DGtal  0.9.3beta
Public Types | Public Member Functions | Protected Attributes | Private Member Functions | Private Attributes
DGtal::LatticePolytope2D< TSpace, TSequence > Class Template Reference

#include <DGtal/arithmetic/LatticePolytope2D.h>

Inheritance diagram for DGtal::LatticePolytope2D< TSpace, TSequence >:
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Collaboration diagram for DGtal::LatticePolytope2D< TSpace, TSequence >:
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Public Types

typedef LatticePolytope2D< TSpace, TSequence > Self
 
typedef TSequence ClockwiseVertexSequence
 
typedef TSpace Space
 
typedef Space::Integer Integer
 
typedef Space::Point Point
 
typedef Space::Vector Vector
 
typedef IntegerComputer< IntegerMyIntegerComputer
 
typedef HyperRectDomain< SpaceDomain
 
typedef ClosedIntegerHalfPlane< SpaceHalfSpace
 
typedef ClockwiseVertexSequence::value_type value_type
 
typedef ClockwiseVertexSequence::reference reference
 
typedef ClockwiseVertexSequence::const_reference const_reference
 
typedef ClockwiseVertexSequence::iterator iterator
 
typedef ClockwiseVertexSequence::const_iterator const_iterator
 
typedef ClockwiseVertexSequence::const_pointer const_pointer
 
typedef ClockwiseVertexSequence::size_type size_type
 
typedef ClockwiseVertexSequence::difference_type difference_type
 
typedef ClockwiseVertexSequence::value_type Value
 
typedef ClockwiseVertexSequence::iterator Iterator
 
typedef ClockwiseVertexSequence::const_iterator ConstIterator
 
typedef std::size_t Size
 
typedef std::pair< Size, SizeSizeCouple
 
typedef MyIntegerComputer::Point2I Point2I
 
typedef MyIntegerComputer::Vector2I Vector2I
 
typedef MyIntegerComputer::Point3I Point3I
 
typedef MyIntegerComputer::Vector3I Vector3I
 

Public Member Functions

 BOOST_STATIC_ASSERT ((concepts::ConceptUtils::SameType< Value, Point >::value))
 
 BOOST_STATIC_ASSERT ((concepts::ConceptUtils::SameType< Point2I, Point >::value))
 
 BOOST_STATIC_ASSERT ((concepts::ConceptUtils::SameType< Vector2I, Vector >::value))
 
 ~LatticePolytope2D ()
 
 LatticePolytope2D ()
 
 LatticePolytope2D (const Self &other)
 
Selfoperator= (const Self &other)
 
MyIntegerComputeric () const
 
ConstIterator begin () const
 
ConstIterator end () const
 
Iterator begin ()
 
Iterator end ()
 
bool empty () const
 
Size size () const
 
Size max_size () const
 
void clear ()
 
Iterator erase (Iterator it)
 
Domain boundingBoxDomain () const
 
void purge ()
 
Iterator insertBefore (const Iterator &pos, const Point &K)
 
void pushBack (const Point &K)
 
void pushFront (const Point &K)
 
void push_back (const Point &K)
 
void push_front (const Point &K)
 
const IntegertwiceArea () const
 
Point3I centroid () const
 
Point3I centroid (const Integer &twice_area) const
 
Integer numberBoundaryPoints () const
 
Integer numberInteriorPoints () const
 
SizeCouple findCut (Iterator &it_next_is_outside, Iterator &it_next_is_inside, const HalfSpace &hs)
 
bool cut (const HalfSpace &hs)
 
