Aim: Useful to compute quickly the lattice points within a polytope, i.e. a convex polyhedron. More...

#include <DGtal/geometry/volumes/BoundedLatticePolytopeCounter.h>

Public Types
typedef BoundedLatticePolytopeCounter< TSpace >	Self

typedef TSpace	Space

typedef BoundedLatticePolytope< TSpace >	Polytope

using	Integer = typename Polytope::Integer

using	Point = typename Polytope::Point

using	Vector = typename Polytope::Vector

using	InequalityMatrix = typename Polytope::InequalityMatrix

using	InequalityVector = typename Polytope::InequalityVector

using	Domain = typename Polytope::Domain

using	HalfSpace = typename Polytope::HalfSpace

using	BigInteger = typename Polytope::BigInteger

using	Intervals = IntegralIntervals< Integer >

using	Interval = typename Intervals::Interval

using	PointRange = std::vector< Point >

using	LatticeSetByInterval = std::map< Point, Interval >
	Internal type used to represent a convex lattice point set.

using	LatticeSetByIntervals = std::map< Point, Intervals >
	Internal type used to represent any lattice point set.

Public Member Functions
	BoundedLatticePolytopeCounter ()=default
	Default constructor.

	BoundedLatticePolytopeCounter (const Polytope &P)

void	init (const Polytope *ptrP)

Interval	intersectionIntervalAlongAxis (Point p, Dimension a) const

Interval	interiorIntersectionIntervalAlongAxis (Point p, Dimension a) const

Integer	countAlongAxis (Dimension a) const

Integer	countInteriorAlongAxis (Dimension a) const

void	getPointsAlongAxis (PointRange &pts, Dimension a) const

void	getInteriorPointsAlongAxis (PointRange &pts, Dimension a) const

LatticeSetByInterval	getLatticeSet (Dimension a) const

LatticeSetByInterval	getLatticeCells (Dimension a) const

Dimension	longestAxis () const

Point	lowerBound () const

Point	upperBound () const

Data Fields
const Polytope *	myPolytope
	The associated polytope.

Point	myLower
	The lower point of the tight bounding box to the associated polytope.

Point	myUpper
	The upper point of the tight bounding box to the associated polytope.

Static Public Attributes
static const Dimension	dimension = Space::dimension

Private Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))

Detailed Description

template<typename TSpace>
class DGtal::BoundedLatticePolytopeCounter< TSpace >

Aim: Useful to compute quickly the lattice points within a polytope, i.e. a convex polyhedron.

Description of template class 'BoundedLatticePolytopeCounter'

It is a model of boost::CopyConstructible, boost::DefaultConstructible, boost::Assignable.

Template Parameters

TSpace an arbitrary model of CSpace.

Definition at line 66 of file BoundedLatticePolytopeCounter.h.

Member Typedef Documentation

◆ BigInteger

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::BigInteger = typename Polytope::BigInteger

Definition at line 80 of file BoundedLatticePolytopeCounter.h.

◆ Domain

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Domain = typename Polytope::Domain

Definition at line 78 of file BoundedLatticePolytopeCounter.h.

◆ HalfSpace

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::HalfSpace = typename Polytope::HalfSpace

Definition at line 79 of file BoundedLatticePolytopeCounter.h.

◆ InequalityMatrix

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::InequalityMatrix = typename Polytope::InequalityMatrix

Definition at line 76 of file BoundedLatticePolytopeCounter.h.

◆ InequalityVector

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::InequalityVector = typename Polytope::InequalityVector

Definition at line 77 of file BoundedLatticePolytopeCounter.h.

◆ Integer

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Integer = typename Polytope::Integer

Definition at line 73 of file BoundedLatticePolytopeCounter.h.

◆ Interval

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Interval = typename Intervals::Interval

Definition at line 82 of file BoundedLatticePolytopeCounter.h.

◆ Intervals

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Intervals = IntegralIntervals< Integer >

Definition at line 81 of file BoundedLatticePolytopeCounter.h.

◆ LatticeSetByInterval

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::LatticeSetByInterval = std::map< Point, Interval >

Internal type used to represent a convex lattice point set.

Definition at line 87 of file BoundedLatticePolytopeCounter.h.

◆ LatticeSetByIntervals

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::LatticeSetByIntervals = std::map< Point, Intervals >

Internal type used to represent any lattice point set.

Definition at line 90 of file BoundedLatticePolytopeCounter.h.

◆ Point

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Point = typename Polytope::Point

Definition at line 74 of file BoundedLatticePolytopeCounter.h.

◆ PointRange

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::PointRange = std::vector< Point >

Definition at line 83 of file BoundedLatticePolytopeCounter.h.

◆ Polytope

template<typename TSpace >

typedef BoundedLatticePolytope<TSpace> DGtal::BoundedLatticePolytopeCounter< TSpace >::Polytope

Definition at line 72 of file BoundedLatticePolytopeCounter.h.

◆ Self

template<typename TSpace >

typedef BoundedLatticePolytopeCounter<TSpace> DGtal::BoundedLatticePolytopeCounter< TSpace >::Self

Definition at line 70 of file BoundedLatticePolytopeCounter.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::BoundedLatticePolytopeCounter< TSpace >::Space

Definition at line 71 of file BoundedLatticePolytopeCounter.h.

