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00001 // Copyright (c) 2008 INRIA Sophia-Antipolis (France). 00002 // All rights reserved. 00003 // 00004 // This file is part of CGAL (www.cgal.org); you may redistribute it under 00005 // the terms of the Q Public License version 1.0. 00006 // See the file LICENSE.QPL distributed with CGAL. 00007 // 00008 // Licensees holding a valid commercial license may use this file in 00009 // accordance with the commercial license agreement provided with the software. 00010 // 00011 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE 00012 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. 00013 // 00014 // $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Circular_kernel_3/include/CGAL/Circular_kernel_3/internal_function_has_on_spherical_kernel.h $ 00015 // $Id: internal_function_has_on_spherical_kernel.h 50731 2009-07-21 09:08:07Z sloriot $ 00016 // 00017 // Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado, 00018 // Sebastien Loriot 00019 00020 // Partially supported by the IST Programme of the EU as a 00021 // STREP (FET Open) Project under Contract No IST-006413 00022 // (ACS -- Algorithms for Complex Shapes) 00023 00024 #ifndef CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H 00025 #define CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H 00026 00027 namespace CGAL { 00028 namespace SphericalFunctors { 00029 00030 template <class SK> 00031 inline 00032 bool 00033 has_on(const typename SK::Sphere_3 &a, 00034 const typename SK::Circular_arc_point_3 &p) 00035 { 00036 typedef typename SK::Algebraic_kernel Algebraic_kernel; 00037 typedef typename SK::Polynomial_for_spheres_2_3 Equation; 00038 Equation equation = get_equation<SK>(a); 00039 return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO); 00040 } 00041 00042 template <class SK> 00043 inline 00044 bool 00045 has_on(const typename SK::Plane_3 &a, 00046 const typename SK::Circular_arc_point_3 &p) 00047 { 00048 typedef typename SK::Algebraic_kernel Algebraic_kernel; 00049 typedef typename SK::Polynomial_1_3 Equation; 00050 Equation equation = get_equation<SK>(a); 00051 return (Algebraic_kernel().sign_at_object()(equation,p.rep().coordinates()) == ZERO); 00052 } 00053 00054 template <class SK> 00055 inline 00056 bool 00057 has_on(const typename SK::Line_3 &a, 00058 const typename SK::Circular_arc_point_3 &p) 00059 { 00060 typedef typename SK::Algebraic_kernel Algebraic_kernel; 00061 typedef typename SK::Polynomials_for_line_3 Equation; 00062 Equation equation = get_equation<SK>(a); 00063 return p.rep().coordinates().is_on_line(equation); 00064 } 00065 00066 template <class SK> 00067 inline 00068 bool 00069 has_on(const typename SK::Circle_3 &a, 00070 const typename SK::Circular_arc_point_3 &p) 00071 { 00072 return has_on<SK>(a.diametral_sphere(),p) && 00073 has_on<SK>(a.supporting_plane(),p); 00074 } 00075 00076 //duplicated code 00077 template <class SK> 00078 inline 00079 bool 00080 has_on(const typename SK::Circle_on_reference_sphere_3 &a, 00081 const typename SK::Point_3 &p) 00082 { 00083 return has_on<SK>(a.diametral_sphere(),p) && 00084 has_on<SK>(a.supporting_plane(),p); 00085 } 00086 00087 template <class SK> 00088 inline 00089 bool 00090 has_on(const typename SK::Circle_on_reference_sphere_3 &a, 00091 const typename SK::Circular_arc_point_on_reference_sphere_3 &p) 00092 { 00093 return has_on<SK>(a.diametral_sphere(),p) && 00094 has_on<SK>(a.supporting_plane(),p); 00095 } 00096 00097 template <class SK> 00098 inline 00099 bool 00100 has_on(const typename SK::Line_arc_3 &l, 00101 const typename SK::Circular_arc_point_3 &p, 00102 const bool has_on_supporting_line = false) 00103 { 00104 if(!has_on_supporting_line) { 00105 if(!has_on<SK>(l.supporting_line(), p)) { 00106 return false; 00107 } 00108 } 00109 return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO && 00110 SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO; 00111 } 00112 00113 template <class SK> 00114 inline 00115 bool 00116 has_on(const typename SK::Line_arc_3 &l, 00117 const typename SK::Point_3 &p, 00118 const bool has_on_supporting_line = false) 00119 { 00120 if(!has_on_supporting_line) { 00121 if(!has_on<SK>(l.supporting_line(), p)) { 00122 return false; 00123 } 00124 } 00125 return SK().compare_xyz_3_object()(l.lower_xyz_extremity(),p) <= ZERO && 00126 SK().compare_xyz_3_object()(p,l.higher_xyz_extremity()) <= ZERO; 00127 } 00128 00129 template <class SK> 00130 inline 00131 bool 00132 has_on(const typename SK::Plane_3 &p, 00133 const typename SK::Line_arc_3 &l) 00134 { 00135 return SK().has_on_3_object()(p, l.supporting_line()); 00136 } 00137 00138 template <class SK> 00139 inline 00140 bool 