/usr/local/include/OpenEXR/ImathMatrix.h
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1 | | /////////////////////////////////////////////////////////////////////////// |
2 | | // |
3 | | // Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas |
4 | | // Digital Ltd. LLC |
5 | | // |
6 | | // All rights reserved. |
7 | | // |
8 | | // Redistribution and use in source and binary forms, with or without |
9 | | // modification, are permitted provided that the following conditions are |
10 | | // met: |
11 | | // * Redistributions of source code must retain the above copyright |
12 | | // notice, this list of conditions and the following disclaimer. |
13 | | // * Redistributions in binary form must reproduce the above |
14 | | // copyright notice, this list of conditions and the following disclaimer |
15 | | // in the documentation and/or other materials provided with the |
16 | | // distribution. |
17 | | // * Neither the name of Industrial Light & Magic nor the names of |
18 | | // its contributors may be used to endorse or promote products derived |
19 | | // from this software without specific prior written permission. |
20 | | // |
21 | | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
22 | | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
23 | | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
24 | | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
25 | | // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
26 | | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
27 | | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
28 | | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
29 | | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
30 | | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
31 | | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
32 | | // |
33 | | /////////////////////////////////////////////////////////////////////////// |
34 | | |
35 | | |
36 | | |
37 | | #ifndef INCLUDED_IMATHMATRIX_H |
38 | | #define INCLUDED_IMATHMATRIX_H |
39 | | |
40 | | //---------------------------------------------------------------- |
41 | | // |
42 | | // 2D (3x3) and 3D (4x4) transformation matrix templates. |
43 | | // |
44 | | //---------------------------------------------------------------- |
45 | | |
46 | | #include "ImathPlatform.h" |
47 | | #include "ImathFun.h" |
48 | | #include "ImathExc.h" |
49 | | #include "ImathVec.h" |
50 | | #include "ImathShear.h" |
51 | | #include "ImathNamespace.h" |
52 | | |
53 | | #include <cstring> |
54 | | #include <iostream> |
55 | | #include <iomanip> |
56 | | #include <string.h> |
57 | | |
58 | | #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER |
59 | | // suppress exception specification warnings |
60 | | #pragma warning(disable:4290) |
61 | | #endif |
62 | | |
63 | | |
64 | | IMATH_INTERNAL_NAMESPACE_HEADER_ENTER |
65 | | |
66 | | enum Uninitialized {UNINITIALIZED}; |
67 | | |
68 | | |
69 | | template <class T> class Matrix22 |
70 | | { |
71 | | public: |
72 | | |
73 | | //------------------- |
74 | | // Access to elements |
75 | | //------------------- |
76 | | |
77 | | T x[2][2]; |
78 | | |
79 | | T * operator [] (int i); |
80 | | const T * operator [] (int i) const; |
81 | | |
82 | | |
83 | | //------------- |
84 | | // Constructors |
85 | | //------------- |
86 | | |
87 | | Matrix22 (Uninitialized) {} |
88 | | |
89 | | Matrix22 (); |
90 | | // 1 0 |
91 | | // 0 1 |
92 | | |
93 | | Matrix22 (T a); |
94 | | // a a |
95 | | // a a |
96 | | |
97 | | Matrix22 (const T a[2][2]); |
98 | | // a[0][0] a[0][1] |
99 | | // a[1][0] a[1][1] |
100 | | |
101 | | Matrix22 (T a, T b, T c, T d); |
102 | | |
103 | | // a b |
104 | | // c d |
105 | | |
106 | | |
107 | | //-------------------------------- |
108 | | // Copy constructor and assignment |
109 | | //-------------------------------- |
110 | | |
111 | | Matrix22 (const Matrix22 &v); |
112 | | template <class S> explicit Matrix22 (const Matrix22<S> &v); |
113 | | |
114 | | const Matrix22 & operator = (const Matrix22 &v); |
115 | | const Matrix22 & operator = (T a); |
116 | | |
117 | | |
118 | | //------------ |
119 | | // Destructor |
120 | | //------------ |
121 | | |
122 | | ~Matrix22 () = default; |
123 | | |
124 | | //---------------------- |
125 | | // Compatibility with Sb |
126 | | //---------------------- |
127 | | |
128 | | T * getValue (); |
129 | | const T * getValue () const; |
130 | | |
131 | | template <class S> |
132 | | void getValue (Matrix22<S> &v) const; |
133 | | template <class S> |
134 | | Matrix22 & setValue (const Matrix22<S> &v); |
135 | | |
136 | | template <class S> |
137 | | Matrix22 & setTheMatrix (const Matrix22<S> &v); |
138 | | |
139 | | |
140 | | //--------- |
141 | | // Identity |
142 | | //--------- |
143 | | |
144 | | void makeIdentity(); |
145 | | |
146 | | |
147 | | //--------- |
148 | | // Equality |
149 | | //--------- |
150 | | |
151 | | bool operator == (const Matrix22 &v) const; |
152 | | bool operator != (const Matrix22 &v) const; |
153 | | |
154 | | //----------------------------------------------------------------------- |
155 | | // Compare two matrices and test if they are "approximately equal": |
156 | | // |
157 | | // equalWithAbsError (m, e) |
158 | | // |
159 | | // Returns true if the coefficients of this and m are the same with |
160 | | // an absolute error of no more than e, i.e., for all i, j |
161 | | // |
162 | | // abs (this[i][j] - m[i][j]) <= e |
163 | | // |
164 | | // equalWithRelError (m, e) |
165 | | // |
166 | | // Returns true if the coefficients of this and m are the same with |
167 | | // a relative error of no more than e, i.e., for all i, j |
168 | | // |
169 | | // abs (this[i] - v[i][j]) <= e * abs (this[i][j]) |
170 | | //----------------------------------------------------------------------- |
171 | | |
172 | | bool equalWithAbsError (const Matrix22<T> &v, T e) const; |
173 | | bool equalWithRelError (const Matrix22<T> &v, T e) const; |
174 | | |
175 | | |
176 | | //------------------------ |
177 | | // Component-wise addition |
178 | | //------------------------ |
179 | | |
180 | | const Matrix22 & operator += (const Matrix22 &v); |
181 | | const Matrix22 & operator += (T a); |
182 | | Matrix22 operator + (const Matrix22 &v) const; |
183 | | |
184 | | |
185 | | //--------------------------- |
186 | | // Component-wise subtraction |
187 | | //--------------------------- |
188 | | |
189 | | const Matrix22 & operator -= (const Matrix22 &v); |
190 | | const Matrix22 & operator -= (T a); |
191 | | Matrix22 operator - (const Matrix22 &v) const; |
192 | | |
193 | | |
194 | | //------------------------------------ |
195 | | // Component-wise multiplication by -1 |
196 | | //------------------------------------ |
197 | | |
198 | | Matrix22 operator - () const; |
199 | | const Matrix22 & negate (); |
200 | | |
201 | | |
202 | | //------------------------------ |
203 | | // Component-wise multiplication |
204 | | //------------------------------ |
205 | | |
206 | | const Matrix22 & operator *= (T a); |
207 | | Matrix22 operator * (T a) const; |
208 | | |
209 | | |
210 | | //----------------------------------- |
211 | | // Matrix-times-matrix multiplication |
212 | | //----------------------------------- |
213 | | |
214 | | const Matrix22 & operator *= (const Matrix22 &v); |
215 | | Matrix22 operator * (const Matrix22 &v) const; |
216 | | |
217 | | |
218 | | //----------------------------------------------------------------- |
219 | | // Vector-times-matrix multiplication; see also the "operator *" |
220 | | // functions defined below. |
221 | | // |
222 | | // m.multDirMatrix(src,dst) multiplies src by the matrix m. |
223 | | //----------------------------------------------------------------- |
224 | | |
225 | | template <class S> |
226 | | void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const; |
227 | | |
228 | | |
229 | | //------------------------ |
230 | | // Component-wise division |
231 | | //------------------------ |
232 | | |
233 | | const Matrix22 & operator /= (T a); |
234 | | Matrix22 operator / (T a) const; |
235 | | |
236 | | |
237 | | //------------------ |
238 | | // Transposed matrix |
239 | | //------------------ |
240 | | |
241 | | const Matrix22 & transpose (); |
242 | | Matrix22 transposed () const; |
243 | | |
244 | | |
245 | | //------------------------------------------------------------ |
246 | | // Inverse matrix: If singExc is false, inverting a singular |
247 | | // matrix produces an identity matrix. If singExc is true, |
248 | | // inverting a singular matrix throws a SingMatrixExc. |
249 | | // |
250 | | // inverse() and invert() invert matrices using determinants. |
251 | | // |
252 | | //------------------------------------------------------------ |
253 | | |
254 | | const Matrix22 & invert (bool singExc = false); |
255 | | |
256 | | Matrix22<T> inverse (bool singExc = false) const; |
257 | | |
258 | | //------------ |
259 | | // Determinant |
260 | | //------------ |
261 | | |
262 | | T determinant() const; |
263 | | |
264 | | //----------------------------------------- |
265 | | // Set matrix to rotation by r (in radians) |
266 | | //----------------------------------------- |
267 | | |
268 | | template <class S> |
269 | | const Matrix22 & setRotation (S r); |
270 | | |
271 | | |
272 | | //----------------------------- |
273 | | // Rotate the given matrix by r |
274 | | //----------------------------- |
275 | | |
276 | | template <class S> |
277 | | const Matrix22 & rotate (S r); |
278 | | |
279 | | |
280 | | //-------------------------------------------- |
281 | | // Set matrix to scale by given uniform factor |
282 | | //-------------------------------------------- |
283 | | |
284 | | const Matrix22 & setScale (T s); |
285 | | |
286 | | |
287 | | //------------------------------------ |
288 | | // Set matrix to scale by given vector |
289 | | //------------------------------------ |
290 | | |
291 | | template <class S> |
292 | | const Matrix22 & setScale (const Vec2<S> &s); |
293 | | |
294 | | |
295 | | //---------------------- |
296 | | // Scale the matrix by s |
297 | | //---------------------- |
298 | | |
299 | | template <class S> |
300 | | const Matrix22 & scale (const Vec2<S> &s); |
301 | | |
302 | | |
303 | | //-------------------------------------------------------- |
304 | | // Number of the row and column dimensions, since |
305 | | // Matrix22 is a square matrix. |
306 | | //-------------------------------------------------------- |
307 | | |
308 | | static unsigned int dimensions() {return 2;} |
309 | | |
310 | | |
311 | | //------------------------------------------------- |
312 | | // Limitations of type T (see also class limits<T>) |
313 | | //------------------------------------------------- |
314 | | |
315 | | static T baseTypeMin() {return limits<T>::min();} |
316 | | static T baseTypeMax() {return limits<T>::max();} |
317 | | static T baseTypeSmallest() {return limits<T>::smallest();} |
318 | | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
319 | | |
320 | | typedef T BaseType; |
321 | | typedef Vec2<T> BaseVecType; |
322 | | |
323 | | private: |
324 | | |
325 | | template <typename R, typename S> |
326 | | struct isSameType |
327 | | { |
328 | | enum {value = 0}; |
329 | | }; |
330 | | |
331 | | template <typename R> |
332 | | struct isSameType<R, R> |
333 | | { |
334 | | enum {value = 1}; |
335 | | }; |
336 | | }; |
337 | | |
338 | | |
339 | | template <class T> class Matrix33 |
340 | | { |
341 | | public: |
342 | | |
343 | | //------------------- |
344 | | // Access to elements |
345 | | //------------------- |
346 | | |
347 | | T x[3][3]; |
348 | | |
349 | | T * operator [] (int i); |
350 | | const T * operator [] (int i) const; |
351 | | |
352 | | |
353 | | //------------- |
354 | | // Constructors |
355 | | //------------- |
356 | | |
357 | | Matrix33 (Uninitialized) {} |
358 | | |
359 | | Matrix33 (); |
360 | | // 1 0 0 |
361 | | // 0 1 0 |
362 | | // 0 0 1 |
363 | | |
364 | | Matrix33 (T a); |
365 | | // a a a |
366 | | // a a a |
367 | | // a a a |
368 | | |
369 | | Matrix33 (const T a[3][3]); |
370 | | // a[0][0] a[0][1] a[0][2] |
371 | | // a[1][0] a[1][1] a[1][2] |
372 | | // a[2][0] a[2][1] a[2][2] |
373 | | |
374 | | Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i); |
375 | | |
376 | | // a b c |
377 | | // d e f |
378 | | // g h i |
379 | | |
380 | | |
381 | | //-------------------------------- |
382 | | // Copy constructor and assignment |
383 | | //-------------------------------- |
384 | | |
385 | | Matrix33 (const Matrix33 &v); |
386 | | template <class S> explicit Matrix33 (const Matrix33<S> &v); |
387 | | |
388 | | const Matrix33 & operator = (const Matrix33 &v); |
389 | | const Matrix33 & operator = (T a); |
390 | | |
391 | | |
392 | | //------------ |
393 | | // Destructor |
394 | | //------------ |
395 | | |
396 | | ~Matrix33 () = default; |
397 | | |
398 | | //---------------------- |
399 | | // Compatibility with Sb |
400 | | //---------------------- |
401 | | |
402 | | T * getValue (); |
403 | | const T * getValue () const; |
404 | | |
405 | | template <class S> |
406 | | void getValue (Matrix33<S> &v) const; |
407 | | template <class S> |
408 | | Matrix33 & setValue (const Matrix33<S> &v); |
409 | | |
410 | | template <class S> |
411 | | Matrix33 & setTheMatrix (const Matrix33<S> &v); |
412 | | |
413 | | |
414 | | //--------- |
415 | | // Identity |
416 | | //--------- |
417 | | |
418 | | void makeIdentity(); |
419 | | |
420 | | |
421 | | //--------- |
422 | | // Equality |
423 | | //--------- |
424 | | |
425 | | bool operator == (const Matrix33 &v) const; |
426 | | bool operator != (const Matrix33 &v) const; |
427 | | |
428 | | //----------------------------------------------------------------------- |
429 | | // Compare two matrices and test if they are "approximately equal": |
430 | | // |
431 | | // equalWithAbsError (m, e) |
432 | | // |
433 | | // Returns true if the coefficients of this and m are the same with |
434 | | // an absolute error of no more than e, i.e., for all i, j |
435 | | // |
436 | | // abs (this[i][j] - m[i][j]) <= e |
437 | | // |
438 | | // equalWithRelError (m, e) |
439 | | // |
440 | | // Returns true if the coefficients of this and m are the same with |
441 | | // a relative error of no more than e, i.e., for all i, j |
442 | | // |
443 | | // abs (this[i] - v[i][j]) <= e * abs (this[i][j]) |
444 | | //----------------------------------------------------------------------- |
445 | | |
446 | | bool equalWithAbsError (const Matrix33<T> &v, T e) const; |
447 | | bool equalWithRelError (const Matrix33<T> &v, T e) const; |
448 | | |
449 | | |
450 | | //------------------------ |
451 | | // Component-wise addition |
452 | | //------------------------ |
453 | | |
454 | | const Matrix33 & operator += (const Matrix33 &v); |
455 | | const Matrix33 & operator += (T a); |
456 | | Matrix33 operator + (const Matrix33 &v) const; |
457 | | |
458 | | |
459 | | //--------------------------- |
460 | | // Component-wise subtraction |
461 | | //--------------------------- |
462 | | |
463 | | const Matrix33 & operator -= (const Matrix33 &v); |
464 | | const Matrix33 & operator -= (T a); |
465 | | Matrix33 operator - (const Matrix33 &v) const; |
466 | | |
467 | | |
468 | | //------------------------------------ |
469 | | // Component-wise multiplication by -1 |
470 | | //------------------------------------ |
471 | | |
472 | | Matrix33 operator - () const; |
473 | | const Matrix33 & negate (); |
474 | | |
475 | | |
476 | | //------------------------------ |
477 | | // Component-wise multiplication |
478 | | //------------------------------ |
479 | | |
480 | | const Matrix33 & operator *= (T a); |
481 | | Matrix33 operator * (T a) const; |
482 | | |
483 | | |
484 | | //----------------------------------- |
485 | | // Matrix-times-matrix multiplication |
486 | | //----------------------------------- |
487 | | |
488 | | const Matrix33 & operator *= (const Matrix33 &v); |
489 | | Matrix33 operator * (const Matrix33 &v) const; |
