det2(a, i1,i2, j0,j1);
1135 }
1136
1137 static const Mat4<T> sIdentity;
1138 static const Mat4<T> sZero;
1139 }; // class Mat4
1140
1141
1142 template <typename T>
1143 const Mat4<T> Mat4<T>::sIdentity = Mat4<T>(1, 0, 0, 0,
1144 0, 1, 0, 0,
1145 0, 0, 1, 0,
1146 0, 0, 0, 1);
1147
1148 template <typename T>
1149 const Mat4<T> Mat4<T>::sZero = Mat4<T>(0, 0, 0, 0,
1150 0, 0, 0, 0,
1151 0, 0, 0, 0,
1152 0, 0, 0, 0);
1153
1156 template <typename T0, typename T1>
1157 bool operator==(const Mat4<T0> &m0, const Mat4<T1> &m1)
1158 {
1159 const T0 *t0 = m0.asPointer();
1160 const T1 *t1 = m1.asPointer();
1161
1162 for (int i=0; i<16; ++i) if (!isExactlyEqual(t0[i], t1[i])) return false;
1163 return true;
1164 }
1165
1168 template <typename T0, typename T1>
1169 bool operator!=(const Mat4<T0> &m0, const Mat4<T1> &m1) { return !(m0 == m1); }
1170
1173 template <typename S, typename T>
1174 Mat4<typename promote<S, T>::type> operator*(S scalar, const Mat4<T> &m)
1175 {
1176 return m*scalar;
1177 }
1178
1181 template <typename S, typename T>
1182 Mat4<typename promote<S, T>::type> operator*(const Mat4<T> &m, S scalar)
1183 {
1184 Mat4<typename promote<S, T>::type> result(m);
1185 result *= scalar;
1186 return result;
1187 }
1188
1191 template<typename T, typename MT>
1192 inline Vec4<typename promote<T, MT>::type>
1193 operator*(const Mat4<MT> &_m,
1194 const Vec4<T> &_v)
1195 {
1196 MT const *m = _m.asPointer();
1197 return Vec4<typename promote<T, MT>::type>(
1198 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + _v[3]*m[3],
1199 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + _v[3]*m[7],
1200 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + _v[3]*m[11],
1201 _v[0]*m[12] + _v[1]*m[13] + _v[2]*m[14] + _v[3]*m[15]);
1202 }
1203
1206 template<typename T, typename MT>
1207 inline Vec4<typename promote<T, MT>::type>
1208 operator*(const Vec4<T> &_v,
1209 const Mat4<MT> &_m)
1210 {
1211 MT const *m = _m.asPointer();
1212 return Vec4<typename promote<T, MT>::type>(
1213 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + _v[3]*m[12],
1214 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + _v[3]*m[13],
1215 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + _v[3]*m[14],
1216 _v[0]*m[3] + _v[1]*m[7] + _v[2]*m[11] + _v[3]*m[15]);
1217 }
1218
1222 template<typename T, typename MT>
1223 inline Vec3<typename promote<T, MT>::type>
1224 operator*(const Mat4<MT> &_m,
1225 const Vec3<T> &_v)
1226 {
1227 MT const *m = _m.asPointer();
1228 return Vec3<typename promote<T, MT>::type>(
1229 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + m[3],
1230 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + m[7],
1231 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + m[11]);
1232 }
1233
1237 template<typename T, typename MT>
1238 inline Vec3<typename promote<T, MT>::type>
1239 operator*(const Vec3<T> &_v,
1240 const Mat4<MT> &_m)
1241 {
1242 MT const *m = _m.asPointer();
1243 return Vec3<typename promote<T, MT>::type>(
1244 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + m[12],
1245 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + m[13],
1246 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + m[14]);
1247 }
1248
1251 template <typename T0, typename T1>
1252 Mat4<typename promote<T0, T1>::type>
1253 operator+(const Mat4<T0> &m0, const Mat4<T1> &m1)
1254 {
1255 Mat4<typename promote<T0, T1>::type> result(m0);
1256 result += m1;
1257 return result;
1258 }
1259
1262 template <typename T0, typename T1>
1263 Mat4<typename promote<T0, T1>::type>