HalfSpace halfSpace (ConstIterator it) const
 
HalfSpace halfSpace (const Point &A, const Point &B, const Point &inP) const
 
template<typename DigitalSet >
void getIncludedDigitalPoints (DigitalSet &aSet) const
 
bool getFirstPointsOfHull (Vector &v, Point &inPt, Point &outPt, const HalfSpace &hs1, const HalfSpace &hs2) const
 
void getAllPointsOfHull (std::vector< Point > &inPts, std::vector< Point > &outPts, const Vector &BV, const HalfSpace &hs2, const HalfSpace &hs3) const
 
template<typename OutputIterator >
OutputIterator computeConvexHullBorder (OutputIterator itOut, const Point &pointRefC1, const Point &pointRefC3, const HalfSpace &hs1, const HalfSpace &hs2, const HalfSpace &hs3) const
 
void swap (LatticePolytope2D &other)
 
void selfDisplay (std::ostream &out) const
 
bool isValid () const
 
std::string className () const
 

Protected Attributes

ClockwiseVertexSequence myVertices
 

Private Member Functions

 BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))
 
 BOOST_STATIC_ASSERT ((TSpace::dimension==2))
 
 BOOST_CONCEPT_ASSERT ((boost::Sequence< TSequence >))
 

Private Attributes

MyIntegerComputer _ic
 
Integer _a
 
Integer _b
 
Integer _c
 
Integer _c1
 
Integer _c3
 
Integer _den
 
Integer _g
 
Integer _fl
 
Integer _ce
 
Point _A
 
Point _B
 
Point _A1
 
Point _B1
 
Point _A2
 
Point _B2
 
Vector _N
 
Vector _DV
 
Vector _u
 
Vector _v
 
std::vector< Point_inPts
 
std::vector< Point_outPts
 

Detailed Description

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
class DGtal::LatticePolytope2D< TSpace, TSequence >

Aim: Represents a 2D polytope, i.e. a convex polygon, in the two-dimensional digital plane. The list of points must follow the clockwise ordering.

Description of template class 'LatticePolytope2D'

It is a model of boost::CopyConstructible, boost::DefaultConstructible, boost::Assignable. It is also a model of boost::Container (it contains the sequence of points). It is also displayable on a Board2D object with two modes: "" or "Transparent", "Filled".

It contains no more data than the sequence of points, except mutable data for intermediate computations.

It is a backport of ImaGene.

Template Parameters
TSpacean arbitrary 2-dimensional model of CSpace.
TSequencea model of boost::Sequence whose elements are points (TSpace::Point). Default is list of points.
Examples:
arithmetic/lower-integer-convex-hull.cpp.

Definition at line 83 of file LatticePolytope2D.h.

Member Typedef Documentation

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef TSequence DGtal::LatticePolytope2D< TSpace, TSequence >::ClockwiseVertexSequence

Definition at line 91 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::const_iterator DGtal::LatticePolytope2D< TSpace, TSequence >::const_iterator

Definition at line 105 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::const_pointer DGtal::LatticePolytope2D< TSpace, TSequence >::const_pointer

Definition at line 106 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::const_reference DGtal::LatticePolytope2D< TSpace, TSequence >::const_reference

Definition at line 103 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::const_iterator DGtal::LatticePolytope2D< TSpace, TSequence >::ConstIterator

Definition at line 112 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::difference_type DGtal::LatticePolytope2D< TSpace, TSequence >::difference_type

Definition at line 108 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef HyperRectDomain< Space > DGtal::LatticePolytope2D< TSpace, TSequence >::Domain

Definition at line 98 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClosedIntegerHalfPlane< Space > DGtal::LatticePolytope2D< TSpace, TSequence >::HalfSpace

Definition at line 99 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef Space::Integer DGtal::LatticePolytope2D< TSpace, TSequence >::Integer

Definition at line 94 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::iterator DGtal::LatticePolytope2D< TSpace, TSequence >::iterator

Definition at line 104 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::iterator DGtal::LatticePolytope2D< TSpace, TSequence >::Iterator

Definition at line 111 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef IntegerComputer<Integer> DGtal::LatticePolytope2D< TSpace, TSequence >::MyIntegerComputer

Definition at line 97 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef Space::Point DGtal::LatticePolytope2D< TSpace, TSequence >::Point

Definition at line 95 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef MyIntegerComputer::Point2I DGtal::LatticePolytope2D< TSpace, TSequence >::Point2I

