GCC Code Coverage Report

Directory: ./
File: openvdb/openvdb/math/Mat4.h
Date: 2022-07-25 17:40:05
Exec Total Coverage
Lines: 383 481 79.6%
Functions: 44 49 89.8%
Branches: 260 570 45.6%
Line Branch Exec Source
1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3
4 #ifndef OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
5 #define OPENVDB_MATH_MAT4_H_HAS_BEEN_INCLUDED
6
7 #include <openvdb/Exceptions.h>
8 #include <openvdb/Platform.h>
9 #include "Math.h"
10 #include "Mat3.h"
11 #include "Vec3.h"
12 #include "Vec4.h"
13 #include <algorithm> // for std::copy(), std::swap()
14 #include <cassert>
15 #include <iomanip>
16 #include <cmath>
17
18
19 namespace openvdb {
20 OPENVDB_USE_VERSION_NAMESPACE
21 namespace OPENVDB_VERSION_NAME {
22 namespace math {
23
24 template<typename T> class Vec4;
25
26
27 /// @class Mat4 Mat4.h
28 /// @brief 4x4 -matrix class.
29 template<typename T>
30 class Mat4: public Mat<4, T>
31 {
32 public:
33 /// Data type held by the matrix.
34 using value_type = T;
35 using ValueType = T;
36 using MyBase = Mat<4, T>;
37
38 /// Trivial constructor, the matrix is NOT initialized
39 #if OPENVDB_ABI_VERSION_NUMBER >= 8
40 /// @note destructor, copy constructor, assignment operator and
41 /// move constructor are left to be defined by the compiler (default)
42 Mat4() = default;
43 #else
44 Mat4() {}
45
46 /// Copy constructor
47 Mat4(const Mat<4, T> &m)
48 {
49 for (int i = 0; i < 4; ++i) {
50 for (int j = 0; j < 4; ++j) {
51 MyBase::mm[i*4 + j] = m[i][j];
52 }
53 }
54 }
55 #endif
56
57 /// Constructor given array of elements, the ordering is in row major form:
58 /** @verbatim
59 a[ 0] a[1] a[ 2] a[ 3]
60 a[ 4] a[5] a[ 6] a[ 7]
61 a[ 8] a[9] a[10] a[11]
62 a[12] a[13] a[14] a[15]
63 @endverbatim */
64 template<typename Source>
65 Mat4(Source *a)
66 {
67 for (int i = 0; i < 16; i++) {
68 MyBase::mm[i] = static_cast<T>(a[i]);
69 }
70 }
71
72 /// Constructor given array of elements, the ordering is in row major form:
73 /** @verbatim
74 a b c d
75 e f g h
76 i j k l
77 m n o p
78 @endverbatim */
79 template<typename Source>
80 743978 Mat4(Source a, Source b, Source c, Source d,
81 Source e, Source f, Source g, Source h,
82 Source i, Source j, Source k, Source l,
83 Source m, Source n, Source o, Source p)
84 {
85 743979 MyBase::mm[ 0] = static_cast<T>(a);
86 743979 MyBase::mm[ 1] = static_cast<T>(b);
87 743979 MyBase::mm[ 2] = static_cast<T>(c);
88 743979 MyBase::mm[ 3] = static_cast<T>(d);
89
90 743979 MyBase::mm[ 4] = static_cast<T>(e);
91 743979 MyBase::mm[ 5] = static_cast<T>(f);
92 743979 MyBase::mm[ 6] = static_cast<T>(g);
93 743979 MyBase::mm[ 7] = static_cast<T>(h);
94
95 743979 MyBase::mm[ 8] = static_cast<T>(i);
96 743979 MyBase::mm[ 9] = static_cast<T>(j);
97 743979 MyBase::mm[10] = static_cast<T>(k);
98 743979 MyBase::mm[11] = static_cast<T>(l);
99
100 743979 MyBase::mm[12] = static_cast<T>(m);
101 743979 MyBase::mm[13] = static_cast<T>(n);
102 743979 MyBase::mm[14] = static_cast<T>(o);
103
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 743970 MyBase::mm[15] = static_cast<T>(p);
104 }
105
106 /// Construct matrix from rows or columns vectors (defaults to rows
107 /// for historical reasons)
108 template<typename Source>
109 Mat4(const Vec4<Source> &v1, const Vec4<Source> &v2,
110 const Vec4<Source> &v3, const Vec4<Source> &v4, bool rows = true)
111 {
112 if (rows) {
113 this->setRows(v1, v2, v3, v4);
114 } else {
115 this->setColumns(v1, v2, v3, v4);
116 }
117 }
118
119 /// Conversion constructor
120 template<typename Source>
121 explicit Mat4(const Mat4<Source> &m)
122 {
123 const Source *src = m.asPointer();
124
125 for (int i=0; i<16; ++i) {
126 MyBase::mm[i] = static_cast<T>(src[i]);
127 }
128 }
129
130 /// Predefined constant for identity matrix
131 738714 static const Mat4<T>& identity() {
132
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 738714 static const Mat4<T> sIdentity = Mat4<T>(
133 1, 0, 0, 0,
134 0, 1, 0, 0,
135 0, 0, 1, 0,
136 0, 0, 0, 1
137 );
138 738714 return sIdentity;
139 }
140
141 /// Predefined constant for zero matrix
142 7284032 static const Mat4<T>& zero() {
143
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 7284032 static const Mat4<T> sZero = Mat4<T>(
144 0, 0, 0, 0,
145 0, 0, 0, 0,
146 0, 0, 0, 0,
147 0, 0, 0, 0
148 );
149 7284032 return sZero;
150 }
151
152 /// Set ith row to vector v
153 void setRow(int i, const Vec4<T> &v)
154 {
155 // assert(i>=0 && i<4);
156 int i4 = i * 4;
157 MyBase::mm[i4+0] = v[0];
158 MyBase::mm[i4+1] = v[1];
159 MyBase::mm[i4+2] = v[2];
160 MyBase::mm[i4+3] = v[3];
161 }
162
163 /// Get ith row, e.g. Vec4f v = m.row(1);
164 Vec4<T> row(int i) const
165 {
166 // assert(i>=0 && i<3);
167 return Vec4<T>((*this)(i,0), (*this)(i,1), (*this)(i,2), (*this)(i,3));
168 }
169
170 /// Set jth column to vector v
171 void setCol(int j, const Vec4<T>& v)
172 {
173 // assert(j>=0 && j<4);
174 ✗ MyBase::mm[ 0+j] = v[0];
175 ✗ MyBase::mm[ 4+j] = v[1];
176 ✗ MyBase::mm[ 8+j] = v[2];
177 ✗ MyBase::mm[12+j] = v[3];
178 }
179
180 /// Get jth column, e.g. Vec4f v = m.col(0);
181 Vec4<T> col(int j) const
182 {
183 // assert(j>=0 && j<4);
184 return Vec4<T>((*this)(0,j), (*this)(1,j), (*this)(2,j), (*this)(3,j));
185 }
186
187 /// Alternative indexed reference to the elements
188 /// Note that the indices are row first and column second.
189 /// e.g. m(0,0) = 1;
190 T& operator()(int i, int j)
191 {
192 // assert(i>=0 && i<4);
193 // assert(j>=0 && j<4);
194 return MyBase::mm[4*i+j];
195 }
196
197 /// Alternative indexed constant reference to the elements,
198 /// Note that the indices are row first and column second.
