|
BWAPI
|
00001 // Copyright (c) 1999 Utrecht University (The Netherlands), 00002 // ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany), 00003 // INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg 00004 // (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria), 00005 // and Tel-Aviv University (Israel). All rights reserved. 00006 // 00007 // This file is part of CGAL (www.cgal.org); you can redistribute it and/or 00008 // modify it under the terms of the GNU Lesser General Public License as 00009 // published by the Free Software Foundation; version 2.1 of the License. 00010 // See the file LICENSE.LGPL distributed with CGAL. 00011 // 00012 // Licensees holding a valid commercial license may use this file in 00013 // accordance with the commercial license agreement provided with the software. 00014 // 00015 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE 00016 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. 00017 // 00018 // $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h $ 00019 // $Id: Aff_transformationH3.h 42811 2008-04-09 13:35:34Z spion $ 00020 // 00021 // 00022 // Author(s) : Stefan Schirra 00023 00024 #ifndef CGAL_AFF_TRANSFORMATIONH3_H 00025 #define CGAL_AFF_TRANSFORMATIONH3_H 00026 00027 #include <CGAL/Handle_for_virtual.h> 00028 #include <CGAL/determinant.h> 00029 00030 CGAL_BEGIN_NAMESPACE 00031 00032 // forward declaration 00033 template < class R > 00034 class Aff_transformationH3; 00035 00036 template < class R > 00037 class Aff_transformation_repH3; 00038 00039 template < class R > 00040 std::ostream & 00041 operator<< ( std::ostream & out, 00042 const Aff_transformationH3<R>& t); 00043 00044 template < class R > 00045 Aff_transformationH3<R> 00046 _general_transformation_composition ( 00047 Aff_transformation_repH3<R> l, 00048 Aff_transformation_repH3<R> r); 00049 00050 template <class R_ > 00051 class Aff_transformation_rep_baseH3 : public Ref_counted_virtual 00052 // abstract base class of aff transformation representations 00053 { 00054 public: 00055 typedef R_ R; 00056 typedef typename R::FT FT; 00057 typedef typename R::RT RT; 00058 typedef typename R::Point_3 Point_3; 00059 typedef typename R::Vector_3 Vector_3; 00060 typedef typename R::Direction_3 Direction_3; 00061 typedef typename R::Plane_3 Plane_3; 00062 typedef typename R::Aff_transformation_3 Aff_transformation_3; 00063 00064 virtual ~Aff_transformation_rep_baseH3(){} 00065 00066 virtual Point_3 00067 transform(const Point_3&) const = 0; 00068 00069 virtual Vector_3 00070 transform(const Vector_3&) const = 0; 00071 00072 virtual Direction_3 00073 transform(const Direction_3&) const = 0; 00074 00075 virtual Plane_3 00076 transform(const Plane_3&) const = 0; 00077 00078 virtual Aff_transformation_3 00079 inverse() const = 0; 00080 00081 virtual Aff_transformation_3 00082 transpose() const = 0; 00083 00084 virtual Aff_transformation_repH3<R> 00085 general_form() const = 0; 00086 00087 virtual bool 00088 is_even() const = 0; 00089 00090 virtual RT 00091 homogeneous(int i, int j) const = 0; 00092 00093 virtual FT 00094 cartesian(int i, int j) const = 0; 00095 }; 00096 00097 template < class R_ > 00098 class