OpenVDB 5.1.0

Mat4.h
Go to the documentation of this file.
1 //
3 // Copyright (c) 2012-2018 DreamWorks Animation LLC
4 //
5 // All rights reserved. This software is distributed under the
6 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
7 //
8 // Redistributions of source code must retain the above copyright
9 // and license notice and the following restrictions and disclaimer.
10 //
11 // * Neither the name of DreamWorks Animation nor the names of
12 // its contributors may be used to endorse or promote products derived
13 // from this software without specific prior written permission.
14 //
15 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
16 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
17 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
18 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
19 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
20 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
21 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
25 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 // IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
27 // LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
28 //
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 "Math.h"
37 #include "Mat3.h"
38 #include "Vec3.h"
39 #include "Vec4.h"
40 #include <algorithm> // for std::copy(), std::swap()
41 #include <cassert>
42 #include <iomanip>
43 #include <cmath>
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 using value_type = T;
62 using ValueType = T;
63 using MyBase = Mat<4, T>;
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 static const Mat4<T> sIdentity = Mat4<T>(
154 1, 0, 0, 0,
155 0, 1, 0, 0,
156 0, 0, 1, 0,
157 0, 0, 0, 1
158 );
159 return sIdentity;
160 }
161
163 static const Mat4<T>& zero() {
164 static const Mat4<T> sZero = Mat4<T>(
165 0, 0, 0, 0,
166 0, 0, 0, 0,
167 0, 0, 0, 0,
168 0, 0, 0, 0
169 );
170 return sZero;
171 }
172
174 void setRow(int i, const Vec4<T> &v)
175 {
176 // assert(i>=0 && i<4);
177 int i4 = i * 4;
178 MyBase::mm[i4+0] = v[0];
179 MyBase::mm[i4+1] = v[1];
180 MyBase::mm[i4+2] = v[2];
181 MyBase::mm[i4+3] = v[3];
182 }
183
185 Vec4<T> row(int i) const
186 {
187 // assert(i>=0 && i<3);
188 return Vec4<T>((*this)(i,0), (*this)(i,1), (*this)(i,2), (*this)(i,3));
189 }
190
192 void setCol(int j, const Vec4<T>& v)
193 {
194 // assert(j>=0 && j<4);
195 MyBase::mm[ 0+j] = v[0];
196 MyBase::mm[ 4+j] = v[1];
197 MyBase::mm[ 8+j] = v[2];
198 MyBase::mm[12+j] = v[3];
199 }
200
202 Vec4<T> col(int j) const
203 {
204 // assert(j>=0 && j<4);
205 return Vec4<T>((*this)(0,j), (*this)(1,j), (*this)(2,j), (*this)(3,j));
206 }
207
209 T* operator[](int i) { return &(MyBase::mm[i<<2]); }
212 const T* operator[](int i) const { return &(MyBase::mm[i<<2]); }
214
216 T* asPointer() {return MyBase::mm;}
217 const T* asPointer() const {return MyBase::mm;}
218
222 T& operator()(int i, int j)
223 {
224 // assert(i>=0 && i<4);
225 // assert(j>=0 && j<4);
226 return MyBase::mm[4*i+j];
227 }
228
232 T operator()(int i, int j) const
233 {
234 // assert(i>=0 && i<4);
235 // assert(j>=0 && j<4);
236 return MyBase::mm[4*i+j];
237 }
238
240 void setRows(const Vec4<T> &v1, const Vec4<T> &v2,
241 const Vec4<T> &v3, const Vec4<T> &v4)
242 {
243 MyBase::mm[ 0] = v1[0];
244 MyBase::mm[ 1] = v1[1];
245 MyBase::mm[ 2] = v1[2];
246 MyBase::mm[ 3] = v1[3];
247
248 MyBase::mm[ 4] = v2[0];
249 MyBase::mm[ 5] = v2[1];
250 MyBase::mm[ 6] = v2[2];
251 MyBase::mm[ 7] = v2[3];
252
253 MyBase::mm[ 8] = v3[0];
254 MyBase::mm[ 9] = v3[1];
255 MyBase::mm[10] = v3[2];
256 MyBase::mm[11] = v3[3];
257
258 MyBase::mm[12] = v4[0];
259 MyBase::mm[13] = v4[1];
260 MyBase::mm[14] = v4[2];
261 MyBase::mm[15] = v4[3];
262 }
263
265 void setColumns(const Vec4<T> &v1, const Vec4<T> &v2,
266 const Vec4<T> &v3, const Vec4<T> &v4)
267 {
268 MyBase::mm[ 0] = v1[0];
269 MyBase::mm[ 1] = v2[0];
270 MyBase::mm[ 2] = v3[0];
271 MyBase::mm[ 3] = v4[0];
272
273 MyBase::mm[ 4] = v1[1];
274 MyBase::mm[ 5] = v2[1];
275 MyBase::mm[ 6] = v3[1];
276 MyBase::mm[ 7] = v4[1];
277
278 MyBase::mm[ 8] = v1[2];
279 MyBase::mm[ 9] = v2[2];
280 MyBase::mm[10] = v3[2];
281 MyBase::mm[11] = v4[2];
282
283 MyBase::mm[12] = v1[3];
284 MyBase::mm[13] = v2[3];
285 MyBase::mm[14] = v3[3];
286 MyBase::mm[15] = v4[3];
287 }
288
289 // Set this matrix to zero
290 void setZero()
291 {
292 MyBase::mm[ 0] = 0;
293 MyBase::mm[ 1] = 0;
294 MyBase::mm[ 2] = 0;
295 MyBase::mm[ 3] = 0;
296 MyBase::mm[ 4] = 0;
297 MyBase::mm[ 5] = 0;
298 MyBase::mm[ 6] = 0;
299 MyBase::mm[ 7] = 0;
300 MyBase::mm[ 8] = 0;
301 MyBase::mm[ 9] = 0;
302 MyBase::mm[10] = 0;
303 MyBase::mm[11] = 0;
304 MyBase::mm[12] = 0;
305 MyBase::mm[13] = 0;
306 MyBase::mm[14] = 0;
307 MyBase::mm[15] = 0;
308 }
309
311 void setIdentity()
312 {
313 MyBase::mm[ 0] = 1;
314 MyBase::mm[ 1] = 0;
315 MyBase::mm[ 2] = 0;
316 MyBase::mm[ 3] = 0;
317
318 MyBase::mm[ 4] = 0;
319 MyBase::mm[ 5] = 1;
320 MyBase::mm[ 6] = 0;
321 MyBase::mm[ 7] = 0;
322
323 MyBase::mm[ 8] = 0;
324 MyBase::mm[ 9] = 0;
325 MyBase::mm[10] = 1;