490 | | |
491 | | |
492 | | //----------------------------------------------------------------- |
493 | | // Vector-times-matrix multiplication; see also the "operator *" |
494 | | // functions defined below. |
495 | | // |
496 | | // m.multVecMatrix(src,dst) implements a homogeneous transformation |
497 | | // by computing Vec3 (src.x, src.y, 1) * m and dividing by the |
498 | | // result's third element. |
499 | | // |
500 | | // m.multDirMatrix(src,dst) multiplies src by the upper left 2x2 |
501 | | // submatrix, ignoring the rest of matrix m. |
502 | | //----------------------------------------------------------------- |
503 | | |
504 | | template <class S> |
505 | | void multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const; |
506 | | |
507 | | template <class S> |
508 | | void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const; |
509 | | |
510 | | |
511 | | //------------------------ |
512 | | // Component-wise division |
513 | | //------------------------ |
514 | | |
515 | | const Matrix33 & operator /= (T a); |
516 | | Matrix33 operator / (T a) const; |
517 | | |
518 | | |
519 | | //------------------ |
520 | | // Transposed matrix |
521 | | //------------------ |
522 | | |
523 | | const Matrix33 & transpose (); |
524 | | Matrix33 transposed () const; |
525 | | |
526 | | |
527 | | //------------------------------------------------------------ |
528 | | // Inverse matrix: If singExc is false, inverting a singular |
529 | | // matrix produces an identity matrix. If singExc is true, |
530 | | // inverting a singular matrix throws a SingMatrixExc. |
531 | | // |
532 | | // inverse() and invert() invert matrices using determinants; |
533 | | // gjInverse() and gjInvert() use the Gauss-Jordan method. |
534 | | // |
535 | | // inverse() and invert() are significantly faster than |
536 | | // gjInverse() and gjInvert(), but the results may be slightly |
537 | | // less accurate. |
538 | | // |
539 | | //------------------------------------------------------------ |
540 | | |
541 | | const Matrix33 & invert (bool singExc = false); |
542 | | |
543 | | Matrix33<T> inverse (bool singExc = false) const; |
544 | | |
545 | | const Matrix33 & gjInvert (bool singExc = false); |
546 | | |
547 | | Matrix33<T> gjInverse (bool singExc = false) const; |
548 | | |
549 | | |
550 | | //------------------------------------------------ |
551 | | // Calculate the matrix minor of the (r,c) element |
552 | | //------------------------------------------------ |
553 | | |
554 | | T minorOf (const int r, const int c) const; |
555 | | |
556 | | //--------------------------------------------------- |
557 | | // Build a minor using the specified rows and columns |
558 | | //--------------------------------------------------- |
559 | | |
560 | | T fastMinor (const int r0, const int r1, |
561 | | const int c0, const int c1) const; |
562 | | |
563 | | //------------ |
564 | | // Determinant |
565 | | //------------ |
566 | | |
567 | | T determinant() const; |
568 | | |
569 | | //----------------------------------------- |
570 | | // Set matrix to rotation by r (in radians) |
571 | | //----------------------------------------- |
572 | | |
573 | | template <class S> |
574 | | const Matrix33 & setRotation (S r); |
575 | | |
576 | | |
577 | | //----------------------------- |
578 | | // Rotate the given matrix by r |
579 | | //----------------------------- |
580 | | |
581 | | template <class S> |
582 | | const Matrix33 & rotate (S r); |
583 | | |
584 | | |
585 | | //-------------------------------------------- |
586 | | // Set matrix to scale by given uniform factor |
587 | | //-------------------------------------------- |
588 | | |
589 | | const Matrix33 & setScale (T s); |
590 | | |
591 | | |
592 | | //------------------------------------ |
593 | | // Set matrix to scale by given vector |
594 | | //------------------------------------ |
595 | | |
596 | | template <class S> |
597 | | const Matrix33 & setScale (const Vec2<S> &s); |
598 | | |
599 | | |
600 | | //---------------------- |
601 | | // Scale the matrix by s |
602 | | //---------------------- |
603 | | |
604 | | template <class S> |
605 | | const Matrix33 & scale (const Vec2<S> &s); |
606 | | |
607 | | |
608 | | //------------------------------------------ |
609 | | // Set matrix to translation by given vector |
610 | | //------------------------------------------ |
611 | | |
612 | | template <class S> |
613 | | const Matrix33 & setTranslation (const Vec2<S> &t); |
614 | | |
615 | | |
616 | | //----------------------------- |
617 | | // Return translation component |
618 | | //----------------------------- |
619 | | |
620 | | Vec2<T> translation () const; |
621 | | |
622 | | |
623 | | //-------------------------- |
624 | | // Translate the matrix by t |
625 | | //-------------------------- |
626 | | |
627 | | template <class S> |
628 | | const Matrix33 & translate (const Vec2<S> &t); |
629 | | |
630 | | |
631 | | //----------------------------------------------------------- |
632 | | // Set matrix to shear x for each y coord. by given factor xy |
633 | | //----------------------------------------------------------- |
634 | | |
635 | | template <class S> |
636 | | const Matrix33 & setShear (const S &h); |
637 | | |
638 | | |
639 | | //------------------------------------------------------------- |
640 | | // Set matrix to shear x for each y coord. by given factor h[0] |
641 | | // and to shear y for each x coord. by given factor h[1] |
642 | | //------------------------------------------------------------- |
643 | | |
644 | | template <class S> |
645 | | const Matrix33 & setShear (const Vec2<S> &h); |
646 | | |
647 | | |
648 | | //----------------------------------------------------------- |
649 | | // Shear the matrix in x for each y coord. by given factor xy |
650 | | //----------------------------------------------------------- |
651 | | |
652 | | template <class S> |
653 | | const Matrix33 & shear (const S &xy); |
654 | | |
655 | | |
656 | | //----------------------------------------------------------- |
657 | | // Shear the matrix in x for each y coord. by given factor xy |
658 | | // and shear y for each x coord. by given factor yx |
659 | | //----------------------------------------------------------- |
660 | | |
661 | | template <class S> |
662 | | const Matrix33 & shear (const Vec2<S> &h); |
663 | | |
664 | | |
665 | | //-------------------------------------------------------- |
666 | | // Number of the row and column dimensions, since |
667 | | // Matrix33 is a square matrix. |
668 | | //-------------------------------------------------------- |
669 | | |
670 | | static unsigned int dimensions() {return 3;} |
671 | | |
672 | | |
673 | | //------------------------------------------------- |
674 | | // Limitations of type T (see also class limits<T>) |
675 | | //------------------------------------------------- |
676 | | |
677 | | static T baseTypeMin() {return limits<T>::min();} |
678 | | static T baseTypeMax() {return limits<T>::max();} |
679 | | static T baseTypeSmallest() {return limits<T>::smallest();} |
680 | | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
681 | | |
682 | | typedef T BaseType; |
683 | | typedef Vec3<T> BaseVecType; |
684 | | |
685 | | private: |
686 | | |
687 | | template <typename R, typename S> |
688 | | struct isSameType |
689 | | { |
690 | | enum {value = 0}; |
691 | | }; |
692 | | |
693 | | template <typename R> |
694 | | struct isSameType<R, R> |
695 | | { |
696 | | enum {value = 1}; |
697 | | }; |
698 | | }; |
699 | | |
700 | | |
701 | | template <class T> class Matrix44 |
702 | | { |
703 | | public: |
704 | | |
705 | | //------------------- |
706 | | // Access to elements |
707 | | //------------------- |
708 | | |
709 | | T x[4][4]; |
710 | | |
711 | | T * operator [] (int i); |
712 | | const T * operator [] (int i) const; |
713 | | |
714 | | |
715 | | //------------- |
716 | | // Constructors |
717 | | //------------- |
718 | | |
719 | | Matrix44 (Uninitialized) {} |
720 | | |
721 | | Matrix44 (); |
722 | | // 1 0 0 0 |
723 | | // 0 1 0 0 |
724 | | // 0 0 1 0 |
725 | | // 0 0 0 1 |
726 | | |
727 | | Matrix44 (T a); |
728 | | // a a a a |
729 | | // a a a a |
730 | | // a a a a |
731 | | // a a a a |
732 | | |
733 | | Matrix44 (const T a[4][4]) ; |
734 | | // a[0][0] a[0][1] a[0][2] a[0][3] |
735 | | // a[1][0] a[1][1] a[1][2] a[1][3] |
736 | | // a[2][0] a[2][1] a[2][2] a[2][3] |
737 | | // a[3][0] a[3][1] a[3][2] a[3][3] |
738 | | |
739 | | Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h, |
740 | | T i, T j, T k, T l, T m, T n, T o, T p); |
741 | | |
742 | | // a b c d |
743 | | // e f g h |
744 | | // i j k l |
745 | | // m n o p |
746 | | |
747 | | Matrix44 (Matrix33<T> r, Vec3<T> t); |
748 | | // r r r 0 |
749 | | // r r r 0 |
750 | | // r r r 0 |
751 | | // t t t 1 |
752 | | |
753 | | //------------ |
754 | | // Destructor |
755 | | //------------ |
756 | | |
757 | | ~Matrix44 () = default; |
758 | | |
759 | | //-------------------------------- |
760 | | // Copy constructor and assignment |
761 | | //-------------------------------- |
762 | | |
763 | | Matrix44 (const Matrix44 &v); |
764 | | template <class S> explicit Matrix44 (const Matrix44<S> &v); |
765 | | |
766 | | const Matrix44 & operator = (const Matrix44 &v); |
767 | | const Matrix44 & operator = (T a); |
768 | | |
769 | | |
770 | | //---------------------- |
771 | | // Compatibility with Sb |
772 | | //---------------------- |
773 | | |
774 | | T * getValue (); |
775 | | const T * getValue () const; |
776 | | |
777 | | template <class S> |
778 | | void getValue (Matrix44<S> &v) const; |
779 | | template <class S> |
780 | | Matrix44 & setValue (const Matrix44<S> &v); |
781 | | |
782 | | template <class S> |
783 | | Matrix44 & setTheMatrix (const Matrix44<S> &v); |
784 | | |
785 | | //--------- |
786 | | // Identity |
787 | | //--------- |
788 | | |
789 | | void makeIdentity(); |
790 | | |
791 | | |
792 | | //--------- |
793 | | // Equality |
794 | | //--------- |
795 | | |
796 | | bool operator == (const Matrix44 &v) const; |
797 | | bool operator != (const Matrix44 &v) const; |
798 | | |
799 | | //----------------------------------------------------------------------- |
800 | | // Compare two matrices and test if they are "approximately equal": |
801 | | // |
802 | | // equalWithAbsError (m, e) |
803 | | // |
804 | | // Returns true if the coefficients of this and m are the same with |
805 | | // an absolute error of no more than e, i.e., for all i, j |
806 | | // |
807 | | // abs (this[i][j] - m[i][j]) <= e |
808 | | // |
809 | | // equalWithRelError (m, e) |
810 | | // |
811 | | // Returns true if the coefficients of this and m are the same with |
812 | | // a relative error of no more than e, i.e., for all i, j |
813 | | // |
814 | | // abs (this[i] - v[i][j]) <= e * abs (this[i][j]) |
815 | | //----------------------------------------------------------------------- |
816 | | |
817 | | bool equalWithAbsError (const Matrix44<T> &v, T e) const; |
818 | | bool equalWithRelError (const Matrix44<T> &v, T e) const; |
819 | | |
820 | | |
821 | | //------------------------ |
822 | | // Component-wise addition |
823 | | //------------------------ |
824 | | |
825 | | const Matrix44 & operator += (const Matrix44 &v); |
826 | | const Matrix44 & operator += (T a); |
827 | | Matrix44 operator + (const Matrix44 &v) const; |
828 | | |
829 | | |
830 | | //--------------------------- |
831 | | // Component-wise subtraction |
832 | | //--------------------------- |
833 | | |
834 | | const Matrix44 & operator -= (const Matrix44 &v); |
835 | | const Matrix44 & operator -= (T a); |
836 | | Matrix44 operator - (const Matrix44 &v) const; |
837 | | |
838 | | |
839 | | //------------------------------------ |
840 | | // Component-wise multiplication by -1 |
841 | | //------------------------------------ |
842 | | |
843 | | Matrix44 operator - () const; |
844 | | const Matrix44 & negate (); |
845 | | |
846 | | |
847 | | //------------------------------ |
848 | | // Component-wise multiplication |
849 | | //------------------------------ |
850 | | |
851 | | const Matrix44 & operator *= (T a); |
852 | | Matrix44 operator * (T a) const; |
853 | | |
854 | | |
855 | | //----------------------------------- |
856 | | // Matrix-times-matrix multiplication |
857 | | //----------------------------------- |
858 | | |
859 | | const Matrix44 & operator *= (const Matrix44 &v); |
860 | | Matrix44 operator * (const Matrix44 &v) const; |
861 | | |
862 | | static void multiply (const Matrix44 &a, // assumes that |
863 | | const Matrix44 &b, // &a != &c and |
864 | | Matrix44 &c); // &b != &c. |
865 | | |
866 | | |
867 | | //----------------------------------------------------------------- |
868 | | // Vector-times-matrix multiplication; see also the "operator *" |
869 | | // functions defined below. |
870 | | // |
871 | | // m.multVecMatrix(src,dst) implements a homogeneous transformation |
872 | | // by computing Vec4 (src.x, src.y, src.z, 1) * m and dividing by |
873 | | // the result's third element. |
874 | | // |
875 | | // m.multDirMatrix(src,dst) multiplies src by the upper left 3x3 |
876 | | // submatrix, ignoring the rest of matrix m. |
877 | | //----------------------------------------------------------------- |
878 | | |
879 | | template <class S> |
880 | | void multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const; |
881 | | |
882 | | template <class S> |
883 | | void multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const; |
884 | | |
885 | | |
886 | | //------------------------ |
887 | | // Component-wise division |
888 | | //------------------------ |
889 | | |
890 | | const Matrix44 & operator /= (T a); |
891 | | Matrix44 operator / (T a) const; |
892 | | |
893 | | |
894 | | //------------------ |
895 | | // Transposed matrix |
896 | | //------------------ |
897 | | |
898 | | const Matrix44 & transpose (); |
899 | | Matrix44 transposed () const; |
900 | | |
901 | | |
902 | | //------------------------------------------------------------ |
903 | | // Inverse matrix: If singExc is false, inverting a singular |
904 | | // matrix produces an identity matrix. If singExc is true, |
905 | | // inverting a singular matrix throws a SingMatrixExc. |
906 | | // |
907 | | // inverse() and invert() invert matrices using determinants; |
908 | | // gjInverse() and gjInvert() use the Gauss-Jordan method. |
909 | | // |
910 | | // inverse() and invert() are significantly faster than |
911 | | // gjInverse() and gjInvert(), but the results may be slightly |
912 | | // less accurate. |
913 | | // |
914 | | //------------------------------------------------------------ |
915 | | |
916 | | const Matrix44 & invert (bool singExc = false); |
917 | | |
918 | | Matrix44<T> inverse (bool singExc = false) const; |
919 | | |
920 | | const Matrix44 & gjInvert (bool singExc = false); |
921 | | |
922 | | Matrix44<T> gjInverse (bool singExc = false) const; |
923 | | |
924 | | |
925 | | //------------------------------------------------ |
926 | | // Calculate the matrix minor of the (r,c) element |
927 | | //------------------------------------------------ |
928 | | |
929 | | T minorOf (const int r, const int c) const; |
930 | | |
931 | | //--------------------------------------------------- |
932 | | // Build a minor using the specified rows and columns |
933 | | //--------------------------------------------------- |
934 | | |
935 | | T fastMinor (const int r0, const int r1, const int r2, |
936 | | const int c0, const int c1, const int c2) const; |
937 | | |
938 | | //------------ |
939 | | // Determinant |
940 | | //------------ |
941 | | |
942 | | T determinant() const; |
943 | | |
944 | | //-------------------------------------------------------- |
945 | | // Set matrix to rotation by XYZ euler angles (in radians) |
946 | | //-------------------------------------------------------- |
947 | | |
948 | | template <class S> |
949 | | const Matrix44 & setEulerAngles (const Vec3<S>& r); |
950 | | |
951 | | |