Aff_transformation_repH3 : public Aff_transformation_rep_baseH3<R_> 00099 { 00100 typedef typename R_::FT FT; 00101 typedef typename R_::RT RT; 00102 typedef typename R_::Point_3 Point_3; 00103 typedef typename R_::Vector_3 Vector_3; 00104 typedef typename R_::Direction_3 Direction_3; 00105 typedef typename R_::Plane_3 Plane_3; 00106 typedef typename R_::Aff_transformation_3 Aff_transformation_3; 00107 00108 public: 00109 typedef R_ R; 00110 00111 Aff_transformation_repH3() {} 00112 00113 Aff_transformation_repH3( 00114 const RT& m00, const RT& m01, const RT& m02, const RT& m03, 00115 const RT& m10, const RT& m11, const RT& m12, const RT& m13, 00116 const RT& m20, const RT& m21, const RT& m22, const RT& m23, 00117 const RT& m33); 00118 virtual ~Aff_transformation_repH3() {} 00119 00120 virtual Point_3 00121 transform(const Point_3& p) const; 00122 00123 virtual Vector_3 00124 transform(const Vector_3& v) const; 00125 00126 virtual Direction_3 00127 transform(const Direction_3& dir) const; 00128 00129 virtual Plane_3 00130 transform(const Plane_3& pl) const; 00131 00132 virtual Aff_transformation_3 00133 inverse() const; 00134 00135 virtual Aff_transformation_repH3<R> 00136 general_form() const; 00137 00138 virtual Aff_transformation_3 00139 transpose() const; 00140 00141 virtual bool 00142 is_even() const; 00143 00144 virtual RT 00145 homogeneous(int i, int j) const ; 00146 00147 virtual FT 00148 cartesian(int i, int j) const ; 00149 00150 friend class Aff_transformationH3<R>; 00151 00152 friend 00153 Aff_transformationH3<R> 00154 _general_transformation_composition <> ( 00155 Aff_transformation_repH3<R> l, 00156 Aff_transformation_repH3<R> r); 00157 00158 friend 00159 std::ostream & 00160 operator<< <> (std::ostream & out, const Aff_transformationH3<R>& t); 00161 00162 private: 00163 RT t00, t01, t02, t03; 00164 RT t10, t11, t12, t13; 00165 RT t20, t21, t22, t23; 00166 RT t33; 00167 }; 00168 00169 template < class R_ > 00170 class Identity_repH3 : public Aff_transformation_rep_baseH3<R_> 00171 { 00172 typedef typename R_::RT RT; 00173 typedef typename R_::FT FT; 00174 typedef typename R_::Point_3 Point_3; 00175 typedef typename R_::Vector_3 Vector_3; 00176 typedef typename R_::Direction_3 Direction_3; 00177 typedef typename R_::Plane_3 Plane_3; 00178 typedef typename R_::Aff_transformation_3 Aff_transformation_3; 00179 00180 public: 00181 typedef R_ R; 00182 00183 Identity_repH3() 00184 {} 00185 00186 virtual ~Identity_repH3() 00187 {} 00188 00189 virtual Point_3 00190 transform(const Point_3& p) const 00191 { return p; } 00192 00193 virtual Vector_3 00194 transform(const Vector_3& v) const 00195 { return v; } 00196 00197 virtual Direction_3 00198 transform(const Direction_3& dir) const 00199 { return dir; } 00200 00201 virtual Plane_3 00202 transform(const Plane_3& pl) const 00203 { return pl; } 00204 00205 virtual Aff_transformation_3 00206 inverse() const 00207 { return Aff_transformation_3( IDENTITY); } 00208 00209 virtual Aff_transformation_repH3<R> 00210 general_form() const; 00211 00212 virtual Aff_transformation_3 00213 transpose() const 00214 { return Aff_transformation_3( IDENTITY); } 00215 00216 virtual bool 00217 is_even() const 