326 MyBase::mm[11] = 0;
327
328 MyBase::mm[12] = 0;
329 MyBase::mm[13] = 0;
330 MyBase::mm[14] = 0;
331 MyBase::mm[15] = 1;
332 }
333
334
336 void setMat3(const Mat3<T> &m)
337 {
338 for (int i = 0; i < 3; i++)
339 for (int j=0; j < 3; j++)
340 MyBase::mm[i*4+j] = m[i][j];
341 }
342
343 Mat3<T> getMat3() const
344 {
345 Mat3<T> m;
346
347 for (int i = 0; i < 3; i++)
348 for (int j = 0; j < 3; j++)
349 m[i][j] = MyBase::mm[i*4+j];
350
351 return m;
352 }
353
355 Vec3<T> getTranslation() const
356 {
357 return Vec3<T>(MyBase::mm[12], MyBase::mm[13], MyBase::mm[14]);
358 }
359
360 void setTranslation(const Vec3<T> &t)
361 {
362 MyBase::mm[12] = t[0];
363 MyBase::mm[13] = t[1];
364 MyBase::mm[14] = t[2];
365 }
366
368 template<typename Source>
369 const Mat4& operator=(const Mat4<Source> &m)
370 {
371 const Source *src = m.asPointer();
372
373 // don't suppress warnings when assigning from different numerical types
374 std::copy(src, (src + this->numElements()), MyBase::mm);
375 return *this;
376 }
377
379 bool eq(const Mat4 &m, T eps=1.0e-8) const
380 {
381 for (int i = 0; i < 16; i++) {
382 if (!isApproxEqual(MyBase::mm[i], m.mm[i], eps))
383 return false;
384 }
385 return true;
386 }
387
389 Mat4<T> operator-() const
390 {
391 return Mat4<T>(
392 -MyBase::mm[ 0], -MyBase::mm[ 1], -MyBase::mm[ 2], -MyBase::mm[ 3],
393 -MyBase::mm[ 4], -MyBase::mm[ 5], -MyBase::mm[ 6], -MyBase::mm[ 7],
394 -MyBase::mm[ 8], -MyBase::mm[ 9], -MyBase::mm[10], -MyBase::mm[11],
395 -MyBase::mm[12], -MyBase::mm[13], -MyBase::mm[14], -MyBase::mm[15]
396 );
397 } // trivial
398
400 template <typename S>
401 const Mat4<T>& operator*=(S scalar)
402 {
403 MyBase::mm[ 0] *= scalar;
404 MyBase::mm[ 1] *= scalar;
405 MyBase::mm[ 2] *= scalar;
406 MyBase::mm[ 3] *= scalar;
407
408 MyBase::mm[ 4] *= scalar;
409 MyBase::mm[ 5] *= scalar;
410 MyBase::mm[ 6] *= scalar;
411 MyBase::mm[ 7] *= scalar;
412
413 MyBase::mm[ 8] *= scalar;
414 MyBase::mm[ 9] *= scalar;
415 MyBase::mm[10] *= scalar;
416 MyBase::mm[11] *= scalar;
417
418 MyBase::mm[12] *= scalar;
419 MyBase::mm[13] *= scalar;
420 MyBase::mm[14] *= scalar;
421 MyBase::mm[15] *= scalar;
422 return *this;
423 }
424
426 template <typename S>
427 const Mat4<T> &operator+=(const Mat4<S> &m1)
428 {
429 const S* s = m1.asPointer();
430
431 MyBase::mm[ 0] += s[ 0];
432 MyBase::mm[ 1] += s[ 1];
433 MyBase::mm[ 2] += s[ 2];
434 MyBase::mm[ 3] += s[ 3];
435
436 MyBase::mm[ 4] += s[ 4];
437 MyBase::mm[ 5] += s[ 5];
438 MyBase::mm[ 6] += s[ 6];
439 MyBase::mm[ 7] += s[ 7];
440
441 MyBase::mm[ 8] += s[ 8];
442 MyBase::mm[ 9] += s[ 9];
443 MyBase::mm[10] += s[10];
444 MyBase::mm[11] += s[11];
445
446 MyBase::mm[12] += s[12];
447 MyBase::mm[13] += s[13];
448 MyBase::mm[14] += s[14];
449 MyBase::mm[15] += s[15];
450
451 return *this;
452 }
453
455 template <typename S>
456 const Mat4<T> &operator-=(const Mat4<S> &m1)
457 {
458 const S* s = m1.asPointer();
459
460 MyBase::mm[ 0] -= s[ 0];
461 MyBase::mm[ 1] -= s[ 1];
462 MyBase::mm[ 2] -= s[ 2];
463 MyBase::mm[ 3] -= s[ 3];
464
465 MyBase::mm[ 4] -= s[ 4];
466 MyBase::mm[ 5] -= s[ 5];
467 MyBase::mm[ 6] -= s[ 6];
468 MyBase::mm[ 7] -= s[ 7];
469
470 MyBase::mm[ 8] -= s[ 8];
471 MyBase::mm[ 9] -= s[ 9];
472 MyBase::mm[10] -= s[10];
473 MyBase::mm[11] -= s[11];
474
475 MyBase::mm[12] -= s[12];
476 MyBase::mm[13] -= s[13];
477 MyBase::mm[14] -= s[14];
478 MyBase::mm[15] -= s[15];
479
480 return *this;
481 }
482
484 template <typename S>
485 const Mat4<T> &operator*=(const Mat4<S> &m1)
486 {
487 Mat4<T> m0(*this);
488
489 const T* s0 = m0.asPointer();
490 const S* s1 = m1.asPointer();
491
492 for (int i = 0; i < 4; i++) {
493 int i4 = 4 * i;
494 MyBase::mm[i4+0] = static_cast<T>(s0[i4+0] * s1[ 0] +
495 s0[i4+1] * s1[ 4] +
496 s0[i4+2] * s1[ 8] +
497 s0[i4+3] * s1[12]);
498
499 MyBase::mm[i4+1] = static_cast<T>(s0[i4+0] * s1[ 1] +
500 s0[i4+1] * s1[ 5] +
501 s0[i4+2] * s1[ 9] +
502 s0[i4+3] * s1[13]);
503
504 MyBase::mm[i4+2] = static_cast<T>(s0[i4+0] * s1[ 2] +
505 s0[i4+1] * s1[ 6] +
506 s0[i4+2] * s1[10] +
507 s0[i4+3] * s1[14]);
508
509 MyBase::mm[i4+3] = static_cast<T>(s0[i4+0] * s1[ 3] +
510 s0[i4+1] * s1[ 7] +
511 s0[i4+2] * s1[11] +
512 s0[i4+3] * s1[15]);
513 }
514 return *this;
515 }
516
518 Mat4 transpose() const
519 {
520 return Mat4<T>(
521 MyBase::mm[ 0], MyBase::mm[ 4], MyBase::mm[ 8], MyBase::mm[12],
522 MyBase::mm[ 1], MyBase::mm[ 5], MyBase::mm[ 9], MyBase::mm[13],
523 MyBase::mm[ 2], MyBase::mm[ 6], MyBase::mm[10], MyBase::mm[14],
524 MyBase::mm[ 3], MyBase::mm[ 7], MyBase::mm[11], MyBase::mm[15]
525 );
526 }
527
528
531 Mat4 inverse(T tolerance = 0) const
532 {
533 //
534 // inv [ A | b ] = [ E | f ] A: 3x3, b: 3x1, c': 1x3 d: 1x1
535 // [ c' | d ] [ g' | h ]
536 //
537 // If A is invertible use
538 //
539 // E = A^-1 + p*h*r
540 // p = A^-1 * b
541 // f = -p * h
542 // g' = -h * c'
543 // h = 1 / (d - c'*p)
544 // r' = c'*A^-1
545 //
546 // Otherwise use gauss-jordan elimination
547 //
548
549 //
550 // We create this alias to ourself so we can easily use own subscript
551 // operator.