Definition at line 121 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef MyIntegerComputer::Point3I DGtal::LatticePolytope2D< TSpace, TSequence >::Point3I

Definition at line 123 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::reference DGtal::LatticePolytope2D< TSpace, TSequence >::reference

Definition at line 102 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef LatticePolytope2D<TSpace,TSequence> DGtal::LatticePolytope2D< TSpace, TSequence >::Self

Definition at line 90 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef std::size_t DGtal::LatticePolytope2D< TSpace, TSequence >::Size

Definition at line 113 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::size_type DGtal::LatticePolytope2D< TSpace, TSequence >::size_type

Definition at line 107 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef std::pair<Size,Size> DGtal::LatticePolytope2D< TSpace, TSequence >::SizeCouple

Definition at line 114 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef TSpace DGtal::LatticePolytope2D< TSpace, TSequence >::Space

Definition at line 93 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::value_type DGtal::LatticePolytope2D< TSpace, TSequence >::Value

Definition at line 110 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef ClockwiseVertexSequence::value_type DGtal::LatticePolytope2D< TSpace, TSequence >::value_type

Definition at line 101 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef Space::Vector DGtal::LatticePolytope2D< TSpace, TSequence >::Vector

Definition at line 96 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef MyIntegerComputer::Vector2I DGtal::LatticePolytope2D< TSpace, TSequence >::Vector2I

Definition at line 122 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
typedef MyIntegerComputer::Vector3I DGtal::LatticePolytope2D< TSpace, TSequence >::Vector3I

Definition at line 124 of file LatticePolytope2D.h.

Constructor & Destructor Documentation

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::~LatticePolytope2D ( )

Destructor.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::LatticePolytope2D ( )

Constructor.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::LatticePolytope2D ( const Self other)

Copy constructor.

Parameters
otherthe object to clone.

Member Function Documentation

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
ConstIterator DGtal::LatticePolytope2D< TSpace, TSequence >::begin ( ) const

Useful to visit the list of vertices in order.

Returns
a const iterator (a forward iterator) pointing on the first vertex.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Iterator DGtal::LatticePolytope2D< TSpace, TSequence >::begin ( )

Useful to visit the list of vertices in order.

Returns
an iterator (a forward iterator) pointing on the first vertex.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >)  )
private
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_CONCEPT_ASSERT ( (boost::Sequence< TSequence >)  )
private
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_STATIC_ASSERT ( (TSpace::dimension==2)  )
private
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_STATIC_ASSERT ( (concepts::ConceptUtils::SameType< Value, Point >::value)  )
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_STATIC_ASSERT ( (concepts::ConceptUtils::SameType< Point2I, Point >::value)  )
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
DGtal::LatticePolytope2D< TSpace, TSequence >::BOOST_STATIC_ASSERT ( (concepts::ConceptUtils::SameType< Vector2I, Vector >::value)  )
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Domain DGtal::LatticePolytope2D< TSpace, TSequence >::boundingBoxDomain ( ) const
Returns
the bounding domain of this polygon, i.e. the smallest bounding box containing all the points of this polygon.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point3I DGtal::LatticePolytope2D< TSpace, TSequence >::centroid ( ) const

if the area of this polygon is not 0, computes centroid, else, if the polygon is reduced to 2 points, computes the middle of the straight line segment, else returns the point itself.

The centroid is a 2D rational point but it is represented as a 3D integer point (a/d,b/d) corresponds to (a,b,d).

Returns
the centroid. The centroid is not in reduced form.
Precondition
The polygon should not be empty.
See also
centroid( const Integer & ) const
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point3I DGtal::LatticePolytope2D< TSpace, TSequence >::centroid ( const Integer twice_area) const

This form is faster than centroid if you have already computed the area.

if the area of this polygon is not 0, computes centroid, else, if the polygon is reduced to 2 points, computes the middle of the straight line segment, else returns the point itself.