952 | | //-------------------------------------------------------- |
953 | | // Set matrix to rotation around given axis by given angle |
954 | | //-------------------------------------------------------- |
955 | | |
956 | | template <class S> |
957 | | const Matrix44 & setAxisAngle (const Vec3<S>& ax, S ang); |
958 | | |
959 | | |
960 | | //------------------------------------------- |
961 | | // Rotate the matrix by XYZ euler angles in r |
962 | | //------------------------------------------- |
963 | | |
964 | | template <class S> |
965 | | const Matrix44 & rotate (const Vec3<S> &r); |
966 | | |
967 | | |
968 | | //-------------------------------------------- |
969 | | // Set matrix to scale by given uniform factor |
970 | | //-------------------------------------------- |
971 | | |
972 | | const Matrix44 & setScale (T s); |
973 | | |
974 | | |
975 | | //------------------------------------ |
976 | | // Set matrix to scale by given vector |
977 | | //------------------------------------ |
978 | | |
979 | | template <class S> |
980 | | const Matrix44 & setScale (const Vec3<S> &s); |
981 | | |
982 | | |
983 | | //---------------------- |
984 | | // Scale the matrix by s |
985 | | //---------------------- |
986 | | |
987 | | template <class S> |
988 | | const Matrix44 & scale (const Vec3<S> &s); |
989 | | |
990 | | |
991 | | //------------------------------------------ |
992 | | // Set matrix to translation by given vector |
993 | | //------------------------------------------ |
994 | | |
995 | | template <class S> |
996 | | const Matrix44 & setTranslation (const Vec3<S> &t); |
997 | | |
998 | | |
999 | | //----------------------------- |
1000 | | // Return translation component |
1001 | | //----------------------------- |
1002 | | |
1003 | | const Vec3<T> translation () const; |
1004 | | |
1005 | | |
1006 | | //-------------------------- |
1007 | | // Translate the matrix by t |
1008 | | //-------------------------- |
1009 | | |
1010 | | template <class S> |
1011 | | const Matrix44 & translate (const Vec3<S> &t); |
1012 | | |
1013 | | |
1014 | | //------------------------------------------------------------- |
1015 | | // Set matrix to shear by given vector h. The resulting matrix |
1016 | | // will shear x for each y coord. by a factor of h[0] ; |
1017 | | // will shear x for each z coord. by a factor of h[1] ; |
1018 | | // will shear y for each z coord. by a factor of h[2] . |
1019 | | //------------------------------------------------------------- |
1020 | | |
1021 | | template <class S> |
1022 | | const Matrix44 & setShear (const Vec3<S> &h); |
1023 | | |
1024 | | |
1025 | | //------------------------------------------------------------ |
1026 | | // Set matrix to shear by given factors. The resulting matrix |
1027 | | // will shear x for each y coord. by a factor of h.xy ; |
1028 | | // will shear x for each z coord. by a factor of h.xz ; |
1029 | | // will shear y for each z coord. by a factor of h.yz ; |
1030 | | // will shear y for each x coord. by a factor of h.yx ; |
1031 | | // will shear z for each x coord. by a factor of h.zx ; |
1032 | | // will shear z for each y coord. by a factor of h.zy . |
1033 | | //------------------------------------------------------------ |
1034 | | |
1035 | | template <class S> |
1036 | | const Matrix44 & setShear (const Shear6<S> &h); |
1037 | | |
1038 | | |
1039 | | //-------------------------------------------------------- |
1040 | | // Shear the matrix by given vector. The composed matrix |
1041 | | // will be <shear> * <this>, where the shear matrix ... |
1042 | | // will shear x for each y coord. by a factor of h[0] ; |
1043 | | // will shear x for each z coord. by a factor of h[1] ; |
1044 | | // will shear y for each z coord. by a factor of h[2] . |
1045 | | //-------------------------------------------------------- |
1046 | | |
1047 | | template <class S> |
1048 | | const Matrix44 & shear (const Vec3<S> &h); |
1049 | | |
1050 | | //-------------------------------------------------------- |
1051 | | // Number of the row and column dimensions, since |
1052 | | // Matrix44 is a square matrix. |
1053 | | //-------------------------------------------------------- |
1054 | | |
1055 | | static unsigned int dimensions() {return 4;} |
1056 | | |
1057 | | |
1058 | | //------------------------------------------------------------ |
1059 | | // Shear the matrix by the given factors. The composed matrix |
1060 | | // will be <shear> * <this>, where the shear matrix ... |
1061 | | // will shear x for each y coord. by a factor of h.xy ; |
1062 | | // will shear x for each z coord. by a factor of h.xz ; |
1063 | | // will shear y for each z coord. by a factor of h.yz ; |
1064 | | // will shear y for each x coord. by a factor of h.yx ; |
1065 | | // will shear z for each x coord. by a factor of h.zx ; |
1066 | | // will shear z for each y coord. by a factor of h.zy . |
1067 | | //------------------------------------------------------------ |
1068 | | |
1069 | | template <class S> |
1070 | | const Matrix44 & shear (const Shear6<S> &h); |
1071 | | |
1072 | | |
1073 | | //------------------------------------------------- |
1074 | | // Limitations of type T (see also class limits<T>) |
1075 | | //------------------------------------------------- |
1076 | | |
1077 | | static T baseTypeMin() {return limits<T>::min();} |
1078 | | static T baseTypeMax() {return limits<T>::max();} |
1079 | | static T baseTypeSmallest() {return limits<T>::smallest();} |
1080 | | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
1081 | | |
1082 | | typedef T BaseType; |
1083 | | typedef Vec4<T> BaseVecType; |
1084 | | |
1085 | | private: |
1086 | | |
1087 | | template <typename R, typename S> |
1088 | | struct isSameType |
1089 | | { |
1090 | | enum {value = 0}; |
1091 | | }; |
1092 | | |
1093 | | template <typename R> |
1094 | | struct isSameType<R, R> |
1095 | | { |
1096 | | enum {value = 1}; |
1097 | | }; |
1098 | | }; |
1099 | | |
1100 | | |
1101 | | //-------------- |
1102 | | // Stream output |
1103 | | //-------------- |
1104 | | |
1105 | | template <class T> |
1106 | | std::ostream & operator << (std::ostream & s, const Matrix22<T> &m); |
1107 | | |
1108 | | template <class T> |
1109 | | std::ostream & operator << (std::ostream & s, const Matrix33<T> &m); |
1110 | | |
1111 | | template <class T> |
1112 | | std::ostream & operator << (std::ostream & s, const Matrix44<T> &m); |
1113 | | |
1114 | | |
1115 | | //--------------------------------------------- |
1116 | | // Vector-times-matrix multiplication operators |
1117 | | //--------------------------------------------- |
1118 | | |
1119 | | |
1120 | | template <class S, class T> |
1121 | | const Vec2<S> & operator *= (Vec2<S> &v, const Matrix22<T> &m); |
1122 | | |
1123 | | template <class S, class T> |
1124 | | Vec2<S> operator * (const Vec2<S> &v, const Matrix22<T> &m); |
1125 | | |
1126 | | template <class S, class T> |
1127 | | const Vec2<S> & operator *= (Vec2<S> &v, const Matrix33<T> &m); |
1128 | | |
1129 | | template <class S, class T> |
1130 | | Vec2<S> operator * (const Vec2<S> &v, const Matrix33<T> &m); |
1131 | | |
1132 | | template <class S, class T> |
1133 | | const Vec3<S> & operator *= (Vec3<S> &v, const Matrix33<T> &m); |
1134 | | |
1135 | | template <class S, class T> |
1136 | | Vec3<S> operator * (const Vec3<S> &v, const Matrix33<T> &m); |
1137 | | |
1138 | | template <class S, class T> |
1139 | | const Vec3<S> & operator *= (Vec3<S> &v, const Matrix44<T> &m); |
1140 | | |
1141 | | template <class S, class T> |
1142 | | Vec3<S> operator * (const Vec3<S> &v, const Matrix44<T> &m); |
1143 | | |
1144 | | template <class S, class T> |
1145 | | const Vec4<S> & operator *= (Vec4<S> &v, const Matrix44<T> &m); |
1146 | | |
1147 | | template <class S, class T> |
1148 | | Vec4<S> operator * (const Vec4<S> &v, const Matrix44<T> &m); |
1149 | | |
1150 | | //------------------------- |
1151 | | // Typedefs for convenience |
1152 | | //------------------------- |
1153 | | |
1154 | | typedef Matrix22 <float> M22f; |
1155 | | typedef Matrix22 <double> M22d; |
1156 | | typedef Matrix33 <float> M33f; |
1157 | | typedef Matrix33 <double> M33d; |
1158 | | typedef Matrix44 <float> M44f; |
1159 | | typedef Matrix44 <double> M44d; |
1160 | | |
1161 | | |
1162 | | //--------------------------- |
1163 | | // Implementation of Matrix22 |
1164 | | //--------------------------- |
1165 | | |
1166 | | template <class T> |
1167 | | inline T * |
1168 | | Matrix22<T>::operator [] (int i) |
1169 | | { |
1170 | | return x[i]; |
1171 | | } |
1172 | | |
1173 | | template <class T> |
1174 | | inline const T * |
1175 | | Matrix22<T>::operator [] (int i) const |
1176 | | { |
1177 | | return x[i]; |
1178 | | } |
1179 | | |
1180 | | template <class T> |
1181 | | inline |
1182 | | Matrix22<T>::Matrix22 () |
1183 | | { |
1184 | | x[0][0] = 1; |
1185 | | x[0][1] = 0; |
1186 | | x[1][0] = 0; |
1187 | | x[1][1] = 1; |
1188 | | } |
1189 | | |
1190 | | template <class T> |
1191 | | inline |
1192 | | Matrix22<T>::Matrix22 (T a) |
1193 | | { |
1194 | | x[0][0] = a; |
1195 | | x[0][1] = a; |
1196 | | x[1][0] = a; |
1197 | | x[1][1] = a; |
1198 | | } |
1199 | | |
1200 | | template <class T> |
1201 | | inline |
1202 | | Matrix22<T>::Matrix22 (const T a[2][2]) |
1203 | | { |
1204 | | memcpy (x, a, sizeof (x)); |
1205 | | } |
1206 | | |
1207 | | template <class T> |
1208 | | inline |
1209 | | Matrix22<T>::Matrix22 (T a, T b, T c, T d) |
1210 | | { |
1211 | | x[0][0] = a; |
1212 | | x[0][1] = b; |
1213 | | x[1][0] = c; |
1214 | | x[1][1] = d; |
1215 | | } |
1216 | | |
1217 | | template <class T> |
1218 | | inline |
1219 | | Matrix22<T>::Matrix22 (const Matrix22 &v) |
1220 | | { |
1221 | | memcpy (x, v.x, sizeof (x)); |
1222 | | } |
1223 | | |
1224 | | template <class T> |
1225 | | template <class S> |
1226 | | inline |
1227 | | Matrix22<T>::Matrix22 (const Matrix22<S> &v) |
1228 | | { |
1229 | | x[0][0] = T (v.x[0][0]); |
1230 | | x[0][1] = T (v.x[0][1]); |
1231 | | x[1][0] = T (v.x[1][0]); |
1232 | | x[1][1] = T (v.x[1][1]); |
1233 | | } |
1234 | | |
1235 | | template <class T> |
1236 | | inline const Matrix22<T> & |
1237 | | Matrix22<T>::operator = (const Matrix22 &v) |
1238 | | { |
1239 | | memcpy (x, v.x, sizeof (x)); |
1240 | | return *this; |
1241 | | } |
1242 | | |
1243 | | template <class T> |
1244 | | inline const Matrix22<T> & |
1245 | | Matrix22<T>::operator = (T a) |
1246 | | { |
1247 | | x[0][0] = a; |
1248 | | x[0][1] = a; |
1249 | | x[1][0] = a; |
1250 | | x[1][1] = a; |
1251 | | return *this; |
1252 | | } |
1253 | | |
1254 | | template <class T> |
1255 | | inline T * |
1256 | | Matrix22<T>::getValue () |
1257 | | { |
1258 | | return (T *) &x[0][0]; |
1259 | | } |
1260 | | |
1261 | | template <class T> |
1262 | | inline const T * |
1263 | | Matrix22<T>::getValue () const |
1264 | | { |
1265 | | return (const T *) &x[0][0]; |
1266 | | } |
1267 | | |
1268 | | template <class T> |
1269 | | template <class S> |
1270 | | inline void |
1271 | | Matrix22<T>::getValue (Matrix22<S> &v) const |
1272 | | { |
1273 | | if (isSameType<S,T>::value) |
1274 | | { |
1275 | | memcpy (v.x, x, sizeof (x)); |
1276 | | } |
1277 | | else |
1278 | | { |
1279 | | v.x[0][0] = x[0][0]; |
1280 | | v.x[0][1] = x[0][1]; |
1281 | | v.x[1][0] = x[1][0]; |
1282 | | v.x[1][1] = x[1][1]; |
1283 | | } |
1284 | | } |
1285 | | |
1286 | | template <class T> |
1287 | | template <class S> |
1288 | | inline Matrix22<T> & |
1289 | | Matrix22<T>::setValue (const Matrix22<S> &v) |
1290 | | { |
1291 | | if (isSameType<S,T>::value) |
1292 | | { |
1293 | | memcpy (x, v.x, sizeof (x)); |
1294 | | } |
1295 | | else |
1296 | | { |
1297 | | x[0][0] = v.x[0][0]; |
1298 | | x[0][1] = v.x[0][1]; |
1299 | | x[1][0] = v.x[1][0]; |
1300 | | x[1][1] = v.x[1][1]; |
1301 | | } |
1302 | | |
1303 | | return *this; |
1304 | | } |
1305 | | |
1306 | | template <class T> |
1307 | | template <class S> |
1308 | | inline Matrix22<T> & |
1309 | | Matrix22<T>::setTheMatrix (const Matrix22<S> &v) |
1310 | | { |
1311 | | if (isSameType<S,T>::value) |
1312 | | { |
1313 | | memcpy (x, v.x, sizeof (x)); |
1314 | | } |
1315 | | else |
1316 | | { |
1317 | | x[0][0] = v.x[0][0]; |
1318 | | x[0][1] = v.x[0][1]; |
1319 | | x[1][0] = v.x[1][0]; |
1320 | | x[1][1] = v.x[1][1]; |
1321 | | } |
1322 | | |
1323 | | return *this; |
1324 | | } |
1325 | | |
1326 | | template <class T> |
1327 | | inline void |
1328 | | Matrix22<T>::makeIdentity() |
1329 | | { |
1330 | | x[0][0] = 1; |
1331 | | x[0][1] = 0; |
1332 | | x[1][0] = 0; |
1333 | | x[1][1] = 1; |
1334 | | } |
1335 | | |
1336 | | template <class T> |
1337 | | bool |
1338 | | Matrix22<T>::operator == (const Matrix22 &v) const |
1339 | | { |
1340 | | return x[0][0] == v.x[0][0] && |
1341 | | x[0][1] == v.x[0][1] && |
1342 | | x[1][0] == v.x[1][0] && |
1343 | | x[1][1] == v.x[1][1]; |
1344 | | } |
1345 | | |
1346 | | template <class T> |
1347 | | bool |
1348 | | Matrix22<T>::operator != (const Matrix22 &v) const |
1349 | | { |
1350 | | return x[0][0] != v.x[0][0] || |
1351 | | x[0][1] != v.x[0][1] || |
1352 | | x[1][0] != v.x[1][0] || |
1353 | | x[1][1] != v.x[1][1]; |
1354 | | } |
1355 | | |
1356 | | template <class T> |
1357 | | bool |
1358 | | Matrix22<T>::equalWithAbsError (const Matrix22<T> &m, T e) const |
1359 | | { |
1360 | | for (int i = 0; i < 2; i++) |
1361 | | for (int j = 0; j < 2; j++) |
1362 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i][j], m[i][j], e)) |
1363 | | return false; |
1364 | | |
1365 | | return true; |
1366 | | } |
1367 | | |
1368 | | template <class T> |
1369 | | bool |
1370 | | Matrix22<T>::equalWithRelError (const Matrix22<T> &m, T e) const |
1371 | | { |
1372 | | for (int i = 0; i < 2; i++) |
1373 | | for (int j = 0; j < 2; j++) |
1374 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i][j], m[i][j], e)) |
1375 | | return false; |
1376 | | |
1377 | | return true; |
1378 | | } |
1379 | | |
1380 | | template <class T> |
1381 | | const Matrix22<T> & |
1382 | | Matrix22<T>::operator += (const Matrix22<T> &v) |
1383 | | { |
1384 | | x[0][0] += v.x[0][0]; |
1385 | | x[0][1] += v.x[0][1]; |
1386 | | x[1][0] += v.x[1][0]; |
1387 | | x[1][1] += v.x[1][1]; |
1388 | | |
1389 | | return *this; |
1390 | | } |
1391 | | |
1392 | | template <class T> |
1393 | | const Matrix22<T> & |
1394 | | Matrix22<T>::operator += (T a) |
1395 | | { |
1396 | | x[0][0] += a; |
1397 | | x[0][1] += a; |
1398 | | x[1][0] += a; |
1399 | | x[1][1] += a; |
1400 | | |
1401 | | return *this; |
1402 | | } |
1403 | | |
1404 | | template <class T> |
1405 | | Matrix22<T> |
1406 | | Matrix22<T>::operator + (const Matrix22<T> &v) const |
1407 | | { |
1408 | | return Matrix22 (x[0][0] + v.x[0][0], |
1409 | | x[0][1] + v.x[0][1], |
1410 | | x[1][0] + v.x[1][0], |
1411 | | x[1][1] + v.x[1][1]); |
1412 | | } |
1413 | | |
1414 | | template <class T> |
1415 | | const Matrix22<T> & |
1416 | | Matrix22<T>::operator -= (const Matrix22<T> &v) |
1417 | | { |
1418 | | x[0][0] -= v.x[0][0]; |
1419 | | x[0][1] -= v.x[0][1]; |
1420 | | x[1][0] -= v.x[1][0]; |
1421 | | x[1][1] -= v.x[1][1]; |
1422 | | |
1423 | | return *this; |
1424 | | } |
1425 | | |
1426 | | template <class T> |
1427 | | const Matrix22<T> & |
1428 | | Matrix22<T>::operator -= (T a) |
1429 | | { |
1430 | | x[0][0] -= a; |
1431 | | x[0][1] -= a; |
1432 | | x[1][0] -= a; |
1433 | | x[1][1] -= a; |
1434 | | |
1435 | | return *this; |
1436 | | } |
1437 | | |
1438 | | template <class T> |
1439 | | Matrix22<T> |
1440 | | Matrix22<T>::operator - (const Matrix22<T> &v) const |
1441 | | { |
1442 | | return Matrix22 (x[0][0] - v.x[0][0], |
1443 | | x[0][1] - v.x[0][1], |
1444 | | x[1][0] - v.x[1][0], |
1445 | | x[1][1] - v.x[1][1]); |
1446 | | } |
1447 | | |
1448 | | template <class T> |
1449 | | Matrix22<T> |
1450 | | Matrix22<T>::operator - () const |
1451 | | { |
1452 | | return Matrix22 (-x[0][0], |
1453 | | -x[0][1], |
1454 | | -x[1][0], |
1455 | | -x[1][1]); |
1456 | | } |
1457 | | |
1458 | | template <class T> |
1459 | | const Matrix22<T> & |
1460 | | Matrix22<T>::negate () |
1461 | | { |