00218 { return true; } 00219 00220 virtual RT 00221 homogeneous(int i, int j) const 00222 { return (i==j) ? RT(1) : RT(0); } 00223 00224 virtual FT 00225 cartesian(int i, int j) const 00226 { return (i==j) ? FT(1) : FT(0); } 00227 }; 00228 00229 template < class R_ > 00230 class Translation_repH3 : public Aff_transformation_rep_baseH3<R_> 00231 { 00232 typedef typename R_::FT FT; 00233 typedef typename R_::RT RT; 00234 typedef typename R_::Point_3 Point_3; 00235 typedef typename R_::Vector_3 Vector_3; 00236 typedef typename R_::Direction_3 Direction_3; 00237 typedef typename R_::Plane_3 Plane_3; 00238 typedef typename R_::Aff_transformation_3 Aff_transformation_3; 00239 00240 public: 00241 typedef R_ R; 00242 00243 Translation_repH3( const Vector_3& v); 00244 00245 virtual ~Translation_repH3() {} 00246 00247 00248 virtual Point_3 00249 transform(const Point_3& p) const; 00250 00251 virtual Vector_3 00252 transform(const Vector_3& v) const; 00253 00254 virtual Direction_3 00255 transform(const Direction_3& dir) const; 00256 00257 virtual Plane_3 00258 transform(const Plane_3& pl) const; 00259 00260 virtual Aff_transformation_3 00261 inverse() const; 00262 00263 virtual Aff_transformation_repH3<R> 00264 general_form() const; 00265 00266 virtual Aff_transformation_3 00267 transpose() const; 00268 00269 virtual bool 00270 is_even() const; 00271 00272 virtual RT 00273 homogeneous(int i, int j) const ; 00274 00275 virtual FT 00276 cartesian(int i, int j) const ; 00277 00278 friend class Aff_transformationH3<R>; 00279 00280 private: 00281 Vector_3 tv; 00282 }; 00283 00284 template < class R_ > 00285 class Aff_transformationH3 00286 : public Handle_for_virtual< Aff_transformation_rep_baseH3<R_> > 00287 { 00288 typedef typename R_::RT RT; 00289 typedef typename R_::FT FT; 00290 typedef typename R_::Point_3 Point_3; 00291 typedef typename R_::Vector_3 Vector_3; 00292 typedef typename R_::Direction_3 Direction_3; 00293 typedef typename R_::Plane_3 Plane_3; 00294 typedef typename R_::Aff_transformation_3 Aff_transformation_3; 00295 00296 public: 00297 typedef R_ R; 00298 00299 Aff_transformationH3(); 00300 00301 // Identity 00302 Aff_transformationH3(const Identity_transformation&); 00303 00304 // Translation 00305 Aff_transformationH3(const Translation& , const Vector_3& v); 00306 00307 // Scaling 00308 Aff_transformationH3(const Scaling&, const RT& num, const RT& den); 00309 00310 // General form 00311 Aff_transformationH3( 00312 const RT& m00, const RT& m01, const RT& m02, const RT& m03, 00313 const RT& m10, const RT& m11, const RT& m12, const RT& m13, 00314 const RT& m20, const RT& m21, const RT& m22, const RT& m23, 00315 const RT& m33); 00316 Aff_transformationH3( 00317 const RT& m00, const RT& m01, const RT& m02, 00318 const RT& m10, const RT& m11, const RT& m12, 00319 const RT& m20, const RT& m21, const RT& m22, 00320 const RT& m33); 00321 00322 Point_3 00323 transform(const Point_3& p) const; 00324 00325 Vector_3 00326 transform(const Vector_3& v) const; 00327 00328 Direction_3 00329 transform(const Direction_3& d) const; 00330 00331 Plane_3 00332 transform(const Plane_3& pl) const; 00333 00334 Aff_transformation_3 00335 