◆ Vector

template<typename TSpace >

using DGtal::BoundedLatticePolytopeCounter< TSpace >::Vector = typename Polytope::Vector

Definition at line 75 of file BoundedLatticePolytopeCounter.h.

Constructor & Destructor Documentation

◆ BoundedLatticePolytopeCounter() [1/2]

template<typename TSpace >

DGtal::BoundedLatticePolytopeCounter< TSpace >::BoundedLatticePolytopeCounter ( )

default

Default constructor.

◆ BoundedLatticePolytopeCounter() [2/2]

template<typename TSpace >

DGtal::BoundedLatticePolytopeCounter< TSpace >::BoundedLatticePolytopeCounter ( const Polytope & P )

Constructor from valid polytope

Parameters

P	any polytope

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<typename TSpace >

DGtal::BoundedLatticePolytopeCounter< TSpace >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

private

◆ countAlongAxis()

template<typename TSpace >

Integer DGtal::BoundedLatticePolytopeCounter< TSpace >::countAlongAxis ( Dimension a ) const

Parameters

a	any axis with 0 <= a < d, where d is the dimension of the space.

Returns: the number of lattice point inside the current polytope.

Note: The result does not depend on parameter a, but the speed of computations depend on this choixe. The best choice is the one that minimizes the projected area of the polytope along this axis.

See also: longestAxis

◆ countInteriorAlongAxis()

template<typename TSpace >

Integer DGtal::BoundedLatticePolytopeCounter< TSpace >::countInteriorAlongAxis ( Dimension a ) const

Parameters

a	any axis with 0 <= a < d, where d is the dimension of the space.

Returns: the number of lattice point strictly inside the current polytope.

Note: The result does not depend on parameter a, but the speed of computation depends on this choice. The best choice is the one that minimizes the projected area of the polytope along this axis.

See also: longestAxis

◆ getInteriorPointsAlongAxis()

template<typename TSpace >

void DGtal::BoundedLatticePolytopeCounter< TSpace >::getInteriorPointsAlongAxis	(	PointRange &	pts,
		Dimension	a ) const

Parameters

[out]	pts	the range of lattice points that are interior to this polytope.
	a	any axis with 0 <= a < d, where d is the dimension of the space.

Returns: the lattice points strictly inside the current polytope.

Note: The result does not depend on parameter a, but the speed of computation depends on this choice. The best choice is the one that minimizes the projected area of the polytope along this axis.

See also: longestAxis

◆ getLatticeCells()

template<typename TSpace >

LatticeSetByInterval DGtal::BoundedLatticePolytopeCounter< TSpace >::getLatticeCells ( Dimension a ) const

Parameters

a	any axis with 0 <= a < d, where d is the dimension of the space.

Returns: the set of cells (as points with Khalimsky coordinates) whose closure touched the current polytope, represented as intervals along the given rows specified by the axis.

Note: The given polytope should have been built from a set of points dilated by the unit cube in order to get exactly the Star of the initial polytope.

◆ getLatticeSet()

template<typename TSpace >

LatticeSetByInterval DGtal::BoundedLatticePolytopeCounter< TSpace >::getLatticeSet ( Dimension a ) const

Parameters

a	any axis with 0 <= a < d, where d is the dimension of the space.

Returns: the set of lattice points within the current polytope, represented as intervals along the given rows specified by the axis.

◆ getPointsAlongAxis()

template<typename TSpace >

void DGtal::BoundedLatticePolytopeCounter< TSpace >::getPointsAlongAxis	(	PointRange &	pts,
		Dimension	a ) const

Parameters

[out]	pts	the range of lattice points that are inside this polytope.
	a	any axis with 0 <= a < d, where d is the dimension of the space.

Note: The result does not depend on parameter a, but the speed of computation depends on this choice. The best choice is the one that minimizes the projected area of the polytope along this axis.

See also: longestAxis

◆ init()

template<typename TSpace >

void DGtal::BoundedLatticePolytopeCounter< TSpace >::init ( const Polytope * ptrP )

Initialization from polytope pointer (nullptr if you want to create an invalid polytope).

Parameters

ptrP	any pointer on a polytope or nullptr.

◆ interiorIntersectionIntervalAlongAxis()

template<typename TSpace >

Interval DGtal::BoundedLatticePolytopeCounter< TSpace >::interiorIntersectionIntervalAlongAxis	(	Point	p,
		Dimension	a ) const

Computes the intersection of the lattice points of the infinite line going through point p along axis a and the interior of the current polytope, returned as an interval [b,e), where bis the a-th coordinate of the first lattice point in common, while e is the a-th coordinate after the last lattice point in common.

Parameters

p	any point with the current domain
a	any axis between 0 (included) and `dimension` (excluded).

Returns: the interval [b,e) of intersection, which is such that b==e when there is no intersection.

◆ intersectionIntervalAlongAxis()

template<typename TSpace >

Interval DGtal::BoundedLatticePolytopeCounter< TSpace >::intersectionIntervalAlongAxis	(	Point	p,
		Dimension	a ) const

Computes the intersection of the lattice points of the infinite line going through point p along axis a and the current polytope, returned as an interval [b,e), where bis the a-th coordinate of the first lattice point in common, while e is the a-th coordinate after the last lattice point in common.

Parameters