OpenVDB 3.2.0

Mat3.h
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30
31 #ifndef OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED
33
34 #include <iomanip>
35 #include <assert.h>
36 #include <math.h>
37 #include <openvdb/Exceptions.h>
38 #include "Vec3.h"
39 #include "Mat.h"
40
41
42 namespace openvdb {
43 OPENVDB_USE_VERSION_NAMESPACE
44 namespace OPENVDB_VERSION_NAME {
45 namespace math {
46
47 template<typename T> class Vec3;
48 template<typename T> class Mat4;
49 template<typename T> class Quat;
50
53 template<typename T>
54 class Mat3: public Mat<3, T>
55 {
56 public:
58 typedef T value_type;
59 typedef T ValueType;
60 typedef Mat<3, T> MyBase;
62 Mat3() {}
63
66 Mat3(const Quat<T> &q)
67 { setToRotation(q); }
68
69
71
76 template<typename Source>
77 Mat3(Source a, Source b, Source c,
78 Source d, Source e, Source f,
79 Source g, Source h, Source i)
80 {
81 MyBase::mm[0] = static_cast<ValueType>(a);
82 MyBase::mm[1] = static_cast<ValueType>(b);
83 MyBase::mm[2] = static_cast<ValueType>(c);
84 MyBase::mm[3] = static_cast<ValueType>(d);
85 MyBase::mm[4] = static_cast<ValueType>(e);
86 MyBase::mm[5] = static_cast<ValueType>(f);
87 MyBase::mm[6] = static_cast<ValueType>(g);
88 MyBase::mm[7] = static_cast<ValueType>(h);
89 MyBase::mm[8] = static_cast<ValueType>(i);
90 } // constructor1Test
91
94 template<typename Source>
95 Mat3(const Vec3<Source> &v1, const Vec3<Source> &v2, const Vec3<Source> &v3, bool rows = true)
96 {
97 if (rows) {
98 this->setRows(v1, v2, v3);
99 } else {
100 this->setColumns(v1, v2, v3);
101 }
102 }
103
108 template<typename Source>
109 Mat3(Source *a)
110 {
111 MyBase::mm[0] = a[0];
112 MyBase::mm[1] = a[1];
113 MyBase::mm[2] = a[2];
114 MyBase::mm[3] = a[3];
115 MyBase::mm[4] = a[4];
116 MyBase::mm[5] = a[5];
117 MyBase::mm[6] = a[6];
118 MyBase::mm[7] = a[7];
119 MyBase::mm[8] = a[8];
120 } // constructor1Test
121
123 Mat3(const Mat<3, T> &m)
124 {
125 for (int i=0; i<3; ++i) {
126 for (int j=0; j<3; ++j) {
127 MyBase::mm[i*3 + j] = m[i][j];
128 }
129 }
130 }
131
133 template<typename Source>
134 explicit Mat3(const Mat3<Source> &m)
135 {
136 for (int i=0; i<3; ++i) {
137 for (int j=0; j<3; ++j) {
138 MyBase::mm[i*3 + j] = static_cast<T>(m[i][j]);
139 }
140 }
141 }
142
144 explicit Mat3(const Mat4<T> &m)
145 {
146 for (int i=0; i<3; ++i) {
147 for (int j=0; j<3; ++j) {
148 MyBase::mm[i*3 + j] = m[i][j];
149 }
150 }
151 }
152
154 static const Mat3<T>& identity() {
155 return sIdentity;
156 }
157
159 static const Mat3<T>& zero() {
160 return sZero;
161 }
162
164 void setRow(int i, const Vec3<T> &v)
165 {
166 // assert(i>=0 && i<3);
167 int i3 = i * 3;
168
169 MyBase::mm[i3+0] = v[0];
170 MyBase::mm[i3+1] = v[1];
171 MyBase::mm[i3+2] = v[2];
172 } // rowColumnTest
173
175 Vec3<T> row(int i) const
176 {
177 // assert(i>=0 && i<3);
178 return Vec3<T>((*this)(i,0), (*this)(i,1), (*this)(i,2));
179 } // rowColumnTest
180
182 void setCol(int j, const Vec3<T>& v)
183 {
184 // assert(j>=0 && j<3);
185 MyBase::mm[0+j] = v[0];
186 MyBase::mm[3+j] = v[1];
187 MyBase::mm[6+j] = v[2];
188 } // rowColumnTest
189
191 Vec3<T> col(int j) const
192 {
193 // assert(j>=0 && j<3);
194 return Vec3<T>((*this)(0,j), (*this)(1,j), (*this)(2,j));
195 } // rowColumnTest
196
197 // NB: The following two methods were changed to
198 // work around a gccWS5 compiler issue related to strict
199 // aliasing (see FX-475).