199 /// e.g. float f = m(1,0);
200 T operator()(int i, int j) const
201 {
202 // assert(i>=0 && i<4);
203 // assert(j>=0 && j<4);
204
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 667515 return MyBase::mm[4*i+j];
205 }
206
207 /// Set the rows of this matrix to the vectors v1, v2, v3, v4
208 void setRows(const Vec4<T> &v1, const Vec4<T> &v2,
209 const Vec4<T> &v3, const Vec4<T> &v4)
210 {
211 MyBase::mm[ 0] = v1[0];
212 MyBase::mm[ 1] = v1[1];
213 MyBase::mm[ 2] = v1[2];
214 MyBase::mm[ 3] = v1[3];
215
216 MyBase::mm[ 4] = v2[0];
217 MyBase::mm[ 5] = v2[1];
218 MyBase::mm[ 6] = v2[2];
219 MyBase::mm[ 7] = v2[3];
220
221 MyBase::mm[ 8] = v3[0];
222 MyBase::mm[ 9] = v3[1];
223 MyBase::mm[10] = v3[2];
224 MyBase::mm[11] = v3[3];
225
226 MyBase::mm[12] = v4[0];
227 MyBase::mm[13] = v4[1];
228 MyBase::mm[14] = v4[2];
229 MyBase::mm[15] = v4[3];
230 }
231
232 /// Set the columns of this matrix to the vectors v1, v2, v3, v4
233 void setColumns(const Vec4<T> &v1, const Vec4<T> &v2,
234 const Vec4<T> &v3, const Vec4<T> &v4)
235 {
236 MyBase::mm[ 0] = v1[0];
237 MyBase::mm[ 1] = v2[0];
238 MyBase::mm[ 2] = v3[0];
239 MyBase::mm[ 3] = v4[0];
240
241 MyBase::mm[ 4] = v1[1];
242 MyBase::mm[ 5] = v2[1];
243 MyBase::mm[ 6] = v3[1];
244 MyBase::mm[ 7] = v4[1];
245
246 MyBase::mm[ 8] = v1[2];
247 MyBase::mm[ 9] = v2[2];
248 MyBase::mm[10] = v3[2];
249 MyBase::mm[11] = v4[2];
250
251 MyBase::mm[12] = v1[3];
252 MyBase::mm[13] = v2[3];
253 MyBase::mm[14] = v3[3];
254 MyBase::mm[15] = v4[3];
255 }
256
257 // Set this matrix to zero
258 void setZero()
259 {
260 MyBase::mm[ 0] = 0;
261 10 MyBase::mm[ 1] = 0;
262 10 MyBase::mm[ 2] = 0;
263 10 MyBase::mm[ 3] = 0;
264 10 MyBase::mm[ 4] = 0;
265 MyBase::mm[ 5] = 0;
266 10 MyBase::mm[ 6] = 0;
267 10 MyBase::mm[ 7] = 0;
268 10 MyBase::mm[ 8] = 0;
269 10 MyBase::mm[ 9] = 0;
270 MyBase::mm[10] = 0;
271 10 MyBase::mm[11] = 0;
272 10 MyBase::mm[12] = 0;
273 10 MyBase::mm[13] = 0;
274
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 10 MyBase::mm[14] = 0;
275 MyBase::mm[15] = 0;
276 }
277
278 /// Set this matrix to identity
279 void setIdentity()
280 {
281 406170 MyBase::mm[ 0] = 1;
282 406171 MyBase::mm[ 1] = 0;
283 406171 MyBase::mm[ 2] = 0;
284 406171 MyBase::mm[ 3] = 0;
285
286 406171 MyBase::mm[ 4] = 0;
287 406170 MyBase::mm[ 5] = 1;
288 406171 MyBase::mm[ 6] = 0;
289 406171 MyBase::mm[ 7] = 0;
290
291 406171 MyBase::mm[ 8] = 0;
292 406171 MyBase::mm[ 9] = 0;
293 406170 MyBase::mm[10] = 1;
294 406171 MyBase::mm[11] = 0;
295
296 406171 MyBase::mm[12] = 0;
297 406171 MyBase::mm[13] = 0;
298 406171 MyBase::mm[14] = 0;
299
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 406170 MyBase::mm[15] = 1;
300 }
301
302
303 /// Set upper left to a Mat3
304 void setMat3(const Mat3<T> &m)
305 {
306
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307
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 192 for (int j=0; j < 3; j++)
308 144 MyBase::mm[i*4+j] = m[i][j];
309 }
310
311 Mat3<T> getMat3() const
312 {
313 Mat3<T> m;
314
315
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316
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 7967136 for (int j = 0; j < 3; j++)
317 5975352 m[i][j] = MyBase::mm[i*4+j];
318
319 return m;
320 }
321
322 /// Return the translation component
323 Vec3<T> getTranslation() const
324 {
325 663558 return Vec3<T>(MyBase::mm[12], MyBase::mm[13], MyBase::mm[14]);
326 }
327
328 void setTranslation(const Vec3<T> &t)
329 {
330 406093 MyBase::mm[12] = t[0];
331 406093 MyBase::mm[13] = t[1];
332
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 331789 MyBase::mm[14] = t[2];
333 74304 }
334
335 /// Assignment operator
336 template<typename Source>
337 const Mat4& operator=(const Mat4<Source> &m)
338 {
339 const Source *src = m.asPointer();
340
341 // don't suppress warnings when assigning from different numerical types
342 std::copy(src, (src + this->numElements()), MyBase::mm);
343 return *this;
344 }
345
346 /// Return @c true if this matrix is equivalent to @a m within a tolerance of @a eps.
347 bool eq(const Mat4 &m, T eps=1.0e-8) const
348 {
349
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350
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 6501324 if (!isApproxEqual(MyBase::mm[i], m.mm[i], eps))
351 return false;
352 }
353 return true;
354 }
355
356 /// Negation operator, for e.g. m1 = -m2;
357 4 Mat4<T> operator-() const
358 {
359 return Mat4<T>(
360 4 -MyBase::mm[ 0], -MyBase::mm[ 1], -MyBase::mm[ 2], -MyBase::mm[ 3],
361 4 -MyBase::mm[ 4], -MyBase::mm[ 5], -MyBase::mm[ 6], -MyBase::mm[ 7],
362 4 -MyBase::mm[ 8], -MyBase::mm[ 9], -MyBase::mm[10], -MyBase::mm[11],
363 4 -MyBase::mm[12], -MyBase::mm[13], -MyBase::mm[14], -MyBase::mm[15]
364 4 );
365 } // trivial
366
367 /// Multiply each element of this matrix by @a scalar.
368 template <typename S>
369 const Mat4<T>& operator*=(S scalar)
370 {
371 MyBase::mm[ 0] *= scalar;
372 MyBase::mm[ 1] *= scalar;
373 MyBase::mm[ 2] *= scalar;
374 MyBase::mm[ 3] *= scalar;
375
376 MyBase::mm[ 4] *= scalar;
377 MyBase::mm[ 5] *= scalar;
378 MyBase::mm[ 6] *= scalar;
379 MyBase::mm[ 7] *= scalar;
380
381 MyBase::mm[ 8] *= scalar;
382 MyBase::mm[ 9] *= scalar;
383 MyBase::mm[10] *= scalar;
384 MyBase::mm[11] *= scalar;
385
386 MyBase::mm[12] *= scalar;
387 MyBase::mm[13] *= scalar;
388 MyBase::mm[14] *= scalar;
389 MyBase::mm[15] *= scalar;
390 return *this;
391 }
392
393 /// Add each element of the given matrix to the corresponding element of this matrix.