The centroid is a 2D rational point but it is represented as a 3D integer point (a/d,b/d) corresponds to (a,b,d).

Parameters
twice_areathe area*2 of this polygon.
Returns
the centroid. The centroid is not in reduced form.
Precondition
The polygon should not be empty.
See also
centroid() const
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
std::string DGtal::LatticePolytope2D< TSpace, TSequence >::className ( ) const
Returns
the class name. It is notably used for drawing this object.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::clear ( )

Clears the lattice polytope. Afterwards, it is composed of 0 vertices.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
template<typename OutputIterator >
OutputIterator DGtal::LatticePolytope2D< TSpace, TSequence >::computeConvexHullBorder ( OutputIterator  itOut,
const Point pointRefC1,
const Point pointRefC3,
const HalfSpace hs1,
const HalfSpace hs2,
const HalfSpace hs3 
) const

Compute the convex hull of grid points satisfying the constraints N1.P<=c1, N2.P<=c2 and N3.P>=c3.

N2.P<=c2 corresponds to the cut two parts of computation: from constraint 1 to constraint 3 and from constraint 3 to constraint 1.

The computed vertices are outputed with the output iterator itOut.

pointRefC1 and pointRefC3 corresponds to grid point lying on the supporting lines of C1 and of C3 resp.

NB: the method also computes grid point satisfying N1.P<=c1 and N3.P>=c3 but not satisfying N2.P<=c2. The algorithm uses these points that's why they appear in the code.

Parameters
itOutThe output iterator.
pointRefC1The grid point lying on C1.
pointRefC3The grid point lying on C3.
hs1The first half-space.
hs2The second half-space.
hs3The third half-space.
Todo:
proper parameters documentation.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
bool DGtal::LatticePolytope2D< TSpace, TSequence >::cut ( const HalfSpace hs)

Cuts the lattice polytope with the given half-space constraint.

Parameters
hsany half-space constraint.
Returns
'true' if the polygon was modified, 'false' otherwise.

NB: complexity is O(N) for finding the involved edges, then log(D) for applying the cut.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
bool DGtal::LatticePolytope2D< TSpace, TSequence >::empty ( ) const
Returns
'true' if the lattice polytope has no vertex, false otherwise.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
ConstIterator DGtal::LatticePolytope2D< TSpace, TSequence >::end ( ) const

Useful to visit the list of vertices in order.

Returns
a const iterator (a forward iterator) pointing after the last vertex.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Iterator DGtal::LatticePolytope2D< TSpace, TSequence >::end ( )

Useful to visit the list of vertices in order.

Returns
an iterator (a forward iterator) pointing after the last vertex.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Iterator DGtal::LatticePolytope2D< TSpace, TSequence >::erase ( Iterator  it)

Erases the vertex pointed by it.

Parameters
itan iterator pointing on the vertex to erase.
Returns
an iterator pointing on the next vertex (the one that follows it).
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
SizeCouple DGtal::LatticePolytope2D< TSpace, TSequence >::findCut ( Iterator it_next_is_outside,
Iterator it_next_is_inside,
const HalfSpace hs 
)

Given some half-plane hs, finds the edges/vertices of this polygon that crosses/borders this half-plane.

Complexity is O(n), where n is size().

Parameters
it_next_is_outside(returns) either the vertex that is in hs and whose successor is not in hs, or end() if none exists.
it_next_is_inside(returns) either the vertex that is not in hs and whose successor is in hs, or end() if none exists.
hsThe half-plane.
Returns
the couple (number of vertices that are in hs, number of vertices).
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::getAllPointsOfHull ( std::vector< Point > &  inPts,
std::vector< Point > &  outPts,
const Vector BV,
const HalfSpace hs2,
const HalfSpace hs3 
) const

Computes the border of the upper and of the lower convex hull from the starting points inPts[0] (up) and outPts[0] down, along the constraint N2.p <= c2 while the vertices satisfy the constraint N3.p <= c3. The vertices of the two borders are stored at the end of inPts and outPts.