552 const Mat4<T>& m(*this);
553
554 T m0011 = m[0][0] * m[1][1];
555 T m0012 = m[0][0] * m[1][2];
556 T m0110 = m[0][1] * m[1][0];
557 T m0210 = m[0][2] * m[1][0];
558 T m0120 = m[0][1] * m[2][0];
559 T m0220 = m[0][2] * m[2][0];
560
561 T detA = m0011 * m[2][2] - m0012 * m[2][1] - m0110 * m[2][2]
562 + m0210 * m[2][1] + m0120 * m[1][2] - m0220 * m[1][1];
563
564 bool hasPerspective =
565 (!isExactlyEqual(m[0][3], T(0.0)) ||
566 !isExactlyEqual(m[1][3], T(0.0)) ||
567 !isExactlyEqual(m[2][3], T(0.0)) ||
568 !isExactlyEqual(m[3][3], T(1.0)));
569
570 T det;
571 if (hasPerspective) {
572 det = m[0][3] * det3(m, 1,2,3, 0,2,1)
573 + m[1][3] * det3(m, 2,0,3, 0,2,1)
574 + m[2][3] * det3(m, 3,0,1, 0,2,1)
575 + m[3][3] * detA;
576 } else {
577 det = detA * m[3][3];
578 }
579
580 Mat4<T> inv;
581 bool invertible;
582
583 if (isApproxEqual(det,T(0.0),tolerance)) {
584 invertible = false;
585
586 } else if (isApproxEqual(detA,T(0.0),T(1e-8))) {
587 // det is too small to rely on inversion by subblocks
588 invertible = m.invert(inv, tolerance);
589
590 } else {
591 invertible = true;
592 detA = 1.0 / detA;
593
594 //
595 // Calculate A^-1
596 //
597 inv[0][0] = detA * ( m[1][1] * m[2][2] - m[1][2] * m[2][1]);
598 inv[0][1] = detA * (-m[0][1] * m[2][2] + m[0][2] * m[2][1]);
599 inv[0][2] = detA * ( m[0][1] * m[1][2] - m[0][2] * m[1][1]);
600
601 inv[1][0] = detA * (-m[1][0] * m[2][2] + m[1][2] * m[2][0]);
602 inv[1][1] = detA * ( m[0][0] * m[2][2] - m0220);
603 inv[1][2] = detA * ( m0210 - m0012);
604
605 inv[2][0] = detA * ( m[1][0] * m[2][1] - m[1][1] * m[2][0]);
606 inv[2][1] = detA * ( m0120 - m[0][0] * m[2][1]);
607 inv[2][2] = detA * ( m0011 - m0110);
608
609 if (hasPerspective) {
610 //
611 // Calculate r, p, and h
612 //
613 Vec3<T> r;
614 r[0] = m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
615 + m[3][2] * inv[2][0];
616 r[1] = m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
617 + m[3][2] * inv[2][1];
618 r[2] = m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
619 + m[3][2] * inv[2][2];
620
621 Vec3<T> p;
622 p[0] = inv[0][0] * m[0][3] + inv[0][1] * m[1][3]
623 + inv[0][2] * m[2][3];
624 p[1] = inv[1][0] * m[0][3] + inv[1][1] * m[1][3]
625 + inv[1][2] * m[2][3];
626 p[2] = inv[2][0] * m[0][3] + inv[2][1] * m[1][3]
627 + inv[2][2] * m[2][3];
628
629 T h = m[3][3] - p.dot(Vec3<T>(m[3][0],m[3][1],m[3][2]));
630 if (isApproxEqual(h,T(0.0),tolerance)) {
631 invertible = false;
632
633 } else {
634 h = 1.0 / h;
635
636 //
637 // Calculate h, g, and f
638 //
639 inv[3][3] = h;
640 inv[3][0] = -h * r[0];
641 inv[3][1] = -h * r[1];
642 inv[3][2] = -h * r[2];
643
644 inv[0][3] = -h * p[0];
645 inv[1][3] = -h * p[1];
646 inv[2][3] = -h * p[2];
647
648 //
649 // Calculate E
650 //
651 p *= h;
652 inv[0][0] += p[0] * r[0];
653 inv[0][1] += p[0] * r[1];
654 inv[0][2] += p[0] * r[2];
655 inv[1][0] += p[1] * r[0];
656 inv[1][1] += p[1] * r[1];
657 inv[1][2] += p[1] * r[2];
658 inv[2][0] += p[2] * r[0];
659 inv[2][1] += p[2] * r[1];
660 inv[2][2] += p[2] * r[2];
661 }
662 } else {
663 // Equations are much simpler in the non-perspective case
664 inv[3][0] = - (m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
665 + m[3][2] * inv[2][0]);
666 inv[3][1] = - (m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
667 + m[3][2] * inv[2][1]);
668 inv[3][2] = - (m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
669 + m[3][2] * inv[2][2]);
670 inv[0][3] = 0.0;
671 inv[1][3] = 0.0;
672 inv[2][3] = 0.0;
673 inv[3][3] = 1.0;
674 }
675 }
676
677 if (!invertible) OPENVDB_THROW(ArithmeticError, "Inversion of singular 4x4 matrix");
678 return inv;
679 }
680
681
683 T det() const
684 {
685 const T *ap;
686 Mat3<T> submat;
687 T det;
688 T *sp;
689 int i, j, k, sign;
690
691 det = 0;
692 sign = 1;
693 for (i = 0; i < 4; i++) {
694 ap = &MyBase::mm[ 0];
695 sp = submat.asPointer();
696 for (j = 0; j < 4; j++) {
697 for (k = 0; k < 4; k++) {
698 if ((k != i) && (j != 0)) {
699 *sp++ = *ap;
700 }
701 ap++;
702 }
703 }
704
705 det += sign * MyBase::mm[i] * submat.det();
706 sign = -sign;
707 }
708
709 return det;
710 }
711
713 static Mat4 translation(const Vec3d& v)
714 {
715 return Mat4(
716 T(1), T(0), T(0), T(0),
717 T(0), T(1), T(0), T(0),
718 T(0), T(0), T(1), T(0),
719 T(v.x()), T(v.y()),T(v.z()), T(1));
720 }
721
723 template <typename T0>
724 void setToTranslation(const Vec3<T0>& v)
725 {
726 MyBase::mm[ 0] = 1;
727 MyBase::mm[ 1] = 0;
728 MyBase::mm[ 2] = 0;
729 MyBase::mm[ 3] = 0;
730
731 MyBase::mm[ 4] = 0;
732 MyBase::mm[ 5] = 1;
733 MyBase::mm[ 6] = 0;
734 MyBase::mm[ 7] = 0;
735
736 MyBase::mm[ 8] = 0;
737 MyBase::mm[ 9] = 0;
738 MyBase::mm[10] = 1;
739 MyBase::mm[11] = 0;
740
741 MyBase::mm[12] = v.x();
742 MyBase::mm[13] = v.y();
743 MyBase::mm[14] = v.z();
744 MyBase::mm[15] = 1;
745 }
746
748 template <typename T0>
749 void preTranslate(const Vec3<T0>& tr)
750 {
751 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
752 Mat4<T> Tr = Mat4<T>::translation(tmp);
753
754 *this = Tr * (*this);
755
756 }
757
759 template <typename T0>
760 void postTranslate(const Vec3<T0>& tr)
761 {
762 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
763 Mat4<T> Tr = Mat4<T>::translation(tmp);
764
765 *this = (*this) * Tr;
766
767 }
768
769
771 template <typename T0>
772 void setToScale(const Vec3<T0>& v)
773 {
774 this->setIdentity();
775 MyBase::mm[ 0] = v.x();
776 MyBase::mm[ 5] = v.y();
777 MyBase::mm[10] = v.z();
778 }
779
780 // Left multiples by the specified scale matrix, i.e. Sc * (*this)
