solver_implicit< C, V > Struct Template Reference

#include <solver_implicit.hpp>

List of all members.

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

template<class C, class V>
struct mmx::shape::solver_implicit< C, V >

Definition at line 49 of file solver_implicit.hpp.

Member Typedef Documentation

typedef bounding_box<C,Ref> BoundingBox

Definition at line 54 of file solver_implicit.hpp.

typedef box_face<C,Ref> BoxFace

Definition at line 55 of file solver_implicit.hpp.

typedef vertex<C,3,V> Point

Definition at line 53 of file solver_implicit.hpp.

typedef use<ref_def,double, V >::Ref Ref

Definition at line 52 of file solver_implicit.hpp.

typedef C Scalar

Definition at line 51 of file solver_implicit.hpp.

Member Function Documentation

static void common_edge_point ( Seq< Point * > &  lp,
const MultivariateDenseBernstein &  p,
const BoxFace &  E,
const BoundingBox &  bx1,
const BoundingBox &  bx2 
) [inline, static]

Definition at line 293 of file solver_implicit.hpp.

References approx(), box_face< C, V >::cvar(), mmx::tensor::face(), box_face< C, V >::lower(), mmx::shape::lower(), mmx::max(), box_face< C, V >::new_point(), box_face< C, V >::side(), mmx::solve(), mmx::ssi::up(), box_face< C, V >::upper(), and mmx::shape::upper().

00297                                                    {
00298       MultivariateDenseBernstein f;
00299 
00300       tensor::face(f,p,E.cvar(0),E.side(0));
00301 
00302       polynomial<double, with<Bernstein> > dw(1,f.size()-1), up(1,f.size()-1);
00303       for(unsigned i=0; i<f.size();i++) {
00304         up[i]= upper(f[i]); 
00305         dw[i]= lower(f[i]);
00306            //up[i]=dw[i]=f[i];
00307       }
00308 
00309       double 
00310         U_b = std::max( E.lower(bx1), E.lower(bx2) ) ,
00311         V_b = std::min( E.upper(bx1), E.upper(bx2) ) ;
00312 
00313       Seq<double> sol;
00314 
00315       solver< double, Sleeve<Approximate> >::solve(sol,dw,up,U_b,V_b);
00316 
00317       sol.sort();// sort from smaller to bigger
00318 
00319       Approximate approx;
00320       for(unsigned i=0;i<sol.size(); i++) 
00321           {
00322             lp<< E.new_point(bx1,sol[i]);
00323           }  
00324     }

static void edge_point ( Seq< Point * > &  lp,
const MultivariateDenseBernstein &  p,
const BoxFace &  E,
const BoundingBox &  bx 
) [inline, static]

Definition at line 94 of file solver_implicit.hpp.

References approx(), box_face< C, V >::cvar(), mmx::tensor::face(), box_face< C, V >::lower(), mmx::shape::lower(), box_face< C, V >::m_s, box_face< C, V >::m_v, box_face< C, V >::new_point(), box_face< C, V >::side(), mmx::solve(), mmx::ssi::up(), box_face< C, V >::upper(), and mmx::shape::upper().

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve(), cell3d_algebraic_surface< C, V >::edge_point(), and bcell3d_algebraic_surface< C, V >::edge_point().

00097                                           {
00098 
00099       MultivariateDenseBernstein f;
00100 
00101       tensor::face(f,p,E.cvar(0),E.side(0));
00102 
00103       polynomial<double, with<Bernstein> > dw(1,f.size()-1), up(1,f.size()-1);
00104       for(unsigned i=0; i<f.size();i++) {
00105         up[i]= upper(f[i]); 
00106         dw[i]= lower(f[i]);
00107       }
00108 
00109       double 
00110         U_b = E.lower(bx),
00111         V_b = E.upper(bx);
00112 
00113       Seq<double> sol;
00114       solver< double, Sleeve<Approximate> >::solve(sol,dw,up,U_b,V_b);
00115 
00116       // std::cout<<"****U= "<<U<<std::endl;
00117       // std::cout<<"****V= "<<V<<std::endl;
00118       // std::cout<<"***dw= "<<dw<<std::endl;
00119       // std::cout<<"***up= "<<up<<std::endl;
00120       //      if(sol.size()>1) std::cout<<"******Sols : "<<sol<<" "<<sol[1]-sol[0]<<std::endl;
00121 
00122       Approximate approx;
00123       std::vector<double> pt(3);
00124       for(unsigned i=0;i<sol.size(); i++) 
00125         if (i==0 || sol[i]-sol[i-1]> approx.eps){
00126           if(true) {//E.is_valid(bx, sol[i], approx.eps)) {
00127             lp<< E.new_point(bx,sol[i]);
00128           } else {
00129             std::cout<<"Not valid: ["<<(*E.new_point(bx,sol[i])) <<"] "
00130                      <<bx<<" "
00131                      <<E.m_v[0]<< " "<< E.m_s[0] <<" "
00132                      <<E.m_v[1]<< " "<< E.m_s[1] << " "
00133                      <<std::endl;
00134             lp<< E.new_point(bx,sol[i]);
00135           }
00136         }
00137     }