200
202 T* operator[](int i) { return &(MyBase::mm[i*3]); }
205 const T* operator[](int i) const { return &(MyBase::mm[i*3]); }
207
208 T* asPointer() {return MyBase::mm;}
209 const T* asPointer() const {return MyBase::mm;}
210
214 T& operator()(int i, int j)
215 {
216 // assert(i>=0 && i<3);
217 // assert(j>=0 && j<3);
218 return MyBase::mm[3*i+j];
219 } // trivial
220
224 T operator()(int i, int j) const
225 {
226 // assert(i>=0 && i<3);
227 // assert(j>=0 && j<3);
228 return MyBase::mm[3*i+j];
229 } // trivial
230
232 void setRows(const Vec3<T> &v1, const Vec3<T> &v2, const Vec3<T> &v3)
233 {
234 MyBase::mm[0] = v1[0];
235 MyBase::mm[1] = v1[1];
236 MyBase::mm[2] = v1[2];
237 MyBase::mm[3] = v2[0];
238 MyBase::mm[4] = v2[1];
239 MyBase::mm[5] = v2[2];
240 MyBase::mm[6] = v3[0];
241 MyBase::mm[7] = v3[1];
242 MyBase::mm[8] = v3[2];
243 } // setRows
244
246 void setColumns(const Vec3<T> &v1, const Vec3<T> &v2, const Vec3<T> &v3)
247 {
248 MyBase::mm[0] = v1[0];
249 MyBase::mm[1] = v2[0];
250 MyBase::mm[2] = v3[0];
251 MyBase::mm[3] = v1[1];
252 MyBase::mm[4] = v2[1];
253 MyBase::mm[5] = v3[1];
254 MyBase::mm[6] = v1[2];
255 MyBase::mm[7] = v2[2];
256 MyBase::mm[8] = v3[2];
257 } // setColumns
258
260 OPENVDB_DEPRECATED void setBasis(const Vec3<T> &v1, const Vec3<T> &v2, const Vec3<T> &v3)
261 {
262 this->setRows(v1, v2, v3);
263 }
264
266 void setSymmetric(const Vec3<T> &vdiag, const Vec3<T> &vtri)
267 {
268 MyBase::mm[0] = vdiag[0];
269 MyBase::mm[1] = vtri[0];
270 MyBase::mm[2] = vtri[1];
271 MyBase::mm[3] = vtri[0];
272 MyBase::mm[4] = vdiag[1];
273 MyBase::mm[5] = vtri[2];
274 MyBase::mm[6] = vtri[1];
275 MyBase::mm[7] = vtri[2];
276 MyBase::mm[8] = vdiag[2];
277 } // setSymmetricTest
278
281 static Mat3 symmetric(const Vec3<T> &vdiag, const Vec3<T> &vtri)
282 {
283 return Mat3(
284 vdiag[0], vtri[0], vtri[1],
285 vtri[0], vdiag[1], vtri[2],
286 vtri[1], vtri[2], vdiag[2]
287 );
288 }
289
291 void setSkew(const Vec3<T> &v)
292 {*this = skew(v);}
293
297 void setToRotation(const Quat<T> &q)
298 {*this = rotation<Mat3<T> >(q);}
299
302 void setToRotation(const Vec3<T> &axis, T angle)
303 {*this = rotation<Mat3<T> >(axis, angle);}
304
306 void setZero()
307 {
308 MyBase::mm[0] = 0;
309 MyBase::mm[1] = 0;
310 MyBase::mm[2] = 0;
311 MyBase::mm[3] = 0;
312 MyBase::mm[4] = 0;
313 MyBase::mm[5] = 0;
314 MyBase::mm[6] = 0;
315 MyBase::mm[7] = 0;
316 MyBase::mm[8] = 0;
317 } // trivial
318
320 void setIdentity()
321 {
322 MyBase::mm[0] = 1;
323 MyBase::mm[1] = 0;
324 MyBase::mm[2] = 0;
325 MyBase::mm[3] = 0;
326 MyBase::mm[4] = 1;
327 MyBase::mm[5] = 0;
328 MyBase::mm[6] = 0;
329 MyBase::mm[7] = 0;
330 MyBase::mm[8] = 1;
331 } // trivial
332
334 template<typename Source>
335 const Mat3& operator=(const Mat3<Source> &m)
336 {
337 const Source *src = m.asPointer();
338
339 // don't suppress type conversion warnings
340 std::copy(src, (src + this->numElements()), MyBase::mm);
341 return *this;
342 } // opEqualToTest
343
345 bool eq(const Mat3 &m, T eps=1.0e-8) const
346 {
347 return (isApproxEqual(MyBase::mm[0],m.mm[0],eps) &&
348 isApproxEqual(MyBase::mm[1],m.mm[1],eps) &&
349 isApproxEqual(MyBase::mm[2],m.mm[2],eps) &&
350 isApproxEqual(MyBase::mm[3],m.mm[3],eps) &&
351 isApproxEqual(MyBase::mm[4],m.mm[4],eps) &&
352 isApproxEqual(MyBase::mm[5],m.mm[5],eps) &&
353 isApproxEqual(MyBase::mm[6],m.mm[6],eps) &&
354 isApproxEqual(MyBase::mm[7],m.mm[7],eps) &&
355 isApproxEqual(MyBase::mm[8],m.mm[8],eps));
356 } // trivial
357
359 Mat3<T> operator-() const