1462 | | x[0][0] = -x[0][0]; |
1463 | | x[0][1] = -x[0][1]; |
1464 | | x[1][0] = -x[1][0]; |
1465 | | x[1][1] = -x[1][1]; |
1466 | | |
1467 | | return *this; |
1468 | | } |
1469 | | |
1470 | | template <class T> |
1471 | | const Matrix22<T> & |
1472 | | Matrix22<T>::operator *= (T a) |
1473 | | { |
1474 | | x[0][0] *= a; |
1475 | | x[0][1] *= a; |
1476 | | x[1][0] *= a; |
1477 | | x[1][1] *= a; |
1478 | | |
1479 | | return *this; |
1480 | | } |
1481 | | |
1482 | | template <class T> |
1483 | | Matrix22<T> |
1484 | | Matrix22<T>::operator * (T a) const |
1485 | | { |
1486 | | return Matrix22 (x[0][0] * a, |
1487 | | x[0][1] * a, |
1488 | | x[1][0] * a, |
1489 | | x[1][1] * a); |
1490 | | } |
1491 | | |
1492 | | template <class T> |
1493 | | inline Matrix22<T> |
1494 | | operator * (T a, const Matrix22<T> &v) |
1495 | | { |
1496 | | return v * a; |
1497 | | } |
1498 | | |
1499 | | template <class T> |
1500 | | const Matrix22<T> & |
1501 | | Matrix22<T>::operator *= (const Matrix22<T> &v) |
1502 | | { |
1503 | | Matrix22 tmp (T (0)); |
1504 | | |
1505 | | for (int i = 0; i < 2; i++) |
1506 | | for (int j = 0; j < 2; j++) |
1507 | | for (int k = 0; k < 2; k++) |
1508 | | tmp.x[i][j] += x[i][k] * v.x[k][j]; |
1509 | | |
1510 | | *this = tmp; |
1511 | | return *this; |
1512 | | } |
1513 | | |
1514 | | template <class T> |
1515 | | Matrix22<T> |
1516 | | Matrix22<T>::operator * (const Matrix22<T> &v) const |
1517 | | { |
1518 | | Matrix22 tmp (T (0)); |
1519 | | |
1520 | | for (int i = 0; i < 2; i++) |
1521 | | for (int j = 0; j < 2; j++) |
1522 | | for (int k = 0; k < 2; k++) |
1523 | | tmp.x[i][j] += x[i][k] * v.x[k][j]; |
1524 | | |
1525 | | return tmp; |
1526 | | } |
1527 | | |
1528 | | template <class T> |
1529 | | template <class S> |
1530 | | void |
1531 | | Matrix22<T>::multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const |
1532 | | { |
1533 | | S a, b; |
1534 | | |
1535 | | a = src[0] * x[0][0] + src[1] * x[1][0]; |
1536 | | b = src[0] * x[0][1] + src[1] * x[1][1]; |
1537 | | |
1538 | | dst.x = a; |
1539 | | dst.y = b; |
1540 | | } |
1541 | | |
1542 | | template <class T> |
1543 | | const Matrix22<T> & |
1544 | | Matrix22<T>::operator /= (T a) |
1545 | | { |
1546 | | x[0][0] /= a; |
1547 | | x[0][1] /= a; |
1548 | | x[1][0] /= a; |
1549 | | x[1][1] /= a; |
1550 | | |
1551 | | return *this; |
1552 | | } |
1553 | | |
1554 | | template <class T> |
1555 | | Matrix22<T> |
1556 | | Matrix22<T>::operator / (T a) const |
1557 | | { |
1558 | | return Matrix22 (x[0][0] / a, |
1559 | | x[0][1] / a, |
1560 | | x[1][0] / a, |
1561 | | x[1][1] / a); |
1562 | | } |
1563 | | |
1564 | | template <class T> |
1565 | | const Matrix22<T> & |
1566 | | Matrix22<T>::transpose () |
1567 | | { |
1568 | | Matrix22 tmp (x[0][0], |
1569 | | x[1][0], |
1570 | | x[0][1], |
1571 | | x[1][1]); |
1572 | | *this = tmp; |
1573 | | return *this; |
1574 | | } |
1575 | | |
1576 | | template <class T> |
1577 | | Matrix22<T> |
1578 | | Matrix22<T>::transposed () const |
1579 | | { |
1580 | | return Matrix22 (x[0][0], |
1581 | | x[1][0], |
1582 | | x[0][1], |
1583 | | x[1][1]); |
1584 | | } |
1585 | | |
1586 | | template <class T> |
1587 | | const Matrix22<T> & |
1588 | | Matrix22<T>::invert (bool singExc) |
1589 | | { |
1590 | | *this = inverse (singExc); |
1591 | | return *this; |
1592 | | } |
1593 | | |
1594 | | template <class T> |
1595 | | Matrix22<T> |
1596 | | Matrix22<T>::inverse (bool singExc) const |
1597 | | { |
1598 | | Matrix22 s ( x[1][1], -x[0][1], |
1599 | | -x[1][0], x[0][0]); |
1600 | | |
1601 | | T r = x[0][0] * x[1][1] - x[1][0] * x[0][1]; |
1602 | | |
1603 | | if (IMATH_INTERNAL_NAMESPACE::abs (r) >= 1) |
1604 | | { |
1605 | | for (int i = 0; i < 2; ++i) |
1606 | | { |
1607 | | for (int j = 0; j < 2; ++j) |
1608 | | { |
1609 | | s[i][j] /= r; |
1610 | | } |
1611 | | } |
1612 | | } |
1613 | | else |
1614 | | { |
1615 | | T mr = IMATH_INTERNAL_NAMESPACE::abs (r) / limits<T>::smallest(); |
1616 | | |
1617 | | for (int i = 0; i < 2; ++i) |
1618 | | { |
1619 | | for (int j = 0; j < 2; ++j) |
1620 | | { |
1621 | | if (mr > IMATH_INTERNAL_NAMESPACE::abs (s[i][j])) |
1622 | | { |
1623 | | s[i][j] /= r; |
1624 | | } |
1625 | | else |
1626 | | { |
1627 | | if (singExc) |
1628 | | throw SingMatrixExc ("Cannot invert " |
1629 | | "singular matrix."); |
1630 | | return Matrix22(); |
1631 | | } |
1632 | | } |
1633 | | } |
1634 | | } |
1635 | | return s; |
1636 | | } |
1637 | | |
1638 | | template <class T> |
1639 | | inline T |
1640 | | Matrix22<T>::determinant () const |
1641 | | { |
1642 | | return x[0][0] * x[1][1] - x[1][0] * x[0][1]; |
1643 | | } |
1644 | | |
1645 | | template <class T> |
1646 | | template <class S> |
1647 | | const Matrix22<T> & |
1648 | | Matrix22<T>::setRotation (S r) |
1649 | | { |
1650 | | S cos_r, sin_r; |
1651 | | |
1652 | | cos_r = Math<T>::cos (r); |
1653 | | sin_r = Math<T>::sin (r); |
1654 | | |
1655 | | x[0][0] = cos_r; |
1656 | | x[0][1] = sin_r; |
1657 | | |
1658 | | x[1][0] = -sin_r; |
1659 | | x[1][1] = cos_r; |
1660 | | |
1661 | | return *this; |
1662 | | } |
1663 | | |
1664 | | template <class T> |
1665 | | template <class S> |
1666 | | const Matrix22<T> & |
1667 | | Matrix22<T>::rotate (S r) |
1668 | | { |
1669 | | *this *= Matrix22<T>().setRotation (r); |
1670 | | return *this; |
1671 | | } |
1672 | | |
1673 | | template <class T> |
1674 | | const Matrix22<T> & |
1675 | | Matrix22<T>::setScale (T s) |
1676 | | { |
1677 | | x[0][0] = s; |
1678 | | x[0][1] = static_cast<T>(0); |
1679 | | x[1][0] = static_cast<T>(0); |
1680 | | x[1][1] = s; |
1681 | | |
1682 | | return *this; |
1683 | | } |
1684 | | |
1685 | | template <class T> |
1686 | | template <class S> |
1687 | | const Matrix22<T> & |
1688 | | Matrix22<T>::setScale (const Vec2<S> &s) |
1689 | | { |
1690 | | x[0][0] = s[0]; |
1691 | | x[0][1] = static_cast<T>(0); |
1692 | | x[1][0] = static_cast<T>(0); |
1693 | | x[1][1] = s[1]; |
1694 | | |
1695 | | return *this; |
1696 | | } |
1697 | | |
1698 | | template <class T> |
1699 | | template <class S> |
1700 | | const Matrix22<T> & |
1701 | | Matrix22<T>::scale (const Vec2<S> &s) |
1702 | | { |
1703 | | x[0][0] *= s[0]; |
1704 | | x[0][1] *= s[0]; |
1705 | | |
1706 | | x[1][0] *= s[1]; |
1707 | | x[1][1] *= s[1]; |
1708 | | |
1709 | | return *this; |
1710 | | } |
1711 | | |
1712 | | |
1713 | | //--------------------------- |
1714 | | // Implementation of Matrix33 |
1715 | | //--------------------------- |
1716 | | |
1717 | | template <class T> |
1718 | | inline T * |
1719 | | Matrix33<T>::operator [] (int i) |
1720 | | { |
1721 | | return x[i]; |
1722 | | } |
1723 | | |
1724 | | template <class T> |
1725 | | inline const T * |
1726 | | Matrix33<T>::operator [] (int i) const |
1727 | | { |
1728 | | return x[i]; |
1729 | | } |
1730 | | |
1731 | | template <class T> |
1732 | | inline |
1733 | | Matrix33<T>::Matrix33 () |
1734 | | { |
1735 | | memset (x, 0, sizeof (x)); |
1736 | | x[0][0] = 1; |
1737 | | x[1][1] = 1; |
1738 | | x[2][2] = 1; |
1739 | | } |
1740 | | |
1741 | | template <class T> |
1742 | | inline |
1743 | | Matrix33<T>::Matrix33 (T a) |
1744 | | { |
1745 | | x[0][0] = a; |
1746 | | x[0][1] = a; |
1747 | | x[0][2] = a; |
1748 | | x[1][0] = a; |
1749 | | x[1][1] = a; |
1750 | | x[1][2] = a; |
1751 | | x[2][0] = a; |
1752 | | x[2][1] = a; |
1753 | | x[2][2] = a; |
1754 | | } |
1755 | | |
1756 | | template <class T> |
1757 | | inline |
1758 | | Matrix33<T>::Matrix33 (const T a[3][3]) |
1759 | | { |
1760 | | memcpy (x, a, sizeof (x)); |
1761 | | } |
1762 | | |
1763 | | template <class T> |
1764 | | inline |
1765 | | Matrix33<T>::Matrix33 (T a, T b, T c, T d, T e, T f, T g, T h, T i) |
1766 | | { |
1767 | | x[0][0] = a; |
1768 | | x[0][1] = b; |
1769 | | x[0][2] = c; |
1770 | | x[1][0] = d; |
1771 | | x[1][1] = e; |
1772 | | x[1][2] = f; |
1773 | | x[2][0] = g; |
1774 | | x[2][1] = h; |
1775 | | x[2][2] = i; |
1776 | | } |
1777 | | |
1778 | | template <class T> |
1779 | | inline |
1780 | | Matrix33<T>::Matrix33 (const Matrix33 &v) |
1781 | | { |
1782 | | memcpy (x, v.x, sizeof (x)); |
1783 | | } |
1784 | | |
1785 | | template <class T> |
1786 | | template <class S> |
1787 | | inline |
1788 | | Matrix33<T>::Matrix33 (const Matrix33<S> &v) |
1789 | | { |
1790 | | x[0][0] = T (v.x[0][0]); |
1791 | | x[0][1] = T (v.x[0][1]); |
1792 | | x[0][2] = T (v.x[0][2]); |
1793 | | x[1][0] = T (v.x[1][0]); |
1794 | | x[1][1] = T (v.x[1][1]); |
1795 | | x[1][2] = T (v.x[1][2]); |
1796 | | x[2][0] = T (v.x[2][0]); |
1797 | | x[2][1] = T (v.x[2][1]); |
1798 | | x[2][2] = T (v.x[2][2]); |
1799 | | } |
1800 | | |
1801 | | template <class T> |
1802 | | inline const Matrix33<T> & |
1803 | | Matrix33<T>::operator = (const Matrix33 &v) |
1804 | | { |
1805 | | memcpy (x, v.x, sizeof (x)); |
1806 | | return *this; |
1807 | | } |
1808 | | |
1809 | | template <class T> |
1810 | | inline const Matrix33<T> & |
1811 | | Matrix33<T>::operator = (T a) |
1812 | | { |
1813 | | x[0][0] = a; |
1814 | | x[0][1] = a; |
1815 | | x[0][2] = a; |
1816 | | x[1][0] = a; |
1817 | | x[1][1] = a; |
1818 | | x[1][2] = a; |
1819 | | x[2][0] = a; |
1820 | | x[2][1] = a; |
1821 | | x[2][2] = a; |
1822 | | return *this; |
1823 | | } |
1824 | | |
1825 | | template <class T> |
1826 | | inline T * |
1827 | | Matrix33<T>::getValue () |
1828 | | { |
1829 | | return (T *) &x[0][0]; |
1830 | | } |
1831 | | |
1832 | | template <class T> |
1833 | | inline const T * |
1834 | | Matrix33<T>::getValue () const |
1835 | | { |
1836 | | return (const T *) &x[0][0]; |
1837 | | } |
1838 | | |
1839 | | template <class T> |
1840 | | template <class S> |
1841 | | inline void |
1842 | | Matrix33<T>::getValue (Matrix33<S> &v) const |
1843 | | { |
1844 | | if (isSameType<S,T>::value) |
1845 | | { |
1846 | | memcpy (v.x, x, sizeof (x)); |
1847 | | } |
1848 | | else |
1849 | | { |
1850 | | v.x[0][0] = x[0][0]; |
1851 | | v.x[0][1] = x[0][1]; |
1852 | | v.x[0][2] = x[0][2]; |
1853 | | v.x[1][0] = x[1][0]; |
1854 | | v.x[1][1] = x[1][1]; |
1855 | | v.x[1][2] = x[1][2]; |
1856 | | v.x[2][0] = x[2][0]; |
1857 | | v.x[2][1] = x[2][1]; |
1858 | | v.x[2][2] = x[2][2]; |
1859 | | } |
1860 | | } |
1861 | | |
1862 | | template <class T> |
1863 | | template <class S> |
1864 | | inline Matrix33<T> & |
1865 | | Matrix33<T>::setValue (const Matrix33<S> &v) |
1866 | | { |
1867 | | if (isSameType<S,T>::value) |
1868 | | { |
1869 | | memcpy (x, v.x, sizeof (x)); |
1870 | | } |
1871 | | else |
1872 | | { |
1873 | | x[0][0] = v.x[0][0]; |
1874 | | x[0][1] = v.x[0][1]; |
1875 | | x[0][2] = v.x[0][2]; |
1876 | | x[1][0] = v.x[1][0]; |
1877 | | x[1][1] = v.x[1][1]; |
1878 | | x[1][2] = v.x[1][2]; |
1879 | | x[2][0] = v.x[2][0]; |
1880 | | x[2][1] = v.x[2][1]; |
1881 | | x[2][2] = v.x[2][2]; |
1882 | | } |
1883 | | |
1884 | | return *this; |
1885 | | } |
1886 | | |
1887 | | template <class T> |
1888 | | template <class S> |
1889 | | inline Matrix33<T> & |
1890 | | Matrix33<T>::setTheMatrix (const Matrix33<S> &v) |
1891 | | { |
1892 | | if (isSameType<S,T>::value) |
1893 | | { |
1894 | | memcpy (x, v.x, sizeof (x)); |
1895 | | } |
1896 | | else |
1897 | | { |
1898 | | x[0][0] = v.x[0][0]; |
1899 | | x[0][1] = v.x[0][1]; |
1900 | | x[0][2] = v.x[0][2]; |
1901 | | x[1][0] = v.x[1][0]; |
1902 | | x[1][1] = v.x[1][1]; |
1903 | | x[1][2] = v.x[1][2]; |
1904 | | x[2][0] = v.x[2][0]; |
1905 | | x[2][1] = v.x[2][1]; |
1906 | | x[2][2] = v.x[2][2]; |
1907 | | } |
1908 | | |
1909 | | return *this; |
1910 | | } |
1911 | | |
1912 | | template <class T> |
1913 | | inline void |
1914 | | Matrix33<T>::makeIdentity() |
1915 | | { |
1916 | | memset (x, 0, sizeof (x)); |
1917 | | x[0][0] = 1; |
1918 | | x[1][1] = 1; |
1919 | | x[2][2] = 1; |
1920 | | } |
1921 | | |
1922 | | template <class T> |
1923 | | bool |
1924 | | Matrix33<T>::operator == (const Matrix33 &v) const |
1925 | | { |
1926 | | return x[0][0] == v.x[0][0] && |
1927 | | x[0][1] == v.x[0][1] && |
1928 | | x[0][2] == v.x[0][2] && |
1929 | | x[1][0] == v.x[1][0] && |
1930 | | x[1][1] == v.x[1][1] && |
1931 | | x[1][2] == v.x[1][2] && |
1932 | | x[2][0] == v.x[2][0] && |
1933 | | x[2][1] == v.x[2][1] && |
1934 | | x[2][2] == v.x[2][2]; |
1935 | | } |
1936 | | |
1937 | | template <class T> |
1938 | | bool |
1939 | | Matrix33<T>::operator != (const Matrix33 &v) const |
1940 | | { |
1941 | | return x[0][0] != v.x[0][0] || |
1942 | | x[0][1] != v.x[0][1] || |
1943 | | x[0][2] != v.x[0][2] || |
1944 | | x[1][0] != v.x[1][0] || |
1945 | | x[1][1] != v.x[1][1] || |
1946 | | x[1][2] != v.x[1][2] || |
1947 | | x[2][0] != v.x[2][0] || |
1948 | | x[2][1] != v.x[2][1] || |
1949 | | x[2][2] != v.x[2][2]; |
1950 | | } |
1951 | | |
1952 | | template <class T> |
1953 | | bool |
1954 | | Matrix33<T>::equalWithAbsError (const Matrix33<T> &m, T e) const |
1955 | | { |
1956 | | for (int i = 0; i < 3; i++) |
1957 | | for (int j = 0; j < 3; j++) |
1958 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i][j], m[i][j], e)) |
1959 | | return false; |
1960 | | |
1961 | | return true; |
1962 | | } |
1963 | | |
1964 | | template <class T> |
1965 | | bool |
1966 | | Matrix33<T>::equalWithRelError (const Matrix33<T> &m, T e) const |
1967 | | { |
1968 | | for (int i = 0; i < 3; i++) |
1969 | | for (int j = 0; j < 3; j++) |
1970 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i][j], m[i][j], e)) |
1971 | | return false; |
1972 | | |
1973 | | return true; |
1974 | | } |
1975 | | |
1976 | | template <class T> |
1977 | | const Matrix33<T> & |
1978 | | Matrix33<T>::operator += (const Matrix33<T> &v) |
1979 | | { |
1980 | | x[0][0] += v.x[0][0]; |
1981 | | x[0][1] += v.x[0][1]; |
1982 | | x[0][2] += v.x[0][2]; |
1983 | | x[1][0] += v.x[1][0]; |
1984 | | x[1][1] += v.x[1][1]; |
1985 | | x[1][2] += v.x[1][2]; |
1986 | | x[2][0] += v.x[2][0]; |
1987 | | x[2][1] += v.x[2][1]; |
1988 | | x[2][2] += v.x[2][2]; |
1989 | | |
1990 | | return *this; |
1991 | | } |
1992 | | |
1993 | | template <class T> |
1994 | | const Matrix33<T> & |
1995 | | Matrix33<T>::operator += (T a) |
1996 | | { |
1997 | | x[0][0] += a; |
1998 | | x[0][1] += a; |
1999 | | x[0][2] += a; |
2000 | | x[1][0] += a; |
2001 | | x[1][1] += a; |
2002 | | x[1][2] += a; |
2003 | | x[2][0] += a; |
2004 | | x[2][1] += a; |
2005 | | x[2][2] += a; |
2006 | | |
2007 | | return *this; |
2008 | | } |
2009 | | |
2010 | | template <class T> |
2011 | | Matrix33<T> |
2012 | | Matrix33<T>::operator + (const Matrix33<T> &v) const |
2013 | | { |
2014 | | return Matrix33 (x[0][0] + v.x[0][0], |
2015 | | x[0][1] + v.x[0][1], |
2016 | | x[0][2] + v.x[0][2], |
2017 | | x[1][0] + v.x[1][0], |
2018 | | x[1][1] + v.x[1][1], |
2019 | | x[1][2] + v.x[1][2], |
2020 | | x[2][0] + v.x[2][0], |
2021 | | x[2][1] + v.x[2][1], |
2022 | | x[2][2] + v.x[2][2]); |
2023 | | } |
2024 | | |
2025 | | template <class T> |
2026 | | const Matrix33<T> & |
2027 | | Matrix33<T>::operator -= (const Matrix33<T> &v) |
2028 | | { |
2029 | | x[0][0] -= v.x[0][0]; |
2030 | | x[0][1] -= v.x[0][1]; |
2031 | | x[0][2] -= v.x[0][2]; |
2032 | | x[1][0] -= v.x[1][0]; |
2033 | | x[1][1] -= v.x[1][1]; |
2034 | | x[1][2] -= v.x[1][2]; |
2035 | | x[2][0] -= v.x[2][0]; |
2036 | | x[2][1] -= v.x[2][1]; |
2037 | | x[2][2] -= v.x[2][2]; |
2038 | | |
2039 | | return *this; |
2040 | | } |
2041 | | |
2042 | | template <class T> |
2043 | | const Matrix33<T> & |
2044 | | Matrix33<T>::operator -= (T a) |
2045 | | { |
2046 | | x[0][0] -= a; |
2047 | | x[0][1] -= a; |
2048 | | x[0][2] -= a; |
2049 | | x[1][0] -= a; |
2050 | | x[1][1] -= a; |
2051 | | x[1][2] -= a; |
2052 | | x[2][0] -= a; |
2053 | | x[2][1] -= a; |
2054 | | x[2][2] -= a; |
2055 | | |
2056 | | return *this; |
2057 | | } |
2058 | | |
2059 | | template <class T> |
2060 | | Matrix33<T> |
2061 | | Matrix33<T>::operator - (const Matrix33<T> &v) const |
2062 | | { |
2063 | | return Matrix33 (x[0][0] - v.x[0][0], |
2064 | | x[0][1] - v.x[0][1], |
2065 | | x[0][2] - v.x[0][2], |
2066 | | x[1][0] - v.x[1][0], |
2067 | | x[1][1] - v.x[1][1], |
2068 | | x[1][2] - v.x[1][2], |
2069 | | x[2][0] - v.x[2][0], |
2070 | | x[2][1] - v.x[2][1], |
2071 | | x[2][2] - v.x[2][2]); |
2072 | | } |