static int edge_sign_var ( const MultivariateDenseBernstein &  p,
const BoxFace &  E 
) [inline, static]

Definition at line 140 of file solver_implicit.hpp.

References box_face< C, V >::cvar(), mmx::tensor::face(), box_face< C, V >::side(), and mmx::sign_variation().

Referenced by cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

00141                                        {
00142       MultivariateDenseBernstein f;
00143       tensor::face(f,p,E.cvar(0),E.side(0));
00144       return sign_variation(f.begin(), f.end());
00145 
00146   }

static void extremal ( Seq< Point * > &  sol,
const Polynomial &  pol,
const BoundingBox &  b 
) [inline, static]

Definition at line 210 of file solver_implicit.hpp.

References mmx::assign(), mmx::diff(), solver_implicit< C, V >::new_point(), Polynomial, bounding_box< C, V >::xmax(), bounding_box< C, V >::xmin(), bounding_box< C, V >::ymax(), and bounding_box< C, V >::ymin().

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve(), cell2d_algebraic_curve< C, V >::cell2d_algebraic_curve(), and mmx::shape::extremal().

00211                                                                     {
00212     
00213       typedef polynomial< double, with<Bernstein> >  MultivariateDenseBernstein;
00214 
00215       // typedef Polynomial MultivariateDenseBernstein;
00216 
00217 
00218       typedef polynomial< GMP::rational, with<Bernstein> > MultivariateDenseBernsteinQ;
00219       
00220       Seq<mmx::GMP::rational> bx;
00221       bx<<as<mmx::GMP::rational>(b.xmin());
00222       bx<<as<mmx::GMP::rational>(b.xmax());
00223       bx<<as<mmx::GMP::rational>(b.ymin());
00224       bx<<as<mmx::GMP::rational>(b.ymax());
00225 
00226 
00227       //tensor::bernstein<mmx::GMP::rational> P(pol.rep(),bx);
00228       //typename Polynomial::Scalar mx = as<typename Polynomial::Scalar>(array::max_abs(P));
00229       //Polynomial Pol=pol/mx, dxpol = diff(Pol,0), dypol = diff(Pol,1);
00230 
00231       Polynomial dxpol = diff(pol,0), dypol = diff(pol,1);
00232       tensor::bernstein<mmx::GMP::rational>
00233          dxP(dxpol.rep(),bx),dyP(dypol.rep(),bx);
00234       
00235       MultivariateDenseBernstein dxp,dyp;
00236       let::assign(dxp.rep(), dxP);
00237       let::assign(dyp.rep(), dyP);
00238 
00239       Seq<MultivariateDenseBernstein> sys;
00240       //      Seq<MultivariateDenseBernsteinQ> sys;
00241       sys<<dxp<<dyp;
00242 
00243       solver<double, ProjRd<SBD_RDRDL> > slv;
00244 
00245       std::vector<double> res; 
00246       slv.solve_bernstein(res,sys);
00247 
00248       double x_sc= (b.xmax()-b.xmin()), y_sc= (b.ymax()-b.ymin());
00249       for(unsigned i=0;i<res.size();i+=2) {
00250         sol << new_point(b.xmin()+res[i]*x_sc, b.ymin()+res[i+1]*y_sc, 0.0);
00251       }
00252     }

static void face_point ( Seq< Point * > &  sol,
const Seq< MultivariateDenseBernstein > &  eqs,
const BoxFace &  F,
const BoundingBox &  bx 
) [inline, static]

Definition at line 149 of file solver_implicit.hpp.

