aff_transformationh2.h

很多二维 三维几何计算算法 C++ 类库

transform( const typename Aff_transformationH2<R>::Direction_2& d) const
{ return this->Ptr()->transform(d); }

template < class R >
typename Aff_transformationH2<R>::Line_2
Aff_transformationH2<R>::
transform( const typename Aff_transformationH2<R>::Line_2& l) const
{ return Line_2( transform( l.point(0)), transform( l.point(1)) ); }

template < class R >
Aff_transformationH2<R>
Aff_transformationH2<R>::
inverse() const
{ return this->Ptr()->inverse(); }

template < class R >
bool
Aff_transformationH2<R>::
is_even() const
{ return this->Ptr()->is_even(); }

template < class R >
bool
Aff_transformationH2<R>::
is_odd() const
{ return ! is_even(); }

template < class R >
inline
typename Aff_transformationH2<R>::FT
Aff_transformationH2<R>::
cartesian(int i, int j) const
{ return this->Ptr()->cartesian(i,j); }

template < class R >
inline
typename Aff_transformationH2<R>::RT
Aff_transformationH2<R>::
homogeneous(int i, int j) const
{ return this->Ptr()->homogeneous(i,j); }

template < class R >
Aff_transformation_repH2<R>
Aff_transformationH2<R>::
general_form() const
{ return this->Ptr()->general_form(); }

template <class R>
Aff_transformationH2<R>
//operator*(const Aff_transformationH2<R>& left_argument,
//          const Aff_transformationH2<R>& right_argument )
Aff_transformationH2<R>::
operator*(const Aff_transformationH2<R>& right_argument) const
{
  return _general_transformation_composition(
                  this->Ptr()->general_form(),
                  right_argument.Ptr()->general_form() );
}

template <class R>
Aff_transformationH2<R>
_general_transformation_composition( Aff_transformation_repH2<R> l,
                                     Aff_transformation_repH2<R> r )
{
return Aff_transformationH2<R>(
       l.a*r.a + l.b*r.d,   l.a*r.b + l.b*r.e,   l.a*r.c + l.b*r.f + l.c*r.g,
       l.d*r.a + l.e*r.d,   l.d*r.b + l.e*r.e,   l.d*r.c + l.e*r.f + l.f*r.g,
                                                 l.g*r.g                     );
}

template < class R >
typename Aff_transformation_repH2<R>::RT
Aff_transformation_repH2<R>::homogeneous(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return a;
              case 1: return b;
              case 2: return c;
            }
    case 1: switch (j)
            {
              case 0: return d;
              case 1: return e;
              case 2: return f;
            }
    case 2: switch (j)
            {
              case 0: return RT(0);
              case 1: return RT(0);
              case 2: return g;
            }
  }
  return RT(0);
}

template < class R >
typename Aff_transformation_repH2<R>::FT
Aff_transformation_repH2<R>::cartesian(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  if ( (i == 2) && (j == 2) )  return FT(1);
  return FT(homogeneous(i,j)) / FT(g);
}

template < class R >
typename Translation_repH2<R>::RT
Translation_repH2<R>::homogeneous(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return _tv.hw();
              case 1: return RT(0);
              case 2: return _tv.hx();
            }
    case 1: switch (j)
            {
              case 0: return RT(0);
              case 1: return _tv.hw();
              case 2: return _tv.hy();
            }
    case 2: switch (j)
            {
              case 0: return RT(0);
              case 1: return RT(0);
              case 2: return _tv.hw();
            }
  }
  return RT(0);
}

template < class R >
typename Translation_repH2<R>::FT
Translation_repH2<R>::cartesian(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return FT(1);
              case 1: return FT(0);
              case 2: return _tv.x();
            }
    case 1: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(1);
              case 2: return _tv.y();
            }
    case 2: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(0);
              case 2: return FT(1);
            }
  }
  return FT(0);
}

template < class R >
typename Rotation_repH2<R>::RT
Rotation_repH2<R>::
homogeneous(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return _cos;
              case 1: return - _sin;
              case 2: return RT(0);
            }
    case 1: switch (j)
            {
              case 0: return _sin;
              case 1: return _cos;
              case 2: return RT(0);
            }
    case 2: switch (j)
            {
              case 0: return RT(0);
              case 1: return RT(0);
              case 2: return _den;
            }
  }
  return RT(0);
}

template < class R >
typename Rotation_repH2<R>::FT
Rotation_repH2<R>::
cartesian(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return FT(_cos) / FT(_den);
              case 1: return - FT(_sin) / FT(_den);
              case 2: return RT(0);
            }
    case 1: switch (j)
            {
              case 0: return FT(_sin) / FT(_den);
              case 1: return FT(_cos) / FT(_den);
              case 2: return FT(0);
            }
    case 2: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(0);
              case 2: return FT(1);
            }
  }
  return FT(0);
}

template < class R >
typename Scaling_repH2<R>::RT
Scaling_repH2<R>::
homogeneous(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return _sf_num;
              case 1: return RT(0);
              case 2: return RT(0);
            }
    case 1: switch (j)
            {
              case 0: return RT(0);
              case 1: return _sf_num;
              case 2: return RT(0);
            }
    case 2: switch (j)
            {
              case 0: return RT(0);
              case 1: return RT(0);
              case 2: return _sf_den;
            }
  }
  return RT(0);
}

template <class R>
typename Scaling_repH2<R>::FT
Scaling_repH2<R>::
cartesian(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return FT(_sf_num) / FT(_sf_den);
              case 1: return FT(0);
              case 2: return FT(0);
            }
    case 1: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(_sf_num) / FT(_sf_den);
              case 2: return FT(0);
            }
    case 2: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(0);
              case 2: return FT(1);
            }
  }
  return FT(0);
}

template < class R >
typename Reflection_repH2<R>::RT
Reflection_repH2<R>::
homogeneous(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  RT mRT2 = -RT(2);
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return l.b()*l.b() - l.a()*l.a();
              case 1: return l.a()*l.b()*mRT2;
              case 2: return l.a()*l.c()*mRT2;
            }
    case 1: switch (j)
            {
              case 0: return l.a()*l.b()*mRT2;
              case 1: return l.a()*l.a() - l.b()*l.b();
              case 2: return l.b()*l.c()*mRT2;
            }
    case 2: switch (j)
            {
              case 0: return RT(0);
              case 1: return RT(0);
              case 2: return l.a()*l.a() + l.b()*l.b();
            }
  }
  return RT(0);
}

template <class R>
typename Reflection_repH2<R>::FT
Reflection_repH2<R>::
cartesian(int i, int j) const
{
  CGAL_kernel_precondition( (i >= 0) && (i <= 2) && (j >= 0) && (j <= 2) );
  FT de = FT( l.a()*l.a() + l.b()*l.b() );
  switch (i)
  {
    case 0: switch (j)
            {
              case 0: return FT( l.b()-l.a() ) / FT( l.a()+l.b());
              case 1: return FT( homogeneous(0,1)) / de;
              case 2: return FT( homogeneous(0,2)) / de;
            }
    case 1: switch (j)
            {
              case 0: return FT( homogeneous(1,0)) / de;
              case 1: return FT( l.a()-l.b() ) / FT( l.a()+l.b());
              case 2: return FT( homogeneous(1,2)) / de;
            }
    case 2: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(0);
              case 2: return FT(1);
            }
  }
  return FT(0);
}

CGAL_END_NAMESPACE

#endif // CGAL_AFF_TRANSFORMATIONH2_H