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// Copyright (c) 2000
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h $
// $Id: include/CGAL/Cartesian/Aff_transformation_rep_3.h 08b27d3db14 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Herve Bronnimann
#ifndef CGAL_CARTESIAN_AFF_TRANSFORMATION_REP_3_H
#define CGAL_CARTESIAN_AFF_TRANSFORMATION_REP_3_H
#include <ostream>
#include <CGAL/determinant.h>
namespace CGAL {
template < class R >
class Aff_transformation_rep_baseC3
: public Ref_counted_virtual
{
public:
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;
virtual ~Aff_transformation_rep_baseC3(){}
virtual Point_3 transform(const Point_3 &p) const = 0;
virtual Vector_3 transform(const Vector_3 &v) const = 0;
virtual Direction_3 transform(const Direction_3 &d) const = 0;
virtual Plane_3 transform(const Plane_3& p) const = 0;
virtual Aff_transformation_3 operator*(
const Aff_transformation_rep_baseC3 &t) const = 0;
virtual Aff_transformation_3 compose(
const Translation_repC3<R> &t) const = 0;
virtual Aff_transformation_3 compose(
const Scaling_repC3<R> &t) const = 0;
virtual Aff_transformation_3 compose(
const Aff_transformation_repC3<R> &t) const = 0;
virtual Aff_transformation_3 inverse() const = 0;
virtual Aff_transformation_3 transpose() const = 0;
virtual bool is_even() const = 0;
virtual bool is_translation() const { return false; }
virtual bool is_scaling() const { return false; }
virtual FT cartesian(int i, int j) const = 0;
virtual std::ostream &print(std::ostream &os) const = 0;
};
template < class R >
class Aff_transformation_repC3
: public Aff_transformation_rep_baseC3<R>
{
friend class Translation_repC3<R>;
friend class Scaling_repC3<R>;
public:
typedef typename R::FT FT;
typedef Aff_transformation_repC3<R> Self;
typedef Aff_transformation_rep_baseC3<R> Transformation_base_3;
typedef Aff_transformation_repC3<R> Transformation_3;
typedef Translation_repC3<R> Translation_3;
typedef Scaling_repC3<R> Scaling_3;
typedef typename Transformation_base_3::Point_3 Point_3;
typedef typename Transformation_base_3::Vector_3 Vector_3;
typedef typename Transformation_base_3::Direction_3 Direction_3;
typedef typename Transformation_base_3::Plane_3 Plane_3;
typedef typename Transformation_base_3::
Aff_transformation_3 Aff_transformation_3;
Aff_transformation_repC3()
{}
Aff_transformation_repC3(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)
: t11(m11), t12(m12), t13(m13), t14(FT(0)),
t21(m21), t22(m22), t23(m23), t24(FT(0)),
t31(m31), t32(m32), t33(m33), t34(FT(0))
{}
Aff_transformation_repC3(
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
)
: t11(m11), t12(m12), t13(m13), t14(m14),
t21(m21), t22(m22), t23(m23), t24(m24),
t31(m31), t32(m32), t33(m33), t34(m34)
{}
virtual ~Aff_transformation_repC3()
{}
virtual Point_3 transform(const Point_3& p) const // FIXME : construction
{
typename R::Construct_point_3 construct_point_3;
return construct_point_3(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);
}
// note that a vector is not translated
virtual Vector_3 transform(const Vector_3& v) const // FIXME : construction
{
return Vector_3(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());
}
// note that a direction is not translated
virtual Direction_3 transform(const Direction_3& dir) const
{ // FIXME : construction
Vector_3 v = dir.to_vector();
return Direction_3(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());
}
virtual Plane_3 transform(const Plane_3& p) const
{
if (is_even())
return Plane_3(transform(p.point()),
transpose().inverse().transform(p.orthogonal_direction()));
else
return Plane_3(transform(p.point()),
- transpose().inverse().transform(p.orthogonal_direction()));
}
// Note that Aff_transformation is not defined yet,
// so the following 6 functions have to be implemented
// outside class body
virtual Aff_transformation_3 inverse() const;
virtual Aff_transformation_3 transpose() const;
virtual Aff_transformation_3 operator*(const Transformation_base_3 &t) const;
virtual Aff_transformation_3 compose(const Transformation_3 &t) const;
virtual Aff_transformation_3 compose(const Translation_3 &t) const;
virtual Aff_transformation_3 compose(const Scaling_3 &t) const;
virtual bool is_even() const
{
return sign_of_determinant(t11, t12, t13,
t21, t22, t23,
t31, t32, t33) == POSITIVE;
}
virtual FT cartesian(int i, int j) const
{
switch (i)
{
case 0: switch (j)
{
case 0: return t11;
case 1: return t12;
case 2: return t13;
default: return t14;
}
case 1: switch (j)
{
case 0: return t21;
case 1: return t22;
case 2: return t23;
default: return t24;
}
case 2: switch (j)
{
case 0: return t31;
case 1: return t32;
case 2: return t33;
default: return t34;
}
case 3: switch (j)
{
case 0: return FT(0);
case 1: return FT(0);
case 2: return FT(0);
default: return FT(1);
}
}
return FT(0);
}
virtual std::ostream &print(std::ostream &os) const
{
os <<"Aff_transformationC3("<<t11<<' '<<t12<<' '<<t13<<' '<<t14<<std::endl;
os <<" "<<t21<<' '<<t22<<' '<<t23<<' '<<t24<<std::endl;
os <<" "<<t31<<' '<<t32<<' '<<t33<<' '<<t34<<")";
return os;
}
private:
FT t11, t12, t13, t14; // FIXME : Wouldn't this be better with an array ?