394 template <typename S>
395 24 const Mat4<T> &operator+=(const Mat4<S> &m1)
396 {
397 const S* s = m1.asPointer();
398
399 24 MyBase::mm[ 0] += s[ 0];
400 24 MyBase::mm[ 1] += s[ 1];
401 24 MyBase::mm[ 2] += s[ 2];
402 24 MyBase::mm[ 3] += s[ 3];
403
404 24 MyBase::mm[ 4] += s[ 4];
405 24 MyBase::mm[ 5] += s[ 5];
406 24 MyBase::mm[ 6] += s[ 6];
407 24 MyBase::mm[ 7] += s[ 7];
408
409 24 MyBase::mm[ 8] += s[ 8];
410 24 MyBase::mm[ 9] += s[ 9];
411 24 MyBase::mm[10] += s[10];
412 24 MyBase::mm[11] += s[11];
413
414 24 MyBase::mm[12] += s[12];
415 24 MyBase::mm[13] += s[13];
416 24 MyBase::mm[14] += s[14];
417 24 MyBase::mm[15] += s[15];
418
419 24 return *this;
420 }
421
422 /// Subtract each element of the given matrix from the corresponding element of this matrix.
423 template <typename S>
424 164074 const Mat4<T> &operator-=(const Mat4<S> &m1)
425 {
426 const S* s = m1.asPointer();
427
428 164074 MyBase::mm[ 0] -= s[ 0];
429 164074 MyBase::mm[ 1] -= s[ 1];
430 164074 MyBase::mm[ 2] -= s[ 2];
431 164074 MyBase::mm[ 3] -= s[ 3];
432
433 164074 MyBase::mm[ 4] -= s[ 4];
434 164074 MyBase::mm[ 5] -= s[ 5];
435 164074 MyBase::mm[ 6] -= s[ 6];
436 164074 MyBase::mm[ 7] -= s[ 7];
437
438 164074 MyBase::mm[ 8] -= s[ 8];
439 164074 MyBase::mm[ 9] -= s[ 9];
440 164074 MyBase::mm[10] -= s[10];
441 164074 MyBase::mm[11] -= s[11];
442
443 164074 MyBase::mm[12] -= s[12];
444 164074 MyBase::mm[13] -= s[13];
445 164074 MyBase::mm[14] -= s[14];
446 164074 MyBase::mm[15] -= s[15];
447
448 164074 return *this;
449 }
450
451 /// Multiply this matrix by the given matrix.
452 template <typename S>
453 1962135 const Mat4<T> &operator*=(const Mat4<S> &m1)
454 {
455 1962135 Mat4<T> m0(*this);
456
457 const T* s0 = m0.asPointer();
458 const S* s1 = m1.asPointer();
459
460
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 9810675 for (int i = 0; i < 4; i++) {
461 7848540 int i4 = 4 * i;
462 7848540 MyBase::mm[i4+0] = static_cast<T>(s0[i4+0] * s1[ 0] +
463 7848540 s0[i4+1] * s1[ 4] +
464 7848540 s0[i4+2] * s1[ 8] +
465 7848540 s0[i4+3] * s1[12]);
466
467 7848540 MyBase::mm[i4+1] = static_cast<T>(s0[i4+0] * s1[ 1] +
468 7848540 s0[i4+1] * s1[ 5] +
469 7848540 s0[i4+2] * s1[ 9] +
470 7848540 s0[i4+3] * s1[13]);
471
472 7848540 MyBase::mm[i4+2] = static_cast<T>(s0[i4+0] * s1[ 2] +
473 7848540 s0[i4+1] * s1[ 6] +
474 7848540 s0[i4+2] * s1[10] +
475 7848540 s0[i4+3] * s1[14]);
476
477 7848540 MyBase::mm[i4+3] = static_cast<T>(s0[i4+0] * s1[ 3] +
478 7848540 s0[i4+1] * s1[ 7] +
479 7848540 s0[i4+2] * s1[11] +
480 7848540 s0[i4+3] * s1[15]);
481 }
482 1962135 return *this;
483 }
484
485 /// @return transpose of this
486 Mat4 transpose() const
487 {
488 return Mat4<T>(
489 87 MyBase::mm[ 0], MyBase::mm[ 4], MyBase::mm[ 8], MyBase::mm[12],
490 87 MyBase::mm[ 1], MyBase::mm[ 5], MyBase::mm[ 9], MyBase::mm[13],
491 87 MyBase::mm[ 2], MyBase::mm[ 6], MyBase::mm[10], MyBase::mm[14],
492
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 87 MyBase::mm[ 3], MyBase::mm[ 7], MyBase::mm[11], MyBase::mm[15]
493 );
494 }
495
496
497 /// @return inverse of this
498 /// @throw ArithmeticError if singular
499 380 Mat4 inverse(T tolerance = 0) const
500 {
501 //
502 // inv [ A | b ] = [ E | f ] A: 3x3, b: 3x1, c': 1x3 d: 1x1
503 // [ c' | d ] [ g' | h ]
504 //
505 // If A is invertible use
506 //
507 // E = A^-1 + p*h*r
508 // p = A^-1 * b
509 // f = -p * h
510 // g' = -h * c'
511 // h = 1 / (d - c'*p)
512 // r' = c'*A^-1
513 //
514 // Otherwise use gauss-jordan elimination
515 //
516
517 //
518 // We create this alias to ourself so we can easily use own subscript
519 // operator.
