pluecker_line_3.h

很多二维 三维几何计算算法 C++ 类库

// Copyright (c) 1997-2002  Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.3-branch/Nef_3/include/CGAL/Nef_3/Pluecker_line_3.h $
// $Id: Pluecker_line_3.h 28567 2006-02-16 14:30:13Z lsaboret $
// 
//
// Author(s)     : Michael Seel    <[e-mail]>
//                 Miguel Granados <[e-mail]>
//                 Susan Hert      <[e-mail]>
//                 Lutz Kettner    <[e-mail]>
#ifndef CGAL_PLUECKER_LINE_3_H
#define CGAL_PLUECKER_LINE_3_H

#include <CGAL/basic.h>
#include <CGAL/Homogeneous.h>
#include <algorithm>
#undef CGAL_NEF_DEBUG
#define CGAL_NEF_DEBUG 61
#include <CGAL/Nef_2/debug.h>

CGAL_BEGIN_NAMESPACE

/*{\Manpage{Pluecker_line_3}{R}{Straight lines in 3-space}{pl}}*/  

/*{\Mdefinition An instance |\Mvar| of the data type |\Mname| is a
directed straight line in the three-dimensional plane. Its
representation is based on Pluecker coordinates. (For a treatment see
the book on projected oriented geometry of Stolfi.)}*/

template <typename Tag, typename R> class Pluecker_line_3;

template <typename R_>
class Pluecker_line_3<Homogeneous_tag,R_> {

/*{\Mtypes 6}*/
typedef R_ R;
/*{\Mtypemember the standard kernel type.}*/
typedef typename R::RT RT;
/*{\Mtypemember the ring type.}*/
typedef typename R::Point_3 Point_3;
/*{\Mtypemember the point type of the standard kernel.}*/
typedef typename R::Line_3  Line_3;
/*{\Mtypemember the line type of the standard kernel.}*/
/*{\Mtypemember iterator over Pluecker coefficients.}*/
typedef Pluecker_line_3<Homogeneous_tag,R> Self;
// typedef Infimaximal_box<typename Is_extended_kernel<R>::value_type, R> Infi_box;
// typedef typename Infi_box::NT NT;
typedef const RT* const_iterator;

RT c_[6];

public:
/*{\Mcreation 3}*/     
Pluecker_line_3() {}
/*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to some line.}*/

Pluecker_line_3(const Line_3& l)
  /*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to |l|.}*/
{
  Point_3 p(l.point(0)), q(l.point(1));
  c_[0] = p.hx()*q.hy() - p.hy()*q.hx();
  c_[1] = p.hx()*q.hz() - p.hz()*q.hx();
  c_[2] = p.hy()*q.hz() - p.hz()*q.hy();
  c_[3] = p.hx()*q.hw() - p.hw()*q.hx();
  c_[4] = p.hy()*q.hw() - p.hw()*q.hy();
  c_[5] = p.hz()*q.hw() - p.hw()*q.hz();
}

Pluecker_line_3(const Point_3& p, const Point_3& q)
/*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to the oriented line through |p| and |q|.}*/
{
  c_[0] = p.hx()*q.hy() - p.hy()*q.hx();
  c_[1] = p.hx()*q.hz() - p.hz()*q.hx();
  c_[2] = p.hy()*q.hz() - p.hz()*q.hy();
  c_[3] = p.hx()*q.hw() - p.hw()*q.hx();
  c_[4] = p.hy()*q.hw() - p.hw()*q.hy();
  c_[5] = p.hz()*q.hw() - p.hw()*q.hz();

}

template <typename Forward_iterator>
Pluecker_line_3(Forward_iterator s, Forward_iterator e) 
/*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to line with the parameters |tuple [s,e)|.}*/
{ int i=0;
  while (s!=e && i<6) c_[i++] = *s;
  CGAL_assertion(i==6);
}

/*{\Moperations 4 2 }*/

const_iterator begin() const { return c_; }
/*{\Mop returns an iterator pointing to the first
Pluecker coefficient.}*/                                                   
const_iterator end() const { return c_+6; }
/*{\Mop returns an iterator pointing beyond the last
Pluecker coefficient.}*/                                                   