inverse() const; 00336 00337 Aff_transformationH3<R> 00338 transpose() const; 00339 00340 bool 00341 is_even() const; 00342 00343 bool 00344 is_odd() const; 00345 00346 FT 00347 cartesian(int i, int j) const 00348 { return this->Ptr()->cartesian(i,j); } 00349 00350 RT 00351 homogeneous(int i, int j) const 00352 { return this->Ptr()->homogeneous(i,j); } 00353 00354 FT 00355 m(int i, int j) const 00356 { return this->Ptr()->cartesian(i,j); } 00357 00358 RT 00359 hm(int i, int j) const 00360 { return this->Ptr()->homogeneous(i,j); } 00361 }; 00362 00363 template < class R > 00364 CGAL_KERNEL_INLINE 00365 Aff_transformation_repH3<R>::Aff_transformation_repH3( 00366 const RT& m00, const RT& m01, const RT& m02, const RT& m03, 00367 const RT& m10, const RT& m11, const RT& m12, const RT& m13, 00368 const RT& m20, const RT& m21, const RT& m22, const RT& m23, 00369 const RT& m33) 00370 : t00(m00), t01(m01), t02(m02), t03(m03), 00371 t10(m10), t11(m11), t12(m12), t13(m13), 00372 t20(m20), t21(m21), t22(m22), t23(m23), 00373 t33(m33) 00374 {} 00375 00376 template < class R > 00377 CGAL_KERNEL_INLINE 00378 typename Aff_transformation_repH3<R>::Point_3 00379 Aff_transformation_repH3<R>:: 00380 transform(const typename Aff_transformation_repH3<R>::Point_3& p) const 00381 { 00382 return Point_3(t00 * p.hx() + t01 * p.hy() + t02 * p.hz() + t03 * p.hw(), 00383 t10 * p.hx() + t11 * p.hy() + t12 * p.hz() + t13 * p.hw(), 00384 t20 * p.hx() + t21 * p.hy() + t22 * p.hz() + t23 * p.hw(), 00385 t33 * p.hw()); 00386 } 00387 00388 template < class R > 00389 CGAL_KERNEL_INLINE 00390 typename Aff_transformation_repH3<R>::Vector_3 00391 Aff_transformation_repH3<R>:: 00392 transform(const typename Aff_transformation_repH3<R>::Vector_3& v) const 00393 { 00394 return Vector_3(t00 * v.hx() + t01 * v.hy() + t02 * v.hz(), 00395 t10 * v.hx() + t11 * v.hy() + t12 * v.hz(), 00396 t20 * v.hx() + t21 * v.hy() + t22 * v.hz(), 00397 t33 * v.hw() ); 00398 } 00399 00400 template < class R > 00401 CGAL_KERNEL_INLINE 00402 typename Aff_transformation_repH3<R>::Direction_3 00403 Aff_transformation_repH3<R>:: 00404 transform(const typename Aff_transformation_repH3<R>::Direction_3& d) const 00405 { 00406 if (t33 > RT(0)) 00407 return Direction_3(t00 * d.hx() + t01 * d.hy() + t02 * d.hz(), 00408 t10 * d.hx() + t11 * d.hy() + t12 * d.hz(), 00409 t20 * d.hx() + t21 * d.hy() + t22 * d.hz()); 00410 else 00411 return - Direction_3(t00 * d.hx() + t01 * d.hy() + t02 * d.hz(), 00412 t10 * d.hx() + t11 * d.hy() + t12 * d.hz(), 00413 t20 * d.hx() + t21 * d.hy() + t22 * d.hz()); 00414 } 00415 00416 template < class R > 00417 CGAL_KERNEL_INLINE 00418 typename Aff_transformation_repH3<R>::Plane_3 00419 Aff_transformation_repH3<R>:: 00420 transform(const typename Aff_transformation_repH3<R>::Plane_3& pl) const 00421 { 00422 if ( is_even() ) 00423 { 00424 return Plane_3( 00425 transform(pl.point() ), 00426 transpose().inverse().transform(pl.orthogonal_direction() )); 00427 } 00428 else 00429 { 00430 return Plane_3( 00431 transform(pl.point() ), 00432 -(transpose().inverse().transform(pl.orthogonal_direction() ))); 00433 } 00434 } 00435 00436 template < class R > 00437 CGAL_KERNEL_INLINE 00438 typename