1264 operator-(const Mat4<T0> &m0, const Mat4<T1> &m1)
1265 {
1266 Mat4<typename promote<T0, T1>::type> result(m0);
1267 result -= m1;
1268 return result;
1269 }
1270
1274 template <typename T0, typename T1>
1275 Mat4<typename promote<T0, T1>::type>
1276 operator*(const Mat4<T0> &m0, const Mat4<T1> &m1)
1277 {
1278 Mat4<typename promote<T0, T1>::type> result(m0);
1279 result *= m1;
1280 return result;
1281 }
1282
1283
1287 template<typename T0, typename T1>
1288 Vec3<T1> transformNormal(const Mat4<T0> &m, const Vec3<T1> &n)
1289 {
1290 return Vec3<T1>(
1291 static_cast<T1>(m[0][0]*n[0] + m[0][1]*n[1] + m[0][2]*n[2]),
1292 static_cast<T1>(m[1][0]*n[0] + m[1][1]*n[1] + m[1][2]*n[2]),
1293 static_cast<T1>(m[2][0]*n[0] + m[2][1]*n[1] + m[2][2]*n[2]));
1294 }
1295
1296
1298 template<typename T>
1299 bool Mat4<T>::invert(Mat4<T> &inverse, T tolerance) const
1300 {
1301 Mat4<T> temp(*this);
1302 inverse.setIdentity();
1303
1304 // Forward elimination step
1305 double det = 1.0;
1306 for (int i = 0; i < 4; ++i) {
1307 int row = i;
1308 double max = fabs(temp[i][i]);
1309
1310 for (int k = i+1; k < 4; ++k) {
1311 if (fabs(temp[k][i]) > max) {
1312 row = k;
1313 max = fabs(temp[k][i]);
1314 }
1315 }
1316
1317 if (isExactlyEqual(max, 0.0)) return false;
1318
1319 // must move pivot to row i
1320 if (row != i) {
1321 det = -det;
1322 for (int k = 0; k < 4; ++k) {
1323 std::swap(temp[row][k], temp[i][k]);
1324 std::swap(inverse[row][k], inverse[i][k]);
1325 }
1326 }
1327
1328 double pivot = temp[i][i];
1329 det *= pivot;
1330
1331 // scale row i
1332 for (int k = 0; k < 4; ++k) {
1333 temp[i][k] /= pivot;
1334 inverse[i][k] /= pivot;
1335 }
1336
1337 // eliminate in rows below i
1338 for (int j = i+1; j < 4; ++j) {
1339 double t = temp[j][i];
1340 if (!isExactlyEqual(t, 0.0)) {
1341 // subtract scaled row i from row j
1342 for (int k = 0; k < 4; ++k) {
1343 temp[j][k] -= temp[i][k] * t;
1344 inverse[j][k] -= inverse[i][k] * t;
1345 }
1346 }
1347 }
1348 }
1349
1350 // Backward elimination step
1351 for (int i = 3; i > 0; --i) {
1352 for (int j = 0; j < i; ++j) {
1353 double t = temp[j][i];
1354
1355 if (!isExactlyEqual(t, 0.0)) {
1356 for (int k = 0; k < 4; ++k) {
1357 inverse[j][k] -= inverse[i][k]*t;
1358 }
1359 }
1360 }
1361 }
1362 return det*det >= tolerance*tolerance;
1363 }
1364
1365 template <typename T>
1366 inline bool isAffine(const Mat4<T>& m) {
1367 return (m.col(3) == Vec4<T>(0, 0, 0, 1));
1368 }
1369
1370 template <typename T>
1371 inline bool hasTranslation(const Mat4<T>& m) {
1372 return (m.row(3) != Vec4<T>(0, 0, 0, 1));
1373 }
1374
1375
1376 typedef Mat4<float> Mat4s;
1377 typedef Mat4<double> Mat4d;
1378
1379 #if DWREAL_IS_DOUBLE == 1
1380 typedef Mat4d Mat4f;
1381 #else
1382 typedef Mat4s Mat4f;
1383 #endif // DWREAL_IS_DOUBLE
1384
1385 } // namespace math
1386
1387
1388 template<> inline math::Mat4s zeroVal<math::Mat4s>() { return math::Mat4s::identity(); }
1389 template<> inline math::Mat4d zeroVal<math::Mat4d>() { return math::Mat4d::identity(); }
1390
1391 } // namespace OPENVDB_VERSION_NAME
1392 } // namespace openvdb
1393
1394 #endif // OPENVDB_UTIL_MAT4_H_HAS_BEEN_INCLUDED
1395
1396 // Copyright (c) 2012-2016 DreamWorks Animation LLC
1397 // All rights reserved. This software is distributed under the
1398 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v3_2_0::math::Mat4::setZero
void setZero()
Definition: Mat4.h:286
openvdb::v3_2_0::math::Mat4::postShear
void postShear(Axis axis0, Axis axis1, T shear)
Right multiplies a shearing transformation into the matrix.