2073 | | |
2074 | | template <class T> |
2075 | | Matrix33<T> |
2076 | | Matrix33<T>::operator - () const |
2077 | | { |
2078 | | return Matrix33 (-x[0][0], |
2079 | | -x[0][1], |
2080 | | -x[0][2], |
2081 | | -x[1][0], |
2082 | | -x[1][1], |
2083 | | -x[1][2], |
2084 | | -x[2][0], |
2085 | | -x[2][1], |
2086 | | -x[2][2]); |
2087 | | } |
2088 | | |
2089 | | template <class T> |
2090 | | const Matrix33<T> & |
2091 | | Matrix33<T>::negate () |
2092 | | { |
2093 | | x[0][0] = -x[0][0]; |
2094 | | x[0][1] = -x[0][1]; |
2095 | | x[0][2] = -x[0][2]; |
2096 | | x[1][0] = -x[1][0]; |
2097 | | x[1][1] = -x[1][1]; |
2098 | | x[1][2] = -x[1][2]; |
2099 | | x[2][0] = -x[2][0]; |
2100 | | x[2][1] = -x[2][1]; |
2101 | | x[2][2] = -x[2][2]; |
2102 | | |
2103 | | return *this; |
2104 | | } |
2105 | | |
2106 | | template <class T> |
2107 | | const Matrix33<T> & |
2108 | | Matrix33<T>::operator *= (T a) |
2109 | | { |
2110 | | x[0][0] *= a; |
2111 | | x[0][1] *= a; |
2112 | | x[0][2] *= a; |
2113 | | x[1][0] *= a; |
2114 | | x[1][1] *= a; |
2115 | | x[1][2] *= a; |
2116 | | x[2][0] *= a; |
2117 | | x[2][1] *= a; |
2118 | | x[2][2] *= a; |
2119 | | |
2120 | | return *this; |
2121 | | } |
2122 | | |
2123 | | template <class T> |
2124 | | Matrix33<T> |
2125 | | Matrix33<T>::operator * (T a) const |
2126 | | { |
2127 | | return Matrix33 (x[0][0] * a, |
2128 | | x[0][1] * a, |
2129 | | x[0][2] * a, |
2130 | | x[1][0] * a, |
2131 | | x[1][1] * a, |
2132 | | x[1][2] * a, |
2133 | | x[2][0] * a, |
2134 | | x[2][1] * a, |
2135 | | x[2][2] * a); |
2136 | | } |
2137 | | |
2138 | | template <class T> |
2139 | | inline Matrix33<T> |
2140 | | operator * (T a, const Matrix33<T> &v) |
2141 | | { |
2142 | | return v * a; |
2143 | | } |
2144 | | |
2145 | | template <class T> |
2146 | | const Matrix33<T> & |
2147 | | Matrix33<T>::operator *= (const Matrix33<T> &v) |
2148 | | { |
2149 | | Matrix33 tmp (T (0)); |
2150 | | |
2151 | | for (int i = 0; i < 3; i++) |
2152 | | for (int j = 0; j < 3; j++) |
2153 | | for (int k = 0; k < 3; k++) |
2154 | | tmp.x[i][j] += x[i][k] * v.x[k][j]; |
2155 | | |
2156 | | *this = tmp; |
2157 | | return *this; |
2158 | | } |
2159 | | |
2160 | | template <class T> |
2161 | | Matrix33<T> |
2162 | | Matrix33<T>::operator * (const Matrix33<T> &v) const |
2163 | | { |
2164 | | Matrix33 tmp (T (0)); |
2165 | | |
2166 | | for (int i = 0; i < 3; i++) |
2167 | | for (int j = 0; j < 3; j++) |
2168 | | for (int k = 0; k < 3; k++) |
2169 | | tmp.x[i][j] += x[i][k] * v.x[k][j]; |
2170 | | |
2171 | | return tmp; |
2172 | | } |
2173 | | |
2174 | | template <class T> |
2175 | | template <class S> |
2176 | | void |
2177 | | Matrix33<T>::multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const |
2178 | | { |
2179 | | S a, b, w; |
2180 | | |
2181 | | a = src[0] * x[0][0] + src[1] * x[1][0] + x[2][0]; |
2182 | | b = src[0] * x[0][1] + src[1] * x[1][1] + x[2][1]; |
2183 | | w = src[0] * x[0][2] + src[1] * x[1][2] + x[2][2]; |
2184 | | |
2185 | | dst.x = a / w; |
2186 | | dst.y = b / w; |
2187 | | } |
2188 | | |
2189 | | template <class T> |
2190 | | template <class S> |
2191 | | void |
2192 | | Matrix33<T>::multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const |
2193 | | { |
2194 | | S a, b; |
2195 | | |
2196 | | a = src[0] * x[0][0] + src[1] * x[1][0]; |
2197 | | b = src[0] * x[0][1] + src[1] * x[1][1]; |
2198 | | |
2199 | | dst.x = a; |
2200 | | dst.y = b; |
2201 | | } |
2202 | | |
2203 | | template <class T> |
2204 | | const Matrix33<T> & |
2205 | | Matrix33<T>::operator /= (T a) |
2206 | | { |
2207 | | x[0][0] /= a; |
2208 | | x[0][1] /= a; |
2209 | | x[0][2] /= a; |
2210 | | x[1][0] /= a; |
2211 | | x[1][1] /= a; |
2212 | | x[1][2] /= a; |
2213 | | x[2][0] /= a; |
2214 | | x[2][1] /= a; |
2215 | | x[2][2] /= a; |
2216 | | |
2217 | | return *this; |
2218 | | } |
2219 | | |
2220 | | template <class T> |
2221 | | Matrix33<T> |
2222 | | Matrix33<T>::operator / (T a) const |
2223 | | { |
2224 | | return Matrix33 (x[0][0] / a, |
2225 | | x[0][1] / a, |
2226 | | x[0][2] / a, |
2227 | | x[1][0] / a, |
2228 | | x[1][1] / a, |
2229 | | x[1][2] / a, |
2230 | | x[2][0] / a, |
2231 | | x[2][1] / a, |
2232 | | x[2][2] / a); |
2233 | | } |
2234 | | |
2235 | | template <class T> |
2236 | | const Matrix33<T> & |
2237 | | Matrix33<T>::transpose () |
2238 | | { |
2239 | | Matrix33 tmp (x[0][0], |
2240 | | x[1][0], |
2241 | | x[2][0], |
2242 | | x[0][1], |
2243 | | x[1][1], |
2244 | | x[2][1], |
2245 | | x[0][2], |
2246 | | x[1][2], |
2247 | | x[2][2]); |
2248 | | *this = tmp; |
2249 | | return *this; |
2250 | | } |
2251 | | |
2252 | | template <class T> |
2253 | | Matrix33<T> |
2254 | | Matrix33<T>::transposed () const |
2255 | | { |
2256 | | return Matrix33 (x[0][0], |
2257 | | x[1][0], |
2258 | | x[2][0], |
2259 | | x[0][1], |
2260 | | x[1][1], |
2261 | | x[2][1], |
2262 | | x[0][2], |
2263 | | x[1][2], |
2264 | | x[2][2]); |
2265 | | } |
2266 | | |
2267 | | template <class T> |
2268 | | const Matrix33<T> & |
2269 | | Matrix33<T>::gjInvert (bool singExc) |
2270 | | { |
2271 | | *this = gjInverse (singExc); |
2272 | | return *this; |
2273 | | } |
2274 | | |
2275 | | template <class T> |
2276 | | Matrix33<T> |
2277 | | Matrix33<T>::gjInverse (bool singExc) const |
2278 | | { |
2279 | | int i, j, k; |
2280 | | Matrix33 s; |
2281 | | Matrix33 t (*this); |
2282 | | |
2283 | | // Forward elimination |
2284 | | |
2285 | | for (i = 0; i < 2 ; i++) |
2286 | | { |
2287 | | int pivot = i; |
2288 | | |
2289 | | T pivotsize = t[i][i]; |
2290 | | |
2291 | | if (pivotsize < 0) |
2292 | | pivotsize = -pivotsize; |
2293 | | |
2294 | | for (j = i + 1; j < 3; j++) |
2295 | | { |
2296 | | T tmp = t[j][i]; |
2297 | | |
2298 | | if (tmp < 0) |
2299 | | tmp = -tmp; |
2300 | | |
2301 | | if (tmp > pivotsize) |
2302 | | { |
2303 | | pivot = j; |
2304 | | pivotsize = tmp; |
2305 | | } |
2306 | | } |
2307 | | |
2308 | | if (pivotsize == 0) |
2309 | | { |
2310 | | if (singExc) |
2311 | | throw ::IMATH_INTERNAL_NAMESPACE::SingMatrixExc ("Cannot invert singular matrix."); |
2312 | | |
2313 | | return Matrix33(); |
2314 | | } |
2315 | | |
2316 | | if (pivot != i) |
2317 | | { |
2318 | | for (j = 0; j < 3; j++) |
2319 | | { |
2320 | | T tmp; |
2321 | | |
2322 | | tmp = t[i][j]; |
2323 | | t[i][j] = t[pivot][j]; |
2324 | | t[pivot][j] = tmp; |
2325 | | |
2326 | | tmp = s[i][j]; |
2327 | | s[i][j] = s[pivot][j]; |
2328 | | s[pivot][j] = tmp; |
2329 | | } |
2330 | | } |
2331 | | |
2332 | | for (j = i + 1; j < 3; j++) |
2333 | | { |
2334 | | T f = t[j][i] / t[i][i]; |
2335 | | |
2336 | | for (k = 0; k < 3; k++) |
2337 | | { |
2338 | | t[j][k] -= f * t[i][k]; |
2339 | | s[j][k] -= f * s[i][k]; |
2340 | | } |
2341 | | } |
2342 | | } |
2343 | | |
2344 | | // Backward substitution |
2345 | | |
2346 | | for (i = 2; i >= 0; --i) |
2347 | | { |
2348 | | T f; |
2349 | | |
2350 | | if ((f = t[i][i]) == 0) |
2351 | | { |
2352 | | if (singExc) |
2353 | | throw ::IMATH_INTERNAL_NAMESPACE::SingMatrixExc ("Cannot invert singular matrix."); |
2354 | | |
2355 | | return Matrix33(); |
2356 | | } |
2357 | | |
2358 | | for (j = 0; j < 3; j++) |
2359 | | { |
2360 | | t[i][j] /= f; |
2361 | | s[i][j] /= f; |
2362 | | } |
2363 | | |
2364 | | for (j = 0; j < i; j++) |
2365 | | { |
2366 | | f = t[j][i]; |
2367 | | |
2368 | | for (k = 0; k < 3; k++) |
2369 | | { |
2370 | | t[j][k] -= f * t[i][k]; |
2371 | | s[j][k] -= f * s[i][k]; |
2372 | | } |
2373 | | } |
2374 | | } |
2375 | | |
2376 | | return s; |
2377 | | } |
2378 | | |
2379 | | template <class T> |
2380 | | const Matrix33<T> & |
2381 | | Matrix33<T>::invert (bool singExc) |
2382 | | { |
2383 | | *this = inverse (singExc); |
2384 | | return *this; |
2385 | | } |
2386 | | |
2387 | | template <class T> |
2388 | | Matrix33<T> |
2389 | | Matrix33<T>::inverse (bool singExc) const |
2390 | | { |
2391 | | if (x[0][2] != 0 || x[1][2] != 0 || x[2][2] != 1) |
2392 | | { |
2393 | | Matrix33 s (x[1][1] * x[2][2] - x[2][1] * x[1][2], |
2394 | | x[2][1] * x[0][2] - x[0][1] * x[2][2], |
2395 | | x[0][1] * x[1][2] - x[1][1] * x[0][2], |
2396 | | |
2397 | | x[2][0] * x[1][2] - x[1][0] * x[2][2], |
2398 | | x[0][0] * x[2][2] - x[2][0] * x[0][2], |
2399 | | x[1][0] * x[0][2] - x[0][0] * x[1][2], |
2400 | | |
2401 | | x[1][0] * x[2][1] - x[2][0] * x[1][1], |
2402 | | x[2][0] * x[0][1] - x[0][0] * x[2][1], |
2403 | | x[0][0] * x[1][1] - x[1][0] * x[0][1]); |
2404 | | |
2405 | | T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0]; |
2406 | | |
2407 | | if (IMATH_INTERNAL_NAMESPACE::abs (r) >= 1) |
2408 | | { |
2409 | | for (int i = 0; i < 3; ++i) |
2410 | | { |
2411 | | for (int j = 0; j < 3; ++j) |
2412 | | { |
2413 | | s[i][j] /= r; |
2414 | | } |
2415 | | } |
2416 | | } |
2417 | | else |
2418 | | { |
2419 | | T mr = IMATH_INTERNAL_NAMESPACE::abs (r) / limits<T>::smallest(); |
2420 | | |
2421 | | for (int i = 0; i < 3; ++i) |
2422 | | { |
2423 | | for (int j = 0; j < 3; ++j) |
2424 | | { |
2425 | | if (mr > IMATH_INTERNAL_NAMESPACE::abs (s[i][j])) |
2426 | | { |
2427 | | s[i][j] /= r; |
2428 | | } |
2429 | | else |
2430 | | { |
2431 | | if (singExc) |
2432 | | throw SingMatrixExc ("Cannot invert " |
2433 | | "singular matrix."); |
2434 | | return Matrix33(); |
2435 | | } |
2436 | | } |
2437 | | } |
2438 | | } |
2439 | | |
2440 | | return s; |
2441 | | } |
2442 | | else |
2443 | | { |
2444 | | Matrix33 s ( x[1][1], |
2445 | | -x[0][1], |
2446 | | 0, |
2447 | | |
2448 | | -x[1][0], |
2449 | | x[0][0], |
2450 | | 0, |
2451 | | |
2452 | | 0, |
2453 | | 0, |
2454 | | 1); |
2455 | | |
2456 | | T r = x[0][0] * x[1][1] - x[1][0] * x[0][1]; |
2457 | | |
2458 | | if (IMATH_INTERNAL_NAMESPACE::abs (r) >= 1) |
2459 | | { |
2460 | | for (int i = 0; i < 2; ++i) |
2461 | | { |
2462 | | for (int j = 0; j < 2; ++j) |
2463 | | { |
2464 | | s[i][j] /= r; |
2465 | | } |
2466 | | } |
2467 | | } |
2468 | | else |
2469 | | { |
2470 | | T mr = IMATH_INTERNAL_NAMESPACE::abs (r) / limits<T>::smallest(); |
2471 | | |
2472 | | for (int i = 0; i < 2; ++i) |
2473 | | { |
2474 | | for (int j = 0; j < 2; ++j) |
2475 | | { |
2476 | | if (mr > IMATH_INTERNAL_NAMESPACE::abs (s[i][j])) |
2477 | | { |
2478 | | s[i][j] /= r; |
2479 | | } |
2480 | | else |
2481 | | { |
2482 | | if (singExc) |
2483 | | throw SingMatrixExc ("Cannot invert " |
2484 | | "singular matrix."); |
2485 | | return Matrix33(); |
2486 | | } |
2487 | | } |
2488 | | } |
2489 | | } |
2490 | | |
2491 | | s[2][0] = -x[2][0] * s[0][0] - x[2][1] * s[1][0]; |
2492 | | s[2][1] = -x[2][0] * s[0][1] - x[2][1] * s[1][1]; |
2493 | | |
2494 | | return s; |
2495 | | } |
2496 | | } |
2497 | | |
2498 | | template <class T> |
2499 | | inline T |
2500 | | Matrix33<T>::minorOf (const int r, const int c) const |
2501 | | { |
2502 | | int r0 = 0 + (r < 1 ? 1 : 0); |
2503 | | int r1 = 1 + (r < 2 ? 1 : 0); |
2504 | | int c0 = 0 + (c < 1 ? 1 : 0); |
2505 | | int c1 = 1 + (c < 2 ? 1 : 0); |
2506 | | |
2507 | | return x[r0][c0]*x[r1][c1] - x[r1][c0]*x[r0][c1]; |
2508 | | } |
2509 | | |
2510 | | template <class T> |
2511 | | inline T |
2512 | | Matrix33<T>::fastMinor( const int r0, const int r1, |
2513 | | const int c0, const int c1) const |
2514 | | { |
2515 | | return x[r0][c0]*x[r1][c1] - x[r0][c1]*x[r1][c0]; |
2516 | | } |
2517 | | |
2518 | | template <class T> |
2519 | | inline T |
2520 | | Matrix33<T>::determinant () const |
2521 | | { |
2522 | | return x[0][0]*(x[1][1]*x[2][2] - x[1][2]*x[2][1]) + |
2523 | | x[0][1]*(x[1][2]*x[2][0] - x[1][0]*x[2][2]) + |
2524 | | x[0][2]*(x[1][0]*x[2][1] - x[1][1]*x[2][0]); |
2525 | | } |
2526 | | |
2527 | | template <class T> |
2528 | | template <class S> |
2529 | | const Matrix33<T> & |
2530 | | Matrix33<T>::setRotation (S r) |
2531 | | { |
2532 | | S cos_r, sin_r; |
2533 | | |
2534 | | cos_r = Math<T>::cos (r); |
2535 | | sin_r = Math<T>::sin (r); |
2536 | | |
2537 | | x[0][0] = cos_r; |
2538 | | x[0][1] = sin_r; |
2539 | | x[0][2] = 0; |
2540 | | |
2541 | | x[1][0] = -sin_r; |
2542 | | x[1][1] = cos_r; |
2543 | | x[1][2] = 0; |
2544 | | |
2545 | | x[2][0] = 0; |
2546 | | x[2][1] = 0; |
2547 | | x[2][2] = 1; |
2548 | | |
2549 | | return *this; |
2550 | | } |
2551 | | |
2552 | | template <class T> |
2553 | | template <class S> |
2554 | | const Matrix33<T> & |
2555 | | Matrix33<T>::rotate (S r) |
2556 | | { |
2557 | | *this *= Matrix33<T>().setRotation (r); |
2558 | | return *this; |
2559 | | } |
2560 | | |
2561 | | template <class T> |
2562 | | const Matrix33<T> & |
2563 | | Matrix33<T>::setScale (T s) |
2564 | | { |
2565 | | memset (x, 0, sizeof (x)); |
2566 | | x[0][0] = s; |
2567 | | x[1][1] = s; |
2568 | | x[2][2] = 1; |
2569 | | |
2570 | | return *this; |
2571 | | } |
2572 | | |
2573 | | template <class T> |
2574 | | template <class S> |
2575 | | const Matrix33<T> & |
2576 | | Matrix33<T>::setScale (const Vec2<S> &s) |
2577 | | { |
2578 | | memset (x, 0, sizeof (x)); |
2579 | | x[0][0] = s[0]; |
2580 | | x[1][1] = s[1]; |
2581 | | x[2][2] = 1; |
2582 | | |
2583 | | return *this; |
2584 | | } |
2585 | | |
2586 | | template <class T> |
2587 | | template <class S> |
2588 | | const Matrix33<T> & |
2589 | | Matrix33<T>::scale (const Vec2<S> &s) |
2590 | | { |
2591 | | x[0][0] *= s[0]; |
2592 | | x[0][1] *= s[0]; |
2593 | | x[0][2] *= s[0]; |
2594 | | |
2595 | | x[1][0] *= s[1]; |
2596 | | x[1][1] *= s[1]; |
2597 | | x[1][2] *= s[1]; |
2598 | | |
2599 | | return *this; |
2600 | | } |
2601 | | |
2602 | | template <class T> |
2603 | | template <class S> |
2604 | | const Matrix33<T> & |
2605 | | Matrix33<T>::setTranslation (const Vec2<S> &t) |
2606 | | { |
2607 | | x[0][0] = 1; |
2608 | | x[0][1] = 0; |
2609 | | x[0][2] = 0; |
2610 | | |
2611 | | x[1][0] = 0; |
2612 | | x[1][1] = 1; |
2613 | | x[1][2] = 0; |
2614 | | |
2615 | | x[2][0] = t[0]; |
2616 | | x[2][1] = t[1]; |
2617 | | x[2][2] = 1; |
2618 | | |
2619 | | return *this; |
2620 | | } |
2621 | | |
2622 | | template <class T> |
2623 | | inline Vec2<T> |
2624 | | Matrix33<T>::translation () const |
2625 | | { |
2626 | | return Vec2<T> (x[2][0], x[2][1]); |
2627 | | } |
2628 | | |
2629 | | template <class T> |
2630 | | template <class S> |
2631 | | const Matrix33<T> & |
2632 | | Matrix33<T>::translate (const Vec2<S> &t) |
2633 | | { |
2634 | | x[2][0] += t[0] * x[0][0] + t[1] * x[1][0]; |
2635 | | x[2][1] += t[0] * x[0][1] + t[1] * x[1][1]; |
2636 | | x[2][2] += t[0] * x[0][2] + t[1] * x[1][2]; |
2637 | | |
2638 | | return *this; |
2639 | | } |
2640 | | |
2641 | | template <class T> |
2642 | | template <class S> |
2643 | | const Matrix33<T> & |
2644 | | Matrix33<T>::setShear (const S &xy) |
2645 | | { |
2646 | | x[0][0] = 1; |
2647 | | x[0][1] = 0; |
2648 | | x[0][2] = 0; |
2649 | | |
2650 | | x[1][0] = xy; |
2651 | | x[1][1] = 1; |
2652 | | x[1][2] = 0; |
2653 | | |
2654 | | x[2][0] = 0; |
2655 | | x[2][1] = 0; |
2656 | | x[2][2] = 1; |
2657 | | |
2658 | | return *this; |
2659 | | } |
2660 | | |
2661 | | template <class T> |
2662 | | template <class S> |
2663 | | const Matrix33<T> & |
2664 | | Matrix33<T>::setShear (const Vec2<S> &h) |
2665 | | { |
2666 | | x[0][0] = 1; |
2667 | | x[0][1] = h[1]; |
2668 | | x[0][2] = 0; |
2669 | | |
2670 | | x[1][0] = h[0]; |
2671 | | x[1][1] = 1; |
2672 | | x[1][2] = 0; |
2673 | | |
2674 | | x[2][0] = 0; |
2675 | | x[2][1] = 0; |
2676 | | x[2][2] = 1; |
2677 | | |
2678 | | return *this; |
2679 | | } |
2680 | | |
2681 | | template <class T> |
2682 | | template <class S> |
2683 | | const Matrix33<T> & |
2684 | | Matrix33<T>::shear (const S &xy) |
2685 | | { |
2686 | | // |
2687 | | // In this case, we don't need a temp. copy of the matrix |
2688 | | // because we never use a value on the RHS after we've |
2689 | | // changed it on the LHS. |
2690 | | // |
2691 | | |
2692 | | x[1][0] += xy * x[0][0]; |
2693 | | x[1][1] += xy * x[0][1]; |
2694 | | x[1][2] += xy * x[0][2]; |
2695 | | |
2696 | | return *this; |
2697 | | } |
2698 | | |
2699 | | template <class T> |
2700 | | template <class S> |
2701 | | const Matrix33<T> & |
2702 | | Matrix33<T>::shear (const Vec2<S> &h) |
2703 | | { |
2704 | | Matrix33<T> P (*this); |
2705 | | |