Aff_transformation_repH3<R>::Aff_transformation_3 00439 Aff_transformation_repH3<R>::inverse() const 00440 { 00441 typedef typename R::RT RT; 00442 const RT RT0(0); 00443 return Aff_transformation_3( 00444 determinant( t11, t12, t13, 00445 t21, t22, t23, // i 00 00446 RT0, RT0, t33 ), 00447 00448 - determinant( t01, t02, t03, 00449 t21, t22, t23, // i 01 00450 RT0, RT0, t33 ), 00451 00452 determinant( t01, t02, t03, 00453 t11, t12, t13, // i 02 00454 RT0, RT0, t33 ), 00455 00456 - determinant( t01, t02, t03, 00457 t11, t12, t13, // i 03 00458 t21, t22, t23 ), 00459 00460 00461 - determinant( t10, t12, t13, 00462 t20, t22, t23, // i 10 00463 RT0, RT0, t33 ), 00464 00465 determinant( t00, t02, t03, 00466 t20, t22, t23, // i 11 00467 RT0, RT0, t33 ), 00468 00469 - determinant( t00, t02, t03, 00470 t10, t12, t13, // i 12 00471 RT0, RT0, t33 ), 00472 00473 determinant( t00, t02, t03, 00474 t10, t12, t13, // i 13 00475 t20, t22, t23 ), 00476 00477 00478 determinant( t10, t11, t13, 00479 t20, t21, t23, // i 20 00480 RT0, RT0, t33 ), 00481 00482 - determinant( t00, t01, t03, 00483 t20, t21, t23, // i 21 00484 RT0, RT0, t33 ), 00485 00486 determinant( t00, t01, t03, 00487 t10, t11, t13, // i 22 00488 RT0, RT0, t33 ), 00489 00490 - determinant( t00, t01, t03, 00491 t10, t11, t13, // i 23 00492 t20, t21, t23 ), 00493 00494 00495 determinant( t00, t01, t02, 00496 t10, t11, t12, // i 33 00497 t20, t21, t22 ) 00498 ) ; 00499 } 00500 00501 template < class R > 00502 inline 00503 Aff_transformation_repH3<R> 00504 Aff_transformation_repH3<R>::general_form() const 00505 { return *this; } 00506 00507 template < class R > 00508 CGAL_KERNEL_INLINE 00509 typename Aff_transformation_repH3<R>::Aff_transformation_3 00510 Aff_transformation_repH3<R>::transpose() const 00511 { 00512 typedef typename R::RT RT; 00513 const RT RT0(0); 00514 return Aff_transformation_3( t00, t10, t20, RT0, 00515 t01, t11, t21, RT0, 00516 t02, t12, t22, RT0, 00517 t33); 00518 } 00519 00520 template < class R > 00521 CGAL_KERNEL_INLINE 00522 bool 00523 Aff_transformation_repH3<R>::is_even() const 00524 { 00525 return (CGAL_NTS sign<RT>( t33 * 00526 determinant(t00, t01, t02, 00527 t10, t11, t12, 00528 t20, t21, t22 ) ) == POSITIVE ); 00529 } 00530 00531 template < class R > 00532 CGAL_KERNEL_LARGE_INLINE 00533 typename Aff_transformation_repH3<R>::RT 00534 Aff_transformation_repH3<R>:: 00535 homogeneous(int i, int j) const 00536 { 00537 typedef typename R::RT RT; 00538 CGAL_kernel_precondition( (i >= 0) && (i <= 3) && (j >= 0) && (j <= 3) ); 00539 const RT RT0(0); 00540 switch (i) 00541 { 00542 case 0: switch (j) 00543 { 00544 case 0: return t00; 00545 case 1: return t01; 00546 case 2: return t02; 00547 case 3: return t03; 00548 } 00549 case 1: switch (j) 00550 { 00551 case 0: return t10; 00552 case 1: return t11; 00553 case 2: return t12; 00554 case 3: return t13; 00555 } 00556 case 2: switch (j) 00557 { 00558 case 0: return t20; 00559 case 1: return t21; 00560 case 2: return t22; 00561 case 3: return t23; 00562 } 00563 case 3: switch (j) 00564 { 00565 case 0: return RT0; 00566 case 1: return RT0; 00567 case 2: return RT0; 00568 case 3: return t33; 00569 } 00570 } 00571 return