Definition: Mat4.h:1025
openvdb::v3_2_0::math::Mat4::preShear
void preShear(Axis axis0, Axis axis1, T shear)
Left multiplies a shearing transformation into the matrix.
Definition: Mat4.h:1010
openvdb::v3_2_0::math::Mat4::operator-
Mat4< typename promote< T0, T1 >::type > operator-(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Returns M, where for .
Definition: Mat4.h:1264
openvdb::v3_2_0::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:203
openvdb::v3_2_0::math::Mat4::operator=
const Mat4 & operator=(const Mat4< Source > &m)
Assignment operator.
Definition: Mat4.h:365
openvdb::v3_2_0::math::Mat4::Mat4
Mat4(const Vec4< Source > &v1, const Vec4< Source > &v2, const Vec4< Source > &v3, const Vec4< Source > &v4, bool rows=true)
Definition: Mat4.h:120
OPENVDB_DEPRECATED
#define OPENVDB_DEPRECATED
Definition: Platform.h:49
Vec3.h
openvdb::v3_2_0::math::Vec3::z
T & z()
Definition: Vec3.h:99
openvdb::v3_2_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:407
openvdb::v3_2_0::math::Mat4::postScale
void postScale(const Vec3< T0 > &v)
Definition: Mat4.h:800
openvdb::v3_2_0::math::Mat4::setToRotation
void setToRotation(Axis axis, T angle)
Sets the matrix to a rotation about the given axis.
Definition: Mat4.h:825
openvdb::v3_2_0::math::Mat4::setRow
void setRow(int i, const Vec4< T > &v)
Set ith row to vector v.
Definition: Mat4.h:162
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v3_2_0::math::Mat4::pretransformH
Vec3< T0 > pretransformH(const Vec3< T0 > &p) const
Transform a Vec3 by pre-multiplication, doing homogenous division.
Definition: Mat4.h:1090
openvdb::v3_2_0::math::X_AXIS
Definition: Math.h:857
openvdb::v3_2_0::math::Mat4::operator[]
const T * operator[](int i) const
Definition: Mat4.h:200
openvdb::v3_2_0::math::Mat4::operator*=
const Mat4< T > & operator*=(const Mat4< S > &m1)
Return m, where for .
Definition: Mat4.h:481
openvdb::v3_2_0::math::Mat4::identity
static const Mat4< T > & identity()
Predefined constant for identity matrix.
Definition: Mat4.h:152
openvdb::v3_2_0::math::Vec3
Definition: Mat.h:146
openvdb::v3_2_0::math::Mat4::Mat4
Mat4(const Mat< 4, T > &m)
Copy constructor.
Definition: Mat4.h:131
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:97
openvdb::v3_2_0::math::Mat::mm
T mm[SIZE *SIZE]
Definition: Mat.h:141
openvdb::v3_2_0::math::Mat4::operator()
T operator()(int i, int j) const
Definition: Mat4.h:220
openvdb::v3_2_0::math::Mat4::eq
bool eq(const Mat4 &m, T eps=1.0e-8) const
Test if "this" is equivalent to m with tolerance of eps value.
Definition: Mat4.h:375
openvdb::v3_2_0::ArithmeticError
Definition: Exceptions.h:78
openvdb::v3_2_0::math::Mat4::asPointer
T * asPointer()
Direct access to the internal data.
