1 | /////////////////////////////////////////////////////////////////////////// |
2 | // |
3 | // Copyright (c) 2004-2012, Industrial Light & Magic, a division of Lucas |
4 | // Digital Ltd. LLC |
5 | // |
6 | // All rights reserved. |
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32 | // |
33 | /////////////////////////////////////////////////////////////////////////// |
34 | |
35 | |
36 | |
37 | #ifndef INCLUDED_IMATHVEC_H |
38 | #define INCLUDED_IMATHVEC_H |
39 | |
40 | //---------------------------------------------------- |
41 | // |
42 | // 2D, 3D and 4D point/vector class templates |
43 | // |
44 | //---------------------------------------------------- |
45 | |
46 | #include "ImathExc.h" |
47 | #include "ImathLimits.h" |
48 | #include "ImathMath.h" |
49 | #include "ImathNamespace.h" |
50 | |
51 | #include <iostream> |
52 | |
53 | #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER |
54 | // suppress exception specification warnings |
55 | #pragma warning(push) |
56 | #pragma warning(disable:4290) |
57 | #endif |
58 | |
59 | |
60 | IMATH_INTERNAL_NAMESPACE_HEADER_ENTER |
61 | |
62 | template <class T> class Vec2; |
63 | template <class T> class Vec3; |
64 | template <class T> class Vec4; |
65 | |
66 | enum InfException {INF_EXCEPTION}; |
67 | |
68 | |
69 | template <class T> class Vec2 |
70 | { |
71 | public: |
72 | |
73 | //------------------- |
74 | // Access to elements |
75 | //------------------- |
76 | |
77 | T x, y; |
78 | |
79 | T & operator [] (int i); |
80 | const T & operator [] (int i) const; |
81 | |
82 | |
83 | //------------- |
84 | // Constructors |
85 | //------------- |
86 | |
87 | Vec2 (); // no initialization |
88 | explicit Vec2 (T a); // (a a) |
89 | Vec2 (T a, T b); // (a b) |
90 | |
91 | |
92 | //--------------------------------- |
93 | // Copy constructors and assignment |
94 | //--------------------------------- |
95 | |
96 | Vec2 (const Vec2 &v); |
97 | template <class S> Vec2 (const Vec2<S> &v); |
98 | |
99 | const Vec2 & operator = (const Vec2 &v); |
100 | |
101 | |
102 | //---------------------- |
103 | // Compatibility with Sb |
104 | //---------------------- |
105 | |
106 | template <class S> |
107 | void setValue (S a, S b); |
108 | |
109 | template <class S> |
110 | void setValue (const Vec2<S> &v); |
111 | |
112 | template <class S> |
113 | void getValue (S &a, S &b) const; |
114 | |
115 | template <class S> |
116 | void getValue (Vec2<S> &v) const; |
117 | |
118 | T * getValue (); |
119 | const T * getValue () const; |
120 | |
121 | |
122 | //--------- |
123 | // Equality |
124 | //--------- |
125 | |
126 | template <class S> |
127 | bool operator == (const Vec2<S> &v) const; |
128 | |
129 | template <class S> |
130 | bool operator != (const Vec2<S> &v) const; |
131 | |
132 | |
133 | //----------------------------------------------------------------------- |
134 | // Compare two vectors and test if they are "approximately equal": |
135 | // |
136 | // equalWithAbsError (v, e) |
137 | // |
138 | // Returns true if the coefficients of this and v are the same with |
139 | // an absolute error of no more than e, i.e., for all i |
140 | // |
141 | // abs (this[i] - v[i]) <= e |
142 | // |
143 | // equalWithRelError (v, e) |
144 | // |
145 | // Returns true if the coefficients of this and v are the same with |
146 | // a relative error of no more than e, i.e., for all i |
147 | // |
148 | // abs (this[i] - v[i]) <= e * abs (this[i]) |
149 | //----------------------------------------------------------------------- |
150 | |
151 | bool equalWithAbsError (const Vec2<T> &v, T e) const; |
152 | bool equalWithRelError (const Vec2<T> &v, T e) const; |
153 | |
154 | //------------ |
155 | // Dot product |
156 | //------------ |
157 | |
158 | T dot (const Vec2 &v) const; |
159 | T operator ^ (const Vec2 &v) const; |
160 | |
161 | |
162 | //------------------------------------------------ |
163 | // Right-handed cross product, i.e. z component of |
164 | // Vec3 (this->x, this->y, 0) % Vec3 (v.x, v.y, 0) |
165 | //------------------------------------------------ |
166 | |
167 | T cross (const Vec2 &v) const; |
168 | T operator % (const Vec2 &v) const; |
169 | |
170 | |
171 | //------------------------ |
172 | // Component-wise addition |
173 | //------------------------ |
174 | |
175 | const Vec2 & operator += (const Vec2 &v); |
176 | Vec2 operator + (const Vec2 &v) const; |
177 | |
178 | |
179 | //--------------------------- |
180 | // Component-wise subtraction |
181 | //--------------------------- |
182 | |
183 | const Vec2 & operator -= (const Vec2 &v); |
184 | Vec2 operator - (const Vec2 &v) const; |
185 | |
186 | |
187 | //------------------------------------ |
188 | // Component-wise multiplication by -1 |
189 | //------------------------------------ |
190 | |
191 | Vec2 operator - () const; |
192 | const Vec2 & negate (); |
193 | |
194 | |
195 | //------------------------------ |
196 | // Component-wise multiplication |
197 | //------------------------------ |
198 | |
199 | const Vec2 & operator *= (const Vec2 &v); |
200 | const Vec2 & operator *= (T a); |
201 | Vec2 operator * (const Vec2 &v) const; |
202 | Vec2 operator * (T a) const; |
203 | |
204 | |
205 | //------------------------ |
206 | // Component-wise division |
207 | //------------------------ |
208 | |
209 | const Vec2 & operator /= (const Vec2 &v); |
210 | const Vec2 & operator /= (T a); |
211 | Vec2 operator / (const Vec2 &v) const; |
212 | Vec2 operator / (T a) const; |
213 | |
214 | |
215 | //---------------------------------------------------------------- |
216 | // Length and normalization: If v.length() is 0.0, v.normalize() |
217 | // and v.normalized() produce a null vector; v.normalizeExc() and |
218 | // v.normalizedExc() throw a NullVecExc. |
219 | // v.normalizeNonNull() and v.normalizedNonNull() are slightly |
220 | // faster than the other normalization routines, but if v.length() |
221 | // is 0.0, the result is undefined. |
222 | //---------------------------------------------------------------- |
223 | |
224 | T length () const; |
225 | T length2 () const; |
226 | |
227 | const Vec2 & normalize (); // modifies *this |
228 | const Vec2 & normalizeExc () throw (IEX_NAMESPACE::MathExc); |
229 | const Vec2 & normalizeNonNull (); |
230 | |
231 | Vec2<T> normalized () const; // does not modify *this |
232 | Vec2<T> normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
233 | Vec2<T> normalizedNonNull () const; |
234 | |
235 | |
236 | //-------------------------------------------------------- |
237 | // Number of dimensions, i.e. number of elements in a Vec2 |
238 | //-------------------------------------------------------- |
239 | |
240 | static unsigned int dimensions() {return 2;} |
241 | |
242 | |
243 | //------------------------------------------------- |
244 | // Limitations of type T (see also class limits<T>) |
245 | //------------------------------------------------- |
246 | |
247 | static T baseTypeMin() {return limits<T>::min();} |
248 | static T baseTypeMax() {return limits<T>::max();} |
249 | static T baseTypeSmallest() {return limits<T>::smallest();} |
250 | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
251 | |
252 | |
253 | //-------------------------------------------------------------- |