00141 has_on(const typename SK::Line_3 &l, 00142 const typename SK::Line_arc_3 &la) 00143 { 00144 return non_oriented_equal<SK>(l, la.supporting_line()); 00145 } 00146 00147 template< class SK> 00148 inline Sign element_cross_product_sign(const typename SK::Root_of_2 & y1, 00149 const typename SK::Root_of_2 &z2, 00150 const typename SK::Root_of_2 &z1, 00151 const typename SK::Root_of_2 &y2) 00152 { 00153 int s1=CGAL_NTS sign(z1); 00154 int s2=CGAL_NTS sign(z2); 00155 if (s1==0){ 00156 if (s2==0) 00157 return CGAL_NTS sign(0); 00158 else 00159 return CGAL_NTS sign(y1) * CGAL_NTS sign(z2); 00160 } 00161 else{ 00162 if (s2==0) 00163 return CGAL_NTS sign(- z1) * CGAL_NTS sign(y2); 00164 else 00165 return CGAL_NTS sign((s1*s2)*compare(y1/z1,y2/z2)); 00166 } 00167 } 00168 00169 template< class SK> 00170 inline 00171 Sign 00172 compute_sign_of_cross_product(const typename SK::Root_of_2 &x1, 00173 const typename SK::Root_of_2 &y1, 00174 const typename SK::Root_of_2 &z1, 00175 const typename SK::Root_of_2 &x2, 00176 const typename SK::Root_of_2 &y2, 00177 const typename SK::Root_of_2 &z2) 00178 { 00179 Sign s = element_cross_product_sign<SK>(y1,z2,z1,y2); 00180 if(s!=0) return s; 00181 s = element_cross_product_sign<SK>(z1,x2,x1,z2); 00182 if(s!=0) return s; 00183 s = element_cross_product_sign<SK>(x1,y2,y1,x2); 00184 return s; 00185 } 00186 00187 template< class SK> 00188 inline 00189 Sign 00190 compute_sign_of_cross_product(const typename SK::Circular_arc_point_3 &p1, 00191 const typename SK::Circular_arc_point_3 &p2, 00192 const typename SK::Circular_arc_point_3 &c) { 00193 return compute_sign_of_cross_product<SK>(p1.x()-c.x(), 00194 p1.y()-c.y(), 00195 p1.z()-c.z(), 00196 p2.x()-c.x(), 00197 p2.y()-c.y(), 00198 p2.z()-c.z()); 00199 } 00200 00201 template <class SK> 00202 inline 00203 bool 00204 has_on(const typename SK::Circular_arc_3 &a, 00205 const typename SK::Point_3 &p, 00206 const bool has_on_supporting_circle = false) 00207 { 00208 if(!has_on_supporting_circle) { 00209 if(!SK().has_on_3_object()(a.supporting_circle(),p)) 00210 return false; 00211 } 00212 if(a.rep().is_full()) return true; 00213 const Sign s_x_t = a.sign_cross_product(); 00214 const Sign s_x_p = 00215 compute_sign_of_cross_product<SK>(a.source(),p,a.center()); 00216 const Sign p_x_t = 00217 compute_sign_of_cross_product<SK>(p,a.target(),a.center()); 00218 if(s_x_t == ZERO) return (s_x_p != NEGATIVE); 00219 if(a.source() == p) return true; 00220 if(a.target() == p) return true; 00221 if(s_x_t == POSITIVE) { 00222 if(s_x_p == POSITIVE) return p_x_t == POSITIVE; 00223 else return false; 00224 } else { 00225 if(s_x_p == NEGATIVE) return p_x_t == POSITIVE; 00226 else return true; 00227 } 00228 } 00229 00230 template <class SK> 00231 inline 00232 bool 00233 has_on(const typename SK::Circular_arc_3 &a, 00234 const typename SK::Circular_arc_point_3 &p, 00235 const bool has_on_supporting_circle = false) 00236 { 00237 if(!has_on_supporting_circle) { 00238 if(!has_on<SK>(a.supporting_circle(),p)) 00239 return false; 00240 } 00241 if(a.rep().is_full()) return true; 00242 const Sign s_x_t = a.sign_cross_product(); 00243 const Sign s_x_p = 00244 compute_sign_of_cross_product<SK>(a.source(),p,a.center()); 00245 const Sign p_x_t = 00246 compute_sign_of_cross_product<SK>(p,a.target(),a.center()); 00247 if(s_x_t == ZERO) return (s_x_p != NEGATIVE); 00248 if(a.source() == p) return true; 00249 if(p == a.target()) return true; 00250 if(s_x_t == POSITIVE) { 00251 if(s_x_p == POSITIVE) return p_x_t == POSITIVE; 00252 else return false; 00253 } else { 00254 if(s_x_p == NEGATIVE) return p_x_t == POSITIVE; 00255 else return true; 00256 } 00257 } 00258 00259 template <class SK> 00260 inline 00261 bool 00262 has_on(const typename SK::Sphere_3 &a, 00263 const typename SK::Circular_arc_3 &p) 00264 { 00265 return a.has_on(p.supporting_circle()); 00266 } 00267 00268 template <class SK> 00269 inline 00270 bool 00271 has_on(const typename SK::Plane_3 &a, 00272 const typename SK::Circular_arc_3 &p) 00273 { 00274 return a.has_on(p.supporting_circle()); 00275 } 00276 00277 template <class SK> 00278 inline 00279 bool 00280 has_on(const typename SK::Circle_3 &c, 00281 const typename SK::Circular_arc_3 &ca) 00282 { 00283 return non_oriented_equal<SK>(c,ca.supporting_circle()); 00284 } 00285 00286 template <class SK> 00287 inline 00288 bool 00289 has_on(const typename SK::Circular_arc_3 &ca, 00290 const typename SK::Circle_3 &c) 00291 { 00292 if(!non_oriented_equal<SK>(c,ca.supporting_circle())) return false; 00293 return ca.rep().is_full(); 00294 } 00295 00296 00297 00298 }//SphericalFunctors 00299 }//CGAL 00300 00301 #endif //CGAL_SPHERICAL_KERNEL_PREDICATES_HAS_ON_3_H
1.7.6.1