781 template <typename T0>
782 void preScale(const Vec3<T0>& v)
783 {
784 MyBase::mm[ 0] *= v.x();
785 MyBase::mm[ 1] *= v.x();
786 MyBase::mm[ 2] *= v.x();
787 MyBase::mm[ 3] *= v.x();
788
789 MyBase::mm[ 4] *= v.y();
790 MyBase::mm[ 5] *= v.y();
791 MyBase::mm[ 6] *= v.y();
792 MyBase::mm[ 7] *= v.y();
793
794 MyBase::mm[ 8] *= v.z();
795 MyBase::mm[ 9] *= v.z();
796 MyBase::mm[10] *= v.z();
797 MyBase::mm[11] *= v.z();
798 }
799
800
801
802 // Right multiples by the specified scale matrix, i.e. (*this) * Sc
803 template <typename T0>
804 void postScale(const Vec3<T0>& v)
805 {
806
807 MyBase::mm[ 0] *= v.x();
808 MyBase::mm[ 1] *= v.y();
809 MyBase::mm[ 2] *= v.z();
810
811 MyBase::mm[ 4] *= v.x();
812 MyBase::mm[ 5] *= v.y();
813 MyBase::mm[ 6] *= v.z();
814
815 MyBase::mm[ 8] *= v.x();
816 MyBase::mm[ 9] *= v.y();
817 MyBase::mm[10] *= v.z();
818
819 MyBase::mm[12] *= v.x();
820 MyBase::mm[13] *= v.y();
821 MyBase::mm[14] *= v.z();
822
823 }
824
825
829 void setToRotation(Axis axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
830
834 void setToRotation(const Vec3<T>& axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
835
838 void setToRotation(const Vec3<T>& v1, const Vec3<T>& v2) {*this = rotation<Mat4<T> >(v1, v2);}
839
840
844 void preRotate(Axis axis, T angle)
845 {
846 T c = static_cast<T>(cos(angle));
847 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
848
849 switch (axis) {
850 case X_AXIS:
851 {
852 T a4, a5, a6, a7;
853
854 a4 = c * MyBase::mm[ 4] - s * MyBase::mm[ 8];
855 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 9];
856 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[10];
857 a7 = c * MyBase::mm[ 7] - s * MyBase::mm[11];
858
859
860 MyBase::mm[ 8] = s * MyBase::mm[ 4] + c * MyBase::mm[ 8];
861 MyBase::mm[ 9] = s * MyBase::mm[ 5] + c * MyBase::mm[ 9];
862 MyBase::mm[10] = s * MyBase::mm[ 6] + c * MyBase::mm[10];
863 MyBase::mm[11] = s * MyBase::mm[ 7] + c * MyBase::mm[11];
864
865 MyBase::mm[ 4] = a4;
866 MyBase::mm[ 5] = a5;
867 MyBase::mm[ 6] = a6;
868 MyBase::mm[ 7] = a7;
869 }
870 break;
871
872 case Y_AXIS:
873 {
874 T a0, a1, a2, a3;
875
876 a0 = c * MyBase::mm[ 0] + s * MyBase::mm[ 8];
877 a1 = c * MyBase::mm[ 1] + s * MyBase::mm[ 9];
878 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[10];
879 a3 = c * MyBase::mm[ 3] + s * MyBase::mm[11];
880
881 MyBase::mm[ 8] = -s * MyBase::mm[ 0] + c * MyBase::mm[ 8];
882 MyBase::mm[ 9] = -s * MyBase::mm[ 1] + c * MyBase::mm[ 9];
883 MyBase::mm[10] = -s * MyBase::mm[ 2] + c * MyBase::mm[10];
884 MyBase::mm[11] = -s * MyBase::mm[ 3] + c * MyBase::mm[11];
885
886
887 MyBase::mm[ 0] = a0;
888 MyBase::mm[ 1] = a1;
889 MyBase::mm[ 2] = a2;
890 MyBase::mm[ 3] = a3;
891 }
892 break;
893
894 case Z_AXIS:
895 {
896 T a0, a1, a2, a3;
897
898 a0 = c * MyBase::mm[ 0] - s * MyBase::mm[ 4];
899 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 5];
900 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 6];
901 a3 = c * MyBase::mm[ 3] - s * MyBase::mm[ 7];
902
903 MyBase::mm[ 4] = s * MyBase::mm[ 0] + c * MyBase::mm[ 4];
904 MyBase::mm[ 5] = s * MyBase::mm[ 1] + c * MyBase::mm[ 5];
905 MyBase::mm[ 6] = s * MyBase::mm[ 2] + c * MyBase::mm[ 6];
906 MyBase::mm[ 7] = s * MyBase::mm[ 3] + c * MyBase::mm[ 7];
907
908 MyBase::mm[ 0] = a0;
909 MyBase::mm[ 1] = a1;
910 MyBase::mm[ 2] = a2;
911 MyBase::mm[ 3] = a3;
912 }
913 break;
914
915 default:
916 assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
917 }
918 }
919
920
924 void postRotate(Axis axis, T angle)
925 {
926 T c = static_cast<T>(cos(angle));
927 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
928
929
930
931 switch (axis) {
932 case X_AXIS:
933 {
934 T a2, a6, a10, a14;
935
936 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 1];
937 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[ 5];
938 a10 = c * MyBase::mm[10] - s * MyBase::mm[ 9];
939 a14 = c * MyBase::mm[14] - s * MyBase::mm[13];
940
941
942 MyBase::mm[ 1] = c * MyBase::mm[ 1] + s * MyBase::mm[ 2];
943 MyBase::mm[ 5] = c * MyBase::mm[ 5] + s * MyBase::mm[ 6];
944 MyBase::mm[ 9] = c * MyBase::mm[ 9] + s * MyBase::mm[10];
945 MyBase::mm[13] = c * MyBase::mm[13] + s * MyBase::mm[14];
946
947 MyBase::mm[ 2] = a2;
948 MyBase::mm[ 6] = a6;
949 MyBase::mm[10] = a10;
950 MyBase::mm[14] = a14;
951 }
952 break;
953
954 case Y_AXIS:
955 {
956 T a2, a6, a10, a14;
957
958 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[ 0];
959 a6 = c * MyBase::mm[ 6] + s * MyBase::mm[ 4];
960 a10 = c * MyBase::mm[10] + s * MyBase::mm[ 8];
961 a14 = c * MyBase::mm[14] + s * MyBase::mm[12];
962
963 MyBase::mm[ 0] = c * MyBase::mm[ 0] - s * MyBase::mm[ 2];
964 MyBase::mm[ 4] = c * MyBase::mm[ 4] - s * MyBase::mm[ 6];
965 MyBase::mm[ 8] = c * MyBase::mm[ 8] - s * MyBase::mm[10];
966 MyBase::mm[12] = c * MyBase::mm[12] - s * MyBase::mm[14];
967
968 MyBase::mm[ 2] = a2;
969 MyBase::mm[ 6] = a6;
970 MyBase::mm[10] = a10;
971 MyBase::mm[14] = a14;
972 }
973 break;
974
975 case Z_AXIS:
976 {
977 T a1, a5, a9, a13;
978
979 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 0];
980 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 4];
981 a9 = c * MyBase::mm[ 9] - s * MyBase::mm[ 8];
982 a13 = c * MyBase::mm[13] - s * MyBase::mm[12];
983
984 MyBase::mm[ 0] = c * MyBase::mm[ 0] + s * MyBase::mm[ 1];
985 MyBase::mm[ 4] = c * MyBase::mm[ 4] + s * MyBase::mm[ 5];
986 MyBase::mm[ 8] = c * MyBase::mm[ 8] + s * MyBase::mm[ 9];