254 | // Base type -- in templates, which accept a parameter, V, which |
255 | // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can |
256 | // refer to T as V::BaseType |
257 | //-------------------------------------------------------------- |
258 | |
259 | typedef T BaseType; |
260 | |
261 | private: |
262 | |
263 | T lengthTiny () const; |
264 | }; |
265 | |
266 | |
267 | template <class T> class Vec3 |
268 | { |
269 | public: |
270 | |
271 | //------------------- |
272 | // Access to elements |
273 | //------------------- |
274 | |
275 | T x, y, z; |
276 | |
277 | T & operator [] (int i); |
278 | const T & operator [] (int i) const; |
279 | |
280 | |
281 | //------------- |
282 | // Constructors |
283 | //------------- |
284 | |
285 | Vec3 (); // no initialization |
286 | explicit Vec3 (T a); // (a a a) |
287 | Vec3 (T a, T b, T c); // (a b c) |
288 | |
289 | |
290 | //--------------------------------- |
291 | // Copy constructors and assignment |
292 | //--------------------------------- |
293 | |
294 | Vec3 (const Vec3 &v); |
295 | template <class S> Vec3 (const Vec3<S> &v); |
296 | |
297 | const Vec3 & operator = (const Vec3 &v); |
298 | |
299 | |
300 | //--------------------------------------------------------- |
301 | // Vec4 to Vec3 conversion, divides x, y and z by w: |
302 | // |
303 | // The one-argument conversion function divides by w even |
304 | // if w is zero. The result depends on how the environment |
305 | // handles floating-point exceptions. |
306 | // |
307 | // The two-argument version thows an InfPointExc exception |
308 | // if w is zero or if division by w would overflow. |
309 | //--------------------------------------------------------- |
310 | |
311 | template <class S> explicit Vec3 (const Vec4<S> &v); |
312 | template <class S> explicit Vec3 (const Vec4<S> &v, InfException); |
313 | |
314 | |
315 | //---------------------- |
316 | // Compatibility with Sb |
317 | //---------------------- |
318 | |
319 | template <class S> |
320 | void setValue (S a, S b, S c); |
321 | |
322 | template <class S> |
323 | void setValue (const Vec3<S> &v); |
324 | |
325 | template <class S> |
326 | void getValue (S &a, S &b, S &c) const; |
327 | |
328 | template <class S> |
329 | void getValue (Vec3<S> &v) const; |
330 | |
331 | T * getValue(); |
332 | const T * getValue() const; |
333 | |
334 | |
335 | //--------- |
336 | // Equality |
337 | //--------- |
338 | |
339 | template <class S> |
340 | bool operator == (const Vec3<S> &v) const; |
341 | |
342 | template <class S> |
343 | bool operator != (const Vec3<S> &v) const; |
344 | |
345 | //----------------------------------------------------------------------- |
346 | // Compare two vectors and test if they are "approximately equal": |
347 | // |
348 | // equalWithAbsError (v, e) |
349 | // |
350 | // Returns true if the coefficients of this and v are the same with |
351 | // an absolute error of no more than e, i.e., for all i |
352 | // |
353 | // abs (this[i] - v[i]) <= e |
354 | // |
355 | // equalWithRelError (v, e) |
356 | // |
357 | // Returns true if the coefficients of this and v are the same with |
358 | // a relative error of no more than e, i.e., for all i |
359 | // |
360 | // abs (this[i] - v[i]) <= e * abs (this[i]) |
361 | //----------------------------------------------------------------------- |
362 | |
363 | bool equalWithAbsError (const Vec3<T> &v, T e) const; |
364 | bool equalWithRelError (const Vec3<T> &v, T e) const; |
365 | |
366 | //------------ |
367 | // Dot product |
368 | //------------ |
369 | |
370 | T dot (const Vec3 &v) const; |
371 | T operator ^ (const Vec3 &v) const; |
372 | |
373 | |
374 | //--------------------------- |
375 | // Right-handed cross product |
376 | //--------------------------- |
377 | |
378 | Vec3 cross (const Vec3 &v) const; |
379 | const Vec3 & operator %= (const Vec3 &v); |
380 | Vec3 operator % (const Vec3 &v) const; |
381 | |
382 | |
383 | //------------------------ |
384 | // Component-wise addition |
385 | //------------------------ |
386 | |
387 | const Vec3 & operator += (const Vec3 &v); |
388 | Vec3 operator + (const Vec3 &v) const; |
389 | |
390 | |
391 | //--------------------------- |
392 | // Component-wise subtraction |
393 | //--------------------------- |
394 | |
395 | const Vec3 & operator -= (const Vec3 &v); |
396 | Vec3 operator - (const Vec3 &v) const; |
397 | |
398 | |
399 | //------------------------------------ |
400 | // Component-wise multiplication by -1 |
401 | //------------------------------------ |
402 | |
403 | Vec3 operator - () const; |
404 | const Vec3 & negate (); |
405 | |
406 | |
407 | //------------------------------ |
408 | // Component-wise multiplication |
409 | //------------------------------ |
410 | |
411 | const Vec3 & operator *= (const Vec3 &v); |
412 | const Vec3 & operator *= (T a); |
413 | Vec3 operator * (const Vec3 &v) const; |
414 | Vec3 operator * (T a) const; |
415 | |
416 | |
417 | //------------------------ |
418 | // Component-wise division |
419 | //------------------------ |
420 | |
421 | const Vec3 & operator /= (const Vec3 &v); |
422 | const Vec3 & operator /= (T a); |
423 | Vec3 operator / (const Vec3 &v) const; |
424 | Vec3 operator / (T a) const; |
425 | |
426 | |
427 | //---------------------------------------------------------------- |
428 | // Length and normalization: If v.length() is 0.0, v.normalize() |
429 | // and v.normalized() produce a null vector; v.normalizeExc() and |
430 | // v.normalizedExc() throw a NullVecExc. |
431 | // v.normalizeNonNull() and v.normalizedNonNull() are slightly |
432 | // faster than the other normalization routines, but if v.length() |
433 | // is 0.0, the result is undefined. |
434 | //---------------------------------------------------------------- |
435 | |
436 | T length () const; |
437 | T length2 () const; |
438 | |
439 | const Vec3 & normalize (); // modifies *this |
440 | const Vec3 & normalizeExc () throw (IEX_NAMESPACE::MathExc); |
441 | const Vec3 & normalizeNonNull (); |
442 | |
443 | Vec3<T> normalized () const; // does not modify *this |
444 | Vec3<T> normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
445 | Vec3<T> normalizedNonNull () const; |
446 | |
447 | |
448 | //-------------------------------------------------------- |
449 | // Number of dimensions, i.e. number of elements in a Vec3 |
450 | //-------------------------------------------------------- |
451 | |
452 | static unsigned int dimensions() {return 3;} |
453 | |
454 | |
455 | //------------------------------------------------- |
456 | // Limitations of type T (see also class limits<T>) |
457 | //------------------------------------------------- |
458 | |
459 | static T baseTypeMin() {return limits<T>::min();} |
460 | static T baseTypeMax() {return limits<T>::max();} |
461 | static T baseTypeSmallest() {return limits<T>::smallest();} |
462 | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
463 | |
464 | |
465 | //-------------------------------------------------------------- |
466 | // Base type -- in templates, which accept a parameter, V, which |
467 | // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can |
468 | // refer to T as V::BaseType |