520 const Mat4<T>& m(*this);
521
522 380 T m0011 = m[0][0] * m[1][1];
523 380 T m0012 = m[0][0] * m[1][2];
524 380 T m0110 = m[0][1] * m[1][0];
525 380 T m0210 = m[0][2] * m[1][0];
526 380 T m0120 = m[0][1] * m[2][0];
527 380 T m0220 = m[0][2] * m[2][0];
528
529 380 T detA = m0011 * m[2][2] - m0012 * m[2][1] - m0110 * m[2][2]
530
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 380 + m0210 * m[2][1] + m0120 * m[1][2] - m0220 * m[1][1];
531
532 bool hasPerspective =
533
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 380 (!isExactlyEqual(m[0][3], T(0.0)) ||
534
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 380 !isExactlyEqual(m[1][3], T(0.0)) ||
535
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 760 !isExactlyEqual(m[2][3], T(0.0)) ||
536 !isExactlyEqual(m[3][3], T(1.0)));
537
538 T det;
539 if (hasPerspective) {
540 ✗ det = m[0][3] * det3(m, 1,2,3, 0,2,1)
541 ✗ + m[1][3] * det3(m, 2,0,3, 0,2,1)
542 ✗ + m[2][3] * det3(m, 3,0,1, 0,2,1)
543 ✗ + m[3][3] * detA;
544 } else {
545 380 det = detA * m[3][3];
546 }
547
548 Mat4<T> inv;
549 bool invertible;
550
551
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 380 if (isApproxEqual(det,T(0.0),tolerance)) {
552 invertible = false;
553
554
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 380 } else if (isApproxEqual(detA,T(0.0),T(1e-8))) {
555 // det is too small to rely on inversion by subblocks
556 ✗ invertible = m.invert(inv, tolerance);
557
558 } else {
559 invertible = true;
560 380 detA = 1.0 / detA;
561
562 //
563 // Calculate A^-1
564 //
565 380 inv[0][0] = detA * ( m[1][1] * m[2][2] - m[1][2] * m[2][1]);
566 380 inv[0][1] = detA * (-m[0][1] * m[2][2] + m[0][2] * m[2][1]);
567 380 inv[0][2] = detA * ( m[0][1] * m[1][2] - m[0][2] * m[1][1]);
568
569 380 inv[1][0] = detA * (-m[1][0] * m[2][2] + m[1][2] * m[2][0]);
570 380 inv[1][1] = detA * ( m[0][0] * m[2][2] - m0220);
571 380 inv[1][2] = detA * ( m0210 - m0012);
572
573 380 inv[2][0] = detA * ( m[1][0] * m[2][1] - m[1][1] * m[2][0]);
574 380 inv[2][1] = detA * ( m0120 - m[0][0] * m[2][1]);
575 380 inv[2][2] = detA * ( m0011 - m0110);
576
577
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 380 if (hasPerspective) {
578 //
579 // Calculate r, p, and h
580 //
581 Vec3<T> r;
582 ✗ r[0] = m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
583 ✗ + m[3][2] * inv[2][0];
584 ✗ r[1] = m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
585 ✗ + m[3][2] * inv[2][1];
586 ✗ r[2] = m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
587 ✗ + m[3][2] * inv[2][2];
588
589 Vec3<T> p;
590 ✗ p[0] = inv[0][0] * m[0][3] + inv[0][1] * m[1][3]
591 ✗ + inv[0][2] * m[2][3];
592 ✗ p[1] = inv[1][0] * m[0][3] + inv[1][1] * m[1][3]
593 ✗ + inv[1][2] * m[2][3];
594 ✗ p[2] = inv[2][0] * m[0][3] + inv[2][1] * m[1][3]
595 ✗ + inv[2][2] * m[2][3];
596
597 ✗ T h = m[3][3] - p.dot(Vec3<T>(m[3][0],m[3][1],m[3][2]));
598 ✗ if (isApproxEqual(h,T(0.0),tolerance)) {
599 invertible = false;
600
601 } else {
602 ✗ h = 1.0 / h;
603
604 //
605 // Calculate h, g, and f
606 //
607 ✗ inv[3][3] = h;
608 ✗ inv[3][0] = -h * r[0];
609 ✗ inv[3][1] = -h * r[1];
610 ✗ inv[3][2] = -h * r[2];
611
612 ✗ inv[0][3] = -h * p[0];
613 ✗ inv[1][3] = -h * p[1];
614 ✗ inv[2][3] = -h * p[2];
615
616 //
617 // Calculate E
618 //
619 p *= h;
620 ✗ inv[0][0] += p[0] * r[0];
621 ✗ inv[0][1] += p[0] * r[1];
622 ✗ inv[0][2] += p[0] * r[2];
623 ✗ inv[1][0] += p[1] * r[0];
624 ✗ inv[1][1] += p[1] * r[1];
625 ✗ inv[1][2] += p[1] * r[2];
626 ✗ inv[2][0] += p[2] * r[0];
627 ✗ inv[2][1] += p[2] * r[1];
628 ✗ inv[2][2] += p[2] * r[2];
629 }
630 } else {
631 // Equations are much simpler in the non-perspective case
632 380 inv[3][0] = - (m[3][0] * inv[0][0] + m[3][1] * inv[1][0]
633 380 + m[3][2] * inv[2][0]);
634 380 inv[3][1] = - (m[3][0] * inv[0][1] + m[3][1] * inv[1][1]
635 380 + m[3][2] * inv[2][1]);
636 380 inv[3][2] = - (m[3][0] * inv[0][2] + m[3][1] * inv[1][2]
637 380 + m[3][2] * inv[2][2]);
638 380 inv[0][3] = 0.0;
639 380 inv[1][3] = 0.0;
640 380 inv[2][3] = 0.0;
641 380 inv[3][3] = 1.0;
642 }
643 }
644
645 ✗ if (!invertible) OPENVDB_THROW(ArithmeticError, "Inversion of singular 4x4 matrix");
646 380 return inv;
647 }
648
649
650 /// Determinant of matrix
651 173 T det() const
652 {
653 const T *ap;
654 Mat3<T> submat;
655 T det;
656 T *sp;
657 int i, j, k, sign;
658
659 det = 0;
660 sign = 1;
661
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 865 for (i = 0; i < 4; i++) {
662 692 ap = &MyBase::mm[ 0];
663 sp = submat.asPointer();
664
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 3460 for (j = 0; j < 4; j++) {
665
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666
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 11072 if ((k != i) && (j != 0)) {
667 6228 *sp++ = *ap;
668 }
669 11072 ap++;
670 }
671 }
672
673 692 det += T(sign) * MyBase::mm[i] * submat.det();
674 692 sign = -sign;
675 }
676
677 173 return det;
678 }
679
680 /// Sets the matrix to a matrix that translates by v
681 static Mat4 translation(const Vec3d& v)
682 {
683 return Mat4(
684 T(1), T(0), T(0), T(0),
685 T(0), T(1), T(0), T(0),
686 T(0), T(0), T(1), T(0),
687 T(v.x()), T(v.y()),T(v.z()), T(1));
688 }
689
690 /// Sets the matrix to a matrix that translates by v
691 template <typename T0>
692 void setToTranslation(const Vec3<T0>& v)
693 {
694 ✗ MyBase::mm[ 0] = 1;
695 ✗ MyBase::mm[ 1] = 0;
696 ✗ MyBase::mm[ 2] = 0;
697 ✗ MyBase::mm[ 3] = 0;
698
699 ✗ MyBase::mm[ 4] = 0;
700 ✗ MyBase::mm[ 5] = 1;
701 ✗ MyBase::mm[ 6] = 0;
702 ✗ MyBase::mm[ 7] = 0;
703
704 ✗ MyBase::mm[ 8] = 0;
705 ✗ MyBase::mm[ 9] = 0;
706 ✗ MyBase::mm[10] = 1;
707 ✗ MyBase::mm[11] = 0;
708
709 ✗ MyBase::mm[12] = v.x();
710 ✗ MyBase::mm[13] = v.y();
711 ✗ MyBase::mm[14] = v.z();
712 ✗ MyBase::mm[15] = 1;
713 }
714
715 /// Left multiples by the specified translation, i.e. Trans * (*this)
716 template <typename T0>
717 743785 void preTranslate(const Vec3<T0>& tr)
718 {
719 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
720 Mat4<T> Tr = Mat4<T>::translation(tmp);
721
722 743785 *this = Tr * (*this);
723
724 743785 }
725
726 /// Right multiplies by the specified translation matrix, i.e. (*this) * Trans
727 template <typename T0>
728 45 void postTranslate(const Vec3<T0>& tr)
729 {
730 Vec3<T> tmp(tr.x(), tr.y(), tr.z());
731 Mat4<T> Tr = Mat4<T>::translation(tmp);
732
733 45 *this = (*this) * Tr;
734
735 45 }
736
737
738 /// Sets the matrix to a matrix that scales by v
739 template <typename T0>
740 void setToScale(const Vec3<T0>& v)
741 {
742 this->setIdentity();
743 1 MyBase::mm[ 0] = v.x();
744 1 MyBase::mm[ 5] = v.y();
745 1 MyBase::mm[10] = v.z();
746 }
747
748 // Left multiples by the specified scale matrix, i.e. Sc * (*this)
749 template <typename T0>
750 149499 void preScale(const Vec3<T0>& v)
751 {
752 149499 MyBase::mm[ 0] *= v.x();
753 149499 MyBase::mm[ 1] *= v.x();
754 149499 MyBase::mm[ 2] *= v.x();
755 149499 MyBase::mm[ 3] *= v.x();
756
757 149499 MyBase::mm[ 4] *= v.y();
758 149499 MyBase::mm[ 5] *= v.y();
759 149499 MyBase::mm[ 6] *= v.y();
760 149499 MyBase::mm[ 7] *= v.y();
761
762 149499 MyBase::mm[ 8] *= v.z();
763 149499 MyBase::mm[ 9] *= v.z();
764 149499 MyBase::mm[10] *= v.z();
765 149499 MyBase::mm[11] *= v.z();
766 149499 }
767
768
769
770 // Right multiples by the specified scale matrix, i.e. (*this) * Sc
771 template <typename T0>
772 704 void postScale(const Vec3<T0>& v)
773 {
774
775 704 MyBase::mm[ 0] *= v.x();
776 704 MyBase::mm[ 1] *= v.y();
777 704 MyBase::mm[ 2] *= v.z();
778
779 704 MyBase::mm[ 4] *= v.x();
780 704 MyBase::mm[ 5] *= v.y();
781 704 MyBase::mm[ 6] *= v.z();
782
783 704 MyBase::mm[ 8] *= v.x();
784 704 MyBase::mm[ 9] *= v.y();
785 704 MyBase::mm[10] *= v.z();
786
787 704 MyBase::mm[12] *= v.x();
788 704 MyBase::mm[13] *= v.y();
789 704 MyBase::mm[14] *= v.z();
790
791 704 }
792
793
794 /// @brief Sets the matrix to a rotation about the given axis.
