aff_transformationh3.h

很多二维 三维几何计算算法 C++ 类库

// Copyright (c) 1999  Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL 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/Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h $
// $Id: Aff_transformationH3.h 29102 2006-03-06 23:51:27Z spion $
// 
//
// Author(s)     : Stefan Schirra

#ifndef CGAL_AFF_TRANSFORMATIONH3_H
#define CGAL_AFF_TRANSFORMATIONH3_H

#include <CGAL/Handle_for_virtual.h>
#include <CGAL/determinant.h>

CGAL_BEGIN_NAMESPACE

// forward declaration
template < class R >
class Aff_transformationH3;

template < class R >
class Aff_transformation_repH3;

template < class R >
std::ostream &
operator<< ( std::ostream & out,
             const Aff_transformationH3<R>& t);

template < class R >
Aff_transformationH3<R>
_general_transformation_composition (
                           Aff_transformation_repH3<R> l,
                           Aff_transformation_repH3<R> r);

template <class R_ >
class Aff_transformation_rep_baseH3 : public Ref_counted_virtual
// abstract base class of aff transformation representations
{
public:
  typedef R_                         R;
  typedef typename R::FT             FT;
  typedef typename R::RT             RT;
  typedef typename R::Point_3        Point_3;
  typedef typename R::Vector_3       Vector_3;
  typedef typename R::Direction_3    Direction_3;
  typedef typename R::Plane_3        Plane_3;
  typedef typename R::Aff_transformation_3 Aff_transformation_3;

  virtual  ~Aff_transformation_rep_baseH3(){}

  virtual  Point_3
           transform(const Point_3&) const = 0;

  virtual  Vector_3
           transform(const Vector_3&) const = 0;

  virtual  Direction_3
           transform(const Direction_3&) const = 0;

  virtual  Plane_3
           transform(const Plane_3&) const = 0;

  virtual  Aff_transformation_3
           inverse() const = 0;

  virtual  Aff_transformation_3
           transpose() const = 0;

  virtual  Aff_transformation_repH3<R>
           general_form() const = 0;

  virtual  bool
           is_even() const = 0;

  virtual  RT
           homogeneous(int i, int j) const = 0;

  virtual  FT
           cartesian(int i, int j) const = 0;
};

template < class R_ >
class Aff_transformation_repH3 : public Aff_transformation_rep_baseH3<R_>
{
  typedef typename R_::FT           FT;
  typedef typename R_::RT           RT;
  typedef typename R_::Point_3              Point_3;
  typedef typename R_::Vector_3             Vector_3;
  typedef typename R_::Direction_3          Direction_3;
  typedef typename R_::Plane_3              Plane_3;
  typedef typename R_::Aff_transformation_3 Aff_transformation_3;

public:
  typedef R_                       R;

  Aff_transformation_repH3() {}

  Aff_transformation_repH3(
                 const RT& m00, const RT& m01, const RT& m02, const RT& m03,
                 const RT& m10, const RT& m11, const RT& m12, const RT& m13,
                 const RT& m20, const RT& m21, const RT& m22, const RT& m23,
                                                              const RT& m33);
  virtual  ~Aff_transformation_repH3() {}

  virtual  Point_3
           transform(const Point_3& p) const;

  virtual  Vector_3
           transform(const Vector_3& v) const;

  virtual  Direction_3
           transform(const Direction_3& dir) const;

  virtual  Plane_3
           transform(const Plane_3& pl) const;

  virtual  Aff_transformation_3
           inverse() const;

  virtual  Aff_transformation_repH3<R>
           general_form() const;

  virtual  Aff_transformation_3
           transpose() const;

  virtual  bool
           is_even() const;

  virtual  RT
           homogeneous(int i, int j) const ;

  virtual  FT
           cartesian(int i, int j) const ;

  friend class Aff_transformationH3<R>;

  friend
  Aff_transformationH3<R>
  _general_transformation_composition <> (
                           Aff_transformation_repH3<R> l,
                           Aff_transformation_repH3<R> r);

  friend
  std::ostream &
  operator<< <> (std::ostream & out, const Aff_transformationH3<R>& t);

private:
    RT   t00, t01, t02, t03;
    RT   t10, t11, t12, t13;
    RT   t20, t21, t22, t23;
    RT                  t33;
};

template < class R_ >
class Identity_repH3 : public Aff_transformation_rep_baseH3<R_>
{
  typedef typename R_::RT    RT;
  typedef typename R_::FT    FT;
  typedef typename R_::Point_3              Point_3;
  typedef typename R_::Vector_3             Vector_3;
  typedef typename R_::Direction_3          Direction_3;
  typedef typename R_::Plane_3              Plane_3;
  typedef typename R_::Aff_transformation_3 Aff_transformation_3;

public:
  typedef R_                R;