360 {
361 return Mat3<T>(
362 -MyBase::mm[0], -MyBase::mm[1], -MyBase::mm[2],
363 -MyBase::mm[3], -MyBase::mm[4], -MyBase::mm[5],
364 -MyBase::mm[6], -MyBase::mm[7], -MyBase::mm[8]
365 );
366 } // trivial
367
369 // friend Mat3 operator*(T scalar, const Mat3& m) {
370 // return m*scalar;
371 // }
372
374 template <typename S>
375 const Mat3<T>& operator*=(S scalar)
376 {
377 MyBase::mm[0] *= scalar;
378 MyBase::mm[1] *= scalar;
379 MyBase::mm[2] *= scalar;
380 MyBase::mm[3] *= scalar;
381 MyBase::mm[4] *= scalar;
382 MyBase::mm[5] *= scalar;
383 MyBase::mm[6] *= scalar;
384 MyBase::mm[7] *= scalar;
385 MyBase::mm[8] *= scalar;
386 return *this;
387 }
388
390 template <typename S>
391 const Mat3<T> &operator+=(const Mat3<S> &m1)
392 {
393 const S *s = m1.asPointer();
394
395 MyBase::mm[0] += s[0];
396 MyBase::mm[1] += s[1];
397 MyBase::mm[2] += s[2];
398 MyBase::mm[3] += s[3];
399 MyBase::mm[4] += s[4];
400 MyBase::mm[5] += s[5];
401 MyBase::mm[6] += s[6];
402 MyBase::mm[7] += s[7];
403 MyBase::mm[8] += s[8];
404 return *this;
405 }
406
408 template <typename S>
409 const Mat3<T> &operator-=(const Mat3<S> &m1)
410 {
411 const S *s = m1.asPointer();
412
413 MyBase::mm[0] -= s[0];
414 MyBase::mm[1] -= s[1];
415 MyBase::mm[2] -= s[2];
416 MyBase::mm[3] -= s[3];
417 MyBase::mm[4] -= s[4];
418 MyBase::mm[5] -= s[5];
419 MyBase::mm[6] -= s[6];
420 MyBase::mm[7] -= s[7];
421 MyBase::mm[8] -= s[8];
422 return *this;
423 }
424
426 template <typename S>
427 const Mat3<T> &operator*=(const Mat3<S> &m1)
428 {
429 Mat3<T> m0(*this);
430 const T* s0 = m0.asPointer();
431 const S* s1 = m1.asPointer();
432
433 MyBase::mm[0] = static_cast<T>(s0[0] * s1[0] +
434 s0[1] * s1[3] +
435 s0[2] * s1[6]);
436 MyBase::mm[1] = static_cast<T>(s0[0] * s1[1] +
437 s0[1] * s1[4] +
438 s0[2] * s1[7]);
439 MyBase::mm[2] = static_cast<T>(s0[0] * s1[2] +
440 s0[1] * s1[5] +
441 s0[2] * s1[8]);
442
443 MyBase::mm[3] = static_cast<T>(s0[3] * s1[0] +
444 s0[4] * s1[3] +
445 s0[5] * s1[6]);
446 MyBase::mm[4] = static_cast<T>(s0[3] * s1[1] +
447 s0[4] * s1[4] +
448 s0[5] * s1[7]);
449 MyBase::mm[5] = static_cast<T>(s0[3] * s1[2] +
450 s0[4] * s1[5] +
451 s0[5] * s1[8]);
452
453 MyBase::mm[6] = static_cast<T>(s0[6] * s1[0] +
454 s0[7] * s1[3] +
455 s0[8] * s1[6]);
456 MyBase::mm[7] = static_cast<T>(s0[6] * s1[1] +
457 s0[7] * s1[4] +
458 s0[8] * s1[7]);
459 MyBase::mm[8] = static_cast<T>(s0[6] * s1[2] +
460 s0[7] * s1[5] +
461 s0[8] * s1[8]);
462
463 return *this;
464 }
465
467 Mat3 cofactor() const
468 {
469 return Mat3<T>(
470 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
471 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
472 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
473 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
474 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
475 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
476 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
477 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
478 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
479 }
480
482 Mat3 adjoint() const
483 {
484 return Mat3<T>(
485 MyBase::mm[4] * MyBase::mm[8] - MyBase::mm[5] * MyBase::mm[7],
486 MyBase::mm[2] * MyBase::mm[7] - MyBase::mm[1] * MyBase::mm[8],
487 MyBase::mm[1] * MyBase::mm[5] - MyBase::mm[2] * MyBase::mm[4],
488 MyBase::mm[5] * MyBase::mm[6] - MyBase::mm[3] * MyBase::mm[8],
489 MyBase::mm[0] * MyBase::mm[8] - MyBase::mm[2] * MyBase::mm[6],
490 MyBase::mm[2] * MyBase::mm[3] - MyBase::mm[0] * MyBase::mm[5],