469 | //-------------------------------------------------------------- |
470 | |
471 | typedef T BaseType; |
472 | |
473 | private: |
474 | |
475 | T lengthTiny () const; |
476 | }; |
477 | |
478 | |
479 | |
480 | template <class T> class Vec4 |
481 | { |
482 | public: |
483 | |
484 | //------------------- |
485 | // Access to elements |
486 | //------------------- |
487 | |
488 | T x, y, z, w; |
489 | |
490 | T & operator [] (int i); |
491 | const T & operator [] (int i) const; |
492 | |
493 | |
494 | //------------- |
495 | // Constructors |
496 | //------------- |
497 | |
498 | Vec4 (); // no initialization |
499 | explicit Vec4 (T a); // (a a a a) |
500 | Vec4 (T a, T b, T c, T d); // (a b c d) |
501 | |
502 | |
503 | //--------------------------------- |
504 | // Copy constructors and assignment |
505 | //--------------------------------- |
506 | |
507 | Vec4 (const Vec4 &v); |
508 | template <class S> Vec4 (const Vec4<S> &v); |
509 | |
510 | const Vec4 & operator = (const Vec4 &v); |
511 | |
512 | |
513 | //------------------------------------- |
514 | // Vec3 to Vec4 conversion, sets w to 1 |
515 | //------------------------------------- |
516 | |
517 | template <class S> explicit Vec4 (const Vec3<S> &v); |
518 | |
519 | |
520 | //--------- |
521 | // Equality |
522 | //--------- |
523 | |
524 | template <class S> |
525 | bool operator == (const Vec4<S> &v) const; |
526 | |
527 | template <class S> |
528 | bool operator != (const Vec4<S> &v) const; |
529 | |
530 | |
531 | //----------------------------------------------------------------------- |
532 | // Compare two vectors and test if they are "approximately equal": |
533 | // |
534 | // equalWithAbsError (v, e) |
535 | // |
536 | // Returns true if the coefficients of this and v are the same with |
537 | // an absolute error of no more than e, i.e., for all i |
538 | // |
539 | // abs (this[i] - v[i]) <= e |
540 | // |
541 | // equalWithRelError (v, e) |
542 | // |
543 | // Returns true if the coefficients of this and v are the same with |
544 | // a relative error of no more than e, i.e., for all i |
545 | // |
546 | // abs (this[i] - v[i]) <= e * abs (this[i]) |
547 | //----------------------------------------------------------------------- |
548 | |
549 | bool equalWithAbsError (const Vec4<T> &v, T e) const; |
550 | bool equalWithRelError (const Vec4<T> &v, T e) const; |
551 | |
552 | |
553 | //------------ |
554 | // Dot product |
555 | //------------ |
556 | |
557 | T dot (const Vec4 &v) const; |
558 | T operator ^ (const Vec4 &v) const; |
559 | |
560 | |
561 | //----------------------------------- |
562 | // Cross product is not defined in 4D |
563 | //----------------------------------- |
564 | |
565 | //------------------------ |
566 | // Component-wise addition |
567 | //------------------------ |
568 | |
569 | const Vec4 & operator += (const Vec4 &v); |
570 | Vec4 operator + (const Vec4 &v) const; |
571 | |
572 | |
573 | //--------------------------- |
574 | // Component-wise subtraction |
575 | //--------------------------- |
576 | |
577 | const Vec4 & operator -= (const Vec4 &v); |
578 | Vec4 operator - (const Vec4 &v) const; |
579 | |
580 | |
581 | //------------------------------------ |
582 | // Component-wise multiplication by -1 |
583 | //------------------------------------ |
584 | |
585 | Vec4 operator - () const; |
586 | const Vec4 & negate (); |
587 | |
588 | |
589 | //------------------------------ |
590 | // Component-wise multiplication |
591 | //------------------------------ |
592 | |
593 | const Vec4 & operator *= (const Vec4 &v); |
594 | const Vec4 & operator *= (T a); |
595 | Vec4 operator * (const Vec4 &v) const; |
596 | Vec4 operator * (T a) const; |
597 | |
598 | |
599 | //------------------------ |
600 | // Component-wise division |
601 | //------------------------ |
602 | |
603 | const Vec4 & operator /= (const Vec4 &v); |
604 | const Vec4 & operator /= (T a); |
605 | Vec4 operator / (const Vec4 &v) const; |
606 | Vec4 operator / (T a) const; |
607 | |
608 | |
609 | //---------------------------------------------------------------- |
610 | // Length and normalization: If v.length() is 0.0, v.normalize() |
611 | // and v.normalized() produce a null vector; v.normalizeExc() and |
612 | // v.normalizedExc() throw a NullVecExc. |
613 | // v.normalizeNonNull() and v.normalizedNonNull() are slightly |
614 | // faster than the other normalization routines, but if v.length() |
615 | // is 0.0, the result is undefined. |
616 | //---------------------------------------------------------------- |
617 | |
618 | T length () const; |
619 | T length2 () const; |
620 | |
621 | const Vec4 & normalize (); // modifies *this |
622 | const Vec4 & normalizeExc () throw (IEX_NAMESPACE::MathExc); |
623 | const Vec4 & normalizeNonNull (); |
624 | |
625 | Vec4<T> normalized () const; // does not modify *this |
626 | Vec4<T> normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
627 | Vec4<T> normalizedNonNull () const; |
628 | |
629 | |
630 | //-------------------------------------------------------- |
631 | // Number of dimensions, i.e. number of elements in a Vec4 |
632 | //-------------------------------------------------------- |
633 | |
634 | static unsigned int dimensions() {return 4;} |
635 | |
636 | |
637 | //------------------------------------------------- |
638 | // Limitations of type T (see also class limits<T>) |
639 | //------------------------------------------------- |
640 | |
641 | static T baseTypeMin() {return limits<T>::min();} |
642 | static T baseTypeMax() {return limits<T>::max();} |
643 | static T baseTypeSmallest() {return limits<T>::smallest();} |
644 | static T baseTypeEpsilon() {return limits<T>::epsilon();} |
645 | |
646 | |
647 | //-------------------------------------------------------------- |
648 | // Base type -- in templates, which accept a parameter, V, which |
649 | // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can |
650 | // refer to T as V::BaseType |
651 | //-------------------------------------------------------------- |
652 | |
653 | typedef T BaseType; |
654 | |
655 | private: |
656 | |
657 | T lengthTiny () const; |
658 | }; |
659 | |
660 | |
661 | //-------------- |
662 | // Stream output |
663 | //-------------- |
664 | |
665 | template <class T> |
666 | std::ostream & operator << (std::ostream &s, const Vec2<T> &v); |
667 | |
668 | template <class T> |
669 | std::ostream & operator << (std::ostream &s, const Vec3<T> &v); |
670 | |
671 | template <class T> |
672 | std::ostream & operator << (std::ostream &s, const Vec4<T> &v); |
673 | |
674 | //---------------------------------------------------- |
675 | // Reverse multiplication: S * Vec2<T> and S * Vec3<T> |
676 | //---------------------------------------------------- |
677 | |
678 | template <class T> Vec2<T> operator * (T a, const Vec2<T> &v); |
679 | template <class T> Vec3<T> operator * (T a, const Vec3<T> &v); |
680 | template <class T> Vec4<T> operator * (T a, const Vec4<T> &v); |
681 | |
682 | |
683 | //------------------------- |
684 | // Typedefs for convenience |
685 | //------------------------- |
686 | |
687 | typedef Vec2 <short> V2s; |
688 | typedef Vec2 <int> V2i; |
689 | typedef Vec2 <float> V2f; |
690 | typedef Vec2 <double> V2d; |