987 MyBase::mm[12] = c * MyBase::mm[12] + s * MyBase::mm[13];
988
989 MyBase::mm[ 1] = a1;
990 MyBase::mm[ 5] = a5;
991 MyBase::mm[ 9] = a9;
992 MyBase::mm[13] = a13;
993
994 }
995 break;
996
997 default:
998 assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
999 }
1000 }
1001
1006 void setToShear(Axis axis0, Axis axis1, T shearby)
1007 {
1008 *this = shear<Mat4<T> >(axis0, axis1, shearby);
1009 }
1010
1011
1014 void preShear(Axis axis0, Axis axis1, T shear)
1015 {
1016 int index0 = static_cast<int>(axis0);
1017 int index1 = static_cast<int>(axis1);
1018
1019 // to row "index1" add a multiple of the index0 row
1020 MyBase::mm[index1 * 4 + 0] += shear * MyBase::mm[index0 * 4 + 0];
1021 MyBase::mm[index1 * 4 + 1] += shear * MyBase::mm[index0 * 4 + 1];
1022 MyBase::mm[index1 * 4 + 2] += shear * MyBase::mm[index0 * 4 + 2];
1023 MyBase::mm[index1 * 4 + 3] += shear * MyBase::mm[index0 * 4 + 3];
1024 }
1025
1026
1029 void postShear(Axis axis0, Axis axis1, T shear)
1030 {
1031 int index0 = static_cast<int>(axis0);
1032 int index1 = static_cast<int>(axis1);
1033
1034 // to collumn "index0" add a multiple of the index1 row
1035 MyBase::mm[index0 + 0] += shear * MyBase::mm[index1 + 0];
1036 MyBase::mm[index0 + 4] += shear * MyBase::mm[index1 + 4];
1037 MyBase::mm[index0 + 8] += shear * MyBase::mm[index1 + 8];
1038 MyBase::mm[index0 + 12] += shear * MyBase::mm[index1 + 12];
1039
1040 }
1041
1043 template<typename T0>
1044 Vec4<T0> transform(const Vec4<T0> &v) const
1045 {
1046 return static_cast< Vec4<T0> >(v * *this);
1047 }
1048
1050 template<typename T0>
1051 Vec3<T0> transform(const Vec3<T0> &v) const
1052 {
1053 return static_cast< Vec3<T0> >(v * *this);
1054 }
1055
1057 template<typename T0>
1058 Vec4<T0> pretransform(const Vec4<T0> &v) const
1059 {
1060 return static_cast< Vec4<T0> >(*this * v);
1061 }
1062
1064 template<typename T0>
1065 Vec3<T0> pretransform(const Vec3<T0> &v) const
1066 {
1067 return static_cast< Vec3<T0> >(*this * v);
1068 }
1069
1071 template<typename T0>
1072 Vec3<T0> transformH(const Vec3<T0> &p) const
1073 {
1074 T0 w;
1075
1076 // w = p * (*this).col(3);
1077 w = static_cast<T0>(p[0] * MyBase::mm[ 3] + p[1] * MyBase::mm[ 7]
1078 + p[2] * MyBase::mm[11] + MyBase::mm[15]);
1079
1080 if ( !isExactlyEqual(w , 0.0) ) {
1081 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 4] +
1082 p[2] * MyBase::mm[ 8] + MyBase::mm[12]) / w),
1083 static_cast<T0>((p[0] * MyBase::mm[ 1] + p[1] * MyBase::mm[ 5] +
1084 p[2] * MyBase::mm[ 9] + MyBase::mm[13]) / w),
1085 static_cast<T0>((p[0] * MyBase::mm[ 2] + p[1] * MyBase::mm[ 6] +
1086 p[2] * MyBase::mm[10] + MyBase::mm[14]) / w));
1087 }
1088
1089 return Vec3<T0>(0, 0, 0);
1090 }
1091
1093 template<typename T0>
1094 Vec3<T0> pretransformH(const Vec3<T0> &p) const
1095 {
1096 T0 w;
1097
1098 // w = p * (*this).col(3);
1099 w = p[0] * MyBase::mm[12] + p[1] * MyBase::mm[13] + p[2] * MyBase::mm[14] + MyBase::mm[15];
1100
1101 if ( !isExactlyEqual(w , 0.0) ) {
1102 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 1] +
1103 p[2] * MyBase::mm[ 2] + MyBase::mm[ 3]) / w),
1104 static_cast<T0>((p[0] * MyBase::mm[ 4] + p[1] * MyBase::mm[ 5] +
1105 p[2] * MyBase::mm[ 6] + MyBase::mm[ 7]) / w),
1106 static_cast<T0>((p[0] * MyBase::mm[ 8] + p[1] * MyBase::mm[ 9] +
1107 p[2] * MyBase::mm[10] + MyBase::mm[11]) / w));
1108 }
1109
1110 return Vec3<T0>(0, 0, 0);
1111 }
1112
1114 template<typename T0>
1115 Vec3<T0> transform3x3(const Vec3<T0> &v) const
1116 {
1117 return Vec3<T0>(
1118 static_cast<T0>(v[0] * MyBase::mm[ 0] + v[1] * MyBase::mm[ 4] + v[2] * MyBase::mm[ 8]),
1119 static_cast<T0>(v[0] * MyBase::mm[ 1] + v[1] * MyBase::mm[ 5] + v[2] * MyBase::mm[ 9]),
1120 static_cast<T0>(v[0] * MyBase::mm[ 2] + v[1] * MyBase::mm[ 6] + v[2] * MyBase::mm[10]));
1121 }
1122
1123
1124 private:
1125 bool invert(Mat4<T> &inverse, T tolerance) const;
1126
1127 T det2(const Mat4<T> &a, int i0, int i1, int j0, int j1) const {
1128 int i0row = i0 * 4;
1129 int i1row = i1 * 4;
1130 return a.mm[i0row+j0]*a.mm[i1row+j1] - a.mm[i0row+j1]*a.mm[i1row+j0];
1131 }
1132
1133 T det3(const Mat4<T> &a, int i0, int i1, int i2,
1134 int j0, int j1, int j2) const {
1135 int i0row = i0 * 4;
1136 return a.mm[i0row+j0]*det2(a, i1,i2, j1,j2) +
1137 a.mm[i0row+j1]*det2(a, i1,i2, j2,j0) +
1138 a.mm[i0row+j2]*det2(a, i1,i2, j0,j1);
1139 }
1140 }; // class Mat4
1141
1142
1145 template <typename T0, typename T1>
1146 bool operator==(const Mat4<T0> &m0, const Mat4<T1> &m1)
1147 {
1148 const T0 *t0 = m0.asPointer();
1149 const T1 *t1 = m1.asPointer();
1150
1151 for (int i=0; i<16; ++i) if (!isExactlyEqual(t0[i], t1[i])) return false;
1152 return true;
1153 }
1154
1157 template <typename T0, typename T1>
1158 bool operator!=(const Mat4<T0> &m0, const Mat4<T1> &m1) { return !(m0 == m1); }
1159
1162 template <typename S, typename T>
1163 Mat4<typename promote<S, T>::type> operator*(S scalar, const Mat4<T> &m)
1164 {
1165 return m*scalar;
1166 }
1167
1170 template <typename S, typename T>
1171 Mat4<typename promote<S, T>::type> operator*(const Mat4<T> &m, S scalar)
1172 {
1173 Mat4<typename promote<S, T>::type> result(m);
1174 result *= scalar;
1175 return result;
1176 }
1177
1180 template<typename T, typename MT>
1181 inline Vec4<typename promote<T, MT>::type>
1182 operator*(const Mat4<MT> &_m,
1183 const Vec4<T> &_v)
1184 {
1185 MT const *m = _m.asPointer();
1186 return Vec4<typename promote<T, MT>::type>(
1187 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + _v[3]*m[3],