491 MyBase::mm[3] * MyBase::mm[7] - MyBase::mm[4] * MyBase::mm[6],
492 MyBase::mm[1] * MyBase::mm[6] - MyBase::mm[0] * MyBase::mm[7],
493 MyBase::mm[0] * MyBase::mm[4] - MyBase::mm[1] * MyBase::mm[3]);
494
495 } // adjointTest
496
498 Mat3 transpose() const
499 {
500 return Mat3<T>(
501 MyBase::mm[0], MyBase::mm[3], MyBase::mm[6],
502 MyBase::mm[1], MyBase::mm[4], MyBase::mm[7],
503 MyBase::mm[2], MyBase::mm[5], MyBase::mm[8]);
504
505 } // transposeTest
506
509 Mat3 inverse(T tolerance = 0) const
510 {
511 Mat3<T> inv(this->adjoint());
512
513 const T det = inv.mm[0]*MyBase::mm[0] + inv.mm[1]*MyBase::mm[3] + inv.mm[2]*MyBase::mm[6];
514
515 // If the determinant is 0, m was singular and "this" will contain junk.
516 if (isApproxEqual(det,T(0.0),tolerance)) {
517 OPENVDB_THROW(ArithmeticError, "Inversion of singular 3x3 matrix");
518 }
519 return inv * (T(1)/det);
520 } // invertTest
521
523 T det() const
524 {
525 const T co00 = MyBase::mm[4]*MyBase::mm[8] - MyBase::mm[5]*MyBase::mm[7];
526 const T co10 = MyBase::mm[5]*MyBase::mm[6] - MyBase::mm[3]*MyBase::mm[8];
527 const T co20 = MyBase::mm[3]*MyBase::mm[7] - MyBase::mm[4]*MyBase::mm[6];
528 return MyBase::mm[0]*co00 + MyBase::mm[1]*co10 + MyBase::mm[2]*co20;
529 } // determinantTest
530
532 T trace() const
533 {
534 return MyBase::mm[0]+MyBase::mm[4]+MyBase::mm[8];
535 }
536
541 Mat3 snapBasis(Axis axis, const Vec3<T> &direction)
542 {
543 return snapMatBasis(*this, axis, direction);
544 }
545
548 template<typename T0>
549 Vec3<T0> transform(const Vec3<T0> &v) const
550 {
551 return static_cast< Vec3<T0> >(v * *this);
552 } // xformVectorTest
553
556 template<typename T0>
557 Vec3<T0> pretransform(const Vec3<T0> &v) const
558 {
559 return static_cast< Vec3<T0> >(*this * v);
560 } // xformTVectorTest
561
562
565 Mat3 timesDiagonal(const Vec3<T>& diag) const
566 {
567 Mat3 ret(*this);
568
569 ret.mm[0] *= diag(0);
570 ret.mm[1] *= diag(1);
571 ret.mm[2] *= diag(2);
572 ret.mm[3] *= diag(0);
573 ret.mm[4] *= diag(1);
574 ret.mm[5] *= diag(2);
575 ret.mm[6] *= diag(0);
576 ret.mm[7] *= diag(1);
577 ret.mm[8] *= diag(2);
578 return ret;
579 }
580
581 private:
582 static const Mat3<T> sIdentity;
583 static const Mat3<T> sZero;
584 }; // class Mat3
585
586
587 template <typename T>
588 const Mat3<T> Mat3<T>::sIdentity = Mat3<T>(1, 0, 0,
589 0, 1, 0,
590 0, 0, 1);
591
592 template <typename T>
593 const Mat3<T> Mat3<T>::sZero = Mat3<T>(0, 0, 0,
594 0, 0, 0,
595 0, 0, 0);
596
599 template <typename T0, typename T1>
600 bool operator==(const Mat3<T0> &m0, const Mat3<T1> &m1)
601 {
602 const T0 *t0 = m0.asPointer();
603 const T1 *t1 = m1.asPointer();
604
605 for (int i=0; i<9; ++i) {
606 if (!isExactlyEqual(t0[i], t1[i])) return false;
607 }
608 return true;
609 }
610
613 template <typename T0, typename T1>
614 bool operator!=(const Mat3<T0> &m0, const Mat3<T1> &m1) { return !(m0 == m1); }
615
618 template <typename S, typename T>
619 Mat3<typename promote<S, T>::type> operator*(S scalar, const Mat3<T> &m)
620 { return m*scalar; }
621
624 template <typename S, typename T>
625 Mat3<typename promote<S, T>::type> operator*(const Mat3<T> &m, S scalar)
626 {
627 Mat3<typename promote<S, T>::type> result(m);
628 result *= scalar;
629 return result;
630 }
631
634 template <typename T0, typename T1>
635 Mat3<typename promote<T0, T1>::type> operator+(const Mat3<T0> &m0, const Mat3<T1> &m1)
636 {
637 Mat3<typename promote<T0, T1>::type> result(m0);
638 result += m1;
639 return result;
640 }
641