691 | typedef Vec3 <short> V3s; |
692 | typedef Vec3 <int> V3i; |
693 | typedef Vec3 <float> V3f; |
694 | typedef Vec3 <double> V3d; |
695 | typedef Vec4 <short> V4s; |
696 | typedef Vec4 <int> V4i; |
697 | typedef Vec4 <float> V4f; |
698 | typedef Vec4 <double> V4d; |
699 | |
700 | |
701 | //------------------------------------------- |
702 | // Specializations for VecN<short>, VecN<int> |
703 | //------------------------------------------- |
704 | |
705 | // Vec2<short> |
706 | |
707 | template <> short |
708 | Vec2<short>::length () const; |
709 | |
710 | template <> const Vec2<short> & |
711 | Vec2<short>::normalize (); |
712 | |
713 | template <> const Vec2<short> & |
714 | Vec2<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
715 | |
716 | template <> const Vec2<short> & |
717 | Vec2<short>::normalizeNonNull (); |
718 | |
719 | template <> Vec2<short> |
720 | Vec2<short>::normalized () const; |
721 | |
722 | template <> Vec2<short> |
723 | Vec2<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
724 | |
725 | template <> Vec2<short> |
726 | Vec2<short>::normalizedNonNull () const; |
727 | |
728 | |
729 | // Vec2<int> |
730 | |
731 | template <> int |
732 | Vec2<int>::length () const; |
733 | |
734 | template <> const Vec2<int> & |
735 | Vec2<int>::normalize (); |
736 | |
737 | template <> const Vec2<int> & |
738 | Vec2<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
739 | |
740 | template <> const Vec2<int> & |
741 | Vec2<int>::normalizeNonNull (); |
742 | |
743 | template <> Vec2<int> |
744 | Vec2<int>::normalized () const; |
745 | |
746 | template <> Vec2<int> |
747 | Vec2<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
748 | |
749 | template <> Vec2<int> |
750 | Vec2<int>::normalizedNonNull () const; |
751 | |
752 | |
753 | // Vec3<short> |
754 | |
755 | template <> short |
756 | Vec3<short>::length () const; |
757 | |
758 | template <> const Vec3<short> & |
759 | Vec3<short>::normalize (); |
760 | |
761 | template <> const Vec3<short> & |
762 | Vec3<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
763 | |
764 | template <> const Vec3<short> & |
765 | Vec3<short>::normalizeNonNull (); |
766 | |
767 | template <> Vec3<short> |
768 | Vec3<short>::normalized () const; |
769 | |
770 | template <> Vec3<short> |
771 | Vec3<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
772 | |
773 | template <> Vec3<short> |
774 | Vec3<short>::normalizedNonNull () const; |
775 | |
776 | |
777 | // Vec3<int> |
778 | |
779 | template <> int |
780 | Vec3<int>::length () const; |
781 | |
782 | template <> const Vec3<int> & |
783 | Vec3<int>::normalize (); |
784 | |
785 | template <> const Vec3<int> & |
786 | Vec3<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
787 | |
788 | template <> const Vec3<int> & |
789 | Vec3<int>::normalizeNonNull (); |
790 | |
791 | template <> Vec3<int> |
792 | Vec3<int>::normalized () const; |
793 | |
794 | template <> Vec3<int> |
795 | Vec3<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
796 | |
797 | template <> Vec3<int> |
798 | Vec3<int>::normalizedNonNull () const; |
799 | |
800 | // Vec4<short> |
801 | |
802 | template <> short |
803 | Vec4<short>::length () const; |
804 | |
805 | template <> const Vec4<short> & |
806 | Vec4<short>::normalize (); |
807 | |
808 | template <> const Vec4<short> & |
809 | Vec4<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
810 | |
811 | template <> const Vec4<short> & |
812 | Vec4<short>::normalizeNonNull (); |
813 | |
814 | template <> Vec4<short> |
815 | Vec4<short>::normalized () const; |
816 | |
817 | template <> Vec4<short> |
818 | Vec4<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
819 | |
820 | template <> Vec4<short> |
821 | Vec4<short>::normalizedNonNull () const; |
822 | |
823 | |
824 | // Vec4<int> |
825 | |
826 | template <> int |
827 | Vec4<int>::length () const; |
828 | |
829 | template <> const Vec4<int> & |
830 | Vec4<int>::normalize (); |
831 | |
832 | template <> const Vec4<int> & |
833 | Vec4<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc); |
834 | |
835 | template <> const Vec4<int> & |
836 | Vec4<int>::normalizeNonNull (); |
837 | |
838 | template <> Vec4<int> |
839 | Vec4<int>::normalized () const; |
840 | |
841 | template <> Vec4<int> |
842 | Vec4<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc); |
843 | |
844 | template <> Vec4<int> |
845 | Vec4<int>::normalizedNonNull () const; |
846 | |
847 | |
848 | //------------------------ |
849 | // Implementation of Vec2: |
850 | //------------------------ |
851 | |
852 | template <class T> |
853 | inline T & |
854 | Vec2<T>::operator [] (int i) |
855 | { |
856 | return (&x)[i]; |
857 | } |
858 | |
859 | template <class T> |
860 | inline const T & |
861 | Vec2<T>::operator [] (int i) const |
862 | { |
863 | return (&x)[i]; |
864 | } |
865 | |
866 | template <class T> |
867 | inline |
868 | Vec2<T>::Vec2 () |
869 | { |
870 | // empty |
871 | } |
872 | |
873 | template <class T> |
874 | inline |
875 | Vec2<T>::Vec2 (T a) |
876 | { |
877 | x = y = a; |
878 | } |
879 | |
880 | template <class T> |
881 | inline |
882 | Vec2<T>::Vec2 (T a, T b) |
883 | { |
884 | x = a; |
885 | y = b; |
886 | } |
887 | |
888 | template <class T> |
889 | inline |
890 | Vec2<T>::Vec2 (const Vec2 &v) |
891 | { |
892 | x = v.x; |
893 | y = v.y; |
894 | } |
895 | |
896 | template <class T> |
897 | template <class S> |
898 | inline |
899 | Vec2<T>::Vec2 (const Vec2<S> &v) |
900 | { |
901 | x = T (v.x); |
902 | y = T (v.y); |
903 | } |
904 | |
905 | template <class T> |
906 | inline const Vec2<T> & |
907 | Vec2<T>::operator = (const Vec2 &v) |
908 | { |
909 | x = v.x; |
910 | y = v.y; |
911 | return *this; |
912 | } |
913 | |
914 | template <class T> |
915 | template <class S> |
916 | inline void |
917 | Vec2<T>::setValue (S a, S b) |
918 | { |
919 | x = T (a); |
920 | y = T (b); |
921 | } |
922 | |
923 | template <class T> |
924 | template <class S> |
925 | inline void |
926 | Vec2<T>::setValue (const Vec2<S> &v) |
927 | { |
928 | x = T (v.x); |
929 | y = T (v.y); |
930 | } |
931 | |
932 | template <class T> |
933 | template <class S> |
934 | inline void |
935 | Vec2<T>::getValue (S &a, S &b) const |
936 | { |
937 | a = S (x); |
938 | b = S (y); |
939 | } |
940 | |
941 | template <class T> |
942 | template <class S> |
943 | inline void |
944 | Vec2<T>::getValue (Vec2<S> &v) const |
945 | { |
946 | v.x = S (x); |
947 | v.y = S (y); |
948 | } |
949 | |
950 | template <class T> |
951 | inline T * |
952 | Vec2<T>::getValue() |
953 | { |
954 | return (T *) &x; |
955 | } |
956 | |
957 | template <class T> |
958 | inline const T * |
959 | Vec2<T>::getValue() const |
960 | { |
961 | return (const T *) &x; |
962 | } |
963 | |
964 | template <class T> |
965 | template <class S> |
966 | inline bool |
967 | Vec2<T>::operator == (const Vec2<S> &v) const |
968 | { |
969 | return x == v.x && y == v.y; |
970 | } |
971 | |
972 | template <class T> |
973 | template <class S> |
974 | inline bool |
975 | Vec2<T>::operator != (const Vec2<S> &v) const |
976 | { |
977 | return x != v.x || y != v.y; |
978 | } |
979 | |
980 | template <class T> |
981 | bool |
982 | Vec2<T>::equalWithAbsError (const Vec2<T> &v, T e) const |
983 | { |
984 | for (int i = 0; i < 2; i++) |