795 /// @param axis The axis (one of X, Y, Z) to rotate about.
796 /// @param angle The rotation angle, in radians.
797
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 1 void setToRotation(Axis axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
798
799 /// @brief Sets the matrix to a rotation about an arbitrary axis
800 /// @param axis The axis of rotation (cannot be zero-length)
801 /// @param angle The rotation angle, in radians.
802 7 void setToRotation(const Vec3<T>& axis, T angle) {*this = rotation<Mat4<T> >(axis, angle);}
803
804 /// @brief Sets the matrix to a rotation that maps v1 onto v2 about the cross
805 /// product of v1 and v2.
806 14 void setToRotation(const Vec3<T>& v1, const Vec3<T>& v2) {*this = rotation<Mat4<T> >(v1, v2);}
807
808
809 /// @brief Left multiplies by a rotation clock-wiseabout the given axis into this matrix.
810 /// @param axis The axis (one of X, Y, Z) of rotation.
811 /// @param angle The clock-wise rotation angle, in radians.
812 446302 void preRotate(Axis axis, T angle)
813 {
814 446302 T c = static_cast<T>(cos(angle));
815 446302 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
816
817
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 446302 switch (axis) {
818 148782 case X_AXIS:
819 {
820 T a4, a5, a6, a7;
821
822 148782 a4 = c * MyBase::mm[ 4] - s * MyBase::mm[ 8];
823 148782 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 9];
824 148782 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[10];
825 148782 a7 = c * MyBase::mm[ 7] - s * MyBase::mm[11];
826
827
828 148782 MyBase::mm[ 8] = s * MyBase::mm[ 4] + c * MyBase::mm[ 8];
829 148782 MyBase::mm[ 9] = s * MyBase::mm[ 5] + c * MyBase::mm[ 9];
830 148782 MyBase::mm[10] = s * MyBase::mm[ 6] + c * MyBase::mm[10];
831 148782 MyBase::mm[11] = s * MyBase::mm[ 7] + c * MyBase::mm[11];
832
833 148782 MyBase::mm[ 4] = a4;
834 148782 MyBase::mm[ 5] = a5;
835 148782 MyBase::mm[ 6] = a6;
836 148782 MyBase::mm[ 7] = a7;
837 }
838 148782 break;
839
840 148762 case Y_AXIS:
841 {
842 T a0, a1, a2, a3;
843
844 148762 a0 = c * MyBase::mm[ 0] + s * MyBase::mm[ 8];
845 148762 a1 = c * MyBase::mm[ 1] + s * MyBase::mm[ 9];
846 148762 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[10];
847 148762 a3 = c * MyBase::mm[ 3] + s * MyBase::mm[11];
848
849 148762 MyBase::mm[ 8] = -s * MyBase::mm[ 0] + c * MyBase::mm[ 8];
850 148762 MyBase::mm[ 9] = -s * MyBase::mm[ 1] + c * MyBase::mm[ 9];
851 148762 MyBase::mm[10] = -s * MyBase::mm[ 2] + c * MyBase::mm[10];
852 148762 MyBase::mm[11] = -s * MyBase::mm[ 3] + c * MyBase::mm[11];
853
854
855 148762 MyBase::mm[ 0] = a0;
856 148762 MyBase::mm[ 1] = a1;
857 148762 MyBase::mm[ 2] = a2;
858 148762 MyBase::mm[ 3] = a3;
859 }
860 148762 break;
861
862 148758 case Z_AXIS:
863 {
864 T a0, a1, a2, a3;
865
866 148758 a0 = c * MyBase::mm[ 0] - s * MyBase::mm[ 4];
867 148758 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 5];
868 148758 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 6];
869 148758 a3 = c * MyBase::mm[ 3] - s * MyBase::mm[ 7];
870
871 148758 MyBase::mm[ 4] = s * MyBase::mm[ 0] + c * MyBase::mm[ 4];
872 148758 MyBase::mm[ 5] = s * MyBase::mm[ 1] + c * MyBase::mm[ 5];
873 148758 MyBase::mm[ 6] = s * MyBase::mm[ 2] + c * MyBase::mm[ 6];
874 148758 MyBase::mm[ 7] = s * MyBase::mm[ 3] + c * MyBase::mm[ 7];
875
876 148758 MyBase::mm[ 0] = a0;
877 148758 MyBase::mm[ 1] = a1;
878 148758 MyBase::mm[ 2] = a2;
879 148758 MyBase::mm[ 3] = a3;
880 }
881 148758 break;
882
883 ✗ default:
884 ✗ assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
885 }
886 446302 }
887
888
889 /// @brief Right multiplies by a rotation clock-wiseabout the given axis into this matrix.
890 /// @param axis The axis (one of X, Y, Z) of rotation.
891 /// @param angle The clock-wise rotation angle, in radians.