644 template <typename T0, typename T1>
645 Mat3<typename promote<T0, T1>::type> operator-(const Mat3<T0> &m0, const Mat3<T1> &m1)
646 {
647 Mat3<typename promote<T0, T1>::type> result(m0);
648 result -= m1;
649 return result;
650 }
651
652
657 template <typename T0, typename T1>
658 Mat3<typename promote<T0, T1>::type>operator*(const Mat3<T0> &m0, const Mat3<T1> &m1)
659 {
660 Mat3<typename promote<T0, T1>::type> result(m0);
661 result *= m1;
662 return result;
663 }
664
667 template<typename T, typename MT>
668 inline Vec3<typename promote<T, MT>::type>
669 operator*(const Mat3<MT> &_m, const Vec3<T> &_v)
670 {
671 MT const *m = _m.asPointer();
672 return Vec3<typename promote<T, MT>::type>(
673 _v[0]*m[0] + _v[1]*m[1] + _v[2]*m[2],
674 _v[0]*m[3] + _v[1]*m[4] + _v[2]*m[5],
675 _v[0]*m[6] + _v[1]*m[7] + _v[2]*m[8]);
676 }
677
680 template<typename T, typename MT>
681 inline Vec3<typename promote<T, MT>::type>
682 operator*(const Vec3<T> &_v, const Mat3<MT> &_m)
683 {
684 MT const *m = _m.asPointer();
685 return Vec3<typename promote<T, MT>::type>(
686 _v[0]*m[0] + _v[1]*m[3] + _v[2]*m[6],
687 _v[0]*m[1] + _v[1]*m[4] + _v[2]*m[7],
688 _v[0]*m[2] + _v[1]*m[5] + _v[2]*m[8]);
689 }
690
693 template<typename T, typename MT>
694 inline Vec3<T> &operator *= (Vec3<T> &_v, const Mat3<MT> &_m)
695 {
696 Vec3<T> mult = _v * _m;
697 _v = mult;
698 return _v;
699 }
700
703 template <typename T>
704 Mat3<T> outerProduct(const Vec3<T>& v1, const Vec3<T>& v2)
705 {
706 return Mat3<T>(v1[0]*v2[0], v1[0]*v2[1], v1[0]*v2[2],
707 v1[1]*v2[0], v1[1]*v2[1], v1[1]*v2[2],
708 v1[2]*v2[0], v1[2]*v2[1], v1[2]*v2[2]);
709 }// outerProduct
710
711 typedef Mat3<float> Mat3s;
712 typedef Mat3<double> Mat3d;
713
714 #if DWREAL_IS_DOUBLE == 1
715 typedef Mat3d Mat3f;
716 #else
717 typedef Mat3s Mat3f;
718 #endif // DWREAL_IS_DOUBLE
719
720
724 template<typename T, typename T0>
725 Mat3<T> powLerp(const Mat3<T0> &m1, const Mat3<T0> &m2, T t)
726 {
727 Mat3<T> x = m1.inverse() * m2;
728 powSolve(x, x, t);
729 Mat3<T> m = m1 * x;
730 return m;
731 }
732
733
734 namespace {
735 template<typename T>
736 void pivot(int i, int j, Mat3<T>& S, Vec3<T>& D, Mat3<T>& Q)
737 {
738 const int& n = Mat3<T>::size; // should be 3
739 T temp;
741 double cotan_of_2_theta;
742 double tan_of_theta;
743 double cosin_of_theta;
744 double sin_of_theta;
745 double z;
746
747 double Sij = S(i,j);
748
749 double Sjj_minus_Sii = D[j] - D[i];
750
751 if (fabs(Sjj_minus_Sii) * (10*math::Tolerance<T>::value()) > fabs(Sij)) {
752 tan_of_theta = Sij / Sjj_minus_Sii;
753 } else {
755 cotan_of_2_theta = 0.5*Sjj_minus_Sii / Sij ;
756
757 if (cotan_of_2_theta < 0.) {
758 tan_of_theta =
759 -1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) - cotan_of_2_theta);
760 } else {
761 tan_of_theta =
762 1./(sqrt(1. + cotan_of_2_theta*cotan_of_2_theta) + cotan_of_2_theta);
763 }
764 }
765
766 cosin_of_theta = 1./sqrt( 1. + tan_of_theta * tan_of_theta);
767 sin_of_theta = cosin_of_theta * tan_of_theta;
768 z = tan_of_theta * Sij;
769 S(i,j) = 0;
770 D[i] -= z;
771 D[j] += z;
772 for (int k = 0; k < i; ++k) {
773 temp = S(k,i);
774 S(k,i) = cosin_of_theta * temp - sin_of_theta * S(k,j);
775 S(k,j)= sin_of_theta * temp + cosin_of_theta * S(k,j);
776 }
777 for (int k = i+1; k < j; ++k) {
778 temp = S(i,k);
779 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(k,j);
780 S(k,j) = sin_of_theta * temp + cosin_of_theta * S(k,j);
781 }
782 for (int k = j+1; k < n; ++k) {
783 temp = S(i,k);
784 S(i,k) = cosin_of_theta * temp - sin_of_theta * S(j,k);