2706 | | x[0][0] = P[0][0] + h[1] * P[1][0]; |
2707 | | x[0][1] = P[0][1] + h[1] * P[1][1]; |
2708 | | x[0][2] = P[0][2] + h[1] * P[1][2]; |
2709 | | |
2710 | | x[1][0] = P[1][0] + h[0] * P[0][0]; |
2711 | | x[1][1] = P[1][1] + h[0] * P[0][1]; |
2712 | | x[1][2] = P[1][2] + h[0] * P[0][2]; |
2713 | | |
2714 | | return *this; |
2715 | | } |
2716 | | |
2717 | | |
2718 | | //--------------------------- |
2719 | | // Implementation of Matrix44 |
2720 | | //--------------------------- |
2721 | | |
2722 | | template <class T> |
2723 | | inline T * |
2724 | | Matrix44<T>::operator [] (int i) |
2725 | 0 | { |
2726 | 0 | return x[i]; |
2727 | 0 | } |
2728 | | |
2729 | | template <class T> |
2730 | | inline const T * |
2731 | | Matrix44<T>::operator [] (int i) const |
2732 | 0 | { |
2733 | 0 | return x[i]; |
2734 | 0 | } |
2735 | | |
2736 | | template <class T> |
2737 | | inline |
2738 | | Matrix44<T>::Matrix44 () |
2739 | 0 | { |
2740 | 0 | memset (x, 0, sizeof (x)); |
2741 | 0 | x[0][0] = 1; |
2742 | 0 | x[1][1] = 1; |
2743 | 0 | x[2][2] = 1; |
2744 | 0 | x[3][3] = 1; |
2745 | 0 | } |
2746 | | |
2747 | | template <class T> |
2748 | | inline |
2749 | | Matrix44<T>::Matrix44 (T a) |
2750 | 0 | { |
2751 | 0 | x[0][0] = a; |
2752 | 0 | x[0][1] = a; |
2753 | 0 | x[0][2] = a; |
2754 | 0 | x[0][3] = a; |
2755 | 0 | x[1][0] = a; |
2756 | 0 | x[1][1] = a; |
2757 | 0 | x[1][2] = a; |
2758 | 0 | x[1][3] = a; |
2759 | 0 | x[2][0] = a; |
2760 | 0 | x[2][1] = a; |
2761 | 0 | x[2][2] = a; |
2762 | 0 | x[2][3] = a; |
2763 | 0 | x[3][0] = a; |
2764 | 0 | x[3][1] = a; |
2765 | 0 | x[3][2] = a; |
2766 | 0 | x[3][3] = a; |
2767 | 0 | } |
2768 | | |
2769 | | template <class T> |
2770 | | inline |
2771 | | Matrix44<T>::Matrix44 (const T a[4][4]) |
2772 | | { |
2773 | | memcpy (x, a, sizeof (x)); |
2774 | | } |
2775 | | |
2776 | | template <class T> |
2777 | | inline |
2778 | | Matrix44<T>::Matrix44 (T a, T b, T c, T d, T e, T f, T g, T h, |
2779 | | T i, T j, T k, T l, T m, T n, T o, T p) |
2780 | 0 | { |
2781 | 0 | x[0][0] = a; |
2782 | 0 | x[0][1] = b; |
2783 | 0 | x[0][2] = c; |
2784 | 0 | x[0][3] = d; |
2785 | 0 | x[1][0] = e; |
2786 | 0 | x[1][1] = f; |
2787 | 0 | x[1][2] = g; |
2788 | 0 | x[1][3] = h; |
2789 | 0 | x[2][0] = i; |
2790 | 0 | x[2][1] = j; |
2791 | 0 | x[2][2] = k; |
2792 | 0 | x[2][3] = l; |
2793 | 0 | x[3][0] = m; |
2794 | 0 | x[3][1] = n; |
2795 | 0 | x[3][2] = o; |
2796 | 0 | x[3][3] = p; |
2797 | 0 | } |
2798 | | |
2799 | | |
2800 | | template <class T> |
2801 | | inline |
2802 | | Matrix44<T>::Matrix44 (Matrix33<T> r, Vec3<T> t) |
2803 | | { |
2804 | | x[0][0] = r[0][0]; |
2805 | | x[0][1] = r[0][1]; |
2806 | | x[0][2] = r[0][2]; |
2807 | | x[0][3] = 0; |
2808 | | x[1][0] = r[1][0]; |
2809 | | x[1][1] = r[1][1]; |
2810 | | x[1][2] = r[1][2]; |
2811 | | x[1][3] = 0; |
2812 | | x[2][0] = r[2][0]; |
2813 | | x[2][1] = r[2][1]; |
2814 | | x[2][2] = r[2][2]; |
2815 | | x[2][3] = 0; |
2816 | | x[3][0] = t[0]; |
2817 | | x[3][1] = t[1]; |
2818 | | x[3][2] = t[2]; |
2819 | | x[3][3] = 1; |
2820 | | } |
2821 | | |
2822 | | template <class T> |
2823 | | inline |
2824 | | Matrix44<T>::Matrix44 (const Matrix44 &v) |
2825 | 0 | { |
2826 | 0 | x[0][0] = v.x[0][0]; |
2827 | 0 | x[0][1] = v.x[0][1]; |
2828 | 0 | x[0][2] = v.x[0][2]; |
2829 | 0 | x[0][3] = v.x[0][3]; |
2830 | 0 | x[1][0] = v.x[1][0]; |
2831 | 0 | x[1][1] = v.x[1][1]; |
2832 | 0 | x[1][2] = v.x[1][2]; |
2833 | 0 | x[1][3] = v.x[1][3]; |
2834 | 0 | x[2][0] = v.x[2][0]; |
2835 | 0 | x[2][1] = v.x[2][1]; |
2836 | 0 | x[2][2] = v.x[2][2]; |
2837 | 0 | x[2][3] = v.x[2][3]; |
2838 | 0 | x[3][0] = v.x[3][0]; |
2839 | 0 | x[3][1] = v.x[3][1]; |
2840 | 0 | x[3][2] = v.x[3][2]; |
2841 | 0 | x[3][3] = v.x[3][3]; |
2842 | 0 | } |
2843 | | |
2844 | | template <class T> |
2845 | | template <class S> |
2846 | | inline |
2847 | | Matrix44<T>::Matrix44 (const Matrix44<S> &v) |
2848 | | { |
2849 | | x[0][0] = T (v.x[0][0]); |
2850 | | x[0][1] = T (v.x[0][1]); |
2851 | | x[0][2] = T (v.x[0][2]); |
2852 | | x[0][3] = T (v.x[0][3]); |
2853 | | x[1][0] = T (v.x[1][0]); |
2854 | | x[1][1] = T (v.x[1][1]); |
2855 | | x[1][2] = T (v.x[1][2]); |
2856 | | x[1][3] = T (v.x[1][3]); |
2857 | | x[2][0] = T (v.x[2][0]); |
2858 | | x[2][1] = T (v.x[2][1]); |
2859 | | x[2][2] = T (v.x[2][2]); |
2860 | | x[2][3] = T (v.x[2][3]); |
2861 | | x[3][0] = T (v.x[3][0]); |
2862 | | x[3][1] = T (v.x[3][1]); |
2863 | | x[3][2] = T (v.x[3][2]); |
2864 | | x[3][3] = T (v.x[3][3]); |
2865 | | } |
2866 | | |
2867 | | template <class T> |
2868 | | inline const Matrix44<T> & |
2869 | | Matrix44<T>::operator = (const Matrix44 &v) |
2870 | 0 | { |
2871 | 0 | x[0][0] = v.x[0][0]; |
2872 | 0 | x[0][1] = v.x[0][1]; |
2873 | 0 | x[0][2] = v.x[0][2]; |
2874 | 0 | x[0][3] = v.x[0][3]; |
2875 | 0 | x[1][0] = v.x[1][0]; |
2876 | 0 | x[1][1] = v.x[1][1]; |
2877 | 0 | x[1][2] = v.x[1][2]; |
2878 | 0 | x[1][3] = v.x[1][3]; |
2879 | 0 | x[2][0] = v.x[2][0]; |
2880 | 0 | x[2][1] = v.x[2][1]; |
2881 | 0 | x[2][2] = v.x[2][2]; |
2882 | 0 | x[2][3] = v.x[2][3]; |
2883 | 0 | x[3][0] = v.x[3][0]; |
2884 | 0 | x[3][1] = v.x[3][1]; |
2885 | 0 | x[3][2] = v.x[3][2]; |
2886 | 0 | x[3][3] = v.x[3][3]; |
2887 | 0 | return *this; |
2888 | 0 | } |
2889 | | |
2890 | | template <class T> |
2891 | | inline const Matrix44<T> & |
2892 | | Matrix44<T>::operator = (T a) |
2893 | | { |
2894 | | x[0][0] = a; |
2895 | | x[0][1] = a; |
2896 | | x[0][2] = a; |
2897 | | x[0][3] = a; |
2898 | | x[1][0] = a; |
2899 | | x[1][1] = a; |
2900 | | x[1][2] = a; |
2901 | | x[1][3] = a; |
2902 | | x[2][0] = a; |
2903 | | x[2][1] = a; |
2904 | | x[2][2] = a; |
2905 | | x[2][3] = a; |
2906 | | x[3][0] = a; |
2907 | | x[3][1] = a; |
2908 | | x[3][2] = a; |
2909 | | x[3][3] = a; |
2910 | | return *this; |
2911 | | } |
2912 | | |
2913 | | template <class T> |
2914 | | inline T * |
2915 | | Matrix44<T>::getValue () |
2916 | | { |
2917 | | return (T *) &x[0][0]; |
2918 | | } |
2919 | | |
2920 | | template <class T> |
2921 | | inline const T * |
2922 | | Matrix44<T>::getValue () const |
2923 | | { |
2924 | | return (const T *) &x[0][0]; |
2925 | | } |
2926 | | |
2927 | | template <class T> |
2928 | | template <class S> |
2929 | | inline void |
2930 | | Matrix44<T>::getValue (Matrix44<S> &v) const |
2931 | | { |
2932 | | if (isSameType<S,T>::value) |
2933 | | { |
2934 | | memcpy (v.x, x, sizeof (x)); |
2935 | | } |
2936 | | else |
2937 | | { |
2938 | | v.x[0][0] = x[0][0]; |
2939 | | v.x[0][1] = x[0][1]; |
2940 | | v.x[0][2] = x[0][2]; |
2941 | | v.x[0][3] = x[0][3]; |
2942 | | v.x[1][0] = x[1][0]; |
2943 | | v.x[1][1] = x[1][1]; |
2944 | | v.x[1][2] = x[1][2]; |
2945 | | v.x[1][3] = x[1][3]; |
2946 | | v.x[2][0] = x[2][0]; |
2947 | | v.x[2][1] = x[2][1]; |
2948 | | v.x[2][2] = x[2][2]; |
2949 | | v.x[2][3] = x[2][3]; |
2950 | | v.x[3][0] = x[3][0]; |
2951 | | v.x[3][1] = x[3][1]; |
2952 | | v.x[3][2] = x[3][2]; |
2953 | | v.x[3][3] = x[3][3]; |
2954 | | } |
2955 | | } |
2956 | | |
2957 | | template <class T> |
2958 | | template <class S> |
2959 | | inline Matrix44<T> & |
2960 | | Matrix44<T>::setValue (const Matrix44<S> &v) |
2961 | | { |
2962 | | if (isSameType<S,T>::value) |
2963 | | { |
2964 | | memcpy (x, v.x, sizeof (x)); |
2965 | | } |
2966 | | else |
2967 | | { |
2968 | | x[0][0] = v.x[0][0]; |
2969 | | x[0][1] = v.x[0][1]; |
2970 | | x[0][2] = v.x[0][2]; |
2971 | | x[0][3] = v.x[0][3]; |
2972 | | x[1][0] = v.x[1][0]; |
2973 | | x[1][1] = v.x[1][1]; |
2974 | | x[1][2] = v.x[1][2]; |
2975 | | x[1][3] = v.x[1][3]; |
2976 | | x[2][0] = v.x[2][0]; |
2977 | | x[2][1] = v.x[2][1]; |
2978 | | x[2][2] = v.x[2][2]; |
2979 | | x[2][3] = v.x[2][3]; |
2980 | | x[3][0] = v.x[3][0]; |
2981 | | x[3][1] = v.x[3][1]; |
2982 | | x[3][2] = v.x[3][2]; |
2983 | | x[3][3] = v.x[3][3]; |
2984 | | } |
2985 | | |
2986 | | return *this; |
2987 | | } |
2988 | | |
2989 | | template <class T> |
2990 | | template <class S> |
2991 | | inline Matrix44<T> & |
2992 | | Matrix44<T>::setTheMatrix (const Matrix44<S> &v) |
2993 | | { |
2994 | | if (isSameType<S,T>::value) |
2995 | | { |
2996 | | memcpy (x, v.x, sizeof (x)); |
2997 | | } |
2998 | | else |
2999 | | { |
3000 | | x[0][0] = v.x[0][0]; |
3001 | | x[0][1] = v.x[0][1]; |
3002 | | x[0][2] = v.x[0][2]; |
3003 | | x[0][3] = v.x[0][3]; |
3004 | | x[1][0] = v.x[1][0]; |
3005 | | x[1][1] = v.x[1][1]; |
3006 | | x[1][2] = v.x[1][2]; |
3007 | | x[1][3] = v.x[1][3]; |
3008 | | x[2][0] = v.x[2][0]; |
3009 | | x[2][1] = v.x[2][1]; |
3010 | | x[2][2] = v.x[2][2]; |
3011 | | x[2][3] = v.x[2][3]; |
3012 | | x[3][0] = v.x[3][0]; |
3013 | | x[3][1] = v.x[3][1]; |
3014 | | x[3][2] = v.x[3][2]; |
3015 | | x[3][3] = v.x[3][3]; |
3016 | | } |
3017 | | |
3018 | | return *this; |
3019 | | } |
3020 | | |
3021 | | template <class T> |
3022 | | inline void |
3023 | | Matrix44<T>::makeIdentity() |
3024 | 0 | { |
3025 | 0 | memset (x, 0, sizeof (x)); |
3026 | 0 | x[0][0] = 1; |
3027 | 0 | x[1][1] = 1; |
3028 | 0 | x[2][2] = 1; |
3029 | 0 | x[3][3] = 1; |
3030 | 0 | } |
3031 | | |
3032 | | template <class T> |
3033 | | bool |
3034 | | Matrix44<T>::operator == (const Matrix44 &v) const |
3035 | | { |
3036 | | return x[0][0] == v.x[0][0] && |
3037 | | x[0][1] == v.x[0][1] && |
3038 | | x[0][2] == v.x[0][2] && |
3039 | | x[0][3] == v.x[0][3] && |
3040 | | x[1][0] == v.x[1][0] && |
3041 | | x[1][1] == v.x[1][1] && |
3042 | | x[1][2] == v.x[1][2] && |
3043 | | x[1][3] == v.x[1][3] && |
3044 | | x[2][0] == v.x[2][0] && |
3045 | | x[2][1] == v.x[2][1] && |
3046 | | x[2][2] == v.x[2][2] && |
3047 | | x[2][3] == v.x[2][3] && |
3048 | | x[3][0] == v.x[3][0] && |
3049 | | x[3][1] == v.x[3][1] && |
3050 | | x[3][2] == v.x[3][2] && |
3051 | | x[3][3] == v.x[3][3]; |
3052 | | } |
3053 | | |
3054 | | template <class T> |
3055 | | bool |
3056 | | Matrix44<T>::operator != (const Matrix44 &v) const |
3057 | | { |
3058 | | return x[0][0] != v.x[0][0] || |
3059 | | x[0][1] != v.x[0][1] || |
3060 | | x[0][2] != v.x[0][2] || |
3061 | | x[0][3] != v.x[0][3] || |
3062 | | x[1][0] != v.x[1][0] || |
3063 | | x[1][1] != v.x[1][1] || |
3064 | | x[1][2] != v.x[1][2] || |
3065 | | x[1][3] != v.x[1][3] || |
3066 | | x[2][0] != v.x[2][0] || |
3067 | | x[2][1] != v.x[2][1] || |
3068 | | x[2][2] != v.x[2][2] || |
3069 | | x[2][3] != v.x[2][3] || |
3070 | | x[3][0] != v.x[3][0] || |
3071 | | x[3][1] != v.x[3][1] || |
3072 | | x[3][2] != v.x[3][2] || |
3073 | | x[3][3] != v.x[3][3]; |
3074 | | } |
3075 | | |
3076 | | template <class T> |
3077 | | bool |
3078 | | Matrix44<T>::equalWithAbsError (const Matrix44<T> &m, T e) const |
3079 | | { |
3080 | | for (int i = 0; i < 4; i++) |
3081 | | for (int j = 0; j < 4; j++) |
3082 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i][j], m[i][j], e)) |
3083 | | return false; |
3084 | | |
3085 | | return true; |
3086 | | } |
3087 | | |
3088 | | template <class T> |
3089 | | bool |
3090 | | Matrix44<T>::equalWithRelError (const Matrix44<T> &m, T e) const |
3091 | | { |
3092 | | for (int i = 0; i < 4; i++) |
3093 | | for (int j = 0; j < 4; j++) |
3094 | | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i][j], m[i][j], e)) |
3095 | | return false; |
3096 | | |
3097 | | return true; |
3098 | | } |
3099 | | |
3100 | | template <class T> |
3101 | | const Matrix44<T> & |
3102 | | Matrix44<T>::operator += (const Matrix44<T> &v) |
3103 | | { |
3104 | | x[0][0] += v.x[0][0]; |
3105 | | x[0][1] += v.x[0][1]; |
3106 | | x[0][2] += v.x[0][2]; |
3107 | | x[0][3] += v.x[0][3]; |
3108 | | x[1][0] += v.x[1][0]; |
3109 | | x[1][1] += v.x[1][1]; |
3110 | | x[1][2] += v.x[1][2]; |
3111 | | x[1][3] += v.x[1][3]; |
3112 | | x[2][0] += v.x[2][0]; |
3113 | | x[2][1] += v.x[2][1]; |
3114 | | x[2][2] += v.x[2][2]; |
3115 | | x[2][3] += v.x[2][3]; |
3116 | | x[3][0] += v.x[3][0]; |
3117 | | x[3][1] += v.x[3][1]; |
3118 | | x[3][2] += v.x[3][2]; |
3119 | | x[3][3] += v.x[3][3]; |
3120 | | |
3121 | | return *this; |
3122 | | } |
3123 | | |
3124 | | template <class T> |
3125 | | const Matrix44<T> & |
3126 | | Matrix44<T>::operator += (T a) |
3127 | | { |
3128 | | x[0][0] += a; |
3129 | | x[0][1] += a; |
3130 | | x[0][2] += a; |
3131 | | x[0][3] += a; |
3132 | | x[1][0] += a; |
3133 | | x[1][1] += a; |
3134 | | x[1][2] += a; |
3135 | | x[1][3] += a; |
3136 | | x[2][0] += a; |
3137 | | x[2][1] += a; |
3138 | | x[2][2] += a; |
3139 | | x[2][3] += a; |
3140 | | x[3][0] += a; |
3141 | | x[3][1] += a; |
3142 | | x[3][2] += a; |
3143 | | x[3][3] += a; |
3144 | | |
3145 | | return *this; |
3146 | | } |
3147 | | |
3148 | | template <class T> |
3149 | | Matrix44<T> |
3150 | | Matrix44<T>::operator + (const Matrix44<T> &v) const |
3151 | | { |
3152 | | return Matrix44 (x[0][0] + v.x[0][0], |
3153 | | x[0][1] + v.x[0][1], |
3154 | | x[0][2] + v.x[0][2], |
3155 | | x[0][3] + v.x[0][3], |
3156 | | x[1][0] + v.x[1][0], |
3157 | | x[1][1] + v.x[1][1], |
3158 | | x[1][2] + v.x[1][2], |
3159 | | x[1][3] + v.x[1][3], |
3160 | | x[2][0] + v.x[2][0], |
3161 | | x[2][1] + v.x[2][1], |
3162 | | x[2][2] + v.x[2][2], |
3163 | | x[2][3] + v.x[2][3], |
3164 | | x[3][0] + v.x[3][0], |
3165 | | x[3][1] + v.x[3][1], |
3166 | | x[3][2] + v.x[3][2], |
3167 | | x[3][3] + v.x[3][3]); |
3168 | | } |
3169 | | |
3170 | | template <class T> |
3171 | | const Matrix44<T> & |
3172 | | Matrix44<T>::operator -= (const Matrix44<T> &v) |
3173 | | { |
3174 | | x[0][0] -= v.x[0][0]; |
3175 | | x[0][1] -= v.x[0][1]; |
3176 | | x[0][2] -= v.x[0][2]; |
3177 | | x[0][3] -= v.x[0][3]; |
3178 | | x[1][0] -= v.x[1][0]; |
3179 | | x[1][1] -= v.x[1][1]; |
3180 | | x[1][2] -= v.x[1][2]; |
3181 | | x[1][3] -= v.x[1][3]; |
3182 | | x[2][0] -= v.x[2][0]; |
3183 | | x[2][1] -= v.x[2][1]; |
3184 | | x[2][2] -= v.x[2][2]; |
3185 | | x[2][3] -= v.x[2][3]; |
3186 | | x[3][0] -= v.x[3][0]; |
3187 | | x[3][1] -= v.x[3][1]; |
3188 | | x[3][2] -= v.x[3][2]; |
3189 | | x[3][3] -= v.x[3][3]; |
3190 | | |
3191 | | return *this; |
3192 | | } |
3193 | | |
3194 | | template <class T> |
3195 | | const Matrix44<T> & |
3196 | | Matrix44<T>::operator -= (T a) |
3197 | | { |
3198 | | x[0][0] -= a; |
3199 | | x[0][1] -= a; |
3200 | | x[0][2] -= a; |
3201 | | x[0][3] -= a; |
3202 | | x[1][0] -= a; |
3203 | | x[1][1] -= a; |
3204 | | x[1][2] -= a; |
3205 | | x[1][3] -= a; |
3206 | | x[2][0] -= a; |
3207 | | x[2][1] -= a; |
3208 | | x[2][2] -= a; |
3209 | | x[2][3] -= a; |
3210 | | x[3][0] -= a; |
3211 | | x[3][1] -= a; |
3212 | | x[3][2] -= a; |
3213 | | x[3][3] -= a; |
3214 | | |
3215 | | return *this; |
3216 | | } |
3217 | | |
3218 | | template <class T> |
3219 | | Matrix44<T> |
3220 | | Matrix44<T>::operator - (const Matrix44<T> &v) const |
3221 | | { |
3222 | | return Matrix44 (x[0][0] - v.x[0][0], |
3223 | | x[0][1] - v.x[0][1], |
3224 | | x[0][2] - v.x[0][2], |
3225 | | x[0][3] - v.x[0][3], |
3226 | | x[1][0] - v.x[1][0], |
3227 | | x[1][1] - v.x[1][1], |
3228 | | x[1][2] - v.x[1][2], |
3229 | | x[1][3] - v.x[1][3], |
3230 | | x[2][0] - v.x[2][0], |
3231 | | x[2][1] - v.x[2][1], |
3232 | | x[2][2] - v.x[2][2], |
3233 | | x[2][3] - v.x[2][3], |
3234 | | x[3][0] - v.x[3][0], |
3235 | | x[3][1] - v.x[3][1], |
3236 | | x[3][2] - v.x[3][2], |
3237 | | x[3][3] - v.x[3][3]); |
3238 | | } |
3239 | | |
3240 | | template <class T> |
3241 | | Matrix44<T> |
3242 | | Matrix44<T>::operator - () const |
3243 | | { |
3244 | | return Matrix44 (-x[0][0], |
3245 | | -x[0][1], |
3246 | | -x[0][2], |
3247 | | -x[0][3], |
3248 | | -x[1][0], |
3249 | | -x[1][1], |
3250 | | -x[1][2], |
3251 | | -x[1][3], |
3252 | | -x[2][0], |
3253 | | -x[2][1], |
3254 | | -x[2][2], |
3255 | | -x[2][3], |
3256 | | -x[3][0], |
3257 | | -x[3][1], |
3258 | | -x[3][2], |
3259 | | -x[3][3]); |
3260 | | } |
3261 | | |
3262 | | template <class T> |
3263 | | const Matrix44<T> & |
3264 | | Matrix44<T>::negate () |
3265 | | { |
3266 | | x[0][0] = -x[0][0]; |
3267 | | x[0][1] = -x[0][1]; |
3268 | | x[0][2] = -x[0][2]; |
3269 | | x[0][3] = -x[0][3]; |
3270 | | x[1][0] = -x[1][0]; |
3271 | | x[1][1] = -x[1][1]; |
3272 | | x[1][2] = -x[1][2]; |
3273 | | x[1][3] = -x[1][3]; |
3274 | | x[2][0] = -x[2][0]; |
3275 | | x[2][1] = -x[2][1]; |
3276 | | x[2][2] = -x[2][2]; |