RT0; 00572 } 00573 00574 template < class R > 00575 inline 00576 typename Aff_transformation_repH3<R>::FT 00577 Aff_transformation_repH3<R>:: 00578 cartesian(int i, int j) const 00579 { 00580 typedef typename R::FT FT; 00581 return FT(homogeneous(i,j)) / FT(t33); 00582 } 00583 00584 template <class R> 00585 Aff_transformation_repH3<R> 00586 Identity_repH3<R>::general_form() const 00587 { 00588 typedef typename R::RT RT; 00589 const RT RT0(0); 00590 const RT RT1(1); 00591 return Aff_transformation_repH3<R>(RT1, RT0, RT0, RT0, 00592 RT0, RT1, RT0, RT0, 00593 RT0, RT0, RT1, RT0, 00594 RT1 ); 00595 } 00596 00597 template < class R > 00598 inline 00599 Translation_repH3<R>:: 00600 Translation_repH3( const typename Translation_repH3<R>::Vector_3& v) 00601 : tv(v) 00602 {} 00603 00604 template < class R > 00605 CGAL_KERNEL_INLINE 00606 typename Translation_repH3<R>::Point_3 00607 Translation_repH3<R>:: 00608 transform(const typename Translation_repH3<R>::Point_3& p) const 00609 { 00610 return Point_3( tv.hw() * p.hx() + tv.hx() * p.hw(), 00611 tv.hw() * p.hy() + tv.hy() * p.hw(), 00612 tv.hw() * p.hz() + tv.hz() * p.hw(), 00613 tv.hw() * p.hw() ); 00614 } 00615 00616 template < class R > 00617 inline 00618 typename Translation_repH3<R>::Vector_3 00619 Translation_repH3<R>:: 00620 transform(const typename Translation_repH3<R>::Vector_3& v) const 00621 { return v; } 00622 00623 template < class R > 00624 inline 00625 typename Translation_repH3<R>::Direction_3 00626 Translation_repH3<R>:: 00627 transform(const typename Translation_repH3<R>::Direction_3& dir) const 00628 { return dir; } 00629 00630 template < class R > 00631 inline 00632 typename Translation_repH3<R>::Plane_3 00633 Translation_repH3<R>:: 00634 transform(const typename Translation_repH3<R>::Plane_3& pl) const 00635 { 00636 return Plane_3( transform( pl.point() ), pl.orthogonal_vector() ); 00637 } 00638 00639 template < class R > 00640 inline 00641 typename Translation_repH3<R>::Aff_transformation_3 00642 Translation_repH3<R>::inverse() const 00643 { return Aff_transformation_3(TRANSLATION, - tv ); } 00644 00645 template < class R > 00646 CGAL_KERNEL_INLINE 00647 Aff_transformation_repH3<R> 00648 Translation_repH3<R>::general_form() const 00649 { 00650 const RT RT0(0); 00651 return Aff_transformation_repH3<R>(tv.hw(), RT0, RT0, tv.hx(), 00652 RT0, tv.hw(), RT0, tv.hy(), 00653 RT0, RT0, tv.hw(), tv.hz(), 00654 tv.hw() ); 00655 } 00656 00657 template < class R > 00658 CGAL_KERNEL_INLINE 00659 typename Translation_repH3<R>::Aff_transformation_3 00660 Translation_repH3<R>::transpose() const 00661 { 00662 typedef typename R::RT RT; 00663 const RT RT0(0); 00664 const RT RT1(1); 00665 return Aff_transformation_3( RT1, RT0, RT0, RT0, 00666 RT0, RT1, RT0, RT0, 00667 RT0, RT0, RT1, RT0, 00668 RT1 ); 00669 } 00670 00671 template < class R > 00672 inline 00673 bool 00674 Translation_repH3<R>::is_even() const 00675 { return true; } 00676 00677 template < class R > 00678 CGAL_KERNEL_LARGE_INLINE 00679 typename Translation_repH3<R>::RT 00680 Translation_repH3<R>::homogeneous(int i, int j) const 00681 { 00682 CGAL_kernel_precondition( (i >= 0) && (i <= 3) && (j >= 0) && (j <= 3) ); 00683 