785 S(j,k) = sin_of_theta * temp + cosin_of_theta * S(j,k);
786 }
787 for (int k = 0; k < n; ++k)
788 {
789 temp = Q(k,i);
790 Q(k,i) = cosin_of_theta * temp - sin_of_theta*Q(k,j);
791 Q(k,j) = sin_of_theta * temp + cosin_of_theta*Q(k,j);
792 }
793 }
794 }
795
796
802 template<typename T>
803 bool diagonalizeSymmetricMatrix(const Mat3<T>& input, Mat3<T>& Q, Vec3<T>& D,
804 unsigned int MAX_ITERATIONS=250)
805 {
808 Q = Mat3<T>::identity();
809 int n = Mat3<T>::size; // should be 3
810
812 Mat3<T> S(input);
813
814 for (int i = 0; i < n; ++i) {
815 D[i] = S(i,i);
816 }
817
818 unsigned int iterations(0);
821 do {
824 double er = 0;
825 for (int i = 0; i < n; ++i) {
826 for (int j = i+1; j < n; ++j) {
827 er += fabs(S(i,j));
828 }
829 }
830 if (std::abs(er) < math::Tolerance<T>::value()) {
831 return true;
832 }
833 iterations++;
834
835 T max_element = 0;
836 int ip = 0;
837 int jp = 0;
839 for (int i = 0; i < n; ++i) {
840 for (int j = i+1; j < n; ++j){
841
842 if ( fabs(D[i]) * (10*math::Tolerance<T>::value()) > fabs(S(i,j))) {
844 S(i,j) = 0;
845 }
846 if (fabs(S(i,j)) > max_element) {
847 max_element = fabs(S(i,j));
848 ip = i;
849 jp = j;
850 }
851 }
852 }
853 pivot(ip, jp, S, D, Q);
854 } while (iterations < MAX_ITERATIONS);
855
856 return false;
857 }
858
859 } // namespace math
860 } // namespace OPENVDB_VERSION_NAME
861 } // namespace openvdb
862
863 #endif // OPENVDB_MATH_MAT3_H_HAS_BEEN_INCLUDED
864
865 // Copyright (c) 2012-2016 DreamWorks Animation LLC
866 // All rights reserved. This software is distributed under the
867 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(const Quat< T > &q)
Definition: Mat3.h:66
openvdb::v3_2_0::math::Mat3::pretransform
Vec3< T0 > pretransform(const Vec3< T0 > &v) const
Definition: Mat3.h:557
openvdb::v3_2_0::math::Mat3::operator=
const Mat3 & operator=(const Mat3< Source > &m)
Assignment operator.
Definition: Mat3.h:335
openvdb::v3_2_0::math::Mat3::symmetric
static Mat3 symmetric(const Vec3< T > &vdiag, const Vec3< T > &vtri)
Definition: Mat3.h:281
OPENVDB_DEPRECATED
#define OPENVDB_DEPRECATED
Definition: Platform.h:49
Vec3.h
openvdb::v3_2_0::math::Mat3::operator!=
bool operator!=(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Inequality operator, does exact floating point comparisons.
Definition: Mat3.h:614
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::Mat3s
Mat3< float > Mat3s
Definition: Mat3.h:711
openvdb::v3_2_0::math::Mat3::cofactor
Mat3 cofactor() const
Return the cofactor matrix of "this".
Definition: Mat3.h:467
openvdb::v3_2_0::math::Mat3::operator-
Mat3< T > operator-() const
Negation operator, for e.g. m1 = -m2;.
Definition: Mat3.h:359
openvdb::v3_2_0::math::Mat3::zero
static const Mat3< T > & zero()
Predefined constant for zero matrix.
Definition: Mat3.h:159
openvdb::v3_2_0::math::Vec3
Definition: Mat.h:146
openvdb::v3_2_0::math::Quat
Definition: Mat.h:145
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::Mat3::asPointer
const T * asPointer() const
Definition: Mat3.h:209
openvdb::v3_2_0::ArithmeticError
Definition: Exceptions.h:78
openvdb::v3_2_0::math::Mat3::operator()
T & operator()(int i, int j)
Definition: Mat3.h:214
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i)
Constructor given array of elements, the ordering is in row major form:
Definition: Mat3.h:77
openvdb::v3_2_0::math::Mat3::setRows
void setRows(const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
Set the rows of "this" matrix to the vectors v1, v2, v3.