892 31 void postRotate(Axis axis, T angle)
893 {
894 31 T c = static_cast<T>(cos(angle));
895 31 T s = -static_cast<T>(sin(angle)); // the "-" makes it clockwise
896
897
898
899
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 31 switch (axis) {
900 24 case X_AXIS:
901 {
902 T a2, a6, a10, a14;
903
904 24 a2 = c * MyBase::mm[ 2] - s * MyBase::mm[ 1];
905 24 a6 = c * MyBase::mm[ 6] - s * MyBase::mm[ 5];
906 24 a10 = c * MyBase::mm[10] - s * MyBase::mm[ 9];
907 24 a14 = c * MyBase::mm[14] - s * MyBase::mm[13];
908
909
910 24 MyBase::mm[ 1] = c * MyBase::mm[ 1] + s * MyBase::mm[ 2];
911 24 MyBase::mm[ 5] = c * MyBase::mm[ 5] + s * MyBase::mm[ 6];
912 24 MyBase::mm[ 9] = c * MyBase::mm[ 9] + s * MyBase::mm[10];
913 24 MyBase::mm[13] = c * MyBase::mm[13] + s * MyBase::mm[14];
914
915 24 MyBase::mm[ 2] = a2;
916 24 MyBase::mm[ 6] = a6;
917 24 MyBase::mm[10] = a10;
918 24 MyBase::mm[14] = a14;
919 }
920 24 break;
921
922 5 case Y_AXIS:
923 {
924 T a2, a6, a10, a14;
925
926 5 a2 = c * MyBase::mm[ 2] + s * MyBase::mm[ 0];
927 5 a6 = c * MyBase::mm[ 6] + s * MyBase::mm[ 4];
928 5 a10 = c * MyBase::mm[10] + s * MyBase::mm[ 8];
929 5 a14 = c * MyBase::mm[14] + s * MyBase::mm[12];
930
931 5 MyBase::mm[ 0] = c * MyBase::mm[ 0] - s * MyBase::mm[ 2];
932 5 MyBase::mm[ 4] = c * MyBase::mm[ 4] - s * MyBase::mm[ 6];
933 5 MyBase::mm[ 8] = c * MyBase::mm[ 8] - s * MyBase::mm[10];
934 5 MyBase::mm[12] = c * MyBase::mm[12] - s * MyBase::mm[14];
935
936 5 MyBase::mm[ 2] = a2;
937 5 MyBase::mm[ 6] = a6;
938 5 MyBase::mm[10] = a10;
939 5 MyBase::mm[14] = a14;
940 }
941 5 break;
942
943 2 case Z_AXIS:
944 {
945 T a1, a5, a9, a13;
946
947 2 a1 = c * MyBase::mm[ 1] - s * MyBase::mm[ 0];
948 2 a5 = c * MyBase::mm[ 5] - s * MyBase::mm[ 4];
949 2 a9 = c * MyBase::mm[ 9] - s * MyBase::mm[ 8];
950 2 a13 = c * MyBase::mm[13] - s * MyBase::mm[12];
951
952 2 MyBase::mm[ 0] = c * MyBase::mm[ 0] + s * MyBase::mm[ 1];
953 2 MyBase::mm[ 4] = c * MyBase::mm[ 4] + s * MyBase::mm[ 5];
954 2 MyBase::mm[ 8] = c * MyBase::mm[ 8] + s * MyBase::mm[ 9];
955 2 MyBase::mm[12] = c * MyBase::mm[12] + s * MyBase::mm[13];
956
957 2 MyBase::mm[ 1] = a1;
958 2 MyBase::mm[ 5] = a5;
959 2 MyBase::mm[ 9] = a9;
960 2 MyBase::mm[13] = a13;
961
962 }
963 2 break;
964
965 ✗ default:
966 ✗ assert(axis==X_AXIS || axis==Y_AXIS || axis==Z_AXIS);
967 }
968 31 }
969
970 /// @brief Sets the matrix to a shear along axis0 by a fraction of axis1.
971 /// @param axis0 The fixed axis of the shear.
972 /// @param axis1 The shear axis.
973 /// @param shearby The shear factor.
974 void setToShear(Axis axis0, Axis axis1, T shearby)
975 {
976 2 *this = shear<Mat4<T> >(axis0, axis1, shearby);
977 }
978
979
980 /// @brief Left multiplies a shearing transformation into the matrix.
981 /// @see setToShear
982 7 void preShear(Axis axis0, Axis axis1, T shear)
983 {
984 7 int index0 = static_cast<int>(axis0);
985 7 int index1 = static_cast<int>(axis1);
986
987 // to row "index1" add a multiple of the index0 row
988 13 MyBase::mm[index1 * 4 + 0] += shear * MyBase::mm[index0 * 4 + 0];
989 13 MyBase::mm[index1 * 4 + 1] += shear * MyBase::mm[index0 * 4 + 1];
990 13 MyBase::mm[index1 * 4 + 2] += shear * MyBase::mm[index0 * 4 + 2];
991 12 MyBase::mm[index1 * 4 + 3] += shear * MyBase::mm[index0 * 4 + 3];
992 7 }
993
994
995 /// @brief Right multiplies a shearing transformation into the matrix.
996 /// @see setToShear
997 7 void postShear(Axis axis0, Axis axis1, T shear)
998 {
999 7 int index0 = static_cast<int>(axis0);
1000 7 int index1 = static_cast<int>(axis1);
1001
1002 // to collumn "index0" add a multiple of the index1 row
1003 12 MyBase::mm[index0 + 0] += shear * MyBase::mm[index1 + 0];
1004 12 MyBase::mm[index0 + 4] += shear * MyBase::mm[index1 + 4];
1005 12 MyBase::mm[index0 + 8] += shear * MyBase::mm[index1 + 8];
1006 11 MyBase::mm[index0 + 12] += shear * MyBase::mm[index1 + 12];
1007
1008 8 }
1009
1010 /// Transform a Vec4 by post-multiplication.
1011 template<typename T0>
1012 Vec4<T0> transform(const Vec4<T0> &v) const
1013 {
1014 return static_cast< Vec4<T0> >(v * *this);
1015 }
1016
1017 /// Transform a Vec3 by post-multiplication, without homogenous division.
1018 template<typename T0>
1019 1108081 Vec3<T0> transform(const Vec3<T0> &v) const
1020 {
1021 1108094 return static_cast< Vec3<T0> >(v * *this);
1022 }
1023
1024 /// Transform a Vec4 by pre-multiplication.
1025 template<typename T0>
1026 Vec4<T0> pretransform(const Vec4<T0> &v) const
1027 {
1028 return static_cast< Vec4<T0> >(*this * v);
1029 }
1030
1031 /// Transform a Vec3 by pre-multiplication, without homogenous division.
1032 template<typename T0>
1033 Vec3<T0> pretransform(const Vec3<T0> &v) const
1034 {
1035 return static_cast< Vec3<T0> >(*this * v);
1036 }
1037
1038 /// Transform a Vec3 by post-multiplication, doing homogenous divison.
1039 template<typename T0>
1040
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 55078 Vec3<T0> transformH(const Vec3<T0> &p) const
1041 {
1042 T0 w;
1043
1044 // w = p * (*this).col(3);
1045 55078 w = static_cast<T0>(p[0] * MyBase::mm[ 3] + p[1] * MyBase::mm[ 7]
1046
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 55078 + p[2] * MyBase::mm[11] + MyBase::mm[15]);
1047
1048
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 55078 if ( !isExactlyEqual(w , 0.0) ) {
1049 55078 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 4] +
1050 55078 p[2] * MyBase::mm[ 8] + MyBase::mm[12]) / w),
1051 55078 static_cast<T0>((p[0] * MyBase::mm[ 1] + p[1] * MyBase::mm[ 5] +
1052 55078 p[2] * MyBase::mm[ 9] + MyBase::mm[13]) / w),
1053 55078 static_cast<T0>((p[0] * MyBase::mm[ 2] + p[1] * MyBase::mm[ 6] +
1054 55078 p[2] * MyBase::mm[10] + MyBase::mm[14]) / w));
1055 }
1056
1057 ✗ return Vec3<T0>(0, 0, 0);
1058 }
1059
1060 /// Transform a Vec3 by pre-multiplication, doing homogenous division.