985 | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e)) |
986 | return false; |
987 | |
988 | return true; |
989 | } |
990 | |
991 | template <class T> |
992 | bool |
993 | Vec2<T>::equalWithRelError (const Vec2<T> &v, T e) const |
994 | { |
995 | for (int i = 0; i < 2; i++) |
996 | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e)) |
997 | return false; |
998 | |
999 | return true; |
1000 | } |
1001 | |
1002 | template <class T> |
1003 | inline T |
1004 | Vec2<T>::dot (const Vec2 &v) const |
1005 | { |
1006 | return x * v.x + y * v.y; |
1007 | } |
1008 | |
1009 | template <class T> |
1010 | inline T |
1011 | Vec2<T>::operator ^ (const Vec2 &v) const |
1012 | { |
1013 | return dot (v); |
1014 | } |
1015 | |
1016 | template <class T> |
1017 | inline T |
1018 | Vec2<T>::cross (const Vec2 &v) const |
1019 | { |
1020 | return x * v.y - y * v.x; |
1021 | |
1022 | } |
1023 | |
1024 | template <class T> |
1025 | inline T |
1026 | Vec2<T>::operator % (const Vec2 &v) const |
1027 | { |
1028 | return x * v.y - y * v.x; |
1029 | } |
1030 | |
1031 | template <class T> |
1032 | inline const Vec2<T> & |
1033 | Vec2<T>::operator += (const Vec2 &v) |
1034 | { |
1035 | x += v.x; |
1036 | y += v.y; |
1037 | return *this; |
1038 | } |
1039 | |
1040 | template <class T> |
1041 | inline Vec2<T> |
1042 | Vec2<T>::operator + (const Vec2 &v) const |
1043 | { |
1044 | return Vec2 (x + v.x, y + v.y); |
1045 | } |
1046 | |
1047 | template <class T> |
1048 | inline const Vec2<T> & |
1049 | Vec2<T>::operator -= (const Vec2 &v) |
1050 | { |
1051 | x -= v.x; |
1052 | y -= v.y; |
1053 | return *this; |
1054 | } |
1055 | |
1056 | template <class T> |
1057 | inline Vec2<T> |
1058 | Vec2<T>::operator - (const Vec2 &v) const |
1059 | { |
1060 | return Vec2 (x - v.x, y - v.y); |
1061 | } |
1062 | |
1063 | template <class T> |
1064 | inline Vec2<T> |
1065 | Vec2<T>::operator - () const |
1066 | { |
1067 | return Vec2 (-x, -y); |
1068 | } |
1069 | |
1070 | template <class T> |
1071 | inline const Vec2<T> & |
1072 | Vec2<T>::negate () |
1073 | { |
1074 | x = -x; |
1075 | y = -y; |
1076 | return *this; |
1077 | } |
1078 | |
1079 | template <class T> |
1080 | inline const Vec2<T> & |
1081 | Vec2<T>::operator *= (const Vec2 &v) |
1082 | { |
1083 | x *= v.x; |
1084 | y *= v.y; |
1085 | return *this; |
1086 | } |
1087 | |
1088 | template <class T> |
1089 | inline const Vec2<T> & |
1090 | Vec2<T>::operator *= (T a) |
1091 | { |
1092 | x *= a; |
1093 | y *= a; |
1094 | return *this; |
1095 | } |
1096 | |
1097 | template <class T> |
1098 | inline Vec2<T> |
1099 | Vec2<T>::operator * (const Vec2 &v) const |
1100 | { |
1101 | return Vec2 (x * v.x, y * v.y); |
1102 | } |
1103 | |
1104 | template <class T> |
1105 | inline Vec2<T> |
1106 | Vec2<T>::operator * (T a) const |
1107 | { |
1108 | return Vec2 (x * a, y * a); |
1109 | } |
1110 | |
1111 | template <class T> |
1112 | inline const Vec2<T> & |
1113 | Vec2<T>::operator /= (const Vec2 &v) |
1114 | { |
1115 | x /= v.x; |
1116 | y /= v.y; |
1117 | return *this; |
1118 | } |
1119 | |
1120 | template <class T> |
1121 | inline const Vec2<T> & |
1122 | Vec2<T>::operator /= (T a) |
1123 | { |
1124 | x /= a; |
1125 | y /= a; |
1126 | return *this; |
1127 | } |
1128 | |
1129 | template <class T> |
1130 | inline Vec2<T> |
1131 | Vec2<T>::operator / (const Vec2 &v) const |
1132 | { |
1133 | return Vec2 (x / v.x, y / v.y); |
1134 | } |
1135 | |
1136 | template <class T> |
1137 | inline Vec2<T> |
1138 | Vec2<T>::operator / (T a) const |
1139 | { |
1140 | return Vec2 (x / a, y / a); |
1141 | } |
1142 | |
1143 | template <class T> |
1144 | T |
1145 | Vec2<T>::lengthTiny () const |
1146 | { |
1147 | T absX = (x >= T (0))? x: -x; |
1148 | T absY = (y >= T (0))? y: -y; |
1149 | |
1150 | T max = absX; |
1151 | |
1152 | if (max < absY) |
1153 | max = absY; |
1154 | |
1155 | if (max == T (0)) |
1156 | return T (0); |
1157 | |
1158 | // |
1159 | // Do not replace the divisions by max with multiplications by 1/max. |
1160 | // Computing 1/max can overflow but the divisions below will always |
1161 | // produce results less than or equal to 1. |
1162 | // |
1163 | |
1164 | absX /= max; |
1165 | absY /= max; |
1166 | |
1167 | return max * Math<T>::sqrt (absX * absX + absY * absY); |
1168 | } |
1169 | |
1170 | template <class T> |
1171 | inline T |
1172 | Vec2<T>::length () const |
1173 | { |
1174 | T length2 = dot (*this); |
1175 | |
1176 | if (length2 < T (2) * limits<T>::smallest()) |
1177 | return lengthTiny(); |
1178 | |
1179 | return Math<T>::sqrt (length2); |
1180 | } |
1181 | |
1182 | template <class T> |
1183 | inline T |
1184 | Vec2<T>::length2 () const |
1185 | { |
1186 | return dot (*this); |
1187 | } |
1188 | |
1189 | template <class T> |
1190 | const Vec2<T> & |
1191 | Vec2<T>::normalize () |
1192 | { |
1193 | T l = length(); |
1194 | |
1195 | if (l != T (0)) |
1196 | { |
1197 | // |
1198 | // Do not replace the divisions by l with multiplications by 1/l. |
1199 | // Computing 1/l can overflow but the divisions below will always |
1200 | // produce results less than or equal to 1. |
1201 | // |
1202 | |
1203 | x /= l; |
1204 | y /= l; |
1205 | } |
1206 | |
1207 | return *this; |
1208 | } |
1209 | |
1210 | template <class T> |
1211 | const Vec2<T> & |
1212 | Vec2<T>::normalizeExc () throw (IEX_NAMESPACE::MathExc) |
1213 | { |
1214 | T l = length(); |
1215 | |
1216 | if (l == T (0)) |
1217 | throw NullVecExc ("Cannot normalize null vector." ); |
1218 | |
1219 | x /= l; |
1220 | y /= l; |
1221 | return *this; |
1222 | } |
1223 | |
1224 | template <class T> |
1225 | inline |
1226 | const Vec2<T> & |
1227 | Vec2<T>::normalizeNonNull () |
1228 | { |
1229 | T l = length(); |
1230 | x /= l; |
1231 | y /= l; |
1232 | return *this; |
1233 | } |
1234 | |
1235 | template <class T> |
1236 | Vec2<T> |
1237 | Vec2<T>::normalized () const |
1238 | { |
1239 | T l = length(); |
1240 | |
1241 | if (l == T (0)) |
1242 | return Vec2 (T (0)); |
1243 | |
1244 | return Vec2 (x / l, y / l); |
1245 | } |
1246 | |
1247 | template <class T> |
1248 | Vec2<T> |
1249 | Vec2<T>::normalizedExc () const throw (IEX_NAMESPACE::MathExc) |
1250 | { |
1251 | T l = length(); |
1252 | |
1253 | if (l == T (0)) |
1254 | throw NullVecExc ("Cannot normalize null vector." ); |
1255 | |
1256 | return Vec2 (x / l, y / l); |
1257 | } |
1258 | |
1259 | template <class T> |
1260 | inline |
1261 | Vec2<T> |
1262 | Vec2<T>::normalizedNonNull () const |
1263 | { |
1264 | T l = length(); |
1265 | return Vec2 (x / l, y / l); |
1266 | } |
1267 | |
1268 | |
1269 | //----------------------- |
1270 | // Implementation of Vec3 |
1271 | //----------------------- |
1272 | |
1273 | template <class T> |
1274 | inline T & |
1275 | Vec3<T>::operator [] (int i) |
1276 | { |
1277 | return (&x)[i]; |
1278 | } |
1279 | |
1280 | template <class T> |
1281 | inline const T & |
1282 | Vec3<T>::operator [] (int i) const |
1283 | { |
1284 | return (&x)[i]; |
1285 | } |
1286 | |
1287 | template <class T> |
1288 | inline |
1289 | Vec3<T>::Vec3 () |
1290 | { |
1291 | // empty |
1292 | } |
1293 | |
1294 | template <class T> |
1295 | inline |
1296 | Vec3<T>::Vec3 (T a) |
1297 | { |
1298 | x = y = z = a; |
1299 | } |
1300 | |
1301 | template <class T> |
1302 | inline |
1303 | Vec3<T>::Vec3 (T a, T b, T c) |