1188 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + _v[3]*m[7],
1189 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + _v[3]*m[11],
1190 _v[0]*m[12] + _v[1]*m[13] + _v[2]*m[14] + _v[3]*m[15]);
1191 }
1192
1195 template<typename T, typename MT>
1196 inline Vec4<typename promote<T, MT>::type>
1197 operator*(const Vec4<T> &_v,
1198 const Mat4<MT> &_m)
1199 {
1200 MT const *m = _m.asPointer();
1201 return Vec4<typename promote<T, MT>::type>(
1202 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + _v[3]*m[12],
1203 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + _v[3]*m[13],
1204 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + _v[3]*m[14],
1205 _v[0]*m[3] + _v[1]*m[7] + _v[2]*m[11] + _v[3]*m[15]);
1206 }
1207
1210 template<typename T, typename MT>
1211 inline Vec3<typename promote<T, MT>::type>
1212 operator*(const Mat4<MT> &_m, const Vec3<T> &_v)
1213 {
1214 MT const *m = _m.asPointer();
1215 return Vec3<typename promote<T, MT>::type>(
1216 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + m[3],
1217 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + m[7],
1218 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + m[11]);
1219 }
1220
1223 template<typename T, typename MT>
1224 inline Vec3<typename promote<T, MT>::type>
1225 operator*(const Vec3<T> &_v, const Mat4<MT> &_m)
1226 {
1227 MT const *m = _m.asPointer();
1228 return Vec3<typename promote<T, MT>::type>(
1229 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + m[12],
1230 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + m[13],
1231 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + m[14]);
1232 }
1233
1236 template <typename T0, typename T1>
1237 Mat4<typename promote<T0, T1>::type>
1238 operator+(const Mat4<T0> &m0, const Mat4<T1> &m1)
1239 {
1240 Mat4<typename promote<T0, T1>::type> result(m0);
1241 result += m1;
1242 return result;
1243 }
1244
1247 template <typename T0, typename T1>
1248 Mat4<typename promote<T0, T1>::type>
1249 operator-(const Mat4<T0> &m0, const Mat4<T1> &m1)
1250 {
1251 Mat4<typename promote<T0, T1>::type> result(m0);
1252 result -= m1;
1253 return result;
1254 }
1255
1258 template <typename T0, typename T1>
1259 Mat4<typename promote<T0, T1>::type>
1260 operator*(const Mat4<T0> &m0, const Mat4<T1> &m1)
1261 {
1262 Mat4<typename promote<T0, T1>::type> result(m0);
1263 result *= m1;
1264 return result;
1265 }
1266
1267
1271 template<typename T0, typename T1>
1272 Vec3<T1> transformNormal(const Mat4<T0> &m, const Vec3<T1> &n)
1273 {
1274 return Vec3<T1>(
1275 static_cast<T1>(m[0][0]*n[0] + m[0][1]*n[1] + m[0][2]*n[2]),
1276 static_cast<T1>(m[1][0]*n[0] + m[1][1]*n[1] + m[1][2]*n[2]),
1277 static_cast<T1>(m[2][0]*n[0] + m[2][1]*n[1] + m[2][2]*n[2]));
1278 }
1279
1280
1282 template<typename T>
1283 bool Mat4<T>::invert(Mat4<T> &inverse, T tolerance) const
1284 {
1285 Mat4<T> temp(*this);
1286 inverse.setIdentity();
1287
1288 // Forward elimination step
1289 double det = 1.0;
1290 for (int i = 0; i < 4; ++i) {
1291 int row = i;
1292 double max = fabs(temp[i][i]);
1293
1294 for (int k = i+1; k < 4; ++k) {
1295 if (fabs(temp[k][i]) > max) {
1296 row = k;
1297 max = fabs(temp[k][i]);
1298 }
1299 }
1300
1301 if (isExactlyEqual(max, 0.0)) return false;
1302
1303 // must move pivot to row i
1304 if (row != i) {
1305 det = -det;
1306 for (int k = 0; k < 4; ++k) {
1307 std::swap(temp[row][k], temp[i][k]);
1308 std::swap(inverse[row][k], inverse[i][k]);
1309 }
1310 }
1311
1312 double pivot = temp[i][i];
1313 det *= pivot;
1314
1315 // scale row i
1316 for (int k = 0; k < 4; ++k) {
1317 temp[i][k] /= pivot;
1318 inverse[i][k] /= pivot;
1319 }
1320
1321 // eliminate in rows below i
1322 for (int j = i+1; j < 4; ++j) {
1323 double t = temp[j][i];
1324 if (!isExactlyEqual(t, 0.0)) {
1325 // subtract scaled row i from row j
1326 for (int k = 0; k < 4; ++k) {
1327 temp[j][k] -= temp[i][k] * t;
1328 inverse[j][k] -= inverse[i][k] * t;
1329 }
1330 }
1331 }
1332 }
1333
1334 // Backward elimination step
1335 for (int i = 3; i > 0; --i) {
1336 for (int j = 0; j < i; ++j) {
1337 double t = temp[j][i];
1338
1339 if (!isExactlyEqual(t, 0.0)) {
1340 for (int k = 0; k < 4; ++k) {
1341 inverse[j][k] -= inverse[i][k]*t;
1342 }
1343 }
1344 }
1345 }
1346 return det*det >= tolerance*tolerance;
1347 }
1348
1349 template <typename T>
1350 inline bool isAffine(const Mat4<T>& m) {
1351 return (m.col(3) == Vec4<T>(0, 0, 0, 1));
1352 }
1353
1354 template <typename T>
1355 inline bool hasTranslation(const Mat4<T>& m) {
1356 return (m.row(3) != Vec4<T>(0, 0, 0, 1));
1357 }
1358
1359
1360 using Mat4s = Mat4<float>;
1361 using Mat4d = Mat4<double>;
1362 using Mat4f = Mat4d;
1363
1364 } // namespace math
1365
1366
1367 template<> inline math::Mat4s zeroVal<math::Mat4s>() { return math::Mat4s::zero(); }
1368 template<> inline math::Mat4d zeroVal<math::Mat4d>() { return math::Mat4d::zero(); }
1369
1370 } // namespace OPENVDB_VERSION_NAME
1371 } // namespace openvdb
1372
1373 #endif // OPENVDB_UTIL_MAT4_H_HAS_BEEN_INCLUDED
1374
1375 // Copyright (c) 2012-2018 DreamWorks Animation LLC
1376 // All rights reserved. This software is distributed under the
1377 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v5_1::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:395
openvdb::v5_1::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::v5_1::math::Mat4::operator-=
const Mat4< T > & operator-=(const Mat4< S > &m1)
Subtract each element of the given matrix from the corresponding element of this matrix.