const RT RT0(0); 00684 switch (i) 00685 { 00686 case 0: switch (j) 00687 { 00688 case 0: return tv.hw(); 00689 case 1: return RT0; 00690 case 2: return RT0; 00691 case 3: return tv.hx(); 00692 } 00693 case 1: switch (j) 00694 { 00695 case 0: return RT0; 00696 case 1: return tv.hw(); 00697 case 2: return RT0; 00698 case 3: return tv.hy(); 00699 } 00700 case 2: switch (j) 00701 { 00702 case 0: return RT0; 00703 case 1: return RT0; 00704 case 2: return tv.hw(); 00705 case 3: return tv.hz(); 00706 } 00707 case 3: switch (j) 00708 { 00709 case 0: return RT0; 00710 case 1: return RT0; 00711 case 2: return RT0; 00712 case 3: return tv.hw(); 00713 } 00714 } 00715 return RT0; 00716 } 00717 00718 template < class R > 00719 inline 00720 typename Translation_repH3<R>::FT 00721 Translation_repH3<R>:: 00722 cartesian(int i, int j) const 00723 { 00724 return FT(homogeneous(i,j)) / FT(tv.hw()); 00725 } 00726 00727 00728 template < class R > 00729 CGAL_KERNEL_INLINE 00730 Aff_transformationH3<R> 00731 _general_transformation_composition( 00732 Aff_transformation_repH3<R> l, 00733 Aff_transformation_repH3<R> r ) 00734 { 00735 return Aff_transformationH3<R>( 00736 l.t00*r.t00 + l.t01*r.t10 + l.t02*r.t20, 00737 l.t00*r.t01 + l.t01*r.t11 + l.t02*r.t21, 00738 l.t00*r.t02 + l.t01*r.t12 + l.t02*r.t22, 00739 l.t00*r.t03 + l.t01*r.t13 + l.t02*r.t23 + l.t03*r.t33, 00740 00741 l.t10*r.t00 + l.t11*r.t10 + l.t12*r.t20, 00742 l.t10*r.t01 + l.t11*r.t11 + l.t12*r.t21, 00743 l.t10*r.t02 + l.t11*r.t12 + l.t12*r.t22, 00744 l.t10*r.t03 + l.t11*r.t13 + l.t12*r.t23 + l.t13*r.t33, 00745 00746 l.t20*r.t00 + l.t21*r.t10 + l.t22*r.t20, 00747 l.t20*r.t01 + l.t21*r.t11 + l.t22*r.t21, 00748 l.t20*r.t02 + l.t21*r.t12 + l.t22*r.t22, 00749 l.t20*r.t03 + l.t21*r.t13 + l.t22*r.t23 + l.t23*r.t33, 00750 00751 l.t33*r.t33 ); 00752 } 00753 00754 template < class R > 00755 CGAL_KERNEL_INLINE 00756 Aff_transformationH3<R>::Aff_transformationH3() 00757 { initialize_with(Aff_transformation_repH3<R>()); } 00758 00759 template < class R > 00760 CGAL_KERNEL_INLINE 00761 Aff_transformationH3<R>:: 00762 Aff_transformationH3(const Identity_transformation&) 00763 { initialize_with(Identity_repH3<R>()); } 00764 00765 template < class R > 00766 CGAL_KERNEL_INLINE 00767 Aff_transformationH3<R>:: 00768 Aff_transformationH3(const Translation&, 00769 const typename Aff_transformationH3<R>::Vector_3& v) 00770 { initialize_with(Translation_repH3<R>( v )); } 00771 00772 template < class R > 00773 CGAL_KERNEL_INLINE 00774 Aff_transformationH3<R>:: 00775 Aff_transformationH3(const Scaling&, const RT& num, const RT& den) 00776 { 00777 const RT RT0(0); 00778 initialize_with(Aff_transformation_repH3<R>(num, RT0, RT0, RT0, 00779 RT0, num, RT0, RT0, 00780 RT0, RT0, num, RT0, 00781 den )); 00782 } 00783 00784 template < class R > 00785 CGAL_KERNEL_INLINE 00786 Aff_transformationH3<R>:: 00787 Aff_transformationH3( 00788 const RT& m00, const RT& m01, const RT& m02, const RT& m03, 00789 const RT& m10, const RT& m11, const RT& m12, const RT& m13, 00790 const RT& m20, const RT& m21, const RT& m22, const RT& m23, 00791 const RT& m33) 00792 { 00793 initialize_with(Aff_transformation_repH3<R>(m00, m01, m02, m03, 00794 