1304 | { |
1305 | x = a; |
1306 | y = b; |
1307 | z = c; |
1308 | } |
1309 | |
1310 | template <class T> |
1311 | inline |
1312 | Vec3<T>::Vec3 (const Vec3 &v) |
1313 | { |
1314 | x = v.x; |
1315 | y = v.y; |
1316 | z = v.z; |
1317 | } |
1318 | |
1319 | template <class T> |
1320 | template <class S> |
1321 | inline |
1322 | Vec3<T>::Vec3 (const Vec3<S> &v) |
1323 | { |
1324 | x = T (v.x); |
1325 | y = T (v.y); |
1326 | z = T (v.z); |
1327 | } |
1328 | |
1329 | template <class T> |
1330 | inline const Vec3<T> & |
1331 | Vec3<T>::operator = (const Vec3 &v) |
1332 | { |
1333 | x = v.x; |
1334 | y = v.y; |
1335 | z = v.z; |
1336 | return *this; |
1337 | } |
1338 | |
1339 | template <class T> |
1340 | template <class S> |
1341 | inline |
1342 | Vec3<T>::Vec3 (const Vec4<S> &v) |
1343 | { |
1344 | x = T (v.x / v.w); |
1345 | y = T (v.y / v.w); |
1346 | z = T (v.z / v.w); |
1347 | } |
1348 | |
1349 | template <class T> |
1350 | template <class S> |
1351 | Vec3<T>::Vec3 (const Vec4<S> &v, InfException) |
1352 | { |
1353 | T vx = T (v.x); |
1354 | T vy = T (v.y); |
1355 | T vz = T (v.z); |
1356 | T vw = T (v.w); |
1357 | |
1358 | T absW = (vw >= T (0))? vw: -vw; |
1359 | |
1360 | if (absW < 1) |
1361 | { |
1362 | T m = baseTypeMax() * absW; |
1363 | |
1364 | if (vx <= -m || vx >= m || vy <= -m || vy >= m || vz <= -m || vz >= m) |
1365 | throw InfPointExc ("Cannot normalize point at infinity." ); |
1366 | } |
1367 | |
1368 | x = vx / vw; |
1369 | y = vy / vw; |
1370 | z = vz / vw; |
1371 | } |
1372 | |
1373 | template <class T> |
1374 | template <class S> |
1375 | inline void |
1376 | Vec3<T>::setValue (S a, S b, S c) |
1377 | { |
1378 | x = T (a); |
1379 | y = T (b); |
1380 | z = T (c); |
1381 | } |
1382 | |
1383 | template <class T> |
1384 | template <class S> |
1385 | inline void |
1386 | Vec3<T>::setValue (const Vec3<S> &v) |
1387 | { |
1388 | x = T (v.x); |
1389 | y = T (v.y); |
1390 | z = T (v.z); |
1391 | } |
1392 | |
1393 | template <class T> |
1394 | template <class S> |
1395 | inline void |
1396 | Vec3<T>::getValue (S &a, S &b, S &c) const |
1397 | { |
1398 | a = S (x); |
1399 | b = S (y); |
1400 | c = S (z); |
1401 | } |
1402 | |
1403 | template <class T> |
1404 | template <class S> |
1405 | inline void |
1406 | Vec3<T>::getValue (Vec3<S> &v) const |
1407 | { |
1408 | v.x = S (x); |
1409 | v.y = S (y); |
1410 | v.z = S (z); |
1411 | } |
1412 | |
1413 | template <class T> |
1414 | inline T * |
1415 | Vec3<T>::getValue() |
1416 | { |
1417 | return (T *) &x; |
1418 | } |
1419 | |
1420 | template <class T> |
1421 | inline const T * |
1422 | Vec3<T>::getValue() const |
1423 | { |
1424 | return (const T *) &x; |
1425 | } |
1426 | |
1427 | template <class T> |
1428 | template <class S> |
1429 | inline bool |
1430 | Vec3<T>::operator == (const Vec3<S> &v) const |
1431 | { |
1432 | return x == v.x && y == v.y && z == v.z; |
1433 | } |
1434 | |
1435 | template <class T> |
1436 | template <class S> |
1437 | inline bool |
1438 | Vec3<T>::operator != (const Vec3<S> &v) const |
1439 | { |
1440 | return x != v.x || y != v.y || z != v.z; |
1441 | } |
1442 | |
1443 | template <class T> |
1444 | bool |
1445 | Vec3<T>::equalWithAbsError (const Vec3<T> &v, T e) const |
1446 | { |
1447 | for (int i = 0; i < 3; i++) |
1448 | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e)) |
1449 | return false; |
1450 | |
1451 | return true; |
1452 | } |
1453 | |
1454 | template <class T> |
1455 | bool |
1456 | Vec3<T>::equalWithRelError (const Vec3<T> &v, T e) const |
1457 | { |
1458 | for (int i = 0; i < 3; i++) |
1459 | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e)) |
1460 | return false; |
1461 | |
1462 | return true; |
1463 | } |
1464 | |
1465 | template <class T> |
1466 | inline T |
1467 | Vec3<T>::dot (const Vec3 &v) const |
1468 | { |
1469 | return x * v.x + y * v.y + z * v.z; |
1470 | } |
1471 | |
1472 | template <class T> |
1473 | inline T |
1474 | Vec3<T>::operator ^ (const Vec3 &v) const |
1475 | { |
1476 | return dot (v); |
1477 | } |
1478 | |
1479 | template <class T> |
1480 | inline Vec3<T> |
1481 | Vec3<T>::cross (const Vec3 &v) const |
1482 | { |
1483 | return Vec3 (y * v.z - z * v.y, |
1484 | z * v.x - x * v.z, |
1485 | x * v.y - y * v.x); |
1486 | } |
1487 | |
1488 | template <class T> |
1489 | inline const Vec3<T> & |
1490 | Vec3<T>::operator %= (const Vec3 &v) |
1491 | { |
1492 | T a = y * v.z - z * v.y; |
1493 | T b = z * v.x - x * v.z; |
1494 | T c = x * v.y - y * v.x; |
1495 | x = a; |
1496 | y = b; |
1497 | z = c; |
1498 | return *this; |
1499 | } |
1500 | |
1501 | template <class T> |
1502 | inline Vec3<T> |
1503 | Vec3<T>::operator % (const Vec3 &v) const |
1504 | { |
1505 | return Vec3 (y * v.z - z * v.y, |
1506 | z * v.x - x * v.z, |
1507 | x * v.y - y * v.x); |
1508 | } |
1509 | |
1510 | template <class T> |
1511 | inline const Vec3<T> & |
1512 | Vec3<T>::operator += (const Vec3 &v) |
1513 | { |
1514 | x += v.x; |
1515 | y += v.y; |
1516 | z += v.z; |
1517 | return *this; |
1518 | } |
1519 | |
1520 | template <class T> |
1521 | inline Vec3<T> |
1522 | Vec3<T>::operator + (const Vec3 &v) const |
1523 | { |
1524 | return Vec3 (x + v.x, y + v.y, z + v.z); |
1525 | } |
1526 | |
1527 | template <class T> |
1528 | inline const Vec3<T> & |
1529 | Vec3<T>::operator -= (const Vec3 &v) |
1530 | { |
1531 | x -= v.x; |
1532 | y -= v.y; |
1533 | z -= v.z; |
1534 | return *this; |
1535 | } |
1536 | |
1537 | template <class T> |
1538 | inline Vec3<T> |
1539 | Vec3<T>::operator - (const Vec3 &v) const |
1540 | { |
1541 | return Vec3 (x - v.x, y - v.y, z - v.z); |
1542 | } |
1543 | |
1544 | template <class T> |
1545 | inline Vec3<T> |
1546 | Vec3<T>::operator - () const |
1547 | { |
1548 | return Vec3 (-x, -y, -z); |
1549 | } |
1550 | |
1551 | template <class T> |
1552 | inline const Vec3<T> & |
1553 | Vec3<T>::negate () |
1554 | { |
1555 | x = -x; |
1556 | y = -y; |
1557 | z = -z; |
1558 | return *this; |
1559 | } |
1560 | |
1561 | template <class T> |
1562 | inline const Vec3<T> & |
1563 | Vec3<T>::operator *= (const Vec3 &v) |
1564 | { |
1565 | x *= v.x; |
1566 | y *= v.y; |
1567 | z *= v.z; |
1568 | return *this; |
1569 | } |
1570 | |
1571 | template <class T> |
1572 | inline const Vec3<T> & |
1573 | Vec3<T>::operator *= (T a) |
1574 | { |
1575 | x *= a; |
1576 | y *= a; |
1577 | z *= a; |
1578 | return *this; |
1579 | } |
1580 | |
1581 | template <class T> |
1582 | inline Vec3<T> |
1583 | Vec3<T>::operator * (const Vec3 &v) const |
1584 | { |
1585 | return Vec3 (x * v.x, y * v.y, z * v.z); |
1586 | } |
1587 | |
1588 | template <class T> |
1589 | inline Vec3<T> |
1590 | Vec3<T>::operator * (T a) const |
1591 | { |
1592 | return Vec3 (x * a, y * a, z * a); |
1593 | } |
1594 | |
1595 | template <class T> |
1596 | inline const Vec3<T> & |
1597 | Vec3<T>::operator /= (const Vec3 &v) |
1598 | { |
1599 | x /= v.x; |
1600 | y /= v.y; |
1601 | z /= v.z; |
1602 | return *this; |
1603 | } |
1604 | |
1605 | template <class T> |
1606 | inline const Vec3<T> & |
1607 | Vec3<T>::operator /= (T a) |
1608 | { |
1609 | x /= a; |
1610 | y /= a; |
1611 | z /= a; |
1612 | return *this; |
1613 | } |
1614 | |
1615 | template <class T> |
1616 | inline Vec3<T> |
1617 | Vec3<T>::operator / (const Vec3 &v) const |