1061 template<typename T0>
1062 Vec3<T0> pretransformH(const Vec3<T0> &p) const
1063 {
1064 T0 w;
1065
1066 // w = p * (*this).col(3);
1067 w = p[0] * MyBase::mm[12] + p[1] * MyBase::mm[13] + p[2] * MyBase::mm[14] + MyBase::mm[15];
1068
1069 if ( !isExactlyEqual(w , 0.0) ) {
1070 return Vec3<T0>(static_cast<T0>((p[0] * MyBase::mm[ 0] + p[1] * MyBase::mm[ 1] +
1071 p[2] * MyBase::mm[ 2] + MyBase::mm[ 3]) / w),
1072 static_cast<T0>((p[0] * MyBase::mm[ 4] + p[1] * MyBase::mm[ 5] +
1073 p[2] * MyBase::mm[ 6] + MyBase::mm[ 7]) / w),
1074 static_cast<T0>((p[0] * MyBase::mm[ 8] + p[1] * MyBase::mm[ 9] +
1075 p[2] * MyBase::mm[10] + MyBase::mm[11]) / w));
1076 }
1077
1078 return Vec3<T0>(0, 0, 0);
1079 }
1080
1081 /// Transform a Vec3 by post-multiplication, without translation.
1082 template<typename T0>
1083 112168 Vec3<T0> transform3x3(const Vec3<T0> &v) const
1084 {
1085 return Vec3<T0>(
1086 112168 static_cast<T0>(v[0] * MyBase::mm[ 0] + v[1] * MyBase::mm[ 4] + v[2] * MyBase::mm[ 8]),
1087 112168 static_cast<T0>(v[0] * MyBase::mm[ 1] + v[1] * MyBase::mm[ 5] + v[2] * MyBase::mm[ 9]),
1088 112168 static_cast<T0>(v[0] * MyBase::mm[ 2] + v[1] * MyBase::mm[ 6] + v[2] * MyBase::mm[10]));
1089 }
1090
1091
1092 private:
1093 bool invert(Mat4<T> &inverse, T tolerance) const;
1094
1095 T det2(const Mat4<T> &a, int i0, int i1, int j0, int j1) const {
1096 int i0row = i0 * 4;
1097 int i1row = i1 * 4;
1098 ✗ return a.mm[i0row+j0]*a.mm[i1row+j1] - a.mm[i0row+j1]*a.mm[i1row+j0];
1099 }
1100
1101 T det3(const Mat4<T> &a, int i0, int i1, int i2,
1102 int j0, int j1, int j2) const {
1103 int i0row = i0 * 4;
1104 ✗ return a.mm[i0row+j0]*det2(a, i1,i2, j1,j2) +
1105 ✗ a.mm[i0row+j1]*det2(a, i1,i2, j2,j0) +
1106 ✗ a.mm[i0row+j2]*det2(a, i1,i2, j0,j1);
1107 }
1108 }; // class Mat4
1109
1110
1111 /// @relates Mat4
1112 /// @brief Equality operator, does exact floating point comparisons
1113 template <typename T0, typename T1>
1114 83927889 bool operator==(const Mat4<T0> &m0, const Mat4<T1> &m1)
1115 {
1116 const T0 *t0 = m0.asPointer();
1117 const T1 *t1 = m1.asPointer();
1118
1119
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 1424438305 for (int i=0; i<16; ++i) if (!isExactlyEqual(t0[i], t1[i])) return false;
1120 return true;
1121 }
1122
1123 /// @relates Mat4
1124 /// @brief Inequality operator, does exact floating point comparisons
1125 template <typename T0, typename T1>
1126 83927080 bool operator!=(const Mat4<T0> &m0, const Mat4<T1> &m1) { return !(m0 == m1); }
1127
1128 /// @relates Mat4
1129 /// @brief Multiply each element of the given matrix by @a scalar and return the result.
1130 template <typename S, typename T>
1131 Mat4<typename promote<S, T>::type> operator*(S scalar, const Mat4<T> &m)
1132 {
1133 return m*scalar;
1134 }
1135
1136 /// @relates Mat4
1137 /// @brief Multiply each element of the given matrix by @a scalar and return the result.
1138 template <typename S, typename T>
1139 Mat4<typename promote<S, T>::type> operator*(const Mat4<T> &m, S scalar)
1140 {
1141 Mat4<typename promote<S, T>::type> result(m);
1142 result *= scalar;
1143 return result;
1144 }
1145
1146 /// @relates Mat4
1147 /// @brief Multiply @a _m by @a _v and return the resulting vector.
1148 template<typename T, typename MT>
1149 inline Vec4<typename promote<T, MT>::type>
1150 296 operator*(const Mat4<MT> &_m,
1151 const Vec4<T> &_v)
1152 {
1153 MT const *m = _m.asPointer();
1154 return Vec4<typename promote<T, MT>::type>(
1155 296 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + _v[3]*m[3],
1156 296 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + _v[3]*m[7],
1157 296 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + _v[3]*m[11],
1158 296 _v[0]*m[12] + _v[1]*m[13] + _v[2]*m[14] + _v[3]*m[15]);
1159 }
1160
1161 /// @relates Mat4
1162 /// @brief Multiply @a _v by @a _m and return the resulting vector.
1163 template<typename T, typename MT>
1164 inline Vec4<typename promote<T, MT>::type>
1165 296 operator*(const Vec4<T> &_v,
1166 const Mat4<MT> &_m)
1167 {
1168 MT const *m = _m.asPointer();
1169 return Vec4<typename promote<T, MT>::type>(
1170 296 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + _v[3]*m[12],
1171 296 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + _v[3]*m[13],
1172 296 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + _v[3]*m[14],
1173 296 _v[0]*m[3] + _v[1]*m[7] + _v[2]*m[11] + _v[3]*m[15]);
1174 }
1175
1176 /// @relates Mat4
1177 /// @brief Multiply @a _m by @a _v and return the resulting vector.
1178 template<typename T, typename MT>
1179 inline Vec3<typename promote<T, MT>::type>
1180 592 operator*(const Mat4<MT> &_m, const Vec3<T> &_v)
1181 {
1182 MT const *m = _m.asPointer();
1183 return Vec3<typename promote<T, MT>::type>(
1184 592 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2] + m[3],
1185 592 _v[0]*m[4] + _v[1]*m[5] + _v[2]*m[6] + m[7],
1186 592 _v[0]*m[8] + _v[1]*m[9] + _v[2]*m[10] + m[11]);
1187 }
1188
1189 /// @relates Mat4
1190 /// @brief Multiply @a _v by @a _m and return the resulting vector.
1191 template<typename T, typename MT>
1192 inline Vec3<typename promote<T, MT>::type>
1193 2646490322 operator*(const Vec3<T> &_v, const Mat4<MT> &_m)
1194 {
1195 MT const *m = _m.asPointer();
1196 return Vec3<typename promote<T, MT>::type>(
1197 2646490322 _v[0]*m[0] + _v[1]*m[4] + _v[2]*m[8] + m[12],
1198 2646490322 _v[0]*m[1] + _v[1]*m[5] + _v[2]*m[9] + m[13],
1199 2646490322 _v[0]*m[2] + _v[1]*m[6] + _v[2]*m[10] + m[14]);
1200 }
1201
1202 /// @relates Mat4
1203 /// @brief Add corresponding elements of @a m0 and @a m1 and return the result.
