DGtal::ClosedIntegerHalfPlane< TSpace > Struct Template Reference

#include <ClosedIntegerHalfPlane.h>

Public Types
typedef ClosedIntegerHalfPlane < TSpace >	Self
typedef TSpace	Space
typedef Space::Integer	Integer
typedef Space::Point	Point
typedef Space::Vector	Vector

Public Member Functions
	BOOST_CONCEPT_ASSERT ((CSpace< TSpace >))
	~ClosedIntegerHalfPlane ()
	ClosedIntegerHalfPlane (const Vector &aN, const Integer &aC)
	ClosedIntegerHalfPlane (const Point &A, const Point &B, const Point &inP, IntegerComputer< Integer > &ic)
bool	operator() (const Point &p) const
bool	isOnBoundary (const Point &p) const
Vector	tangent () const
void	negate ()
void	selfDisplay (std::ostream &out) const
bool	isValid () const

Data Fields
Vector	N
Integer	c

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Detailed Description

template<typename TSpace>
struct DGtal::ClosedIntegerHalfPlane< TSpace >

Aim: A half-space specified by a vector N and a constant c. The half-space is the set \( \{ P \in Z^2, N.P \le c \} \).

Description of template class 'ClosedIntegerHalfPlane'

A model of boost::DefaultConstructible, boost::CopyConstructible, boost::Assignable, CPointPredicate.

Examples:

arithmetic/lower-integer-convex-hull.cpp.

Definition at line 63 of file ClosedIntegerHalfPlane.h.

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Member Typedef Documentation

template<typename TSpace>

typedef Space::Integer DGtal::ClosedIntegerHalfPlane< TSpace >::Integer

Definition at line 69 of file ClosedIntegerHalfPlane.h.

template<typename TSpace>

typedef Space::Point DGtal::ClosedIntegerHalfPlane< TSpace >::Point

Definition at line 70 of file ClosedIntegerHalfPlane.h.

template<typename TSpace>

typedef ClosedIntegerHalfPlane<TSpace> DGtal::ClosedIntegerHalfPlane< TSpace >::Self

Definition at line 65 of file ClosedIntegerHalfPlane.h.

template<typename TSpace>

typedef TSpace DGtal::ClosedIntegerHalfPlane< TSpace >::Space

Definition at line 68 of file ClosedIntegerHalfPlane.h.

template<typename TSpace>

typedef Space::Vector DGtal::ClosedIntegerHalfPlane< TSpace >::Vector

Definition at line 71 of file ClosedIntegerHalfPlane.h.

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Constructor & Destructor Documentation

template<typename TSpace >

DGtal::ClosedIntegerHalfPlane< TSpace >::~ClosedIntegerHalfPlane ( )

inline

Destructor.

Definition at line 44 of file ClosedIntegerHalfPlane.ih.

{}

template<typename TSpace >

DGtal::ClosedIntegerHalfPlane< TSpace >::ClosedIntegerHalfPlane ( const Vector &  aN, const Integer &  aC  )

inline

Constructor from normal and constant.

Parameters:

aN	a vector that defines the normal direction to the half-plane.
aC	the constant that defines the bound.

Definition at line 50 of file ClosedIntegerHalfPlane.ih.

  : N( aN ), c( aC ) 
{}

template<typename TSpace >

DGtal::ClosedIntegerHalfPlane< TSpace >::ClosedIntegerHalfPlane ( const Point &  A, const Point &  B, const Point &  inP, IntegerComputer< Integer > &  ic  )

inline

Constructor. Computes the half-space of the form N.P<=c whose supporting line passes through A and B such that the point inP satisfies the constraint.

Parameters:

A	any point.
B	any point different from A.
inP	any point not on the straight line (AB).
ic	any compatible integer computer.

Returns:

the corresponding half-space.

Definition at line 95 of file ClosedIntegerHalfPlane.ih.

References DGtal::IntegerComputer< TInteger >::floorDiv(), DGtal::IntegerComputer< TInteger >::gcd(), and DGtal::IntegerComputer< TInteger >::getDotProduct().