1618 | { |
1619 | return Vec3 (x / v.x, y / v.y, z / v.z); |
1620 | } |
1621 | |
1622 | template <class T> |
1623 | inline Vec3<T> |
1624 | Vec3<T>::operator / (T a) const |
1625 | { |
1626 | return Vec3 (x / a, y / a, z / a); |
1627 | } |
1628 | |
1629 | template <class T> |
1630 | T |
1631 | Vec3<T>::lengthTiny () const |
1632 | { |
1633 | T absX = (x >= T (0))? x: -x; |
1634 | T absY = (y >= T (0))? y: -y; |
1635 | T absZ = (z >= T (0))? z: -z; |
1636 | |
1637 | T max = absX; |
1638 | |
1639 | if (max < absY) |
1640 | max = absY; |
1641 | |
1642 | if (max < absZ) |
1643 | max = absZ; |
1644 | |
1645 | if (max == T (0)) |
1646 | return T (0); |
1647 | |
1648 | // |
1649 | // Do not replace the divisions by max with multiplications by 1/max. |
1650 | // Computing 1/max can overflow but the divisions below will always |
1651 | // produce results less than or equal to 1. |
1652 | // |
1653 | |
1654 | absX /= max; |
1655 | absY /= max; |
1656 | absZ /= max; |
1657 | |
1658 | return max * Math<T>::sqrt (absX * absX + absY * absY + absZ * absZ); |
1659 | } |
1660 | |
1661 | template <class T> |
1662 | inline T |
1663 | Vec3<T>::length () const |
1664 | { |
1665 | T length2 = dot (*this); |
1666 | |
1667 | if (length2 < T (2) * limits<T>::smallest()) |
1668 | return lengthTiny(); |
1669 | |
1670 | return Math<T>::sqrt (length2); |
1671 | } |
1672 | |
1673 | template <class T> |
1674 | inline T |
1675 | Vec3<T>::length2 () const |
1676 | { |
1677 | return dot (*this); |
1678 | } |
1679 | |
1680 | template <class T> |
1681 | const Vec3<T> & |
1682 | Vec3<T>::normalize () |
1683 | { |
1684 | T l = length(); |
1685 | |
1686 | if (l != T (0)) |
1687 | { |
1688 | // |
1689 | // Do not replace the divisions by l with multiplications by 1/l. |
1690 | // Computing 1/l can overflow but the divisions below will always |
1691 | // produce results less than or equal to 1. |
1692 | // |
1693 | |
1694 | x /= l; |
1695 | y /= l; |
1696 | z /= l; |
1697 | } |
1698 | |
1699 | return *this; |
1700 | } |
1701 | |
1702 | template <class T> |
1703 | const Vec3<T> & |
1704 | Vec3<T>::normalizeExc () throw (IEX_NAMESPACE::MathExc) |
1705 | { |
1706 | T l = length(); |
1707 | |
1708 | if (l == T (0)) |
1709 | throw NullVecExc ("Cannot normalize null vector." ); |
1710 | |
1711 | x /= l; |
1712 | y /= l; |
1713 | z /= l; |
1714 | return *this; |
1715 | } |
1716 | |
1717 | template <class T> |
1718 | inline |
1719 | const Vec3<T> & |
1720 | Vec3<T>::normalizeNonNull () |
1721 | { |
1722 | T l = length(); |
1723 | x /= l; |
1724 | y /= l; |
1725 | z /= l; |
1726 | return *this; |
1727 | } |
1728 | |
1729 | template <class T> |
1730 | Vec3<T> |
1731 | Vec3<T>::normalized () const |
1732 | { |
1733 | T l = length(); |
1734 | |
1735 | if (l == T (0)) |
1736 | return Vec3 (T (0)); |
1737 | |
1738 | return Vec3 (x / l, y / l, z / l); |
1739 | } |
1740 | |
1741 | template <class T> |
1742 | Vec3<T> |
1743 | Vec3<T>::normalizedExc () const throw (IEX_NAMESPACE::MathExc) |
1744 | { |
1745 | T l = length(); |
1746 | |
1747 | if (l == T (0)) |
1748 | throw NullVecExc ("Cannot normalize null vector." ); |
1749 | |
1750 | return Vec3 (x / l, y / l, z / l); |
1751 | } |
1752 | |
1753 | template <class T> |
1754 | inline |
1755 | Vec3<T> |
1756 | Vec3<T>::normalizedNonNull () const |
1757 | { |
1758 | T l = length(); |
1759 | return Vec3 (x / l, y / l, z / l); |
1760 | } |
1761 | |
1762 | |
1763 | //----------------------- |
1764 | // Implementation of Vec4 |
1765 | //----------------------- |
1766 | |
1767 | template <class T> |
1768 | inline T & |
1769 | Vec4<T>::operator [] (int i) |
1770 | { |
1771 | return (&x)[i]; |
1772 | } |
1773 | |
1774 | template <class T> |
1775 | inline const T & |
1776 | Vec4<T>::operator [] (int i) const |
1777 | { |
1778 | return (&x)[i]; |
1779 | } |
1780 | |
1781 | template <class T> |
1782 | inline |
1783 | Vec4<T>::Vec4 () |
1784 | { |
1785 | // empty |
1786 | } |
1787 | |
1788 | template <class T> |
1789 | inline |
1790 | Vec4<T>::Vec4 (T a) |
1791 | { |
1792 | x = y = z = w = a; |
1793 | } |
1794 | |
1795 | template <class T> |
1796 | inline |
1797 | Vec4<T>::Vec4 (T a, T b, T c, T d) |
1798 | { |
1799 | x = a; |
1800 | y = b; |
1801 | z = c; |
1802 | w = d; |
1803 | } |
1804 | |
1805 | template <class T> |
1806 | inline |
1807 | Vec4<T>::Vec4 (const Vec4 &v) |
1808 | { |
1809 | x = v.x; |
1810 | y = v.y; |
1811 | z = v.z; |
1812 | w = v.w; |
1813 | } |
1814 | |
1815 | template <class T> |
1816 | template <class S> |
1817 | inline |
1818 | Vec4<T>::Vec4 (const Vec4<S> &v) |
1819 | { |
1820 | x = T (v.x); |
1821 | y = T (v.y); |
1822 | z = T (v.z); |
1823 | w = T (v.w); |
1824 | } |
1825 | |
1826 | template <class T> |
1827 | inline const Vec4<T> & |
1828 | Vec4<T>::operator = (const Vec4 &v) |
1829 | { |
1830 | x = v.x; |
1831 | y = v.y; |
1832 | z = v.z; |
1833 | w = v.w; |
1834 | return *this; |
1835 | } |
1836 | |
1837 | template <class T> |
1838 | template <class S> |
1839 | inline |
1840 | Vec4<T>::Vec4 (const Vec3<S> &v) |
1841 | { |
1842 | x = T (v.x); |
1843 | y = T (v.y); |
1844 | z = T (v.z); |
1845 | w = T (1); |
1846 | } |
1847 | |
1848 | template <class T> |
1849 | template <class S> |
1850 | inline bool |
1851 | Vec4<T>::operator == (const Vec4<S> &v) const |
1852 | { |
1853 | return x == v.x && y == v.y && z == v.z && w == v.w; |
1854 | } |
1855 | |
1856 | template <class T> |
1857 | template <class S> |
1858 | inline bool |
1859 | Vec4<T>::operator != (const Vec4<S> &v) const |
1860 | { |
1861 | return x != v.x || y != v.y || z != v.z || w != v.w; |
1862 | } |
1863 | |
1864 | template <class T> |
1865 | bool |
1866 | Vec4<T>::equalWithAbsError (const Vec4<T> &v, T e) const |
1867 | { |
1868 | for (int i = 0; i < 4; i++) |
1869 | if (!IMATH_INTERNAL_NAMESPACE::equalWithAbsError ((*this)[i], v[i], e)) |
1870 | return false; |
1871 | |
1872 | return true; |
1873 | } |
1874 | |
1875 | template <class T> |
1876 | bool |
1877 | Vec4<T>::equalWithRelError (const Vec4<T> &v, T e) const |
1878 | { |
1879 | for (int i = 0; i < 4; i++) |
1880 | if (!IMATH_INTERNAL_NAMESPACE::equalWithRelError ((*this)[i], v[i], e)) |
1881 | return false; |
1882 | |
1883 | return true; |
1884 | } |
1885 | |
1886 | template <class T> |
1887 | inline T |
1888 | Vec4<T>::dot (const Vec4 &v) const |
1889 | { |
1890 | return x * v.x + y * v.y + z * v.z + w * v.w; |
1891 | } |
1892 | |
1893 | template <class T> |
1894 | inline T |
1895 | Vec4<T>::operator ^ (const Vec4 &v) const |
1896 | { |
1897 | return dot (v); |
1898 | } |
1899 | |
1900 | |
1901 | template <class T> |
1902 | inline const Vec4<T> & |
1903 | Vec4<T>::operator += (const Vec4 &v) |
1904 | { |
1905 | x += v.x; |
1906 | y += v.y; |
1907 | z += v.z; |
1908 | w += v.w; |
1909 | return *this; |
1910 | } |
1911 | |
1912 | template <class T> |
1913 | inline Vec4<T> |
1914 | Vec4<T>::operator + (const Vec4 &v) const |
1915 | { |
1916 | return Vec4 (x + v.x, y + v.y, z + v.z, w + v.w); |
1917 | } |
1918 | |
1919 | template <class T> |
1920 | inline const Vec4<T> & |
1921 | Vec4<T>::operator -= (const Vec4 &v) |
1922 | { |
1923 | x -= v.x; |
1924 | y -= v.y; |
1925 | z -= v.z; |
1926 | w -= v.w; |
1927 | return *this; |
1928 | } |
1929 | |
1930 | template <class T> |