1204 template <typename T0, typename T1>
1205 Mat4<typename promote<T0, T1>::type>
1206 24 operator+(const Mat4<T0> &m0, const Mat4<T1> &m1)
1207 {
1208 24 Mat4<typename promote<T0, T1>::type> result(m0);
1209 24 result += m1;
1210 24 return result;
1211 }
1212
1213 /// @relates Mat4
1214 /// @brief Subtract corresponding elements of @a m0 and @a m1 and return the result.
1215 template <typename T0, typename T1>
1216 Mat4<typename promote<T0, T1>::type>
1217 164074 operator-(const Mat4<T0> &m0, const Mat4<T1> &m1)
1218 {
1219 164074 Mat4<typename promote<T0, T1>::type> result(m0);
1220 164074 result -= m1;
1221 164074 return result;
1222 }
1223
1224 /// @relates Mat4
1225 /// @brief Multiply @a m0 by @a m1 and return the resulting matrix.
1226 template <typename T0, typename T1>
1227 Mat4<typename promote<T0, T1>::type>
1228 1962135 operator*(const Mat4<T0> &m0, const Mat4<T1> &m1)
1229 {
1230 1962135 Mat4<typename promote<T0, T1>::type> result(m0);
1231 1962135 result *= m1;
1232 1962135 return result;
1233 }
1234
1235
1236 /// Transform a Vec3 by pre-multiplication, without translation.
1237 /// Presumes this matrix is inverse of coordinate transform
1238 /// Synonymous to "pretransform3x3"
1239 template<typename T0, typename T1>
1240 Vec3<T1> transformNormal(const Mat4<T0> &m, const Vec3<T1> &n)
1241 {
1242 return Vec3<T1>(
1243 static_cast<T1>(m[0][0]*n[0] + m[0][1]*n[1] + m[0][2]*n[2]),
1244 static_cast<T1>(m[1][0]*n[0] + m[1][1]*n[1] + m[1][2]*n[2]),
1245 static_cast<T1>(m[2][0]*n[0] + m[2][1]*n[1] + m[2][2]*n[2]));
1246 }
1247
1248
1249 /// Invert via gauss-jordan elimination. Modified from dreamworks internal mx library
1250 template<typename T>
1251 ✗ bool Mat4<T>::invert(Mat4<T> &inverse, T tolerance) const
1252 {
1253 ✗ Mat4<T> temp(*this);
1254 inverse.setIdentity();
1255
1256 // Forward elimination step
1257 double det = 1.0;
1258 ✗ for (int i = 0; i < 4; ++i) {
1259 int row = i;
1260 ✗ double max = fabs(temp[i][i]);
1261
1262 ✗ for (int k = i+1; k < 4; ++k) {
1263 ✗ if (fabs(temp[k][i]) > max) {
1264 row = k;
1265 max = fabs(temp[k][i]);
1266 }
1267 }
1268
1269 ✗ if (isExactlyEqual(max, 0.0)) return false;
1270
1271 // must move pivot to row i
1272 ✗ if (row != i) {
1273 ✗ det = -det;
1274 ✗ for (int k = 0; k < 4; ++k) {
1275 ✗ std::swap(temp[row][k], temp[i][k]);
1276 ✗ std::swap(inverse[row][k], inverse[i][k]);
1277 }
1278 }
1279
1280 ✗ double pivot = temp[i][i];
1281 ✗ det *= pivot;
1282
1283 // scale row i
1284 ✗ for (int k = 0; k < 4; ++k) {
1285 ✗ temp[i][k] /= pivot;
1286 ✗ inverse[i][k] /= pivot;
1287 }
1288
1289 // eliminate in rows below i
1290 ✗ for (int j = i+1; j < 4; ++j) {
1291 ✗ double t = temp[j][i];
1292 ✗ if (!isExactlyEqual(t, 0.0)) {
1293 // subtract scaled row i from row j
1294 ✗ for (int k = 0; k < 4; ++k) {
1295 ✗ temp[j][k] -= temp[i][k] * t;
1296 ✗ inverse[j][k] -= inverse[i][k] * t;
1297 }
1298 }
1299 }
1300 }
1301
1302 // Backward elimination step
1303 ✗ for (int i = 3; i > 0; --i) {
1304 ✗ for (int j = 0; j < i; ++j) {
1305 ✗ double t = temp[j][i];
1306
1307 ✗ if (!isExactlyEqual(t, 0.0)) {
1308 ✗ for (int k = 0; k < 4; ++k) {
1309 ✗ inverse[j][k] -= inverse[i][k]*t;
1310 }
1311 }
1312 }
1313 }
1314 ✗ return det*det >= tolerance*tolerance;
1315 }
1316
1317 template <typename T>
1318 inline bool isAffine(const Mat4<T>& m) {
1319 return (m.col(3) == Vec4<T>(0, 0, 0, 1));
1320 }
1321
1322 template <typename T>
1323 inline bool hasTranslation(const Mat4<T>& m) {
1324 return (m.row(3) != Vec4<T>(0, 0, 0, 1));
1325 }
1326
1327 template<typename T>
1328 inline Mat4<T>
1329 Abs(const Mat4<T>& m)
1330 {
1331 Mat4<T> out;
1332 const T* ip = m.asPointer();
1333 T* op = out.asPointer();
1334
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 1394561 for (unsigned i = 0; i < 16; ++i, ++op, ++ip) *op = math::Abs(*ip);
1335 return out;
1336 }
1337
1338 template<typename Type1, typename Type2>
1339 inline Mat4<Type1>
1340 cwiseAdd(const Mat4<Type1>& m, const Type2 s)
1341 {
1342 Mat4<Type1> out;
1343 const Type1* ip = m.asPointer();
1344 Type1* op = out.asPointer();
1345 ✗ for (unsigned i = 0; i < 16; ++i, ++op, ++ip) {
1346 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
1347 ✗ *op = *ip + s;
1348 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
1349 }
1350 return out;
1351 }
1352
1353 template<typename T>
1354 inline bool
1355 cwiseLessThan(const Mat4<T>& m0, const Mat4<T>& m1)
1356 {
1357 return cwiseLessThan<4, T>(m0, m1);
1358 }
1359
1360 template<typename T>
1361 inline bool
1362 cwiseGreaterThan(const Mat4<T>& m0, const Mat4<T>& m1)
1363 {
1364 return cwiseGreaterThan<4, T>(m0, m1);
1365 }
1366
1367 using Mat4s = Mat4<float>;
1368 using Mat4d = Mat4<double>;
1369 using Mat4f = Mat4d;
1370
1371 #if OPENVDB_ABI_VERSION_NUMBER >= 8
1372 OPENVDB_IS_POD(Mat4s)
1373 OPENVDB_IS_POD(Mat4d)
1374 #endif
1375
1376 } // namespace math
1377
1378
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 1714017 template<> inline math::Mat4s zeroVal<math::Mat4s>() { return math::Mat4s::zero(); }
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 1928135 template<> inline math::Mat4d zeroVal<math::Mat4d>() { return math::Mat4d::zero(); }
1381
1382 } // namespace OPENVDB_VERSION_NAME
1383 } // namespace openvdb
1384
1385 #endif // OPENVDB_UTIL_MAT4_H_HAS_BEEN_INCLUDED
1386