FT t21, t22, t23, t24;
FT t31, t32, t33, t34;
};
template < class R >
CGAL_KERNEL_LARGE_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::inverse() const // FIXME : construction
{
return Aff_transformation_3(
determinant( t22, t23, t32, t33), // i 11
-determinant( t12, t13, t32, t33), // i 12
determinant( t12, t13, t22, t23), // i 13
-determinant( t12, t13, t14, t22, t23, t24, t32, t33, t34 ),
-determinant( t21, t23, t31, t33), // i 21
determinant( t11, t13, t31, t33), // i 22
-determinant( t11, t13, t21, t23), // i 23
determinant( t11, t13, t14, t21, t23, t24, t31, t33, t34 ),
determinant( t21, t22, t31, t32), // i 31
-determinant( t11, t12, t31, t32), // i 32
determinant( t11, t12, t21, t22), // i 33
-determinant( t11, t12, t14, t21, t22, t24, t31, t32, t34 ),
determinant( t11, t12, t13, t21, t22, t23, t31, t32, t33 ));
}
template < class R >
CGAL_KERNEL_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::
operator*(const Aff_transformation_rep_baseC3<R> &t) const
{
return t.compose(*this);
}
template < class R >
CGAL_KERNEL_LARGE_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::
compose(const Aff_transformation_repC3<R> &t) const // FIXME : construction
{
return Aff_transformation_3(t.t11*t11 + t.t12*t21 + t.t13*t31,
t.t11*t12 + t.t12*t22 + t.t13*t32,
t.t11*t13 + t.t12*t23 + t.t13*t33,
t.t11*t14 + t.t12*t24 + t.t13*t34 + t.t14,
t.t21*t11 + t.t22*t21 + t.t23*t31,
t.t21*t12 + t.t22*t22 + t.t23*t32,
t.t21*t13 + t.t22*t23 + t.t23*t33,
t.t21*t14 + t.t22*t24 + t.t23*t34 + t.t24,
t.t31*t11 + t.t32*t21 + t.t33*t31,
t.t31*t12 + t.t32*t22 + t.t33*t32,
t.t31*t13 + t.t32*t23 + t.t33*t33,
t.t31*t14 + t.t32*t24 + t.t33*t34 + t.t34);
}
template < class R >
CGAL_KERNEL_LARGE_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::
compose(const Translation_repC3<R> &t) const // FIXME : construction
{
return Aff_transformation_3(t11,
t12,
t13,
t14 + t.translationvector_.x(),
t21,
t22,
t23,
t24 + t.translationvector_.y(),
t31,
t32,
t33,
t34 + t.translationvector_.z());
}
template < class R >
CGAL_KERNEL_LARGE_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::
compose(const Scaling_repC3<R> &t) const // FIXME : construction
{
return Aff_transformation_3(t.scalefactor_ * t11,
t.scalefactor_ * t12,
t.scalefactor_ * t13,
t.scalefactor_ * t14,
t.scalefactor_ * t21,
t.scalefactor_ * t22,
t.scalefactor_ * t23,
t.scalefactor_ * t24,
t.scalefactor_ * t31,
t.scalefactor_ * t32,
t.scalefactor_ * t33,
t.scalefactor_ * t34);
}
template < class R >
CGAL_KERNEL_LARGE_INLINE
typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::transpose() const
{
return Aff_transformation_3( t11, t21, t31, t14,
t12, t22, t32, t24,
t13, t23, t33, t34);
}
} //namespace CGAL
#endif // CGAL_CARTESIAN_AFF_TRANSFORMATION_REP_3_H
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