Parameters
inPts(in, out) as input, contains the first point, as output the sequence of points satisfying hs2 and hs3.
outPts(in, out) as input, contains the first point, as output the sequence of points not satisfying hs2 and satisfying hs3.
BVthe Bezout vector of the vector between inPts[ 0 ] and outPts[ 0 ].
hs2the half-space that is approached by the two sequences of points.
hs3the limiting half-space which defines the bounds of the approximation.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
bool DGtal::LatticePolytope2D< TSpace, TSequence >::getFirstPointsOfHull ( Vector v,
Point inPt,
Point outPt,
const HalfSpace hs1,
const HalfSpace hs2 
) const

Given a point inPt on the boundary of hs1, computes the closest integer points along the boundary of hs1 that are separated by hs2. Either the intersection is exact and the returned points lies at this intersection, or inPt designates the point that satisfies hs2 while outPt does not satisfy hs2. The two points are then separated by the direction vector of the half-space.

Parameters
v(returns) the Bezout vector of the direction vector between inPt and outPt.
inPt(in/out) as input, a point on hs1, as output, a point on hs1 satisfying hs2.
Precondition
inPt must belong to hs1.
Parameters
outPt(returns) a point on hs1 not satisfying hs2.
hs1The first half-space.
hs2The second half-space.
Returns
'true' iff the intersection oh hs1 and hs2 is exact. In this case, outPt is equal to inPt and is at the intersection of the two half-space boundaries.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
template<typename DigitalSet >
void DGtal::LatticePolytope2D< TSpace, TSequence >::getIncludedDigitalPoints ( DigitalSet &  aSet) const

Computes the set aSet all the digital points that belongs to this polygon (interior plus boundary).

Parameters
aSet(returns) the set that contains as output all the digital points of this polygon.
Todo:
this method is for now not efficient and is just for visualization purposes.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
HalfSpace DGtal::LatticePolytope2D< TSpace, TSequence >::halfSpace ( ConstIterator  it) const

Computes the constraint of the form N.P<=c whose supporting line passes through point *it and *(it+1), such that the other points of the polygon are inside. Parameters of the hafl-space are minimal. Complexity is O(log(D)).

Parameters
itan iterator on a point of this polygon.
Returns
the corresponding half-space.
Precondition
the polygon should have at least two vertices.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
HalfSpace DGtal::LatticePolytope2D< TSpace, TSequence >::halfSpace ( const Point A,
const Point B,
const Point inP 
) const

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

Parameters
Aany point.
Bany point different from A.
inPany point not on the straight line (AB).
Returns
the corresponding half-space.

NB: It is not a static method because this method uses the internal IntegerComputer object member.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
MyIntegerComputer& DGtal::LatticePolytope2D< TSpace, TSequence >::ic ( ) const
Returns
the object that performs integer calculation.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Iterator DGtal::LatticePolytope2D< TSpace, TSequence >::insertBefore ( const Iterator pos,
const Point K 
)

Inserts the point K to the lattice polytope before position "pos".

Parameters
posany iterator
Kthe point to add
Returns
an iterator on the newly created element.
Precondition
if C_1, ..., C_N is the lattice polytope, then C_1, C_pos-1, K ..., C_N should be the vertices of the output lattice polytope.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
bool DGtal::LatticePolytope2D< TSpace, TSequence >::isValid ( ) const

Checks the validity/consistency of the object.

Returns
'true' if the object is valid, 'false' otherwise.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Size DGtal::LatticePolytope2D< TSpace, TSequence >::max_size ( ) const
Returns
the maximal possible number of vertices (or edges) that can be stored (here, greatest possible Size integer).
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::numberBoundaryPoints ( ) const
Returns
the exact number of digital points on the polygon boundary (greater or equal to the number of vertices. NB: complexity in O(n log(D) ), where n is the number of vertices.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::numberInteriorPoints ( ) const
Returns
the exact number of digital points in the polygon interior.

Calls numberBoundaryPoints and twiceArea. Uses Pick's formula.

