// 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.
//
// $Source: /CVSROOT/CGAL/Packages/H2/include/CGAL/Homogeneous/LineH2.h,v $
// $Revision: 1.15 $ $Date: 2004/02/22 22:52:28 $
// $Name: $
//
// Author(s) : Stefan Schirra
#ifndef CGAL_LINEH2_H
#define CGAL_LINEH2_H
#include <CGAL/Threetuple.h>
CGAL_BEGIN_NAMESPACE
template < class R_ >
class LineH2
{
typedef typename R_::FT FT;
typedef typename R_::RT RT;
typedef typename R_::Point_2 Point_2;
typedef typename R_::Vector_2 Vector_2;
typedef typename R_::Direction_2 Direction_2;
typedef typename R_::Segment_2 Segment_2;
typedef typename R_::Ray_2 Ray_2;
typedef typename R_::Line_2 Line_2;
typedef typename R_::Aff_transformation_2 Aff_transformation_2;
typedef Threetuple<RT> Rep;
typedef typename R_::template Handle<Rep>::type Base;
Base base;
public:
typedef R_ R;
LineH2() {}
LineH2(const Point_2& p, const Point_2& q);
LineH2(const RT& a, const RT& b, const RT& c);
LineH2(const Segment_2& s);
LineH2(const Ray_2& r);
LineH2(const Point_2& p, const Direction_2& d);
LineH2(const Point_2& p, const Vector_2& v);
bool operator==(const LineH2<R>& l) const ;
bool operator!=(const LineH2<R>& l) const ;
const RT & a() const { return get(base).e0; }
const RT & b() const { return get(base).e1; }
const RT & c() const { return get(base).e2; }
FT x_at_y(FT y) const;
FT y_at_x(FT x) const;
Line_2 perpendicular(const Point_2& p ) const;
Line_2 opposite() const;
Point_2 point() const;
Point_2 point(int i) const;
Point_2 projection(const Point_2& p) const;
Direction_2 direction() const;
Vector_2 to_vector() const;
Oriented_side oriented_side( const Point_2& p ) const;
bool has_on( const Point_2& p ) const;
bool has_on_boundary( const Point_2& p ) const;
bool has_on_positive_side( const Point_2& p ) const;
bool has_on_negative_side( const Point_2& p ) const;
bool is_horizontal() const;
bool is_vertical() const;
bool is_degenerate() const;
Line_2 transform(const Aff_transformation_2&) const;
};
template < class R >
CGAL_KERNEL_MEDIUM_INLINE
LineH2<R>::LineH2(const typename LineH2<R>::Point_2& p,
const typename LineH2<R>::Point_2& q)
: base(
// a() * X + b() * Y + c() * W() == 0
// | X Y W |
// | p.hx() p.hy() p.hw() |
// | q.hx() q.hy() q.hw() |
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx())
{}
template < class R >
CGAL_KERNEL_INLINE
LineH2<R>::LineH2(const RT& a, const RT& b, const RT& c)
: base(a, b, c)
{}
template < class R >
CGAL_KERNEL_INLINE
LineH2<R>::LineH2(const typename LineH2<R>::Segment_2& s)
{
Point_2 p = s.start();
Point_2 q = s.end();
base = Rep (
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx());
}
template < class R >
CGAL_KERNEL_INLINE
LineH2<R>::LineH2(const typename LineH2<R>::Ray_2& r)
{
Point_2 p = r.start();
Point_2 q = r.second_point();
base = Rep (
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
template < class R >
CGAL_KERNEL_INLINE
LineH2<R>::LineH2(const typename LineH2<R>::Point_2& p,
const typename LineH2<R>::Vector_2& v)
{
Point_2 q = p + v;
base = Rep (
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
template < class R >
CGAL_KERNEL_INLINE
LineH2<R>::LineH2(const typename LineH2<R>::Point_2& p,
const typename LineH2<R>::Direction_2& d)
{
Point_2 q = p + d.to_vector();
base = Rep (
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::FT
LineH2<R>::x_at_y(FT y) const
{
CGAL_kernel_precondition( !is_degenerate() );
return (FT(-b())*y - FT(c()) )/FT(a());
}
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::FT
LineH2<R>::y_at_x(FT x) const
{
CGAL_kernel_precondition( !is_degenerate() );
return (FT(-a())*x - FT(c()) )/FT(b());
}
template < class R >
CGAL_KERNEL_INLINE
typename R::Line_2
LineH2<R>::perpendicular(const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
return typename R::Line_2( -b()*p.hw(), a()*p.hw(), b()*p.hx() - a()*p.hy());
}
template < class R >
inline
typename R::Line_2
LineH2<R>::opposite() const
{ return typename R::Line_2( -a(), -b(), -c() ); }
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::Point_2
LineH2<R>::point() const
{
CGAL_kernel_precondition( !is_degenerate() );
if (is_vertical() )
{
return Point_2(-c(), RT(0) , a() );
}
else
{