References approx(), mmx::assign(), box_face< C, V >::cvar(), mmx::tensor::face(), box_face< C, V >::is_valid(), box_face< C, V >::new_point(), Polynomial, Seq< C, R >::rep(), box_face< C, V >::side(), and Seq< C, R >::size().

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), and bcell3d_algebraic_curve< C, V >::subdivide().

00152                                          {
00153       
00154       typedef polynomial< double, with<Bernstein> > Polynomial;
00155 
00156       Polynomial f, p;
00157       Seq<Polynomial> sys;
00158       for(unsigned i=0;i< eqs.size(); i++) {
00159         let::assign(p.rep(), eqs[i].rep());
00160         tensor::face(f.rep(), p.rep(), F.cvar(0), F.side(0));
00161         sys<<f;
00162       }
00163 
00164       solver<double, ProjRd<SBD_RDRDL> > slv;
00165       std::vector<double> res; 
00166       slv.solve_bernstein(res,sys);
00167       Approximate approx;
00168 
00169       for(int i=0;i<(int)res.size()-1;i+=2) {
00170 
00171 //      if (res[i]<approx.eps) res[i]=0;
00172 //      else if (res[i]>1-approx.eps) res[i]=1;
00173 
00174 //      if (res[i+1]<approx.eps) res[i+1]=0;
00175 //      else if (res[i+1]>1-approx.eps) res[i+1]=1;
00176 
00177         Point * p = F.new_point(bx, res[i], res[i+1]);
00178         if (F.is_valid(*p, bx))  sol<< p;
00179         //      else delete p;
00180       }
00181     }

static void intersection ( Seq< Point * > &  sol,
const Polynomial &  f1,
const Polynomial &  f2,
const BoundingBox &  bx 
) [inline, static]

Definition at line 184 of file solver_implicit.hpp.

References mmx::assign(), solver_implicit< C, V >::new_point(), bounding_box< C, V >::xmax(), bounding_box< C, V >::xmin(), bounding_box< C, V >::ymax(), and bounding_box< C, V >::ymin().

00186                                                                          {
00187 
00188       typedef polynomial< double, with<Bernstein> > MultivariateDenseBernstein;
00189       MultivariateDenseBernstein p1, p2;
00190 
00191       
00192       let::assign(p1.rep(), f1.rep() );
00193       let::assign(p2.rep(), f2.rep() );
00194       
00195       Seq<MultivariateDenseBernstein> sys;
00196       sys<<p1<<p2;
00197 
00198       solver<double, ProjRd<SBD_RDRDL> > slv;
00199       std::vector<double> res; 
00200       slv.solve_bernstein(res,sys);
00201 
00202       double x_sc= (bx.xmax()-bx.xmin()), y_sc= (bx.ymax()-bx.ymin());
00203       for(unsigned i=0;i<res.size();i+=2)
00204         {
00205           sol << new_point(bx.xmin()+res[i]*x_sc, bx.ymin()+res[i+1]*y_sc, 0.0);
00206         }
00207     }

static Point* new_point ( double  a,
double  b,
double  c 
) [inline, static]

Definition at line 86 of file solver_implicit.hpp.

Referenced by solver_implicit< C, V >::extremal(), solver_implicit< C, V >::intersection(), and solver_implicit< C, V >::singular().

00086                                                                {
00087     return new Point(a,b,c);
00088   }

static void singular ( Seq< Point * > &  sol,
const Polynomial &  pol,
const BoundingBox &  b 
) [inline, static]

Definition at line 255 of file solver_implicit.hpp.

References mmx::assign(), mmx::diff(), solver_implicit< C, V >::new_point(), Polynomial, bounding_box< C, V >::xmax(), bounding_box< C, V >::xmin(), bounding_box< C, V >::ymax(), and bounding_box< C, V >::ymin().