Definition: Mat3.h:232
openvdb::v3_2_0::math::operator*
Mat3< typename promote< T0, T1 >::type > operator*(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Matrix multiplication.
Definition: Mat3.h:658
openvdb::v3_2_0::math::Mat3::operator==
bool operator==(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat3.h:600
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(const Mat4< T > &m)
Conversion from Mat4 (copies top left)
Definition: Mat3.h:144
openvdb::v3_2_0::math::Mat3::col
Vec3< T > col(int j) const
Get jth column, e.g. Vec3d v = m.col(0);.
Definition: Mat3.h:191
openvdb::v3_2_0::math::Mat3::transpose
Mat3 transpose() const
returns transpose of this
Definition: Mat3.h:498
openvdb::v3_2_0::math::Mat3::transform
Vec3< T0 > transform(const Vec3< T0 > &v) const
Definition: Mat3.h:549
openvdb::v3_2_0::math::Mat3::operator*
Mat3< typename promote< S, T >::type > operator*(const Mat3< T > &m, S scalar)
Returns M, where for .
Definition: Mat3.h:625
openvdb::v3_2_0::math::Mat4
4x4 -matrix class.
Definition: Mat3.h:48
openvdb::v3_2_0::math::Mat3::operator-
Mat3< typename promote< T0, T1 >::type > operator-(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Returns M, where for .
Definition: Mat3.h:645
openvdb::v3_2_0::math::powLerp
Mat3< T > powLerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)
Definition: Mat3.h:725
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::Mat3::setZero
void setZero()
Set this matrix to zero.
Definition: Mat3.h:306
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(Source *a)
Definition: Mat3.h:109
Exceptions.h
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
Definition: version.h:43
openvdb::v3_2_0::math::Mat3::operator*
Mat3< typename promote< S, T >::type > operator*(S scalar, const Mat3< T > &m)
Returns M, where for .
Definition: Mat3.h:619
openvdb::v3_2_0::math::Mat3::row
Vec3< T > row(int i) const
Get ith row, e.g. Vec3d v = m.row(1);.
Definition: Mat3.h:175
openvdb::v3_2_0::math::Mat3::setColumns
void setColumns(const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
Set the columns of "this" matrix to the vectors v1, v2, v3.
Definition: Mat3.h:246
openvdb::v3_2_0::math::Mat3::setToRotation
void setToRotation(const Vec3< T > &axis, T angle)
Set this matrix to the rotation specified by axis and angle.
Definition: Mat3.h:302
openvdb::v3_2_0::math::Mat3::operator*
Vec3< typename promote< T, MT >::type > operator*(const Vec3< T > &_v, const Mat3< MT > &_m)
Returns v, where for .
Definition: Mat3.h:682
openvdb::v3_2_0::math::Mat3d
Mat3< double > Mat3d
Definition: Mat3.h:712
openvdb::v3_2_0::math::Mat3::ValueType
T ValueType
Definition: Mat3.h:59
openvdb::v3_2_0::math::Mat3::setSymmetric
void setSymmetric(const Vec3< T > &vdiag, const Vec3< T > &vtri)
Set diagonal and symmetric triangular components.
Definition: Mat3.h:266
openvdb::v3_2_0::math::Mat3::operator-=
const Mat3< T > & operator-=(const Mat3< S > &m1)
Returns m0, where for .
Definition: Mat3.h:409
openvdb::v3_2_0::math::Mat3::setSkew
void setSkew(const Vec3< T > &v)
Set the matrix as cross product of the given vector.
Definition: Mat3.h:291
openvdb
Definition: Exceptions.h:39
openvdb::v3_2_0::math::Tolerance
Tolerance for floating-point comparison.
Definition: Math.h:125
openvdb::v3_2_0::math::Mat3
3x3 matrix class.
Definition: Mat3.h:54
openvdb::v3_2_0::math::Mat3::eq
bool eq(const Mat3 &m, T eps=1.0e-8) const
Test if "this" is equivalent to m with tolerance of eps value.
Definition: Mat3.h:345
openvdb::v3_2_0::math::Mat3::inverse
Mat3 inverse(T tolerance=0) const
Definition: Mat3.h:509
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::Mat3::operator*=
const Mat3< T > & operator*=(S scalar)
Multiplication operator, e.g. M = scalar * M;.
Definition: Mat3.h:375
openvdb::v3_2_0::math::diagonalizeSymmetricMatrix
bool diagonalizeSymmetricMatrix(const Mat3< T > &input, Mat3< T > &Q, Vec3< T > &D, unsigned int MAX_ITERATIONS=250)
Use Jacobi iterations to decompose a symmetric 3x3 matrix (diagonalize and compute eigenvectors) ...