3277 | | x[2][3] = -x[2][3]; |
3278 | | x[3][0] = -x[3][0]; |
3279 | | x[3][1] = -x[3][1]; |
3280 | | x[3][2] = -x[3][2]; |
3281 | | x[3][3] = -x[3][3]; |
3282 | | |
3283 | | return *this; |
3284 | | } |
3285 | | |
3286 | | template <class T> |
3287 | | const Matrix44<T> & |
3288 | | Matrix44<T>::operator *= (T a) |
3289 | | { |
3290 | | x[0][0] *= a; |
3291 | | x[0][1] *= a; |
3292 | | x[0][2] *= a; |
3293 | | x[0][3] *= a; |
3294 | | x[1][0] *= a; |
3295 | | x[1][1] *= a; |
3296 | | x[1][2] *= a; |
3297 | | x[1][3] *= a; |
3298 | | x[2][0] *= a; |
3299 | | x[2][1] *= a; |
3300 | | x[2][2] *= a; |
3301 | | x[2][3] *= a; |
3302 | | x[3][0] *= a; |
3303 | | x[3][1] *= a; |
3304 | | x[3][2] *= a; |
3305 | | x[3][3] *= a; |
3306 | | |
3307 | | return *this; |
3308 | | } |
3309 | | |
3310 | | template <class T> |
3311 | | Matrix44<T> |
3312 | | Matrix44<T>::operator * (T a) const |
3313 | | { |
3314 | | return Matrix44 (x[0][0] * a, |
3315 | | x[0][1] * a, |
3316 | | x[0][2] * a, |
3317 | | x[0][3] * a, |
3318 | | x[1][0] * a, |
3319 | | x[1][1] * a, |
3320 | | x[1][2] * a, |
3321 | | x[1][3] * a, |
3322 | | x[2][0] * a, |
3323 | | x[2][1] * a, |
3324 | | x[2][2] * a, |
3325 | | x[2][3] * a, |
3326 | | x[3][0] * a, |
3327 | | x[3][1] * a, |
3328 | | x[3][2] * a, |
3329 | | x[3][3] * a); |
3330 | | } |
3331 | | |
3332 | | template <class T> |
3333 | | inline Matrix44<T> |
3334 | | operator * (T a, const Matrix44<T> &v) |
3335 | | { |
3336 | | return v * a; |
3337 | | } |
3338 | | |
3339 | | template <class T> |
3340 | | inline const Matrix44<T> & |
3341 | | Matrix44<T>::operator *= (const Matrix44<T> &v) |
3342 | | { |
3343 | | Matrix44 tmp (T (0)); |
3344 | | |
3345 | | multiply (*this, v, tmp); |
3346 | | *this = tmp; |
3347 | | return *this; |
3348 | | } |
3349 | | |
3350 | | template <class T> |
3351 | | inline Matrix44<T> |
3352 | | Matrix44<T>::operator * (const Matrix44<T> &v) const |
3353 | 0 | { |
3354 | 0 | Matrix44 tmp (T (0)); |
3355 | |
|
3356 | 0 | multiply (*this, v, tmp); |
3357 | 0 | return tmp; |
3358 | 0 | } |
3359 | | |
3360 | | template <class T> |
3361 | | void |
3362 | | Matrix44<T>::multiply (const Matrix44<T> &a, |
3363 | | const Matrix44<T> &b, |
3364 | | Matrix44<T> &c) |
3365 | 0 | { |
3366 | 0 | const T * IMATH_RESTRICT ap = &a.x[0][0]; |
3367 | 0 | const T * IMATH_RESTRICT bp = &b.x[0][0]; |
3368 | 0 | T * IMATH_RESTRICT cp = &c.x[0][0]; |
3369 | |
|
3370 | 0 | T a0, a1, a2, a3; |
3371 | |
|
3372 | 0 | a0 = ap[0]; |
3373 | 0 | a1 = ap[1]; |
3374 | 0 | a2 = ap[2]; |
3375 | 0 | a3 = ap[3]; |
3376 | |
|
3377 | 0 | cp[0] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
3378 | 0 | cp[1] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
3379 | 0 | cp[2] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
3380 | 0 | cp[3] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
3381 | |
|
3382 | 0 | a0 = ap[4]; |
3383 | 0 | a1 = ap[5]; |
3384 | 0 | a2 = ap[6]; |
3385 | 0 | a3 = ap[7]; |
3386 | |
|
3387 | 0 | cp[4] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
3388 | 0 | cp[5] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
3389 | 0 | cp[6] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
3390 | 0 | cp[7] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
3391 | |
|
3392 | 0 | a0 = ap[8]; |
3393 | 0 | a1 = ap[9]; |
3394 | 0 | a2 = ap[10]; |
3395 | 0 | a3 = ap[11]; |
3396 | |
|
3397 | 0 | cp[8] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
3398 | 0 | cp[9] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
3399 | 0 | cp[10] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
3400 | 0 | cp[11] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
3401 | |
|
3402 | 0 | a0 = ap[12]; |
3403 | 0 | a1 = ap[13]; |
3404 | 0 | a2 = ap[14]; |
3405 | 0 | a3 = ap[15]; |
3406 | |
|
3407 | 0 | cp[12] = a0 * bp[0] + a1 * bp[4] + a2 * bp[8] + a3 * bp[12]; |
3408 | 0 | cp[13] = a0 * bp[1] + a1 * bp[5] + a2 * bp[9] + a3 * bp[13]; |
3409 | 0 | cp[14] = a0 * bp[2] + a1 * bp[6] + a2 * bp[10] + a3 * bp[14]; |
3410 | 0 | cp[15] = a0 * bp[3] + a1 * bp[7] + a2 * bp[11] + a3 * bp[15]; |
3411 | 0 | } |
3412 | | |
3413 | | template <class T> template <class S> |
3414 | | void |
3415 | | Matrix44<T>::multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const |
3416 | | { |
3417 | | S a, b, c, w; |
3418 | | |
3419 | | a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0] + x[3][0]; |
3420 | | b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1] + x[3][1]; |
3421 | | c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2] + x[3][2]; |
3422 | | w = src[0] * x[0][3] + src[1] * x[1][3] + src[2] * x[2][3] + x[3][3]; |
3423 | | |
3424 | | dst.x = a / w; |
3425 | | dst.y = b / w; |
3426 | | dst.z = c / w; |
3427 | | } |
3428 | | |
3429 | | template <class T> template <class S> |
3430 | | void |
3431 | | Matrix44<T>::multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const |
3432 | | { |
3433 | | S a, b, c; |
3434 | | |
3435 | | a = src[0] * x[0][0] + src[1] * x[1][0] + src[2] * x[2][0]; |
3436 | | b = src[0] * x[0][1] + src[1] * x[1][1] + src[2] * x[2][1]; |
3437 | | c = src[0] * x[0][2] + src[1] * x[1][2] + src[2] * x[2][2]; |
3438 | | |
3439 | | dst.x = a; |
3440 | | dst.y = b; |
3441 | | dst.z = c; |
3442 | | } |
3443 | | |
3444 | | template <class T> |
3445 | | const Matrix44<T> & |
3446 | | Matrix44<T>::operator /= (T a) |
3447 | | { |
3448 | | x[0][0] /= a; |
3449 | | x[0][1] /= a; |
3450 | | x[0][2] /= a; |
3451 | | x[0][3] /= a; |
3452 | | x[1][0] /= a; |
3453 | | x[1][1] /= a; |
3454 | | x[1][2] /= a; |
3455 | | x[1][3] /= a; |
3456 | | x[2][0] /= a; |
3457 | | x[2][1] /= a; |
3458 | | x[2][2] /= a; |
3459 | | x[2][3] /= a; |
3460 | | x[3][0] /= a; |
3461 | | x[3][1] /= a; |
3462 | | x[3][2] /= a; |
3463 | | x[3][3] /= a; |
3464 | | |
3465 | | return *this; |
3466 | | } |
3467 | | |
3468 | | template <class T> |
3469 | | Matrix44<T> |
3470 | | Matrix44<T>::operator / (T a) const |
3471 | | { |
3472 | | return Matrix44 (x[0][0] / a, |
3473 | | x[0][1] / a, |
3474 | | x[0][2] / a, |
3475 | | x[0][3] / a, |
3476 | | x[1][0] / a, |
3477 | | x[1][1] / a, |
3478 | | x[1][2] / a, |
3479 | | x[1][3] / a, |
3480 | | x[2][0] / a, |
3481 | | x[2][1] / a, |
3482 | | x[2][2] / a, |
3483 | | x[2][3] / a, |
3484 | | x[3][0] / a, |
3485 | | x[3][1] / a, |
3486 | | x[3][2] / a, |
3487 | | x[3][3] / a); |
3488 | | } |
3489 | | |
3490 | | template <class T> |
3491 | | const Matrix44<T> & |
3492 | | Matrix44<T>::transpose () |
3493 | | { |
3494 | | Matrix44 tmp (x[0][0], |
3495 | | x[1][0], |
3496 | | x[2][0], |
3497 | | x[3][0], |
3498 | | x[0][1], |
3499 | | x[1][1], |
3500 | | x[2][1], |
3501 | | x[3][1], |
3502 | | x[0][2], |
3503 | | x[1][2], |
3504 | | x[2][2], |
3505 | | x[3][2], |
3506 | | x[0][3], |
3507 | | x[1][3], |
3508 | | x[2][3], |
3509 | | x[3][3]); |
3510 | | *this = tmp; |
3511 | | return *this; |
3512 | | } |
3513 | | |
3514 | | template <class T> |
3515 | | Matrix44<T> |
3516 | | Matrix44<T>::transposed () const |
3517 | | { |
3518 | | return Matrix44 (x[0][0], |
3519 | | x[1][0], |
3520 | | x[2][0], |
3521 | | x[3][0], |
3522 | | x[0][1], |
3523 | | x[1][1], |
3524 | | x[2][1], |
3525 | | x[3][1], |
3526 | | x[0][2], |
3527 | | x[1][2], |
3528 | | x[2][2], |
3529 | | x[3][2], |
3530 | | x[0][3], |
3531 | | x[1][3], |
3532 | | x[2][3], |
3533 | | x[3][3]); |
3534 | | } |
3535 | | |
3536 | | template <class T> |
3537 | | const Matrix44<T> & |
3538 | | Matrix44<T>::gjInvert (bool singExc) |
3539 | | { |
3540 | | *this = gjInverse (singExc); |
3541 | | return *this; |
3542 | | } |
3543 | | |
3544 | | template <class T> |
3545 | | Matrix44<T> |
3546 | | Matrix44<T>::gjInverse (bool singExc) const |
3547 | | { |
3548 | | int i, j, k; |
3549 | | Matrix44 s; |
3550 | | Matrix44 t (*this); |
3551 | | |
3552 | | // Forward elimination |
3553 | | |
3554 | | for (i = 0; i < 3 ; i++) |
3555 | | { |
3556 | | int pivot = i; |
3557 | | |
3558 | | T pivotsize = t[i][i]; |
3559 | | |
3560 | | if (pivotsize < 0) |
3561 | | pivotsize = -pivotsize; |
3562 | | |
3563 | | for (j = i + 1; j < 4; j++) |
3564 | | { |
3565 | | T tmp = t[j][i]; |
3566 | | |
3567 | | if (tmp < 0) |
3568 | | tmp = -tmp; |
3569 | | |
3570 | | if (tmp > pivotsize) |
3571 | | { |
3572 | | pivot = j; |
3573 | | pivotsize = tmp; |
3574 | | } |
3575 | | } |
3576 | | |
3577 | | if (pivotsize == 0) |
3578 | | { |
3579 | | if (singExc) |
3580 | | throw ::IMATH_INTERNAL_NAMESPACE::SingMatrixExc ("Cannot invert singular matrix."); |
3581 | | |
3582 | | return Matrix44(); |
3583 | | } |
3584 | | |
3585 | | if (pivot != i) |
3586 | | { |
3587 | | for (j = 0; j < 4; j++) |
3588 | | { |
3589 | | T tmp; |
3590 | | |
3591 | | tmp = t[i][j]; |
3592 | | t[i][j] = t[pivot][j]; |
3593 | | t[pivot][j] = tmp; |
3594 | | |
3595 | | tmp = s[i][j]; |
3596 | | s[i][j] = s[pivot][j]; |
3597 | | s[pivot][j] = tmp; |
3598 | | } |
3599 | | } |
3600 | | |
3601 | | for (j = i + 1; j < 4; j++) |
3602 | | { |
3603 | | T f = t[j][i] / t[i][i]; |
3604 | | |
3605 | | for (k = 0; k < 4; k++) |
3606 | | { |
3607 | | t[j][k] -= f * t[i][k]; |
3608 | | s[j][k] -= f * s[i][k]; |
3609 | | } |
3610 | | } |
3611 | | } |
3612 | | |
3613 | | // Backward substitution |
3614 | | |
3615 | | for (i = 3; i >= 0; --i) |
3616 | | { |
3617 | | T f; |
3618 | | |
3619 | | if ((f = t[i][i]) == 0) |
3620 | | { |
3621 | | if (singExc) |
3622 | | throw ::IMATH_INTERNAL_NAMESPACE::SingMatrixExc ("Cannot invert singular matrix."); |
3623 | | |
3624 | | return Matrix44(); |
3625 | | } |
3626 | | |
3627 | | for (j = 0; j < 4; j++) |
3628 | | { |
3629 | | t[i][j] /= f; |
3630 | | s[i][j] /= f; |
3631 | | } |
3632 | | |
3633 | | for (j = 0; j < i; j++) |
3634 | | { |
3635 | | f = t[j][i]; |
3636 | | |
3637 | | for (k = 0; k < 4; k++) |
3638 | | { |
3639 | | t[j][k] -= f * t[i][k]; |
3640 | | s[j][k] -= f * s[i][k]; |
3641 | | } |
3642 | | } |
3643 | | } |
3644 | | |
3645 | | return s; |
3646 | | } |
3647 | | |
3648 | | template <class T> |
3649 | | const Matrix44<T> & |
3650 | | Matrix44<T>::invert (bool singExc) |
3651 | | { |
3652 | | *this = inverse (singExc); |
3653 | | return *this; |
3654 | | } |
3655 | | |
3656 | | template <class T> |
3657 | | Matrix44<T> |
3658 | | Matrix44<T>::inverse (bool singExc) const |
3659 | | { |
3660 | | if (x[0][3] != 0 || x[1][3] != 0 || x[2][3] != 0 || x[3][3] != 1) |
3661 | | return gjInverse(singExc); |
3662 | | |
3663 | | Matrix44 s (x[1][1] * x[2][2] - x[2][1] * x[1][2], |
3664 | | x[2][1] * x[0][2] - x[0][1] * x[2][2], |
3665 | | x[0][1] * x[1][2] - x[1][1] * x[0][2], |
3666 | | 0, |
3667 | | |
3668 | | x[2][0] * x[1][2] - x[1][0] * x[2][2], |
3669 | | x[0][0] * x[2][2] - x[2][0] * x[0][2], |
3670 | | x[1][0] * x[0][2] - x[0][0] * x[1][2], |
3671 | | 0, |
3672 | | |
3673 | | x[1][0] * x[2][1] - x[2][0] * x[1][1], |
3674 | | x[2][0] * x[0][1] - x[0][0] * x[2][1], |
3675 | | x[0][0] * x[1][1] - x[1][0] * x[0][1], |
3676 | | 0, |
3677 | | |
3678 | | 0, |
3679 | | 0, |
3680 | | 0, |
3681 | | 1); |
3682 | | |
3683 | | T r = x[0][0] * s[0][0] + x[0][1] * s[1][0] + x[0][2] * s[2][0]; |
3684 | | |
3685 | | if (IMATH_INTERNAL_NAMESPACE::abs (r) >= 1) |
3686 | | { |
3687 | | for (int i = 0; i < 3; ++i) |
3688 | | { |
3689 | | for (int j = 0; j < 3; ++j) |
3690 | | { |
3691 | | s[i][j] /= r; |
3692 | | } |
3693 | | } |
3694 | | } |
3695 | | else |
3696 | | { |
3697 | | T mr = IMATH_INTERNAL_NAMESPACE::abs (r) / limits<T>::smallest(); |
3698 | | |
3699 | | for (int i = 0; i < 3; ++i) |
3700 | | { |
3701 | | for (int j = 0; j < 3; ++j) |
3702 | | { |
3703 | | if (mr > IMATH_INTERNAL_NAMESPACE::abs (s[i][j])) |
3704 | | { |
3705 | | s[i][j] /= r; |
3706 | | } |
3707 | | else |
3708 | | { |
3709 | | if (singExc) |
3710 | | throw SingMatrixExc ("Cannot invert singular matrix."); |
3711 | | |
3712 | | return Matrix44(); |
3713 | | } |
3714 | | } |
3715 | | } |
3716 | | } |
3717 | | |
3718 | | s[3][0] = -x[3][0] * s[0][0] - x[3][1] * s[1][0] - x[3][2] * s[2][0]; |
3719 | | s[3][1] = -x[3][0] * s[0][1] - x[3][1] * s[1][1] - x[3][2] * s[2][1]; |
3720 | | s[3][2] = -x[3][0] * s[0][2] - x[3][1] * s[1][2] - x[3][2] * s[2][2]; |
3721 | | |
3722 | | return s; |
3723 | | } |
3724 | | |
3725 | | template <class T> |
3726 | | inline T |
3727 | | Matrix44<T>::fastMinor( const int r0, const int r1, const int r2, |
3728 | | const int c0, const int c1, const int c2) const |
3729 | | { |
3730 | | return x[r0][c0] * (x[r1][c1]*x[r2][c2] - x[r1][c2]*x[r2][c1]) |
3731 | | + x[r0][c1] * (x[r1][c2]*x[r2][c0] - x[r1][c0]*x[r2][c2]) |
3732 | | + x[r0][c2] * (x[r1][c0]*x[r2][c1] - x[r1][c1]*x[r2][c0]); |
3733 | | } |
3734 | | |
3735 | | template <class T> |
3736 | | inline T |
3737 | | Matrix44<T>::minorOf (const int r, const int c) const |
3738 | | { |
3739 | | int r0 = 0 + (r < 1 ? 1 : 0); |
3740 | | int r1 = 1 + (r < 2 ? 1 : 0); |
3741 | | int r2 = 2 + (r < 3 ? 1 : 0); |
3742 | | int c0 = 0 + (c < 1 ? 1 : 0); |
3743 | | int c1 = 1 + (c < 2 ? 1 : 0); |
3744 | | int c2 = 2 + (c < 3 ? 1 : 0); |
3745 | | |
3746 | | Matrix33<T> working (x[r0][c0],x[r1][c0],x[r2][c0], |
3747 | | x[r0][c1],x[r1][c1],x[r2][c1], |
3748 | | x[r0][c2],x[r1][c2],x[r2][c2]); |
3749 | | |
3750 | | return working.determinant(); |
3751 | | } |
3752 | | |
3753 | | template <class T> |
3754 | | inline T |
3755 | | Matrix44<T>::determinant () const |
3756 | | { |
3757 | | T sum = (T)0; |
3758 | | |
3759 | | if (x[0][3] != 0.) sum -= x[0][3] * fastMinor(1,2,3,0,1,2); |
3760 | | if (x[1][3] != 0.) sum += x[1][3] * fastMinor(0,2,3,0,1,2); |
3761 | | if (x[2][3] != 0.) sum -= x[2][3] * fastMinor(0,1,3,0,1,2); |
3762 | | if (x[3][3] != 0.) sum += x[3][3] * fastMinor(0,1,2,0,1,2); |
3763 | | |
3764 | | return sum; |
3765 | | } |
3766 | | |
3767 | | template <class T> |
3768 | | template <class S> |
3769 | | const Matrix44<T> & |
3770 | | Matrix44<T>::setEulerAngles (const Vec3<S>& r) |
3771 | | { |
3772 | | S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx; |
3773 | | |
3774 | | cos_rz = Math<T>::cos (r[2]); |
3775 | | cos_ry = Math<T>::cos (r[1]); |
3776 | | cos_rx = Math<T>::cos (r[0]); |
3777 | | |
3778 | | sin_rz = Math<T>::sin (r[2]); |
3779 | | sin_ry = Math<T>::sin (r[1]); |
3780 | | sin_rx = Math<T>::sin (r[0]); |
3781 | | |
3782 | | x[0][0] = cos_rz * cos_ry; |
3783 | | x[0][1] = sin_rz * cos_ry; |
3784 | | x[0][2] = -sin_ry; |
3785 | | x[0][3] = 0; |
3786 | | |
3787 | | x[1][0] = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx; |
3788 | | x[1][1] = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx; |
3789 | | x[1][2] = cos_ry * sin_rx; |
3790 | | x[1][3] = 0; |
3791 | | |
3792 | | x[2][0] = sin_rz * sin_rx + cos_rz * sin_ry * cos_rx; |
3793 | | x[2][1] = -cos_rz * sin_rx + sin_rz * sin_ry * cos_rx; |
3794 | | x[2][2] = cos_ry * cos_rx; |
3795 | | x[2][3] = 0; |
3796 | | |
3797 | | x[3][0] = 0; |
3798 | | x[3][1] = 0; |
3799 | | x[3][2] = 0; |
3800 | | x[3][3] = 1; |
3801 | | |
3802 | | return *this; |
3803 | | } |
3804 | | |
3805 | | template <class T> |
3806 | | template <class S> |
3807 | | const Matrix44<T> & |
3808 | | Matrix44<T>::setAxisAngle (const Vec3<S>& axis, S angle) |
3809 | 0 | { |
3810 | 0 | Vec3<S> unit (axis.normalized()); |
3811 | 0 | S sine = Math<T>::sin (angle); |
3812 | 0 | S cosine = Math<T>::cos (angle); |
3813 | |
|
3814 | 0 | x[0][0] = unit[0] * unit[0] * (1 - cosine) + cosine; |
3815 | 0 | x[0][1] = unit[0] * unit[1] * (1 - cosine) + unit[2] * sine; |
3816 | 0 | x[0][2] = unit[0] * unit[2] * (1 - cosine) - unit[1] * sine; |
3817 | 0 | x[0][3] = 0; |
3818 | |
|
3819 | 0 | x[1][0] = unit[0] * unit[1] * (1 - cosine) - unit[2] * sine; |
3820 | 0 | x[1][1] = unit[1] * unit[1] * (1 - cosine) + cosine; |
3821 | 0 | x[1][2] = unit[1] * unit[2] * (1 - cosine) + unit[0] * sine; |
3822 | 0 | x[1][3] = 0; |
3823 | |
|
3824 | 0 | x[2][0] = unit[0] * unit[2] * (1 - cosine) + unit[1] * sine; |
3825 | 0 | x[2][1] = unit[1] * unit[2] * (1 - cosine) - unit[0] * sine; |
3826 | 0 | x[2][2] = unit[2] * unit[2] * (1 - cosine) + cosine; |
3827 | 0 | x[2][3] = 0; |
3828 | |
|
3829 | 0 | x[3][0] = 0; |
3830 | 0 | x[3][1] = 0; |