return Point_2(RT(0) , -c(), b() );
}
}
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::Point_2
LineH2<R>::point(int i) const
{ return point() + RT(i) * to_vector(); }
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::Point_2
LineH2<R>::projection(const typename LineH2<R>::Point_2& p) const
{
CGAL_kernel_precondition( !is_degenerate() );
LineH2<R> l( p, Direction_2( a(), b() ));
return Point_2( b()*l.c() - l.b()*c(),
l.a()*c() - a()*l.c(),
a()*l.b() - l.a()*b() );
}
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::Vector_2
LineH2<R>::to_vector() const
{
CGAL_kernel_precondition( !is_degenerate() );
return Vector_2( b(), -a() );
}
template < class R >
CGAL_KERNEL_INLINE
typename LineH2<R>::Direction_2
LineH2<R>::direction() const
{
CGAL_kernel_precondition( !is_degenerate() );
return Direction_2( b(), -a() );
}
template < class R >
CGAL_KERNEL_INLINE
typename R::Line_2
LineH2<R>::transform(const typename LineH2<R>::Aff_transformation_2& t) const
{
CGAL_kernel_precondition( !is_degenerate() );
Point_2 p = point() + to_vector();
return typename R::Line_2( t.transform(point() ), t.transform(p) );
}
#ifndef CGAL_NO_OSTREAM_INSERT_LINEH2
template < class R >
std::ostream &
operator<<(std::ostream &os, const LineH2<R> &l)
{
switch(os.iword(IO::mode))
{
case IO::ASCII :
return os << l.a() << ' ' << l.b() << ' ' << l.c();
case IO::BINARY :
write(os, l.a());
write(os, l.b());
write(os, l.c());
return os;
default:
return os << "LineH2(" << l.a() << ", " << l.b() << ", " << l.c() <<')';
}
}
#endif // CGAL_NO_OSTREAM_INSERT_LINEH2
#ifndef CGAL_NO_ISTREAM_EXTRACT_LINEH2
template < class R >
std::istream &
operator>>(std::istream &is, LineH2<R> &p)
{
typename R::RT a, b, c;
switch(is.iword(IO::mode))
{
case IO::ASCII :
is >> a >> b >> c;
break;
case IO::BINARY :
read(is, a);
read(is, b);
read(is, c);
break;
default:
std::cerr << "" << std::endl;
std::cerr << "Stream must be in ascii or binary mode" << std::endl;
break;
}
p = LineH2<R>(a, b, c);
return is;
}
#endif // CGAL_NO_ISTREAM_EXTRACT_LINEH2
template < class R >
CGAL_KERNEL_INLINE
bool
LineH2<R>::has_on( const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
return ( ( a()*p.hx() + b()*p.hy() + c()*p.hw() ) == RT(0) );
}
template < class R >
CGAL_KERNEL_INLINE
bool
LineH2<R>::has_on_boundary( const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
return ( ( a()*p.hx() + b()*p.hy() + c()*p.hw() ) == RT(0) );
}
template < class R >
CGAL_KERNEL_INLINE
bool
LineH2<R>::has_on_positive_side( const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
return ( ( a()*p.hx() + b()*p.hy() + c()*p.hw() ) > RT(0) );
}
template < class R >
CGAL_KERNEL_INLINE
bool
LineH2<R>::has_on_negative_side( const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
return ( ( a()*p.hx() + b()*p.hy() + c()*p.hw() ) < RT(0) );
}
template < class R >
CGAL_KERNEL_INLINE
Oriented_side
LineH2<R>::oriented_side( const typename LineH2<R>::Point_2& p ) const
{
CGAL_kernel_precondition( !is_degenerate() );
RT v = a()*p.hx() + b()*p.hy() + c()*p.hw();
if (v > RT(0) )
{
return ON_POSITIVE_SIDE;
}
else
{
return (v < RT(0) ) ? ON_NEGATIVE_SIDE : ON_ORIENTED_BOUNDARY;
}
}
template < class R >
inline
bool
LineH2<R>::is_horizontal() const
{ return ( a() == RT(0) ); }
template < class R >
inline
bool
LineH2<R>::is_vertical() const
{ return ( b() == RT(0) ); }
template < class R >
inline
bool
LineH2<R>::is_degenerate() const
{ return (a() == RT(0) )&&(b() == RT(0) ) ; }
template < class R >
CGAL_KERNEL_MEDIUM_INLINE
bool
LineH2<R>::operator==(const LineH2<R>& l) const
{
if ( (a() * l.c() != l.a() * c() )
||(b() * l.c() != l.b() * c() ) )
{
return false;
}
int sc = static_cast<int>(CGAL_NTS sign(c()));
int slc = static_cast<int>(CGAL_NTS sign(l.c()));
if ( sc == slc )
{
if (sc == 0)
return ( (a()*l.b() == b()*l.a() )
&&(CGAL_NTS sign(a() )== CGAL_NTS sign( l.a() ))
&&(CGAL_NTS sign(b() )== CGAL_NTS sign( l.b() )) );
else
return true;
}
else
return false;
}
template < class R >
inline
bool
LineH2<R>::operator!=(const LineH2<R>& l) const
{ return !(*this == l); }
CGAL_END_NAMESPACE
#endif // CGAL_LINEH2_H
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