Definition: Mat3.h:803
openvdb::v3_2_0::math::Mat3::setBasis
OPENVDB_DEPRECATED void setBasis(const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
Set the rows of "this" matrix to the vectors v1, v2, v3.
Definition: Mat3.h:260
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(const Mat3< Source > &m)
Conversion constructor.
Definition: Mat3.h:134
openvdb::v3_2_0::math::outerProduct
Mat3< T > outerProduct(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Mat3.h:704
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(const Mat< 3, T > &m)
Copy constructor.
Definition: Mat3.h:123
openvdb::v3_2_0::math::Mat3::setIdentity
void setIdentity()
Set "this" matrix to identity.
Definition: Mat3.h:320
openvdb::v3_2_0::math::Mat3::MyBase
Mat< 3, T > MyBase
Definition: Mat3.h:60
openvdb::v3_2_0::math::Mat3::setRow
void setRow(int i, const Vec3< T > &v)
Set ith row to vector v.
Definition: Mat3.h:164
openvdb::v3_2_0::math::Mat3::identity
static const Mat3< T > & identity()
Predefined constant for identity matrix.
Definition: Mat3.h:154
openvdb::v3_2_0::math::Mat3::operator*
Vec3< typename promote< T, MT >::type > operator*(const Mat3< MT > &_m, const Vec3< T > &_v)
Returns v, where for .
Definition: Mat3.h:669
openvdb::v3_2_0::math::Mat3::setCol
void setCol(int j, const Vec3< T > &v)
Set jth column to vector v.
Definition: Mat3.h:182
openvdb::v3_2_0::math::Mat3::timesDiagonal
Mat3 timesDiagonal(const Vec3< T > &diag) const
Definition: Mat3.h:565
openvdb::v3_2_0::math::Mat3::Mat3
Mat3()
Trivial constructor, the matrix is NOT initialized.
Definition: Mat3.h:62
openvdb::v3_2_0::math::snapMatBasis
MatType snapMatBasis(const MatType &source, Axis axis, const Vec3< typename MatType::value_type > &direction)
This function snaps a specific axis to a specific direction, preserving scaling.
Definition: Mat.h:730
openvdb::v3_2_0::math::Mat3::value_type
T value_type
Data type held by the matrix.
Definition: Mat3.h:58
openvdb::v3_2_0::math::Mat3f
Mat3s Mat3f
Definition: Mat3.h:717
openvdb::v3_2_0::math::Axis
Axis
Definition: Math.h:856
openvdb::v3_2_0::math::skew
MatType skew(const Vec3< typename MatType::value_type > &skew)
Return a matrix as the cross product of the given vector.
Definition: Mat.h:687
openvdb::v3_2_0::math::Mat3::det
T det() const
Determinant of matrix.
Definition: Mat3.h:523
openvdb::v3_2_0::math::powSolve
void powSolve(const MatType &aA, MatType &aB, double aPower, double aTol=0.01)
Definition: Mat.h:810
openvdb::v3_2_0::math::Mat3::operator*=
const Mat3< T > & operator*=(const Mat3< S > &m1)
Returns m0, where for .
Definition: Mat3.h:427
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::Mat3::trace
T trace() const
Trace of matrix.
Definition: Mat3.h:532
openvdb::v3_2_0::math::Mat3::operator[]
const T * operator[](int i) const
Definition: Mat3.h:205
openvdb::v3_2_0::math::Mat3::adjoint
Mat3 adjoint() const
returns adjoint of "this", i.e. the transpose of the cofactor of "this"
Definition: Mat3.h:482
openvdb::v3_2_0::math::Mat3::setToRotation
void setToRotation(const Quat< T > &q)
Set this matrix to the rotation matrix specified by the quaternion.
Definition: Mat3.h:297
Mat.h
openvdb::v3_2_0::math::Mat3::Mat3
Mat3(const Vec3< Source > &v1, const Vec3< Source > &v2, const Vec3< Source > &v3, bool rows=true)
Definition: Mat3.h:95
openvdb::v3_2_0::math::Mat3::snapBasis
Mat3 snapBasis(Axis axis, const Vec3< T > &direction)
Definition: Mat3.h:541
openvdb::v3_2_0::math::Mat3::operator()
T operator()(int i, int j) const
Definition: Mat3.h:224
openvdb::v3_2_0::math::Mat3::operator+=
const Mat3< T > & operator+=(const Mat3< S > &m1)
Returns m0, where for .
Definition: Mat3.h:391
openvdb::v3_2_0::math::Mat3::asPointer
T * asPointer()
Definition: Mat3.h:208
openvdb::v3_2_0::math::Mat3::operator+
Mat3< typename promote< T0, T1 >::type > operator+(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Returns M, where for .
Definition: Mat3.h:635