           Identity_repH3()
           {}

  virtual  ~Identity_repH3()
           {}

  virtual  Point_3
           transform(const Point_3& p) const
           { return p; }

  virtual  Vector_3
           transform(const Vector_3& v) const
           { return v; }

  virtual  Direction_3
           transform(const Direction_3& dir) const
           { return dir; }

  virtual  Plane_3
           transform(const Plane_3& pl) const
           { return pl; }

  virtual  Aff_transformation_3
           inverse() const
           { return Aff_transformation_3( IDENTITY); }

  virtual  Aff_transformation_repH3<R>
           general_form() const;

  virtual  Aff_transformation_3
           transpose() const
           { return Aff_transformation_3( IDENTITY); }

  virtual  bool
           is_even() const
           { return true; }

  virtual  RT
           homogeneous(int i, int j) const
           { return (i==j) ? RT(1) : RT(0); }

  virtual  FT
           cartesian(int i, int j) const
           { return (i==j) ? FT(1) : FT(0); }
};

template < class R_ >
class Translation_repH3 : public Aff_transformation_rep_baseH3<R_>
{
  typedef typename R_::FT       FT;
  typedef typename R_::RT       RT;
  typedef typename R_::Point_3              Point_3;
  typedef typename R_::Vector_3             Vector_3;
  typedef typename R_::Direction_3          Direction_3;
  typedef typename R_::Plane_3              Plane_3;
  typedef typename R_::Aff_transformation_3 Aff_transformation_3;

public:
  typedef R_                    R;

           Translation_repH3( const Vector_3& v);

  virtual  ~Translation_repH3() {}


  virtual  Point_3
           transform(const Point_3& p) const;

  virtual  Vector_3
           transform(const Vector_3& v) const;

  virtual  Direction_3
           transform(const Direction_3& dir) const;

  virtual  Plane_3
           transform(const Plane_3& pl) const;

  virtual  Aff_transformation_3
           inverse() const;

  virtual  Aff_transformation_repH3<R>
           general_form() const;

  virtual  Aff_transformation_3
           transpose() const;

  virtual  bool
           is_even() const;

  virtual  RT
           homogeneous(int i, int j) const ;

  virtual  FT
           cartesian(int i, int j) const ;

friend class Aff_transformationH3<R>;

private:
  Vector_3  tv;
};

template < class R_ >
class Aff_transformationH3
  : public Handle_for_virtual< Aff_transformation_rep_baseH3<R_> >
{
  typedef typename R_::RT                   RT;
  typedef typename R_::FT                   FT;
  typedef typename R_::Point_3              Point_3;
  typedef typename R_::Vector_3             Vector_3;
  typedef typename R_::Direction_3          Direction_3;
  typedef typename R_::Plane_3              Plane_3;
  typedef typename R_::Aff_transformation_3 Aff_transformation_3;

public:
  typedef R_                R;

  Aff_transformationH3();

  // Identity
  Aff_transformationH3(const Identity_transformation&);

  // Translation
  Aff_transformationH3(const Translation& , const Vector_3& v);

  //  Scaling
  Aff_transformationH3(const Scaling&, const RT& num, const RT& den);

  //  General form
  Aff_transformationH3(
                  const RT& m00, const RT& m01, const RT& m02, const RT& m03,
                  const RT& m10, const RT& m11, const RT& m12, const RT& m13,
                  const RT& m20, const RT& m21, const RT& m22, const RT& m23,
                                                               const RT& m33);
  Aff_transformationH3(
                  const RT& m00, const RT& m01, const RT& m02,
                  const RT& m10, const RT& m11, const RT& m12,
                  const RT& m20, const RT& m21, const RT& m22,
                                                               const RT& m33);

