LineS2< FT > Class Template Reference

#include <LineS2.h>

Public Member Functions
	LineS2 ()
	LineS2 (const PointS2< FT > &p, const PointS2< FT > &q)
	LineS2 (const FT &a, const FT &b, const FT &c)
	LineS2 (const SegmentS2< FT > &s)
	LineS2 (const RayS2< FT > &r)
	LineS2 (const PointS2< FT > &p, const DirectionS2< FT > &d)
bool	operator== (const LineS2< FT > &l) const
bool	operator!= (const LineS2< FT > &l) const
FT	a () const
FT	b () const
FT	c () const
FT	x_at_y (const FT &y) const
FT	y_at_x (const FT &x) const
LineS2< FT >	perpendicular (const PointS2< FT > &p) const
LineS2< FT >	opposite () const
PointS2< FT >	point (int i) const
PointS2< FT >	point () const
PointS2< FT >	projection (const PointS2< FT > &p) const
DirectionS2< FT >	direction () const
Oriented_side	oriented_side (const PointS2< FT > &p) const
bool	has_on_boundary (const PointS2< FT > &p) const
bool	has_on_positive_side (const PointS2< FT > &p) const
bool	has_on_negative_side (const PointS2< FT > &p) const
bool	is_horizontal () const
bool	is_vertical () const
bool	is_degenerate () const
LineS2< FT >	transform (const Aff_transformationS2< FT > &t) const
void	new_rep (const PointS2< FT > &p, const PointS2< FT > &q)
void	new_rep (const FT &a, const FT &b, const FT &c)

Public Attributes
FT	e0
FT	e1
FT	e2

Detailed Description

template<class FT>
class LineS2< FT >

Definition at line 62 of file LineS2.h.

Constructor & Destructor Documentation

LineS2 ( )

inline

Definition at line 117 of file LineS2.h.

{}

LineS2 ( const PointS2< FT > &  p, const PointS2< FT > &  q  )

inline

Definition at line 140 of file LineS2.h.

{ new_rep(p,q); }

LineS2 ( const FT &  a, const FT &  b, const FT &  c  )

inline

Definition at line 145 of file LineS2.h.

{ new_rep(a,b,c); }

LineS2 ( const SegmentS2< FT > &  s )

inline

Definition at line 150 of file LineS2.h.

References SegmentS2< FT >::end(), and SegmentS2< FT >::start().

{ new_rep( s.start(), s.end()); }

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LineS2 ( const RayS2< FT > &  r )

inline

Definition at line 155 of file LineS2.h.

References RayS2< FT >::second_point(), and RayS2< FT >::start().

{ new_rep(r.start(), r.second_point()); }

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CGAL_KERNEL_INLINE LineS2	(	const PointS2< FT > &	p,
		const DirectionS2< FT > &	d
	)

Definition at line 160 of file LineS2.h.

References DirectionS2< FT >::dx(), DirectionS2< FT >::dy(), PointS2< FT >::x(), and PointS2< FT >::y().

{ new_rep(-d.dy(), d.dx(), -d.dx()* p.y()  + d.dy() * p.x()); }

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Member Function Documentation

FT a ( ) const

inline

Definition at line 188 of file LineS2.h.

Referenced by LineS2< FT >::operator==().

{ return e0; }

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FT b ( ) const

inline

Definition at line 193 of file LineS2.h.

Referenced by LineS2< FT >::operator==().

{ return e1; }

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FT c ( ) const

inline

Definition at line 198 of file LineS2.h.

Referenced by LineS2< FT >::operator==().

{ return e2; }

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DirectionS2< FT > direction ( ) const

inline

Definition at line 270 of file LineS2.h.

Referenced by Aff_transformationS2< FT >::transform().

{ return DirectionS2<FT>( b(), -a() ); }

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bool has_on_boundary ( const PointS2< FT > &  p ) const

inline

Definition at line 280 of file LineS2.h.

References PointS2< FT >::x(), and PointS2< FT >::y().

{ return (a()*p.x() + b()*p.y() + c()) == FT(0); }

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CGAL_KERNEL_INLINE bool has_on_negative_side

(

const PointS2< FT > &

p

)

const

Definition at line 290 of file LineS2.h.

References PointS2< FT >::x(), and PointS2< FT >::y().

{ return (a()*p.x() + b()*p.y() + c()) <  FT(0); }

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bool has_on_positive_side ( const PointS2< FT > &  p ) const

inline

Definition at line 285 of file LineS2.h.

References PointS2< FT >::x(), and PointS2< FT >::y().

{ return (a()*p.x() + b()*p.y() + c()) >  FT(0); }

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bool is_degenerate ( ) const

inline

Definition at line 305 of file LineS2.h.

{ return (a() == FT(0)) && (b() == FT(0)) ; }

bool is_horizontal ( ) const

inline

Definition at line 295 of file LineS2.h.

{ return a() == FT(0) ; }

bool is_vertical ( ) const

inline

Definition at line 300 of file LineS2.h.

{ return b() == FT(0) ; }

CGAL_KERNEL_INLINE void new_rep	(	const PointS2< FT > &	p,
		const PointS2< FT > &	q
	)

Definition at line 122 of file LineS2.h.

References PointS2< FT >::x(), and PointS2< FT >::y().