Pluecker_line_3(const Self& l) 
{ std::copy(l.begin(),l.end(),c_); }

Self& operator=(const Self& l) 
{ if (&l!=this) std::copy(l.begin(),l.end(),c_); 
  return *this; }

const RT& operator[](unsigned i) const
/*{\Marrop returns constant access to the $i$th Pluecker coefficient.}*/    
{ CGAL_assertion(i<6); return c_[i]; }

int sign() const
/*{\Mop returns the sign of the first nonzero Pluecker coefficient
within the ordered tuple of coefficients.}*/
{ for (unsigned i=0; i<6; ++i) 
    if (c_[i]!=RT(0)) return CGAL_NTS sign(c_[i]); 
 CGAL_assertion_msg(0,"Pluecker line 0 0 0 0 0 0 shouldn't appear!!!"); 
  return CGAL_NTS sign(c_[5]); 
}

void normalize()
//{\Mop reduces the Pluecker coefficients to a minimal 
//representation. This is done by dividing all Pluecker 
//coefficients by their common gcd.}
{ 
  CGAL_NEF_TRACEN("normalize");
  int i=0;
  while(i<6 && c_[i]==0)
    i++;
    
  if(i>5)
    return;

  RT D = c_[i];
  CGAL_assertion(D!=0);

  for(++i; i<6; ++i) 
    D = (c_[i]==0 ? D : CGAL_NTS gcd(D, c_[i]));
  if (D==0) return;
  CGAL_NEF_TRACEN("gcd" << D);
  for(int i=0; i<6; ++i) c_[i]/=D;
}

void negate()
/*{\Mop negates all Pluecker coefficients.}*/
{ for(int i=0; i<6; ++i) c_[i] = -c_[i]; }

Self opposite() const
/*{\Mop returns the line opposite to |\Mvar|. }*/
{ Self res;
  std::negate<RT> N;
  std::transform(begin(), end(), res.c_, N);
  return res;
}

static int cmp(const Self& l1,
               const Self& l2)
/*{\Mstatic returns the lexicographic order on lines defined
on their Pluecker coefficient tuples.}*/
{ for (unsigned i=0; i<5; ++i) {
    typename R::RT diff = l1[i]-l2[i];
    if ( diff != typename R::RT(0) ) return CGAL_NTS sign(diff);
  }
  return CGAL_NTS sign(l1[5]-l2[5]);
}

}; // Pluecker_line_3


template <typename R_>
class Pluecker_line_3<Cartesian_tag,R_> {

/*{\Mtypes 6}*/
typedef R_ R;
/*{\Mtypemember the standard kernel type.}*/
typedef typename R::FT FT;
/*{\Mtypemember the ring type.}*/
typedef typename R::Point_3 Point_3;
/*{\Mtypemember the point type of the standard kernel.}*/
typedef typename R::Line_3  Line_3;
/*{\Mtypemember the line type of the standard kernel.}*/
/*{\Mtypemember iterator over Pluecker coefficients.}*/
typedef Pluecker_line_3<Cartesian_tag,R> Self;
// typedef Infimaximal_box<typename Is_extended_kernel<R>::value_type, R> Infi_box;
// typedef typename Infi_box::NT NT;
typedef const FT* const_iterator;

FT c_[6];

public:
/*{\Mcreation 3}*/     
Pluecker_line_3() {}
/*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to some line.}*/

Pluecker_line_3(const Line_3& l)
  /*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to |l|.}*/
{
  Point_3 p(l.point(0)), q(l.point(1));
  c_[0] = p.x()*q.y() - p.y()*q.x();
  c_[1] = p.x()*q.z() - p.z()*q.x();
  c_[2] = p.y()*q.z() - p.z()*q.y();
  c_[3] = p.x() - q.x();
  c_[4] = p.y() - q.y();
  c_[5] = p.z() - q.z();
}


Pluecker_line_3(const Point_3& p, const Point_3& q)
//{\Mcreate creates an instance |\Mvar| of type |\Mname| and
// initializes it to the oriented line through |p| and |q|.}
{
  c_[0] = p.x()*q.y() - p.y()*q.x();
  c_[1] = p.x()*q.z() - p.z()*q.x();
  c_[2] = p.y()*q.z() - p.z()*q.y();
  c_[3] = p.x() - q.x();
  c_[4] = p.y() - q.y();
  c_[5] = p.z() - q.z();
}

template <typename Forward_iterator>
Pluecker_line_3(Forward_iterator s, Forward_iterator e) 
/*{\Mcreate creates an instance |\Mvar| of type |\Mname| and
initializes it to line with the parameters |tuple [s,e)|.}*/
{ int i=0;
  while (s!=e && i<6) c_[i++] = *s;
  CGAL_assertion(i==6);
}