  Point_3
  transform(const Point_3& p) const;

  Vector_3
  transform(const Vector_3& v) const;

  Direction_3
  transform(const Direction_3& d) const;

  Plane_3
  transform(const Plane_3& pl) const;

  Aff_transformation_3
  inverse()   const;

  Aff_transformationH3<R>
  transpose() const;

  bool
  is_even()   const;

  bool
  is_odd()    const;

  FT
  cartesian(int i, int j) const
  { return this->Ptr()->cartesian(i,j); }

  RT
  homogeneous(int i, int j) const
  { return this->Ptr()->homogeneous(i,j); }

  FT
  m(int i, int j) const
  { return this->Ptr()->cartesian(i,j); }

  RT
  hm(int i, int j) const
  { return this->Ptr()->homogeneous(i,j); }
};

template < class R >
CGAL_KERNEL_INLINE
Aff_transformation_repH3<R>::Aff_transformation_repH3(
                   const RT& m00, const RT& m01, const RT& m02, const RT& m03,
                   const RT& m10, const RT& m11, const RT& m12, const RT& m13,
                   const RT& m20, const RT& m21, const RT& m22, const RT& m23,
                                                                const RT& m33)
  :  t00(m00), t01(m01), t02(m02), t03(m03),
     t10(m10), t11(m11), t12(m12), t13(m13),
     t20(m20), t21(m21), t22(m22), t23(m23),
                                   t33(m33)
{}

template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repH3<R>::Point_3
Aff_transformation_repH3<R>::
transform(const typename Aff_transformation_repH3<R>::Point_3& p) const
{
  return Point_3(t00 * p.hx() + t01 * p.hy() + t02 * p.hz() + t03 * p.hw(),
                 t10 * p.hx() + t11 * p.hy() + t12 * p.hz() + t13 * p.hw(),
                 t20 * p.hx() + t21 * p.hy() + t22 * p.hz() + t23 * p.hw(),
                 t33 * p.hw());
}

template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repH3<R>::Vector_3
Aff_transformation_repH3<R>::
transform(const typename Aff_transformation_repH3<R>::Vector_3& v) const
{
  return Vector_3(t00 * v.hx() + t01 * v.hy() + t02 * v.hz(),
                  t10 * v.hx() + t11 * v.hy() + t12 * v.hz(),
                  t20 * v.hx() + t21 * v.hy() + t22 * v.hz(),
                  t33 * v.hw() );
}

template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repH3<R>::Direction_3
Aff_transformation_repH3<R>::
transform(const typename Aff_transformation_repH3<R>::Direction_3& d) const
{
    if (t33 > RT(0))
        return Direction_3(t00 * d.hx() + t01 * d.hy() + t02 * d.hz(),
                           t10 * d.hx() + t11 * d.hy() + t12 * d.hz(),
                           t20 * d.hx() + t21 * d.hy() + t22 * d.hz());
    else
        return - Direction_3(t00 * d.hx() + t01 * d.hy() + t02 * d.hz(),
                             t10 * d.hx() + t11 * d.hy() + t12 * d.hz(),
                             t20 * d.hx() + t21 * d.hy() + t22 * d.hz());
}

template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repH3<R>::Plane_3
Aff_transformation_repH3<R>::
transform(const typename Aff_transformation_repH3<R>::Plane_3& pl) const
{
  if ( is_even() )
  {
      return Plane_3(
               transform(pl.point() ),
               transpose().inverse().transform(pl.orthogonal_direction() ));
  }
  else
  {
     return Plane_3(
               transform(pl.point() ),
               -(transpose().inverse().transform(pl.orthogonal_direction() )));
  }
}

template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repH3<R>::Aff_transformation_3
Aff_transformation_repH3<R>::inverse() const
{
  typedef typename R::RT RT;
  const RT  RT0(0);
  return Aff_transformation_3(
                           det3x3_by_formula( t11, t12, t13,
                                                   t21, t22, t23,     // i 00
                                                   RT0, RT0, t33 ),

                        -  det3x3_by_formula( t01, t02, t03,