{
  e0 = p.y() - q.y();
  e1 = q.x() - p.x();
  e2 = p.x()*q.y() - p.y()*q.x();
}

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CGAL_KERNEL_INLINE void new_rep	(	const FT &	a,
		const FT &	b,
		const FT &	c
	)

Definition at line 131 of file LineS2.h.

{
  e0 = a;
  e1 = b;
  e2 = c;
}

bool operator!= ( const LineS2< FT > &  l ) const

inline

Definition at line 183 of file LineS2.h.

{ return !(*this == l); }

CGAL_KERNEL_MEDIUM_INLINE bool operator==

(

const LineS2< FT > &

l

)

const

Definition at line 166 of file LineS2.h.

References LineS2< FT >::a(), LineS2< FT >::b(), LineS2< FT >::c(), CGAL_NTS, and sign().

{
  if (  (a() * l.c() != l.a() * c())
      ||(b() * l.c() != l.b() * c()) )
      return false;
  int sc  = CGAL_NTS sign(c());
  int slc = CGAL_NTS sign(l.c());
  if ( sc == slc )
      return (sc == 0) ?  ( a()*l.b() ==  b()*l.a() )
                         && (CGAL_NTS sign(a() ) == CGAL_NTS sign( l.a() ))
                         && (CGAL_NTS sign(b() ) == CGAL_NTS sign( l.b() ))
                       : true;
  return false;
}

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LineS2< FT > opposite ( ) const

inline

Definition at line 226 of file LineS2.h.

{ return LineS2<FT>( -a(), -b(), -c() ); }

CGAL_KERNEL_INLINE Oriented_side oriented_side

(

const PointS2< FT > &

p

)

const

Definition at line 275 of file LineS2.h.

References CGAL_NTS, sign(), PointS2< FT >::x(), and PointS2< FT >::y().

{ return Oriented_side(CGAL_NTS sign(a()*p.x() + b()*p.y() + c())); }

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LineS2< FT > perpendicular ( const PointS2< FT > &  p ) const

inline

Definition at line 221 of file LineS2.h.

References PointS2< FT >::x(), and PointS2< FT >::y().

{ return LineS2<FT>( -b() , a() , b() * p.x() - a() * p.y()  ); }

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CGAL_KERNEL_MEDIUM_INLINE PointS2< FT > point

(

int

i

)

const

Definition at line 231 of file LineS2.h.

Referenced by Aff_transformationS2< FT >::transform().

{
  if (i == 0)
    return is_vertical() ? PointS2<FT>( (-b()-c())/a(), FT(1) )
                         : PointS2<FT>( FT(1), -(a()+c())/b());
  if (i == 1)
    return is_vertical() ? PointS2<FT>( (-b()-c())/a() + b(), FT(1) - a() )
                         : PointS2<FT>( FT(1) + b(), -(a()+c())/b() - a() );
  // we add i times the direction
  if (is_vertical())
    return PointS2<FT>( (-b()-c())/a() + FT(i)*b(), FT(1) - FT(i)*a() );
  return PointS2<FT>( FT(1) + FT(i)*b(), -(a()+c())/b() - FT(i)*a() );
}

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CGAL_KERNEL_INLINE PointS2< FT > point

(

)

const

Definition at line 247 of file LineS2.h.

{
  return is_vertical() ? PointS2<FT>( (-b()-c())/a(), FT(1) )
                       : PointS2<FT>( FT(1), -(a()+c())/b());
}

CGAL_KERNEL_MEDIUM_INLINE PointS2< FT > projection

(

const PointS2< FT > &

p

)

const

Definition at line 255 of file LineS2.h.

References PointS2< FT >::x(), PointS2< FT >::y(), and y.

{
  if (is_horizontal())
      return PointS2<FT>(p.x(), -c()/b());

  if (is_vertical())
      return PointS2<FT>( -c()/a(), p.y());

  FT ab = a()/b(), ba = b()/a(), ca = c()/a();
  FT y = ( -p.x() + ab*p.y() - ca ) / ( ba + ab );
  return PointS2<FT>(-ba * y - ca, y);
}

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LineS2< FT > transform ( const Aff_transformationS2< FT > &  t ) const

inline

Definition at line 310 of file LineS2.h.

References Aff_transformationS2< FT >::transform().

{ return LineS2<FT>( t.transform(point(0) ), t.transform(direction() )); }

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CGAL_KERNEL_INLINE FT x_at_y

(

const FT &

y

)

const

Definition at line 203 of file LineS2.h.

References CGAL_kernel_precondition_msg.

{
  CGAL_kernel_precondition_msg( (a() != FT(0)),
               "Line::x_at_y(const FT& y) is undefined for horizontal line" );
  return ( -b()*y - c() ) / a();
}

CGAL_KERNEL_INLINE FT y_at_x

(

const FT &

x

)

const

Definition at line 212 of file LineS2.h.

References CGAL_kernel_precondition_msg.

{
  CGAL_kernel_precondition_msg( (b() != FT(0)),
              "Line::x_at_y(const FT& y) is undefined for vertical line");
  return ( -a()*x - c() ) / b();
}

Member Data Documentation

FT e0

Definition at line 108 of file LineS2.h.

FT e1

Definition at line 109 of file LineS2.h.

FT e2

Definition at line 110 of file LineS2.h.

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

• LineS2.h