1931 | inline Vec4<T> |
1932 | Vec4<T>::operator - (const Vec4 &v) const |
1933 | { |
1934 | return Vec4 (x - v.x, y - v.y, z - v.z, w - v.w); |
1935 | } |
1936 | |
1937 | template <class T> |
1938 | inline Vec4<T> |
1939 | Vec4<T>::operator - () const |
1940 | { |
1941 | return Vec4 (-x, -y, -z, -w); |
1942 | } |
1943 | |
1944 | template <class T> |
1945 | inline const Vec4<T> & |
1946 | Vec4<T>::negate () |
1947 | { |
1948 | x = -x; |
1949 | y = -y; |
1950 | z = -z; |
1951 | w = -w; |
1952 | return *this; |
1953 | } |
1954 | |
1955 | template <class T> |
1956 | inline const Vec4<T> & |
1957 | Vec4<T>::operator *= (const Vec4 &v) |
1958 | { |
1959 | x *= v.x; |
1960 | y *= v.y; |
1961 | z *= v.z; |
1962 | w *= v.w; |
1963 | return *this; |
1964 | } |
1965 | |
1966 | template <class T> |
1967 | inline const Vec4<T> & |
1968 | Vec4<T>::operator *= (T a) |
1969 | { |
1970 | x *= a; |
1971 | y *= a; |
1972 | z *= a; |
1973 | w *= a; |
1974 | return *this; |
1975 | } |
1976 | |
1977 | template <class T> |
1978 | inline Vec4<T> |
1979 | Vec4<T>::operator * (const Vec4 &v) const |
1980 | { |
1981 | return Vec4 (x * v.x, y * v.y, z * v.z, w * v.w); |
1982 | } |
1983 | |
1984 | template <class T> |
1985 | inline Vec4<T> |
1986 | Vec4<T>::operator * (T a) const |
1987 | { |
1988 | return Vec4 (x * a, y * a, z * a, w * a); |
1989 | } |
1990 | |
1991 | template <class T> |
1992 | inline const Vec4<T> & |
1993 | Vec4<T>::operator /= (const Vec4 &v) |
1994 | { |
1995 | x /= v.x; |
1996 | y /= v.y; |
1997 | z /= v.z; |
1998 | w /= v.w; |
1999 | return *this; |
2000 | } |
2001 | |
2002 | template <class T> |
2003 | inline const Vec4<T> & |
2004 | Vec4<T>::operator /= (T a) |
2005 | { |
2006 | x /= a; |
2007 | y /= a; |
2008 | z /= a; |
2009 | w /= a; |
2010 | return *this; |
2011 | } |
2012 | |
2013 | template <class T> |
2014 | inline Vec4<T> |
2015 | Vec4<T>::operator / (const Vec4 &v) const |
2016 | { |
2017 | return Vec4 (x / v.x, y / v.y, z / v.z, w / v.w); |
2018 | } |
2019 | |
2020 | template <class T> |
2021 | inline Vec4<T> |
2022 | Vec4<T>::operator / (T a) const |
2023 | { |
2024 | return Vec4 (x / a, y / a, z / a, w / a); |
2025 | } |
2026 | |
2027 | template <class T> |
2028 | T |
2029 | Vec4<T>::lengthTiny () const |
2030 | { |
2031 | T absX = (x >= T (0))? x: -x; |
2032 | T absY = (y >= T (0))? y: -y; |
2033 | T absZ = (z >= T (0))? z: -z; |
2034 | T absW = (w >= T (0))? w: -w; |
2035 | |
2036 | T max = absX; |
2037 | |
2038 | if (max < absY) |
2039 | max = absY; |
2040 | |
2041 | if (max < absZ) |
2042 | max = absZ; |
2043 | |
2044 | if (max < absW) |
2045 | max = absW; |
2046 | |
2047 | if (max == T (0)) |
2048 | return T (0); |
2049 | |
2050 | // |
2051 | // Do not replace the divisions by max with multiplications by 1/max. |
2052 | // Computing 1/max can overflow but the divisions below will always |
2053 | // produce results less than or equal to 1. |
2054 | // |
2055 | |
2056 | absX /= max; |
2057 | absY /= max; |
2058 | absZ /= max; |
2059 | absW /= max; |
2060 | |
2061 | return max * |
2062 | Math<T>::sqrt (absX * absX + absY * absY + absZ * absZ + absW * absW); |
2063 | } |
2064 | |
2065 | template <class T> |
2066 | inline T |
2067 | Vec4<T>::length () const |
2068 | { |
2069 | T length2 = dot (*this); |
2070 | |
2071 | if (length2 < T (2) * limits<T>::smallest()) |
2072 | return lengthTiny(); |
2073 | |
2074 | return Math<T>::sqrt (length2); |
2075 | } |
2076 | |
2077 | template <class T> |
2078 | inline T |
2079 | Vec4<T>::length2 () const |
2080 | { |
2081 | return dot (*this); |
2082 | } |
2083 | |
2084 | template <class T> |
2085 | const Vec4<T> & |
2086 | Vec4<T>::normalize () |
2087 | { |
2088 | T l = length(); |
2089 | |
2090 | if (l != T (0)) |
2091 | { |
2092 | // |
2093 | // Do not replace the divisions by l with multiplications by 1/l. |
2094 | // Computing 1/l can overflow but the divisions below will always |
2095 | // produce results less than or equal to 1. |
2096 | // |
2097 | |
2098 | x /= l; |
2099 | y /= l; |
2100 | z /= l; |
2101 | w /= l; |
2102 | } |
2103 | |
2104 | return *this; |
2105 | } |
2106 | |
2107 | template <class T> |
2108 | const Vec4<T> & |
2109 | Vec4<T>::normalizeExc () throw (IEX_NAMESPACE::MathExc) |
2110 | { |
2111 | T l = length(); |
2112 | |
2113 | if (l == T (0)) |
2114 | throw NullVecExc ("Cannot normalize null vector." ); |
2115 | |
2116 | x /= l; |
2117 | y /= l; |
2118 | z /= l; |
2119 | w /= l; |
2120 | return *this; |
2121 | } |
2122 | |
2123 | template <class T> |
2124 | inline |
2125 | const Vec4<T> & |
2126 | Vec4<T>::normalizeNonNull () |
2127 | { |
2128 | T l = length(); |
2129 | x /= l; |
2130 | y /= l; |
2131 | z /= l; |
2132 | w /= l; |
2133 | return *this; |
2134 | } |
2135 | |
2136 | template <class T> |
2137 | Vec4<T> |
2138 | Vec4<T>::normalized () const |
2139 | { |
2140 | T l = length(); |
2141 | |
2142 | if (l == T (0)) |
2143 | return Vec4 (T (0)); |
2144 | |
2145 | return Vec4 (x / l, y / l, z / l, w / l); |
2146 | } |
2147 | |
2148 | template <class T> |
2149 | Vec4<T> |
2150 | Vec4<T>::normalizedExc () const throw (IEX_NAMESPACE::MathExc) |
2151 | { |
2152 | T l = length(); |
2153 | |
2154 | if (l == T (0)) |
2155 | throw NullVecExc ("Cannot normalize null vector." ); |
2156 | |
2157 | return Vec4 (x / l, y / l, z / l, w / l); |
2158 | } |
2159 | |
2160 | template <class T> |
2161 | inline |
2162 | Vec4<T> |
2163 | Vec4<T>::normalizedNonNull () const |
2164 | { |
2165 | T l = length(); |
2166 | return Vec4 (x / l, y / l, z / l, w / l); |
2167 | } |
2168 | |
2169 | //----------------------------- |
2170 | // Stream output implementation |
2171 | //----------------------------- |
2172 | |
2173 | template <class T> |
2174 | std::ostream & |
2175 | operator << (std::ostream &s, const Vec2<T> &v) |
2176 | { |
2177 | return s << '(' << v.x << ' ' << v.y << ')'; |
2178 | } |
2179 | |
2180 | template <class T> |
2181 | std::ostream & |
2182 | operator << (std::ostream &s, const Vec3<T> &v) |
2183 | { |
2184 | return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ')'; |
2185 | } |
2186 | |
2187 | template <class T> |
2188 | std::ostream & |
2189 | operator << (std::ostream &s, const Vec4<T> &v) |
2190 | { |
2191 | return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ' ' << v.w << ')'; |
2192 | } |
2193 | |
2194 | |
2195 | //----------------------------------------- |
2196 | // Implementation of reverse multiplication |
2197 | //----------------------------------------- |
2198 | |
2199 | template <class T> |
2200 | inline Vec2<T> |
2201 | operator * (T a, const Vec2<T> &v) |
2202 | { |
2203 | return Vec2<T> (a * v.x, a * v.y); |
2204 | } |
2205 | |
2206 | template <class T> |
2207 | inline Vec3<T> |
2208 | operator * (T a, const Vec3<T> &v) |
2209 | { |
2210 | return Vec3<T> (a * v.x, a * v.y, a * v.z); |
2211 | } |
2212 | |
2213 | template <class T> |
2214 | inline Vec4<T> |
2215 | operator * (T a, const Vec4<T> &v) |
2216 | { |
2217 | return Vec4<T> (a * v.x, a * v.y, a * v.z, a * v.w); |
2218 | } |
2219 | |
2220 | |
2221 | #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER |
2222 | #pragma warning(pop) |
2223 | #endif |
2224 | |
2225 | IMATH_INTERNAL_NAMESPACE_HEADER_EXIT |
2226 | |
2227 | #endif // INCLUDED_IMATHVEC_H |
2228 | |