Definition: Mat4.h:456
openvdb::v5_1::math::Mat4::setIdentity
void setIdentity()
Set this matrix to identity.
Definition: Mat4.h:311
openvdb::v5_1::math::Vec4
Definition: Mat4.h:51
openvdb::v5_1::math::Mat4::transform3x3
Vec3< T0 > transform3x3(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without translation.
Definition: Mat4.h:1115
openvdb::v5_1::math::Mat4::setTranslation
void setTranslation(const Vec3< T > &t)
Definition: Mat4.h:360
Vec3.h
openvdb::v5_1::math::Mat4::inverse
Mat4 inverse(T tolerance=0) const
Definition: Mat4.h:531
openvdb::v5_1::math::mat3_internal::pivot
void pivot(int i, int j, Mat3< T > &S, Vec3< T > &D, Mat3< T > &Q)
Definition: Mat3.h:716
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v5_1::math::Mat4::identity
static const Mat4< T > & identity()
Predefined constant for identity matrix.
Definition: Mat4.h:152
openvdb::v5_1::math::Mat4::postScale
void postScale(const Vec3< T0 > &v)
Definition: Mat4.h:804
openvdb::v5_1::math::transformNormal
Vec3< T1 > transformNormal(const Mat4< T0 > &m, const Vec3< T1 > &n)
Definition: Mat4.h:1272
openvdb::v5_1::math::Axis
Axis
Definition: Math.h:856
openvdb::v5_1::math::Mat4::operator==
bool operator==(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat4.h:1146
openvdb::v5_1::math::Mat4::preScale
void preScale(const Vec3< T0 > &v)
Definition: Mat4.h:782
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
openvdb::v5_1::math::Mat4::zero
static const Mat4< T > & zero()
Predefined constant for zero matrix.
Definition: Mat4.h:163
openvdb::v5_1::math::Mat4::translation
static Mat4 translation(const Vec3d &v)
Sets the matrix to a matrix that translates by v.
Definition: Mat4.h:713
openvdb::v5_1::math::Mat4
4x4 -matrix class.
Definition: Mat3.h:49
openvdb::v5_1::math::Mat4::operator*
Mat4< typename promote< S, T >::type > operator*(S scalar, const Mat4< T > &m)
Multiply each element of the given matrix by scalar and return the result.
Definition: Mat4.h:1163
openvdb::v5_1::math::Mat4::operator-
Mat4< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition: Mat4.h:389
openvdb::v5_1::math::Mat4::setZero
void setZero()
Definition: Mat4.h:290
openvdb::v5_1::math::Mat4::preShear
void preShear(Axis axis0, Axis axis1, T shear)
Left multiplies a shearing transformation into the matrix.
Definition: Mat4.h:1014
openvdb::v5_1::math::Mat4::operator*
Vec3< typename promote< T, MT >::type > operator*(const Vec3< T > &_v, const Mat4< MT > &_m)
Multiply _v by _m and return the resulting vector.
Definition: Mat4.h:1225
openvdb::v5_1::math::Mat4::operator*
Vec4< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec4< T > &_v)
Multiply _m by _v and return the resulting vector.
Definition: Mat4.h:1182
openvdb::v5_1::math::Mat4::operator-
Mat4< typename promote< T0, T1 >::type > operator-(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Subtract corresponding elements of m0 and m1 and return the result.
Definition: Mat4.h:1249
openvdb::v5_1::math::Vec3
Definition: Mat.h:197
openvdb::v5_1::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::v5_1::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:472
openvdb::v5_1::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:265
openvdb::v5_1::math::Mat4::setMat3
void setMat3(const Mat3< T > &m)
Set upper left to a Mat3.
Definition: Mat4.h:336
Mat3.h
openvdb::v5_1::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:1006
openvdb::v5_1::math::Mat4::pretransformH
Vec3< T0 > pretransformH(const Vec3< T0 > &p) const
Transform a Vec3 by pre-multiplication, doing homogenous division.
Definition: Mat4.h:1094
openvdb::v5_1::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:844
openvdb::v5_1::math::Mat4::row
Vec4< T > row(int i) const
Get ith row, e.g. Vec4f v = m.row(1);.
Definition: Mat4.h:185
openvdb::v5_1::math::Mat
Definition: Mat.h:53
openvdb::v5_1::math::Mat4::setCol
void setCol(int j, const Vec4< T > &v)
Set jth column to vector v.
Definition: Mat4.h:192
openvdb::v5_1::math::Mat4::operator*
Vec3< typename promote< T, MT >::type > operator*(const Mat4< MT > &_m, const Vec3< T > &_v)
Multiply _m by _v and return the resulting vector.
Definition: Mat4.h:1212
openvdb::v5_1::math::Mat3::asPointer
T * asPointer()
Definition: Mat3.h:219
openvdb::v5_1::math::Mat3
3x3 matrix class.
Definition: Mat3.h:55
openvdb::v5_1::math::Mat4::Mat4
Mat4(const Mat< 4, T > &m)
Copy constructor.
Definition: Mat4.h:131
openvdb::v5_1::math::Mat4::operator()
T & operator()(int i, int j)
Definition: Mat4.h:222
openvdb::v5_1::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:838
openvdb::v5_1::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:718
openvdb::v5_1::math::Mat4::operator*
Vec4< typename promote< T, MT >::type > operator*(const Vec4< T > &_v, const Mat4< MT > &_m)
Multiply _v by _m and return the resulting vector.
Definition: Mat4.h:1197
Exceptions.h
openvdb::v5_1::math::Mat3::det
T det() const
Determinant of matrix.
Definition: Mat3.h:527
openvdb::v5_1::math::Mat4::pretransform
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Transform a Vec3 by pre-multiplication, without homogenous division.