Definition: Mat4.h:204
openvdb::v3_2_0::math::Mat4::setIdentity
void setIdentity()
Set "this" matrix to identity.
Definition: Mat4.h:307
openvdb::v3_2_0::math::Mat4::operator*
Vec3< typename promote< T, MT >::type > operator*(const Vec3< T > &_v, const Mat4< MT > &_m)
Returns v, where for .
Definition: Mat4.h:1239
openvdb::v3_2_0::math::Mat4::det
T det() const
Determinant of matrix.
Definition: Mat4.h:679
openvdb::v3_2_0::math::Mat4::operator*
Mat4< typename promote< S, T >::type > operator*(S scalar, const Mat4< T > &m)
Returns M, where for .
Definition: Mat4.h:1174
openvdb::v3_2_0::math::Y_AXIS
Definition: Math.h:858
openvdb::v3_2_0::math::shear
MatType shear(Axis axis0, Axis axis1, typename MatType::value_type shear)
Set the matrix to a shear along axis0 by a fraction of axis1.
Definition: Mat.h:667
openvdb::v3_2_0::math::Mat4::setColumns
void setColumns(const Vec4< T > &v1, const Vec4< T > &v2, const Vec4< T > &v3, const Vec4< T > &v4)
Set the columns of "this" matrix to the vectors v1, v2, v3, v4.
Definition: Mat4.h:253
openvdb::v3_2_0::math::Mat4::ValueType
T ValueType
Definition: Mat4.h:62
openvdb::v3_2_0::math::Mat4::setBasis
OPENVDB_DEPRECATED void setBasis(const Vec4< T > &v1, const Vec4< T > &v2, const Vec4< T > &v3, const Vec4< T > &v4)
Set the rows of "this" matrix to the vectors v1, v2, v3, v4.
Definition: Mat4.h:278
openvdb::v3_2_0::tools::composite::max
const boost::disable_if_c< VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:132
openvdb::v3_2_0::math::Mat4::transformH
Vec3< T0 > transformH(const Vec3< T0 > &p) const
Transform a Vec3 by post-multiplication, doing homogenous divison.
Definition: Mat4.h:1068
Mat3.h
openvdb::v3_2_0::math::Mat4f
Mat4s Mat4f
Definition: Mat4.h:1382
openvdb::v3_2_0::math::Mat4::preRotate
void preRotate(Axis axis, T angle)
Left multiplies by a rotation clock-wiseabout the given axis into this matrix.
Definition: Mat4.h:840
openvdb::v3_2_0::math::Mat4
4x4 -matrix class.
Definition: Mat3.h:48
openvdb::v3_2_0::math::Mat4::preTranslate
void preTranslate(const Vec3< T0 > &tr)
Left multiples by the specified translation, i.e. Trans * (*this)
Definition: Mat4.h:745
openvdb::v3_2_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:370
openvdb::v3_2_0::math::Mat4::operator*
Vec4< typename promote< T, MT >::type > operator*(const Vec4< T > &_v, const Mat4< MT > &_m)
Returns v, where for .
Definition: Mat4.h:1208
openvdb::v3_2_0::math::Mat4::operator+=
const Mat4< T > & operator+=(const Mat4< S > &m1)
Returns m0, where for .
Definition: Mat4.h:423
openvdb::v3_2_0::math::Mat4::Mat4
Mat4(Source *a)
Constructor given array of elements, the ordering is in row major form:
Definition: Mat4.h:76
Exceptions.h
openvdb::v3_2_0::math::Mat4::pretransform
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Transform a Vec3 by pre-multiplication, without homogenous division.
Definition: Mat4.h:1061
openvdb::v3_2_0::math::Mat4::setToScale
void setToScale(const Vec3< T0 > &v)
Sets the matrix to a matrix that scales by v.
Definition: Mat4.h:768
openvdb::v3_2_0::math::Mat4::inverse
Mat4 inverse(T tolerance=0) const
Definition: Mat4.h:527
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
Definition: version.h:43
openvdb::v3_2_0::math::Mat4::transpose
Mat4 transpose() const
Definition: Mat4.h:514
openvdb::v3_2_0::math::Mat4::setMat3
void setMat3(const Mat3< T > &m)
Set upper left to a Mat3.