/*{\Moperations 4 2 }*/

const_iterator begin() const { return c_; }
/*{\Mop returns an iterator pointing to the first
Pluecker coefficient.}*/                                                   
const_iterator end() const { return c_+6; }
/*{\Mop returns an iterator pointing beyond the last
Pluecker coefficient.}*/                                                   

Pluecker_line_3(const Self& l) 
{ std::copy(l.begin(),l.end(),c_); }

Self& operator=(const Self& l) 
{ if (&l!=this) std::copy(l.begin(),l.end(),c_); 
  return *this; }

const FT& operator[](unsigned i) const
/*{\Marrop returns constant access to the $i$th Pluecker coefficient.}*/    
{ CGAL_assertion(i<6); return c_[i]; }

int sign() const
/*{\Mop returns the sign of the first nonzero Pluecker coefficient
within the ordered tuple of coefficients.}*/
{ for (unsigned i=0; i<6; ++i) 
    if (c_[i]!=FT(0)) return CGAL_NTS sign(c_[i]); 
 CGAL_assertion_msg(0,"Pluecker line 0 0 0 0 0 0 shouldn't appear!!!"); 
  return CGAL_NTS sign(c_[5]); 
}

void normalize()
//{\Mop reduces the Pluecker coefficients to a minimal 
//representation. This is done by dividing all Pluecker 
//coefficients by their common gcd.}
{
  CGAL_NEF_TRACEN("normalize");
  int i=0;
  while(i<6 && c_[i]==FT(0))
    ++i;
    
  if(i>5)
    return;

  FT D = c_[i];
  if(D<FT(0)) D=-D;
  CGAL_assertion(D!=0);

  for(int i=0; i<6; ++i) {
    c_[i]/=D;
    //    c_[i].normalize();
  }
}

void negate()
/*{\Mop negates all Pluecker coefficients.}*/
{ for(int i=0; i<6; ++i) c_[i] = -c_[i]; }

Self opposite() const
/*{\Mop returns the line opposite to |\Mvar|. }*/
{ Self res;
  std::negate<FT> N;
  std::transform(begin(), end(), res.c_, N);
  return res;
}

static int cmp(const Self& l1,
               const Self& l2)
/*{\Mstatic returns the lexicographic order on lines defined
on their Pluecker coefficient tuples.}*/
{ for (unsigned i=0; i<5; ++i) {
    typename R::FT diff = l1[i]-l2[i];
    if ( diff != typename R::FT(0) ) return CGAL_NTS sign(diff);
  }
  return CGAL_NTS sign(l1[5]-l2[5]);
}

}; // Pluecker_line_3

template <typename Tag, typename R>
std::ostream& operator<<(std::ostream& os, const Pluecker_line_3<Tag,R>& l)
{ 
  switch( os.iword(CGAL::IO::mode) ) {
    case CGAL::IO::ASCII :
      for (unsigned i=0; i<6; ++i) os << l[i] << " "; 
      return os; 
    case CGAL::IO::BINARY :
      for (unsigned i=0; i<6; ++i) CGAL::write(os, l[i]);
      return os;
    default:
      os << "Pluecker_line_3(";
      for (unsigned i=0; i<5; ++i) os << l[i] << ", "; 
      os << l[5] << ")";
  } return os;
}

template <typename Tag, typename R>
Pluecker_line_3<Tag,R> categorize(const Pluecker_line_3<Tag,R>& l, int& inverted)
{ Pluecker_line_3<Tag,R> res(l);
  if ( res.sign()<0 ) { res.negate(); inverted=1; }
  else inverted=-1;
  res.normalize();
  CGAL_assertion(res.sign()!=0);
  return res;
}

struct Pluecker_line_lt {
  template <typename Tag, typename R>
  bool operator()(const CGAL::Pluecker_line_3<Tag,R>& l1,
                  const CGAL::Pluecker_line_3<Tag,R>& l2) const
  { return CGAL::Pluecker_line_3<Tag,R>::cmp(l1,l2)<0; }
};

CGAL_END_NAMESPACE
#endif //CGAL_PLUECKER_LINE_3_H