m10, m11, m12, m13, 00795 m20, m21, m22, m23, 00796 m33 )); 00797 } 00798 00799 template < class R > 00800 CGAL_KERNEL_INLINE 00801 Aff_transformationH3<R>:: 00802 Aff_transformationH3( 00803 const RT& m00, const RT& m01, const RT& m02, 00804 const RT& m10, const RT& m11, const RT& m12, 00805 const RT& m20, const RT& m21, const RT& m22, 00806 const RT& m33) 00807 { 00808 const RT RT0 = RT(0); 00809 initialize_with(Aff_transformation_repH3<R>(m00, m01, m02, RT0, 00810 m10, m11, m12, RT0, 00811 m20, m21, m22, RT0, 00812 m33 )); 00813 } 00814 00815 template < class R > 00816 inline 00817 typename Aff_transformationH3<R>::Point_3 00818 Aff_transformationH3<R>:: 00819 transform(const typename Aff_transformationH3<R>::Point_3& p) const 00820 { return this->Ptr()->transform(p); } 00821 00822 template < class R > 00823 inline 00824 typename Aff_transformationH3<R>::Vector_3 00825 Aff_transformationH3<R>:: 00826 transform(const typename Aff_transformationH3<R>::Vector_3& v) const 00827 { return this->Ptr()->transform(v); } 00828 00829 template < class R > 00830 inline 00831 typename Aff_transformationH3<R>::Direction_3 00832 Aff_transformationH3<R>:: 00833 transform(const typename Aff_transformationH3<R>::Direction_3& d) const 00834 { return this->Ptr()->transform(d); } 00835 00836 template < class R > 00837 inline 00838 typename Aff_transformationH3<R>::Plane_3 00839 Aff_transformationH3<R>:: 00840 transform(const typename Aff_transformationH3<R>::Plane_3& pl) const 00841 { return this->Ptr()->transform(pl); } 00842 00843 template < class R > 00844 inline 00845 typename Aff_transformationH3<R>::Aff_transformation_3 00846 Aff_transformationH3<R>::inverse() const 00847 { return this->Ptr()->inverse(); } 00848 00849 template < class R > 00850 inline 00851 Aff_transformationH3<R> 00852 Aff_transformationH3<R>::transpose() const 00853 { return this->Ptr()->transpose(); } 00854 00855 template < class R > 00856 inline 00857 bool 00858 Aff_transformationH3<R>::is_even() const 00859 { return this->Ptr()->is_even(); } 00860 00861 template < class R > 00862 inline 00863 bool 00864 Aff_transformationH3<R>::is_odd() const 00865 { return ( ! (this->Ptr()->is_even() )); } 00866 00867 template < class R > 00868 CGAL_KERNEL_INLINE 00869 Aff_transformationH3<R> 00870 operator*(const Aff_transformationH3<R>& left_argument, 00871 const Aff_transformationH3<R>& right_argument ) 00872 { 00873 return _general_transformation_composition( 00874 left_argument.Ptr() ->general_form(), 00875 right_argument.Ptr()->general_form() ); 00876 } 00877 00878 template < class R > 00879 std::ostream & 00880 operator<< ( std::ostream & out, 00881 const Aff_transformationH3<R>& t) 00882 { 00883 typename R::RT RT0(0); 00884 Aff_transformation_repH3<R> r = t.Ptr()->general_form(); 00885 return out 00886 << "| "<< r.t00 <<' '<< r.t01 <<' '<< r.t02 <<' '<< r.t03 << " |\n" 00887 << "| "<< r.t10 <<' '<< r.t11 <<' '<< r.t12 <<' '<< r.t13 << " |\n" 00888 << "| "<< r.t20 <<' '<< r.t21 <<' '<< r.t22 <<' '<< r.t23 << " |\n" 00889 << "| "<< RT0 <<' '<< RT0 <<' '<< RT0 <<' '<< r.t33 << " |\n"; 00890 } 00891 00892 CGAL_END_NAMESPACE 00893 00894 #endif // CGAL_AFF_TRANSFORMATIONH3_H
1.7.6.1