Definition: Mat4.h:332
openvdb::v3_2_0::math::Mat4::operator==
bool operator==(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat4.h:1157
openvdb::v3_2_0::math::Mat4::postRotate
void postRotate(Axis axis, T angle)
Right multiplies by a rotation clock-wiseabout the given axis into this matrix.
Definition: Mat4.h:920
openvdb::v3_2_0::math::Mat4::Mat4
Mat4(Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i, Source j, Source k, Source l, Source m, Source n, Source o, Source p)
Constructor given array of elements, the ordering is in row major form:
Definition: Mat4.h:91
openvdb::v3_2_0::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:97
openvdb::v3_2_0::math::isAffine
bool isAffine(const Mat4< T > &m)
Definition: Mat4.h:1366
openvdb
Definition: Exceptions.h:39
openvdb::v3_2_0::math::Mat4::transform
Vec3< T0 > transform(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without homogenous division.
Definition: Mat4.h:1047
openvdb::v3_2_0::math::Mat4::row
Vec4< T > row(int i) const
Get ith row, e.g. Vec4f v = m.row(1);.
Definition: Mat4.h:173
openvdb::v3_2_0::math::Mat3
3x3 matrix class.
Definition: Mat3.h:54
openvdb::v3_2_0::math::Mat4::setToShear
void setToShear(Axis axis0, Axis axis1, T shearby)
Sets the matrix to a shear along axis0 by a fraction of axis1.
Definition: Mat4.h:1002
openvdb::v3_2_0::math::Mat4::value_type
T value_type
Data type held by the matrix.
Definition: Mat4.h:61
openvdb::v3_2_0::math::Mat4::operator-=
const Mat4< T > & operator-=(const Mat4< S > &m1)
Returns m0, where for .
Definition: Mat4.h:452
openvdb::v3_2_0::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:446
openvdb::v3_2_0::math::Mat4s
Mat4< float > Mat4s
Definition: Mat4.h:1376
openvdb::v3_2_0::math::Mat4::getMat3
Mat3< T > getMat3() const
Definition: Mat4.h:339
openvdb::v3_2_0::math::Mat4::operator()
T & operator()(int i, int j)
Definition: Mat4.h:210
openvdb::v3_2_0::math::Mat4::setToRotation
void setToRotation(const Vec3< T > &v1, const Vec3< T > &v2)
Sets the matrix to a rotation that maps v1 onto v2 about the cross product of v1 and v2...
Definition: Mat4.h:834
openvdb::v3_2_0::math::Mat4::MyBase
Mat< 4, T > MyBase
Definition: Mat4.h:63
openvdb::v3_2_0::math::Mat4::operator*=
const Mat4< T > & operator*=(S scalar)
Return m, where for .
Definition: Mat4.h:397
openvdb::v3_2_0::math::Z_AXIS
Definition: Math.h:859
openvdb::v3_2_0::math::Mat4::setTranslation
void setTranslation(const Vec3< T > &t)
Definition: Mat4.h:356
openvdb::v3_2_0::math::Mat4d
Mat4< double > Mat4d
Definition: Mat4.h:1377
openvdb::v3_2_0::math::Mat4::pretransform
Vec4< T0 > pretransform(const Vec4< T0 > &v) const
Transform a Vec4 by pre-multiplication.
Definition: Mat4.h:1054
openvdb::v3_2_0::math::Vec3::y
T & y()
Definition: Vec3.h:98
openvdb::v3_2_0::math::Mat4::setToRotation
void setToRotation(const Vec3< T > &axis, T angle)
Sets the matrix to a rotation about an arbitrary axis.
Definition: Mat4.h:830
openvdb::v3_2_0::math::Mat4::translation
static Mat4 translation(const Vec3d &v)
Sets the matrix to a matrix that translates by v.
Definition: Mat4.h:709
openvdb::v3_2_0::math::Mat4::zero
static const Mat4< T > & zero()
Predefined constant for zero matrix.
