Aff_transformation_repS3< FT > Class Template Reference

#include <Aff_transformationS3.h>

Inheritance diagram for Aff_transformation_repS3< FT >:

Collaboration diagram for Aff_transformation_repS3< FT >:

Public Member Functions
	Aff_transformation_repS3 ()
	Aff_transformation_repS3 (const FT &m11, const FT &m12, const FT &m13, const FT &m21, const FT &m22, const FT &m23, const FT &m31, const FT &m32, const FT &m33)
	Aff_transformation_repS3 (const FT &m11, const FT &m12, const FT &m13, const FT &m14, const FT &m21, const FT &m22, const FT &m23, const FT &m24, const FT &m31, const FT &m32, const FT &m33, const FT &m34)
	~Aff_transformation_repS3 ()
PointS3< FT >	transform (const PointS3< FT > &p) const
VectorS3< FT >	transform (const VectorS3< FT > &v) const
DirectionS3< FT >	transform (const DirectionS3< FT > &dir) const
Aff_transformationS3< FT >	inverse () const
virtual Aff_transformationS3< FT >	general_form () const
virtual Aff_transformationS3< FT >	transpose () const
virtual bool	is_even () const
virtual FT	cartesian (int i, int j) const
std::ostream &	print (std::ostream &os) const
Public Member Functions inherited from Aff_transformation_rep_baseS3< FT >
virtual	~Aff_transformation_rep_baseS3 ()

Private Attributes
FT	t11
FT	t12
FT	t13
FT	t14
FT	t21
FT	t22
FT	t23
FT	t24
FT	t31
FT	t32
FT	t33
FT	t34

Friends
class	Aff_transformationS3< FT >
Aff_transformationS3< FT > _general_transformation_composition	CGAL_NULL_TMPL_ARGS (Aff_transformation_repS3< FT > &l, Aff_transformation_repS3< FT > &r)
Aff_transformationS3< FT >	operator*CGAL_NULL_TMPL_ARGS (const Aff_transformationS3< FT > &a, const Aff_transformationS3< FT > &b)

Additional Inherited Members
Protected Member Functions inherited from Leda_like_rep
	Leda_like_rep ()
virtual	~Leda_like_rep ()
Protected Attributes inherited from Leda_like_rep
int	count

Detailed Description

template<class FT>
class Aff_transformation_repS3< FT >

Definition at line 66 of file Aff_transformationS3.h.

Constructor & Destructor Documentation

Aff_transformation_repS3 ( )

inline

Definition at line 129 of file Aff_transformationS3.h.

  {}

Aff_transformation_repS3 ( const FT &  m11, const FT &  m12, const FT &  m13, const FT &  m21, const FT &  m22, const FT &  m23, const FT &  m31, const FT &  m32, const FT &  m33  )

inline

Definition at line 132 of file Aff_transformationS3.h.

    : t11(m11), t12(m12), t13(m13), t14(0),
      t21(m21), t22(m22), t23(m23), t24(0),
      t31(m31), t32(m32), t33(m33), t34(0)
  {}

Aff_transformation_repS3 ( const FT &  m11, const FT &  m12, const FT &  m13, const FT &  m14, const FT &  m21, const FT &  m22, const FT &  m23, const FT &  m24, const FT &  m31, const FT &  m32, const FT &  m33, const FT &  m34  )

inline

Definition at line 140 of file Aff_transformationS3.h.

    : t11(m11), t12(m12), t13(m13), t14(m14),
      t21(m21), t22(m22), t23(m23), t24(m24),
      t31(m31), t32(m32), t33(m33), t34(m34)
  {}

~Aff_transformation_repS3 ( )

inline

Definition at line 153 of file Aff_transformationS3.h.

  {}

Member Function Documentation

virtual FT cartesian ( int  i, int  j  ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 253 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t14, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t24, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, and Aff_transformation_repS3< FT >::t34.

  {
    switch (i)
    {
    case 0: switch (j)
            {
              case 0: return t11;
              case 1: return t12;
              case 2: return t13;
              case 3: return t14;
            }
    case 1: switch (j)
            {
              case 0: return t21;
              case 1: return t22;
              case 2: return t23;
              case 3: return t24;
            }
    case 2: switch (j)
            {
              case 0: return t31;
              case 1: return t32;
              case 2: return t33;
              case 3: return t34;
            }
    case 3: switch (j)
            {
              case 0: return FT(0);
              case 1: return FT(0);
              case 2: return FT(0);
              case 3: return FT(1);
            }
    }
  return FT(0);
  }

virtual Aff_transformationS3<FT> general_form ( ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 231 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t14, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t24, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, and Aff_transformation_repS3< FT >::t34.

  {
    return Aff_transformationS3<FT>(t11, t12, t13, t14,
                                    t21, t22, t23, t24,
                                    t31, t32, t33, t34);
  }

Aff_transformationS3<FT> inverse ( ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 182 of file Aff_transformationS3.h.

References det2x2_by_formula(), det3x3_by_formula(), Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t14, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t24, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, and Aff_transformation_repS3< FT >::t34.