00256                                                                     {
00257 
00258       typedef polynomial< double, with<Bernstein> >        MultivariateDenseBernstein;
00259       typedef polynomial< GMP::rational, with<Bernstein> > MultivariateDenseBernsteinQ;
00260       
00261       Seq<mmx::GMP::rational> bx;
00262       bx<<as<mmx::GMP::rational>(b.xmin());
00263       bx<<as<mmx::GMP::rational>(b.xmax());
00264       bx<<as<mmx::GMP::rational>(b.ymin());
00265       bx<<as<mmx::GMP::rational>(b.ymax());
00266 
00267       Polynomial dxpol = diff(pol,0), dypol = diff(pol,1);
00268       tensor::bernstein<mmx::GMP::rational>
00269          P(pol.rep(),bx), dxP(dxpol.rep(),bx),dyP(dypol.rep(),bx);
00270       
00271       MultivariateDenseBernstein p,dxp,dyp;
00272       let::assign(p.rep()  , P);
00273       let::assign(dxp.rep(), dxP);
00274       let::assign(dyp.rep(), dyP);
00275 
00276       Seq<MultivariateDenseBernstein> sys;
00277       sys<<p<<dxp<<dyp;
00278 
00279       solver<double, ProjRd<SBD_RDRDL> > slv;
00280       //      solver<ring<double,Bernstein>, ProjRd<SBD_RDRDL> >::eps=1e-10;
00281 
00282       std::vector<double> res; 
00283       slv.solve_bernstein(res,sys);
00284 
00285       double x_sc= (b.xmax()-b.xmin()), y_sc= (b.ymax()-b.ymin());
00286       for(unsigned i=0;i<res.size();i+=2) {
00287         sol << new_point(b.xmin()+res[i]*x_sc, b.ymin()+res[i+1]*y_sc, 0.0);
00288       }
00289     }

Member Data Documentation

box_face< C, typename use< ref_def, double, V >::Ref > back_edge [inline, static]

Definition at line 62 of file solver_implicit.hpp.

box_face< C, typename use< ref_def, double, V >::Ref > back_face [inline, static]

Definition at line 84 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > east_back_edge [inline, static]

Definition at line 67 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > east_edge [inline, static]

Definition at line 60 of file solver_implicit.hpp.

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve().

box_face< C, typename use< ref_def, double, V >::Ref > east_face [inline, static]

Definition at line 82 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > east_front_edge [inline, static]

Definition at line 72 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > front_edge [inline, static]

Definition at line 61 of file solver_implicit.hpp.

box_face< C, typename use< ref_def, double, V >::Ref > front_face [inline, static]

Definition at line 83 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > north_back_edge [inline, static]

Definition at line 64 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > north_east_edge [inline, static]

Definition at line 76 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > north_edge [inline, static]

Definition at line 57 of file solver_implicit.hpp.

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve().

box_face< C, typename use< ref_def, double, V >::Ref > north_face [inline, static]

Definition at line 79 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > north_front_edge [inline, static]

Definition at line 69 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > north_west_edge [inline, static]

Definition at line 74 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > south_back_edge [inline, static]

Definition at line 65 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > south_east_edge [inline, static]

Definition at line 77 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > south_edge [inline, static]

Definition at line 58 of file solver_implicit.hpp.

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve().

box_face< C, typename use< ref_def, double, V >::Ref > south_face [inline, static]

Definition at line 80 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > south_front_edge [inline, static]

Definition at line 70 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > south_west_edge [inline, static]

Definition at line 75 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > west_back_edge [inline, static]

Definition at line 66 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

box_face< C, typename use< ref_def, double, V >::Ref > west_edge [inline, static]

Definition at line 59 of file solver_implicit.hpp.

Referenced by bcell2d_algebraic_curve< C, V >::bcell2d_algebraic_curve().

box_face< C, typename use< ref_def, double, V >::Ref > west_face [inline, static]

Definition at line 81 of file solver_implicit.hpp.

Referenced by bcell3d_algebraic_curve< C, V >::bcell3d_algebraic_curve(), bcell3d< C, V >::intersections(), and bcell3d_algebraic_curve< C, V >::subdivide().

box_face< C, typename use< ref_def, double, V >::Ref > west_front_edge [inline, static]

Definition at line 71 of file solver_implicit.hpp.

Referenced by cell3d_algebraic_surface< C, V >::edge_point(), bcell3d_algebraic_surface< C, V >::edge_point(), cell3d_algebraic_surface< C, V >::is_regular(), and bcell3d_algebraic_surface< C, V >::is_regular().

The documentation for this struct was generated from the following file:
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