Definition: Mat4.h:157
openvdb::v3_2_0::math::hasTranslation
bool hasTranslation(const Mat4< T > &m)
Definition: Mat4.h:1371
openvdb::v3_2_0::math::Mat4::asPointer
const T * asPointer() const
Definition: Mat4.h:205
openvdb::v3_2_0::math::Mat4::Mat4
Mat4()
Trivial constructor, the matrix is NOT initialized.
Definition: Mat4.h:66
openvdb::v3_2_0::math::Mat4::operator*
Vec4< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec4< T > &_v)
Returns v, where for .
Definition: Mat4.h:1193
openvdb::v3_2_0::math::Mat4::transform3x3
Vec3< T0 > transform3x3(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without translation.
Definition: Mat4.h:1111
openvdb::v3_2_0::math::Mat4::operator*
Mat4< typename promote< T0, T1 >::type > operator*(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Returns M, where for .
Definition: Mat4.h:1276
openvdb::v3_2_0::math::Mat4::operator*
Vec3< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec3< T > &_v)
Returns v, where for .
Definition: Mat4.h:1224
openvdb::v3_2_0::math::Mat4::operator+
Mat4< typename promote< T0, T1 >::type > operator+(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Returns M, where for .
Definition: Mat4.h:1253
openvdb::v3_2_0::math::Mat4::setToTranslation
void setToTranslation(const Vec3< T0 > &v)
Sets the matrix to a matrix that translates by v.
Definition: Mat4.h:720
openvdb::v3_2_0::math::Axis
Axis
Definition: Math.h:856
openvdb::v3_2_0::math::Mat4::setCol
void setCol(int j, const Vec4< T > &v)
Set jth column to vector v.
Definition: Mat4.h:180
openvdb::v3_2_0::math::Mat4::operator*
Mat4< typename promote< S, T >::type > operator*(const Mat4< T > &m, S scalar)
Returns M, where for .
Definition: Mat4.h:1182
openvdb::v3_2_0::math::Mat3::det
T det() const
Determinant of matrix.
Definition: Mat3.h:523
openvdb::v3_2_0::math::Mat4::col
Vec4< T > col(int j) const
Get jth column, e.g. Vec4f v = m.col(0);.
Definition: Mat4.h:190
openvdb::v3_2_0::math::Mat4::operator-
Mat4< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition: Mat4.h:385
openvdb::v3_2_0::math::Mat4::transform
Vec4< T0 > transform(const Vec4< T0 > &v) const
Transform a Vec4 by post-multiplication.
Definition: Mat4.h:1040
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:71
openvdb::v3_2_0::math::Mat
Definition: Mat.h:52
openvdb::v3_2_0::math::Mat4::setRows
void setRows(const Vec4< T > &v1, const Vec4< T > &v2, const Vec4< T > &v3, const Vec4< T > &v4)
Set the rows of "this" matrix to the vectors v1, v2, v3, v4.
Definition: Mat4.h:228
openvdb::v3_2_0::math::Mat4::getTranslation
Vec3< T > getTranslation() const
Return the translation component.
Definition: Mat4.h:351
openvdb::v3_2_0::math::Mat4::Mat4
Mat4(const Mat4< Source > &m)
Conversion constructor.
Definition: Mat4.h:142
openvdb::v3_2_0::math::Mat4::preScale
void preScale(const Vec3< T0 > &v)
Definition: Mat4.h:778
openvdb::v3_2_0::math::Mat4::postTranslate
void postTranslate(const Vec3< T0 > &tr)
Right multiplies by the specified translation matrix, i.e. (*this) * Trans.
Definition: Mat4.h:756
openvdb::v3_2_0::math::Vec4
Definition: Mat4.h:51
openvdb::v3_2_0::math::Mat4::operator!=
bool operator!=(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition: Mat4.h:1169
Platform.h
openvdb::v3_2_0::math::Mat3::asPointer
T * asPointer()
Definition: Mat3.h:208
Vec4.h
openvdb::v3_2_0::math::transformNormal
Vec3< T1 > transformNormal(const Mat4< T0 > &m, const Vec3< T1 > &n)
Definition: Mat4.h:1288