{
  N[ 0 ] = A[ 1 ] - B[ 1 ];
  N[ 1 ] = B[ 0 ] - A[ 0 ];
  ic.getDotProduct( c, N, A );
  Integer c1;
  ic.getDotProduct( c1, N, inP );
  if ( c1 > c )
    {
      N.negate();
      c = -c;
    }
  //simplification of the constraint
  Integer g = ic.gcd( N[ 0 ], N[ 1 ] );
  N /= g;
  ic.floorDiv( c, g );  
}

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Member Function Documentation

template<typename TSpace>

DGtal::ClosedIntegerHalfPlane< TSpace >::BOOST_CONCEPT_ASSERT

(

(CSpace< TSpace >)

)

template<typename TSpace >

bool DGtal::ClosedIntegerHalfPlane< TSpace >::isOnBoundary ( const Point &  p ) const

inline

Parameters:

p	any point in the plane.

Returns:

'true' if p is on the boundary of the half-space (i.e. N.p == c ).

Definition at line 67 of file ClosedIntegerHalfPlane.ih.

Referenced by DGtal::LatticePolytope2D< TSpace, TSequence >::getAllPointsOfHull(), and DGtal::LatticePolytope2D< TSpace, TSequence >::getFirstPointsOfHull().

{
  return N.dot( p ) == c;
}

template<typename TSpace >

bool DGtal::ClosedIntegerHalfPlane< TSpace >::isValid ( ) const

inline

Checks the validity/consistency of the object.

Returns:

'true' if the object is valid, 'false' otherwise.

Definition at line 136 of file ClosedIntegerHalfPlane.ih.

{
    return true;
}

template<typename TSpace >

void DGtal::ClosedIntegerHalfPlane< TSpace >::negate ( )

inline

Negates the half-space. Only the boundary is common.

Definition at line 85 of file ClosedIntegerHalfPlane.ih.

References DGtal::ClosedIntegerHalfPlane< TSpace >::negate().

Referenced by DGtal::LatticePolytope2D< TSpace, TSequence >::getIncludedDigitalPoints(), DGtal::LatticePolytope2D< TSpace, TSequence >::halfSpace(), and DGtal::ClosedIntegerHalfPlane< TSpace >::negate().

{
  N.negate(); // = Point( -N[ 0 ], -N[ 1 ] ); 
  c = -c;
}

template<typename TSpace >

bool DGtal::ClosedIntegerHalfPlane< TSpace >::operator() ( const Point &  p ) const

inline

Parameters:

p	any point in the plane.

Returns:

'true' if p is inside the half-space (i.e. N.p <= c ).

Definition at line 58 of file ClosedIntegerHalfPlane.ih.

{
  return N.dot( p ) <= c;
}

template<typename TSpace >

void DGtal::ClosedIntegerHalfPlane< TSpace >::selfDisplay ( std::ostream &  out ) const

inline

Writes/Displays the object on an output stream.

Parameters:

out	the output stream where the object is written.

Definition at line 124 of file ClosedIntegerHalfPlane.ih.

{
  out << "[ClosedIntegerHalfPlane N=" << N << " c=" << c << " ]";
}

template<typename TSpace >

DGtal::ClosedIntegerHalfPlane< TSpace >::Vector DGtal::ClosedIntegerHalfPlane< TSpace >::tangent ( ) const

inline

Returns:

the tangent vector to the half-plane boundary (ie. ( -N.y, N.x ) ).

Definition at line 76 of file ClosedIntegerHalfPlane.ih.

Referenced by DGtal::LatticePolytope2D< TSpace, TSequence >::getFirstPointsOfHull().

{
  return Vector( -N[ 1 ], N[ 0 ] );
}

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Field Documentation

template<typename TSpace>

Integer DGtal::ClosedIntegerHalfPlane< TSpace >::c

Definition at line 77 of file ClosedIntegerHalfPlane.h.

Referenced by DGtal::LatticePolytope2D< TSpace, TSequence >::cut(), DGtal::LatticePolytope2D< TSpace, TSequence >::getAllPointsOfHull(), and DGtal::LatticePolytope2D< TSpace, TSequence >::getFirstPointsOfHull().

template<typename TSpace>

Vector DGtal::ClosedIntegerHalfPlane< TSpace >::N

Definition at line 76 of file ClosedIntegerHalfPlane.h.

Referenced by DGtal::LatticePolytope2D< TSpace, TSequence >::cut(), DGtal::LatticePolytope2D< TSpace, TSequence >::getAllPointsOfHull(), DGtal::LatticePolytope2D< TSpace, TSequence >::getFirstPointsOfHull(), and DGtal::LatticePolytope2D< TSpace, TSequence >::getIncludedDigitalPoints().

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The documentation for this struct was generated from the following files:

• ClosedIntegerHalfPlane.h
• ClosedIntegerHalfPlane.ih