NB: complexity in O(n log(D) ), where n is the number of vertices.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Self& DGtal::LatticePolytope2D< TSpace, TSequence >::operator= ( const Self other)

Assignment.

Parameters
otherthe object to copy.
Returns
a reference on 'this'.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::purge ( )

Removes (duplicate) consecutive vertices. NB: complexity is O(N), where N is the number of vertices.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::push_back ( const Point K)

Adds the point K to the end of the polygon (stl version for BackInsertable).

Parameters
Kthe point to add
Precondition
if C_1, ..., C_N is the lattice polytope, then C_1, ..., C_N, K should be the vertices of the output lattice polytope.
See also
pushBack
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::push_front ( const Point K)

Adds the point K to the beginning of the polygon (stl version)

Parameters
Kthe point to add
Precondition
if C_1, ..., C_N is the lattice polytope, then K, C_1, ..., C_N should be the vertices of the output lattice polytope.
See also
pushFront
Examples:
arithmetic/lower-integer-convex-hull.cpp.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::pushBack ( const Point K)

adds the point K to the end of the polygon.

Parameters
Kthe point to add
Precondition
if C_1, ..., C_N is the lattice polytope, then C_1, ..., C_N, K should be the vertices of the output lattice polytope.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::pushFront ( const Point K)

Adds the point K to the beginning of the polygon (stl version)

Parameters
Kthe point to add
Precondition
if C_1, ..., C_N is the lattice polytope, then K, C_1, ..., C_N should be the vertices of the output lattice polytope.
See also
push_front
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::selfDisplay ( std::ostream &  out) const

Writes/Displays the object on an output stream.

Parameters
outthe output stream where the object is written.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Size DGtal::LatticePolytope2D< TSpace, TSequence >::size ( ) const
Returns
the number of vertices (or edges) of the lattice polytope.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
void DGtal::LatticePolytope2D< TSpace, TSequence >::swap ( LatticePolytope2D< TSpace, TSequence > &  other)

Swaps the content of this object with other. O(1) complexity.

Parameters
otherany other LatticePolytope2D.
template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
const Integer& DGtal::LatticePolytope2D< TSpace, TSequence >::twiceArea ( ) const
Returns
2*area of polygon.

Field Documentation

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_a
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_A
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_A1
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_A2
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_b
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_B
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_B1
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Point DGtal::LatticePolytope2D< TSpace, TSequence >::_B2
mutableprivate

Definition at line 537 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_c
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_c1
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_c3
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_ce
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_den
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Vector DGtal::LatticePolytope2D< TSpace, TSequence >::_DV
mutableprivate

Definition at line 538 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_fl
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Integer DGtal::LatticePolytope2D< TSpace, TSequence >::_g
mutableprivate

Definition at line 536 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
MyIntegerComputer DGtal::LatticePolytope2D< TSpace, TSequence >::_ic
mutableprivate

A utility object to perform computation on integers. Need not to be copied when cloning this object. Avoids many dynamic allocations when using big integers.

Definition at line 535 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
std::vector<Point> DGtal::LatticePolytope2D< TSpace, TSequence >::_inPts
mutableprivate

Definition at line 539 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Vector DGtal::LatticePolytope2D< TSpace, TSequence >::_N
mutableprivate

Definition at line 538 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
std::vector<Point> DGtal::LatticePolytope2D< TSpace, TSequence >::_outPts
mutableprivate

Definition at line 539 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Vector DGtal::LatticePolytope2D< TSpace, TSequence >::_u
mutableprivate

Definition at line 538 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
Vector DGtal::LatticePolytope2D< TSpace, TSequence >::_v
mutableprivate

Definition at line 538 of file LatticePolytope2D.h.

template<typename TSpace, typename TSequence = std::list< typename TSpace::Point >>
ClockwiseVertexSequence DGtal::LatticePolytope2D< TSpace, TSequence >::myVertices
protected

Definition at line 528 of file LatticePolytope2D.h.


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