Definition: Mat4.h:1065
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
openvdb::v5_1::math::hasTranslation
bool hasTranslation(const Mat4< T > &m)
Definition: Mat4.h:1355
openvdb::v5_1::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:216
openvdb::v5_1::math::Mat4::setRow
void setRow(int i, const Vec4< T > &v)
Set ith row to vector v.
Definition: Mat4.h:174
openvdb::v5_1::ArithmeticError
Definition: Exceptions.h:83
openvdb::v5_1::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:110
openvdb::v5_1::math::Mat4::eq
bool eq(const Mat4 &m, T eps=1.0e-8) const
Return true if this matrix is equivalent to m within a tolerance of eps.
Definition: Mat4.h:379
openvdb::v5_1::math::Mat4::getTranslation
Vec3< T > getTranslation() const
Return the translation component.
Definition: Mat4.h:355
openvdb
Definition: Exceptions.h:40
openvdb::v5_1::math::Z_AXIS
Definition: Math.h:859
openvdb::v5_1::math::Mat4::operator+
Mat4< typename promote< T0, T1 >::type > operator+(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Add corresponding elements of m0 and m1 and return the result.
Definition: Mat4.h:1238
openvdb::v5_1::math::Mat4::operator*
Mat4< typename promote< T0, T1 >::type > operator*(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Multiply m0 by m1 and return the resulting matrix.
Definition: Mat4.h:1260
openvdb::v5_1::math::Mat4::Mat4
Mat4(Source *a)
Constructor given array of elements, the ordering is in row major form:
Definition: Mat4.h:76
openvdb::v5_1::math::isAffine
bool isAffine(const Mat4< T > &m)
Definition: Mat4.h:1350
openvdb::v5_1::math::Mat4::operator*=
const Mat4< T > & operator*=(const Mat4< S > &m1)
Multiply this matrix by the given matrix.
Definition: Mat4.h:485
openvdb::v5_1::math::Mat< 4, Real >::value_type
Real value_type
Definition: Mat.h:56
openvdb::v5_1::math::Mat4::postTranslate
void postTranslate(const Vec3< T0 > &tr)
Right multiplies by the specified translation matrix, i.e. (*this) * Trans.
Definition: Mat4.h:760
openvdb::v5_1::math::Mat4::setToTranslation
void setToTranslation(const Vec3< T0 > &v)
Sets the matrix to a matrix that translates by v.
Definition: Mat4.h:724
openvdb::v5_1::math::Mat4::transpose
Mat4 transpose() const
Definition: Mat4.h:518
openvdb::v5_1::math::Mat4::operator+=
const Mat4< T > & operator+=(const Mat4< S > &m1)
Add each element of the given matrix to the corresponding element of this matrix. ...
Definition: Mat4.h:427
openvdb::v5_1::math::Mat4::asPointer
T * asPointer()
Direct access to the internal data.
Definition: Mat4.h:216
openvdb::v5_1::math::Y_AXIS
Definition: Math.h:858
openvdb::v5_1::math::Mat4::preTranslate
void preTranslate(const Vec3< T0 > &tr)
Left multiples by the specified translation, i.e. Trans * (*this)
Definition: Mat4.h:749
openvdb::v5_1::math::Mat4::transformH
Vec3< T0 > transformH(const Vec3< T0 > &p) const
Transform a Vec3 by post-multiplication, doing homogenous divison.
Definition: Mat4.h:1072
openvdb::v5_1::math::Mat4::setToRotation
void setToRotation(const Vec3< T > &axis, T angle)
Sets the matrix to a rotation about an arbitrary axis.
Definition: Mat4.h:834
openvdb::v5_1::math::Mat4::setToRotation
void setToRotation(Axis axis, T angle)
Sets the matrix to a rotation about the given axis.
Definition: Mat4.h:829
openvdb::v5_1::math::Mat4::getMat3
Mat3< T > getMat3() const
Definition: Mat4.h:343
openvdb::v5_1::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:358
openvdb::v5_1::math::Mat4::operator()
T operator()(int i, int j) const
Definition: Mat4.h:232
openvdb::v5_1::math::Mat::mm
T mm[SIZE *SIZE]
Definition: Mat.h:192
openvdb::v5_1::math::Mat4d
Mat4< double > Mat4d
Definition: Mat4.h:1361
openvdb::v5_1::math::Mat4::postShear
void postShear(Axis axis0, Axis axis1, T shear)
Right multiplies a shearing transformation into the matrix.
Definition: Mat4.h:1029
openvdb::v5_1::math::Mat4::col
Vec4< T > col(int j) const
Get jth column, e.g. Vec4f v = m.col(0);.
Definition: Mat4.h:202
openvdb::v5_1::math::Mat4::pretransform
Vec4< T0 > pretransform(const Vec4< T0 > &v) const
Transform a Vec4 by pre-multiplication.
Definition: Mat4.h:1058
openvdb::v5_1::math::Mat4::setToScale
void setToScale(const Vec3< T0 > &v)
Sets the matrix to a matrix that scales by v.
Definition: Mat4.h:772
openvdb::v5_1::math::X_AXIS
Definition: Math.h:857
openvdb::v5_1::math::Mat4::operator=
const Mat4 & operator=(const Mat4< Source > &m)
Assignment operator.
Definition: Mat4.h:369
openvdb::v5_1::math::Mat4::det
T det() const
Determinant of matrix.
Definition: Mat4.h:683
openvdb::v5_1::math::Mat4::Mat4
Mat4()
Trivial constructor, the matrix is NOT initialized.
Definition: Mat4.h:66
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
openvdb::v5_1::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:924
openvdb::v5_1::math::Mat4::transform
Vec4< T0 > transform(const Vec4< T0 > &v) const
Transform a Vec4 by post-multiplication.
Definition: Mat4.h:1044
openvdb::v5_1::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v5_1::math::Mat4::operator!=
bool operator!=(const Mat4< T0 > &m0, const Mat4< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition: Mat4.h:1158
openvdb::v5_1::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:240
openvdb::v5_1::math::Mat4::transform
Vec3< T0 > transform(const Vec3< T0 > &v) const
Transform a Vec3 by post-multiplication, without homogenous division.
Definition: Mat4.h:1051
openvdb::v5_1::math::Mat4::asPointer
const T * asPointer() const
Definition: Mat4.h:217
openvdb::v5_1::math::Mat4::operator[]
const T * operator[](int i) const
Definition: Mat4.h:212
openvdb::v5_1::math::Mat4::Mat4
Mat4(const Mat4< Source > &m)
Conversion constructor.
Definition: Mat4.h:142
openvdb::v5_1::math::Vec3::z
T & z()
Definition: Vec3.h:112
openvdb::v5_1::math::Mat< 4, Real >::ValueType
Real ValueType
Definition: Mat.h:57
Platform.h
openvdb::v5_1::math::Mat4::operator*=
const Mat4< T > & operator*=(S scalar)
Multiply each element of this matrix by scalar.
Definition: Mat4.h:401
Vec4.h
openvdb::v5_1::math::Mat4::operator*
Mat4< typename promote< S, T >::type > operator*(const Mat4< T > &m, S scalar)
Multiply each element of the given matrix by scalar and return the result.
Definition: Mat4.h:1171
openvdb::v5_1::math::Vec3::y
T & y()
Definition: Vec3.h:111