  {
 return Aff_transformationS3<FT>(
                           det2x2_by_formula( t22, t23,
                                              t32, t33),         // i 11

                        -  det2x2_by_formula( t12, t13,
                                              t32, t33),         // i 12

                           det2x2_by_formula( t12, t13,
                                              t22, t23),         // i 13

                        -  det3x3_by_formula( t12, t13, t14,
                                              t22, t23, t24,     // i 14
                                              t32, t33, t34 ),

                        -  det2x2_by_formula( t21, t23,
                                              t31, t33),         // i 21

                           det2x2_by_formula( t11, t13,
                                              t31, t33),         // i 22

                        -  det2x2_by_formula( t11, t13,
                                              t21, t23),         // i 23

                           det3x3_by_formula( t11, t13, t14,
                                              t21, t23, t24,     // i 24
                                              t31, t33, t34 ),

                           det2x2_by_formula( t21, t22,
                                              t31, t32),         // i 31

                        -  det2x2_by_formula( t11, t12,
                                              t31, t32),         // i 32

                           det2x2_by_formula( t11, t12,
                                              t21, t22),         // i 33

                        -  det3x3_by_formula( t11, t12, t14,
                                              t21, t22, t24,     // i 34
                                              t31, t32, t34 ),

                           det3x3_by_formula( t11, t12, t13,
                                              t21, t22, t23,     // i 44
                                              t31, t32, t33 )
                                                       ) ;
  }

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virtual bool is_even ( ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 246 of file Aff_transformationS3.h.

References POSITIVE, sign_of_determinant3x3(), Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, and Aff_transformation_repS3< FT >::t33.

  {
    return sign_of_determinant3x3(t11, t12, t13,
                                  t21, t22, t23,
                                  t31, t32, t33) == POSITIVE;
  }

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std::ostream& print ( std::ostream &  os ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 290 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t14, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t24, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, and Aff_transformation_repS3< FT >::t34.

  {
    os <<"                   "<< t11 <<' '<< t12 <<' '<< t13 <<' '<< t14 <<"\n";
    os <<"                   "<< t21 <<' '<< t22 <<' '<< t23 <<' '<< t24 <<"\n";
    os <<"                   "<< t31 <<' '<< t32 <<' '<< t33 <<' '<< t34 <<")\n";

    return os;
  }

PointS3<FT> transform ( const PointS3< FT > &  p ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 156 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t14, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t24, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, Aff_transformation_repS3< FT >::t34, PointS3< FT >::x(), PointS3< FT >::y(), and PointS3< FT >::z().

  {
    return PointS3<FT>(t11 * p.x() + t12 * p.y() + t13 * p.z() + t14,
                       t21 * p.x() + t22 * p.y() + t23 * p.z() + t24,
                       t31 * p.x() + t32 * p.y() + t33 * p.z() + t34);
  }

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VectorS3<FT> transform ( const VectorS3< FT > &  v ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 165 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, VectorS3< FT >::x(), VectorS3< FT >::y(), and VectorS3< FT >::z().

  {
    return VectorS3<FT>(t11 * v.x() + t12 * v.y() + t13 * v.z(),
                        t21 * v.x() + t22 * v.y() + t23 * v.z(),
                        t31 * v.x() + t32 * v.y() + t33 * v.z());
  }

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DirectionS3<FT> transform ( const DirectionS3< FT > &  dir ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 174 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, Aff_transformation_repS3< FT >::t33, v, DirectionS3< FT >::vector(), VectorS3< FT >::x(), VectorS3< FT >::y(), and VectorS3< FT >::z().

  {
    VectorS3<FT> v = dir.vector();
    return DirectionS3<FT>(t11 * v.x() + t12 * v.y() + t13 * v.z(),
                           t21 * v.x() + t22 * v.y() + t23 * v.z(),
                           t31 * v.x() + t32 * v.y() + t33 * v.z());
  }

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virtual Aff_transformationS3<FT> transpose ( ) const

inlinevirtual

Implements Aff_transformation_rep_baseS3< FT >.

Definition at line 238 of file Aff_transformationS3.h.

References Aff_transformation_repS3< FT >::t11, Aff_transformation_repS3< FT >::t12, Aff_transformation_repS3< FT >::t13, Aff_transformation_repS3< FT >::t21, Aff_transformation_repS3< FT >::t22, Aff_transformation_repS3< FT >::t23, Aff_transformation_repS3< FT >::t31, Aff_transformation_repS3< FT >::t32, and Aff_transformation_repS3< FT >::t33.

  {
    FT ft0(0);
    return Aff_transformationS3<FT>( t11, t21, t31, ft0,
                                     t12, t22, t32, ft0,
                                     t13, t23, t33, ft0);
  }

Friends And Related Function Documentation

friend class Aff_transformationS3< FT >

friend

Definition at line 117 of file Aff_transformationS3.h.

Aff_transformationS3<FT> _general_transformation_composition CGAL_NULL_TMPL_ARGS ( Aff_transformation_repS3< FT > &  l, Aff_transformation_repS3< FT > &  r  )

friend

Aff_transformationS3<FT> operator*CGAL_NULL_TMPL_ARGS ( const Aff_transformationS3< FT > &  a, const Aff_transformationS3< FT > &  b  )

friend

Member Data Documentation

FT t11

private

Definition at line 300 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t12

private

Definition at line 300 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t13

private

Definition at line 300 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t14

private

Definition at line 300 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::print(), and Aff_transformation_repS3< FT >::transform().

FT t21

private

Definition at line 301 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t22

private

Definition at line 301 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t23

private

Definition at line 301 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t24

private

Definition at line 301 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::print(), and Aff_transformation_repS3< FT >::transform().

FT t31

private

Definition at line 302 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t32

private

Definition at line 302 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t33

private

Definition at line 302 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::is_even(), Aff_transformation_repS3< FT >::print(), Aff_transformation_repS3< FT >::transform(), and Aff_transformation_repS3< FT >::transpose().

FT t34

private

Definition at line 302 of file Aff_transformationS3.h.

Referenced by _general_transformation_composition(), Aff_transformation_repS3< FT >::cartesian(), Aff_transformation_repS3< FT >::general_form(), Aff_transformation_repS3< FT >::inverse(), Aff_transformation_repS3< FT >::print(), and Aff_transformation_repS3< FT >::transform().

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

• Aff_transformationS3.h