3831 | 0 | x[3][2] = 0; |
3832 | 0 | x[3][3] = 1; |
3833 | |
|
3834 | 0 | return *this; |
3835 | 0 | } |
3836 | | |
3837 | | template <class T> |
3838 | | template <class S> |
3839 | | const Matrix44<T> & |
3840 | | Matrix44<T>::rotate (const Vec3<S> &r) |
3841 | 0 | { |
3842 | 0 | S cos_rz, sin_rz, cos_ry, sin_ry, cos_rx, sin_rx; |
3843 | 0 | S m00, m01, m02; |
3844 | 0 | S m10, m11, m12; |
3845 | 0 | S m20, m21, m22; |
3846 | |
|
3847 | 0 | cos_rz = Math<S>::cos (r[2]); |
3848 | 0 | cos_ry = Math<S>::cos (r[1]); |
3849 | 0 | cos_rx = Math<S>::cos (r[0]); |
3850 | | |
3851 | 0 | sin_rz = Math<S>::sin (r[2]); |
3852 | 0 | sin_ry = Math<S>::sin (r[1]); |
3853 | 0 | sin_rx = Math<S>::sin (r[0]); |
3854 | |
|
3855 | 0 | m00 = cos_rz * cos_ry; |
3856 | 0 | m01 = sin_rz * cos_ry; |
3857 | 0 | m02 = -sin_ry; |
3858 | 0 | m10 = -sin_rz * cos_rx + cos_rz * sin_ry * sin_rx; |
3859 | 0 | m11 = cos_rz * cos_rx + sin_rz * sin_ry * sin_rx; |
3860 | 0 | m12 = cos_ry * sin_rx; |
3861 | 0 | m20 = -sin_rz * -sin_rx + cos_rz * sin_ry * cos_rx; |
3862 | 0 | m21 = cos_rz * -sin_rx + sin_rz * sin_ry * cos_rx; |
3863 | 0 | m22 = cos_ry * cos_rx; |
3864 | |
|
3865 | 0 | Matrix44<T> P (*this); |
3866 | |
|
3867 | 0 | x[0][0] = P[0][0] * m00 + P[1][0] * m01 + P[2][0] * m02; |
3868 | 0 | x[0][1] = P[0][1] * m00 + P[1][1] * m01 + P[2][1] * m02; |
3869 | 0 | x[0][2] = P[0][2] * m00 + P[1][2] * m01 + P[2][2] * m02; |
3870 | 0 | x[0][3] = P[0][3] * m00 + P[1][3] * m01 + P[2][3] * m02; |
3871 | |
|
3872 | 0 | x[1][0] = P[0][0] * m10 + P[1][0] * m11 + P[2][0] * m12; |
3873 | 0 | x[1][1] = P[0][1] * m10 + P[1][1] * m11 + P[2][1] * m12; |
3874 | 0 | x[1][2] = P[0][2] * m10 + P[1][2] * m11 + P[2][2] * m12; |
3875 | 0 | x[1][3] = P[0][3] * m10 + P[1][3] * m11 + P[2][3] * m12; |
3876 | |
|
3877 | 0 | x[2][0] = P[0][0] * m20 + P[1][0] * m21 + P[2][0] * m22; |
3878 | 0 | x[2][1] = P[0][1] * m20 + P[1][1] * m21 + P[2][1] * m22; |
3879 | 0 | x[2][2] = P[0][2] * m20 + P[1][2] * m21 + P[2][2] * m22; |
3880 | 0 | x[2][3] = P[0][3] * m20 + P[1][3] * m21 + P[2][3] * m22; |
3881 | |
|
3882 | 0 | return *this; |
3883 | 0 | } |
3884 | | |
3885 | | template <class T> |
3886 | | const Matrix44<T> & |
3887 | | Matrix44<T>::setScale (T s) |
3888 | | { |
3889 | | memset (x, 0, sizeof (x)); |
3890 | | x[0][0] = s; |
3891 | | x[1][1] = s; |
3892 | | x[2][2] = s; |
3893 | | x[3][3] = 1; |
3894 | | |
3895 | | return *this; |
3896 | | } |
3897 | | |
3898 | | template <class T> |
3899 | | template <class S> |
3900 | | const Matrix44<T> & |
3901 | | Matrix44<T>::setScale (const Vec3<S> &s) |
3902 | 0 | { |
3903 | 0 | memset (x, 0, sizeof (x)); |
3904 | 0 | x[0][0] = s[0]; |
3905 | 0 | x[1][1] = s[1]; |
3906 | 0 | x[2][2] = s[2]; |
3907 | 0 | x[3][3] = 1; |
3908 | |
|
3909 | 0 | return *this; |
3910 | 0 | } |
3911 | | |
3912 | | template <class T> |
3913 | | template <class S> |
3914 | | const Matrix44<T> & |
3915 | | Matrix44<T>::scale (const Vec3<S> &s) |
3916 | | { |
3917 | | x[0][0] *= s[0]; |
3918 | | x[0][1] *= s[0]; |
3919 | | x[0][2] *= s[0]; |
3920 | | x[0][3] *= s[0]; |
3921 | | |
3922 | | x[1][0] *= s[1]; |
3923 | | x[1][1] *= s[1]; |
3924 | | x[1][2] *= s[1]; |
3925 | | x[1][3] *= s[1]; |
3926 | | |
3927 | | x[2][0] *= s[2]; |
3928 | | x[2][1] *= s[2]; |
3929 | | x[2][2] *= s[2]; |
3930 | | x[2][3] *= s[2]; |
3931 | | |
3932 | | return *this; |
3933 | | } |
3934 | | |
3935 | | template <class T> |
3936 | | template <class S> |
3937 | | const Matrix44<T> & |
3938 | | Matrix44<T>::setTranslation (const Vec3<S> &t) |
3939 | 0 | { |
3940 | 0 | x[0][0] = 1; |
3941 | 0 | x[0][1] = 0; |
3942 | 0 | x[0][2] = 0; |
3943 | 0 | x[0][3] = 0; |
3944 | |
|
3945 | 0 | x[1][0] = 0; |
3946 | 0 | x[1][1] = 1; |
3947 | 0 | x[1][2] = 0; |
3948 | 0 | x[1][3] = 0; |
3949 | |
|
3950 | 0 | x[2][0] = 0; |
3951 | 0 | x[2][1] = 0; |
3952 | 0 | x[2][2] = 1; |
3953 | 0 | x[2][3] = 0; |
3954 | |
|
3955 | 0 | x[3][0] = t[0]; |
3956 | 0 | x[3][1] = t[1]; |
3957 | 0 | x[3][2] = t[2]; |
3958 | 0 | x[3][3] = 1; |
3959 | |
|
3960 | 0 | return *this; |
3961 | 0 | } |
3962 | | |
3963 | | template <class T> |
3964 | | inline const Vec3<T> |
3965 | | Matrix44<T>::translation () const |
3966 | 0 | { |
3967 | 0 | return Vec3<T> (x[3][0], x[3][1], x[3][2]); |
3968 | 0 | } |
3969 | | |
3970 | | template <class T> |
3971 | | template <class S> |
3972 | | const Matrix44<T> & |
3973 | | Matrix44<T>::translate (const Vec3<S> &t) |
3974 | | { |
3975 | | x[3][0] += t[0] * x[0][0] + t[1] * x[1][0] + t[2] * x[2][0]; |
3976 | | x[3][1] += t[0] * x[0][1] + t[1] * x[1][1] + t[2] * x[2][1]; |
3977 | | x[3][2] += t[0] * x[0][2] + t[1] * x[1][2] + t[2] * x[2][2]; |
3978 | | x[3][3] += t[0] * x[0][3] + t[1] * x[1][3] + t[2] * x[2][3]; |
3979 | | |
3980 | | return *this; |
3981 | | } |
3982 | | |
3983 | | template <class T> |
3984 | | template <class S> |
3985 | | const Matrix44<T> & |
3986 | | Matrix44<T>::setShear (const Vec3<S> &h) |
3987 | | { |
3988 | | x[0][0] = 1; |
3989 | | x[0][1] = 0; |
3990 | | x[0][2] = 0; |
3991 | | x[0][3] = 0; |
3992 | | |
3993 | | x[1][0] = h[0]; |
3994 | | x[1][1] = 1; |
3995 | | x[1][2] = 0; |
3996 | | x[1][3] = 0; |
3997 | | |
3998 | | x[2][0] = h[1]; |
3999 | | x[2][1] = h[2]; |
4000 | | x[2][2] = 1; |
4001 | | x[2][3] = 0; |
4002 | | |
4003 | | x[3][0] = 0; |
4004 | | x[3][1] = 0; |
4005 | | x[3][2] = 0; |
4006 | | x[3][3] = 1; |
4007 | | |
4008 | | return *this; |
4009 | | } |
4010 | | |
4011 | | template <class T> |
4012 | | template <class S> |
4013 | | const Matrix44<T> & |
4014 | | Matrix44<T>::setShear (const Shear6<S> &h) |
4015 | | { |
4016 | | x[0][0] = 1; |
4017 | | x[0][1] = h.yx; |
4018 | | x[0][2] = h.zx; |
4019 | | x[0][3] = 0; |
4020 | | |
4021 | | x[1][0] = h.xy; |
4022 | | x[1][1] = 1; |
4023 | | x[1][2] = h.zy; |
4024 | | x[1][3] = 0; |
4025 | | |
4026 | | x[2][0] = h.xz; |
4027 | | x[2][1] = h.yz; |
4028 | | x[2][2] = 1; |
4029 | | x[2][3] = 0; |
4030 | | |
4031 | | x[3][0] = 0; |
4032 | | x[3][1] = 0; |
4033 | | x[3][2] = 0; |
4034 | | x[3][3] = 1; |
4035 | | |
4036 | | return *this; |
4037 | | } |
4038 | | |
4039 | | template <class T> |
4040 | | template <class S> |
4041 | | const Matrix44<T> & |
4042 | | Matrix44<T>::shear (const Vec3<S> &h) |
4043 | | { |
4044 | | // |
4045 | | // In this case, we don't need a temp. copy of the matrix |
4046 | | // because we never use a value on the RHS after we've |
4047 | | // changed it on the LHS. |
4048 | | // |
4049 | | |
4050 | | for (int i=0; i < 4; i++) |
4051 | | { |
4052 | | x[2][i] += h[1] * x[0][i] + h[2] * x[1][i]; |
4053 | | x[1][i] += h[0] * x[0][i]; |
4054 | | } |
4055 | | |
4056 | | return *this; |
4057 | | } |
4058 | | |
4059 | | template <class T> |
4060 | | template <class S> |
4061 | | const Matrix44<T> & |
4062 | | Matrix44<T>::shear (const Shear6<S> &h) |
4063 | | { |
4064 | | Matrix44<T> P (*this); |
4065 | | |
4066 | | for (int i=0; i < 4; i++) |
4067 | | { |
4068 | | x[0][i] = P[0][i] + h.yx * P[1][i] + h.zx * P[2][i]; |
4069 | | x[1][i] = h.xy * P[0][i] + P[1][i] + h.zy * P[2][i]; |
4070 | | x[2][i] = h.xz * P[0][i] + h.yz * P[1][i] + P[2][i]; |
4071 | | } |
4072 | | |
4073 | | return *this; |
4074 | | } |
4075 | | |
4076 | | |
4077 | | //-------------------------------- |
4078 | | // Implementation of stream output |
4079 | | //-------------------------------- |
4080 | | |
4081 | | template <class T> |
4082 | | std::ostream & |
4083 | | operator << (std::ostream &s, const Matrix22<T> &m) |
4084 | | { |
4085 | | std::ios_base::fmtflags oldFlags = s.flags(); |
4086 | | int width; |
4087 | | |
4088 | | if (s.flags() & std::ios_base::fixed) |
4089 | | { |
4090 | | s.setf (std::ios_base::showpoint); |
4091 | | width = static_cast<int>(s.precision()) + 5; |
4092 | | } |
4093 | | else |
4094 | | { |
4095 | | s.setf (std::ios_base::scientific); |
4096 | | s.setf (std::ios_base::showpoint); |
4097 | | width = static_cast<int>(s.precision()) + 8; |
4098 | | } |
4099 | | |
4100 | | s << "(" << std::setw (width) << m[0][0] << |
4101 | | " " << std::setw (width) << m[0][1] << "\n" << |
4102 | | |
4103 | | " " << std::setw (width) << m[1][0] << |
4104 | | " " << std::setw (width) << m[1][1] << ")\n"; |
4105 | | |
4106 | | s.flags (oldFlags); |
4107 | | return s; |
4108 | | } |
4109 | | |
4110 | | template <class T> |
4111 | | std::ostream & |
4112 | | operator << (std::ostream &s, const Matrix33<T> &m) |
4113 | | { |
4114 | | std::ios_base::fmtflags oldFlags = s.flags(); |
4115 | | int width; |
4116 | | |
4117 | | if (s.flags() & std::ios_base::fixed) |
4118 | | { |
4119 | | s.setf (std::ios_base::showpoint); |
4120 | | width = static_cast<int>(s.precision()) + 5; |
4121 | | } |
4122 | | else |
4123 | | { |
4124 | | s.setf (std::ios_base::scientific); |
4125 | | s.setf (std::ios_base::showpoint); |
4126 | | width = static_cast<int>(s.precision()) + 8; |
4127 | | } |
4128 | | |
4129 | | s << "(" << std::setw (width) << m[0][0] << |
4130 | | " " << std::setw (width) << m[0][1] << |
4131 | | " " << std::setw (width) << m[0][2] << "\n" << |
4132 | | |
4133 | | " " << std::setw (width) << m[1][0] << |
4134 | | " " << std::setw (width) << m[1][1] << |
4135 | | " " << std::setw (width) << m[1][2] << "\n" << |
4136 | | |
4137 | | " " << std::setw (width) << m[2][0] << |
4138 | | " " << std::setw (width) << m[2][1] << |
4139 | | " " << std::setw (width) << m[2][2] << ")\n"; |
4140 | | |
4141 | | s.flags (oldFlags); |
4142 | | return s; |
4143 | | } |
4144 | | |
4145 | | template <class T> |
4146 | | std::ostream & |
4147 | | operator << (std::ostream &s, const Matrix44<T> &m) |
4148 | | { |
4149 | | std::ios_base::fmtflags oldFlags = s.flags(); |
4150 | | int width; |
4151 | | |
4152 | | if (s.flags() & std::ios_base::fixed) |
4153 | | { |
4154 | | s.setf (std::ios_base::showpoint); |
4155 | | width = static_cast<int>(s.precision()) + 5; |
4156 | | } |
4157 | | else |
4158 | | { |
4159 | | s.setf (std::ios_base::scientific); |
4160 | | s.setf (std::ios_base::showpoint); |
4161 | | width = static_cast<int>(s.precision()) + 8; |
4162 | | } |
4163 | | |
4164 | | s << "(" << std::setw (width) << m[0][0] << |
4165 | | " " << std::setw (width) << m[0][1] << |
4166 | | " " << std::setw (width) << m[0][2] << |
4167 | | " " << std::setw (width) << m[0][3] << "\n" << |
4168 | | |
4169 | | " " << std::setw (width) << m[1][0] << |
4170 | | " " << std::setw (width) << m[1][1] << |
4171 | | " " << std::setw (width) << m[1][2] << |
4172 | | " " << std::setw (width) << m[1][3] << "\n" << |
4173 | | |
4174 | | " " << std::setw (width) << m[2][0] << |
4175 | | " " << std::setw (width) << m[2][1] << |
4176 | | " " << std::setw (width) << m[2][2] << |
4177 | | " " << std::setw (width) << m[2][3] << "\n" << |
4178 | | |
4179 | | " " << std::setw (width) << m[3][0] << |
4180 | | " " << std::setw (width) << m[3][1] << |
4181 | | " " << std::setw (width) << m[3][2] << |
4182 | | " " << std::setw (width) << m[3][3] << ")\n"; |
4183 | | |
4184 | | s.flags (oldFlags); |
4185 | | return s; |
4186 | | } |
4187 | | |
4188 | | |
4189 | | //--------------------------------------------------------------- |
4190 | | // Implementation of vector-times-matrix multiplication operators |
4191 | | //--------------------------------------------------------------- |
4192 | | |
4193 | | template <class S, class T> |
4194 | | inline const Vec2<S> & |
4195 | | operator *= (Vec2<S> &v, const Matrix22<T> &m) |
4196 | | { |
4197 | | S x = S(v.x * m[0][0] + v.y * m[1][0]); |
4198 | | S y = S(v.x * m[0][1] + v.y * m[1][1]); |
4199 | | |
4200 | | v.x = x; |
4201 | | v.y = y; |
4202 | | |
4203 | | return v; |
4204 | | } |
4205 | | |
4206 | | template <class S, class T> |
4207 | | inline Vec2<S> |
4208 | | operator * (const Vec2<S> &v, const Matrix22<T> &m) |
4209 | | { |
4210 | | S x = S(v.x * m[0][0] + v.y * m[1][0]); |
4211 | | S y = S(v.x * m[0][1] + v.y * m[1][1]); |
4212 | | |
4213 | | return Vec2<S> (x, y); |
4214 | | } |
4215 | | |
4216 | | template <class S, class T> |
4217 | | inline const Vec2<S> & |
4218 | | operator *= (Vec2<S> &v, const Matrix33<T> &m) |
4219 | | { |
4220 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]); |
4221 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]); |
4222 | | S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]); |
4223 | | |
4224 | | v.x = x / w; |
4225 | | v.y = y / w; |
4226 | | |
4227 | | return v; |
4228 | | } |
4229 | | |
4230 | | template <class S, class T> |
4231 | | inline Vec2<S> |
4232 | | operator * (const Vec2<S> &v, const Matrix33<T> &m) |
4233 | | { |
4234 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + m[2][0]); |
4235 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + m[2][1]); |
4236 | | S w = S(v.x * m[0][2] + v.y * m[1][2] + m[2][2]); |
4237 | | |
4238 | | return Vec2<S> (x / w, y / w); |
4239 | | } |
4240 | | |
4241 | | |
4242 | | template <class S, class T> |
4243 | | inline const Vec3<S> & |
4244 | | operator *= (Vec3<S> &v, const Matrix33<T> &m) |
4245 | | { |
4246 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]); |
4247 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]); |
4248 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]); |
4249 | | |
4250 | | v.x = x; |
4251 | | v.y = y; |
4252 | | v.z = z; |
4253 | | |
4254 | | return v; |
4255 | | } |
4256 | | |
4257 | | template <class S, class T> |
4258 | | inline Vec3<S> |
4259 | | operator * (const Vec3<S> &v, const Matrix33<T> &m) |
4260 | | { |
4261 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0]); |
4262 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1]); |
4263 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2]); |
4264 | | |
4265 | | return Vec3<S> (x, y, z); |
4266 | | } |
4267 | | |
4268 | | |
4269 | | template <class S, class T> |
4270 | | inline const Vec3<S> & |
4271 | | operator *= (Vec3<S> &v, const Matrix44<T> &m) |
4272 | | { |
4273 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]); |
4274 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]); |
4275 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]); |
4276 | | S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]); |
4277 | | |
4278 | | v.x = x / w; |
4279 | | v.y = y / w; |
4280 | | v.z = z / w; |
4281 | | |
4282 | | return v; |
4283 | | } |
4284 | | |
4285 | | template <class S, class T> |
4286 | | inline Vec3<S> |
4287 | | operator * (const Vec3<S> &v, const Matrix44<T> &m) |
4288 | | { |
4289 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + m[3][0]); |
4290 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + m[3][1]); |
4291 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + m[3][2]); |
4292 | | S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + m[3][3]); |
4293 | | |
4294 | | return Vec3<S> (x / w, y / w, z / w); |
4295 | | } |
4296 | | |
4297 | | |
4298 | | template <class S, class T> |
4299 | | inline const Vec4<S> & |
4300 | | operator *= (Vec4<S> &v, const Matrix44<T> &m) |
4301 | | { |
4302 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + v.w * m[3][0]); |
4303 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + v.w * m[3][1]); |
4304 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + v.w * m[3][2]); |
4305 | | S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + v.w * m[3][3]); |
4306 | | |
4307 | | v.x = x; |
4308 | | v.y = y; |
4309 | | v.z = z; |
4310 | | v.w = w; |
4311 | | |
4312 | | return v; |
4313 | | } |
4314 | | |
4315 | | template <class S, class T> |
4316 | | inline Vec4<S> |
4317 | | operator * (const Vec4<S> &v, const Matrix44<T> &m) |
4318 | | { |
4319 | | S x = S(v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0] + v.w * m[3][0]); |
4320 | | S y = S(v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1] + v.w * m[3][1]); |
4321 | | S z = S(v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2] + v.w * m[3][2]); |
4322 | | S w = S(v.x * m[0][3] + v.y * m[1][3] + v.z * m[2][3] + v.w * m[3][3]); |
4323 | | |
4324 | | return Vec4<S> (x, y, z, w); |
4325 | | } |
4326 | | |
4327 | | IMATH_INTERNAL_NAMESPACE_HEADER_EXIT |
4328 | | |
4329 | | #endif // INCLUDED_IMATHMATRIX_H |