Aim: This concept describes a cellular grid space in nD. In these spaces obtained by cartesian product, cells have a cubic shape that depends on the dimension: 0-cells are points, 1-cells are unit segments, 2-cells are squares, 3-cells are cubes, and so on. More...

#include <DGtal/topology/CCellularGridSpaceND.h>

Inheritance diagram for DGtal::concepts::CCellularGridSpaceND< T >:

Public Types
typedef T::Size	Size

Public Types inherited from DGtal::concepts::CPreCellularGridSpaceND< T >
typedef T::Integer	Integer

typedef T::Space	Space

typedef T::PreCellularGridSpace	PreCellularGridSpace

typedef T::Cell	Cell

typedef T::SCell	SCell

typedef T::Surfel	Surfel

typedef T::Sign	Sign

typedef T::DirIterator	DirIterator

typedef T::Point	Point

typedef T::Vector	Vector

typedef T::Cells	Cells

typedef T::SCells	SCells

typedef T::CellSet	CellSet

typedef T::SCellSet	SCellSet

typedef T::SurfelSet	SurfelSet

typedef int	Dummy

typedef T::template CellMap< Dummy >::Type	CellMap

typedef T::template SCellMap< Dummy >::Type	SCellMap

typedef T::template SurfelMap< Dummy >::Type	SurfelMap

Public Member Functions
	BOOST_CONCEPT_ASSERT ((CUnsignedNumber< Size >))

	BOOST_CONCEPT_ASSERT ((CIntegralNumber< Size >))

	BOOST_CONCEPT_USAGE (CCellularGridSpaceND)

void	checkConstConstraints () const

Public Member Functions inherited from DGtal::concepts::CPreCellularGridSpaceND< T >
	BOOST_CONCEPT_ASSERT ((CInteger< Integer >))

	BOOST_STATIC_ASSERT ((ConceptUtils::SameType< Integer, typename Space::Integer >::value))

	BOOST_STATIC_ASSERT ((ConceptUtils::SameType< Point, typename Space::Point >::value))

	BOOST_STATIC_ASSERT ((ConceptUtils::SameType< Vector, typename Space::Vector >::value))

	BOOST_CONCEPT_ASSERT ((CConstSinglePassRange< Cells >))

	BOOST_CONCEPT_ASSERT ((CConstSinglePassRange< SCells >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< CellSet >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< SCellSet >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< SurfelSet >))

	BOOST_CONCEPT_ASSERT ((boost::SimpleAssociativeContainer< CellSet >))

	BOOST_CONCEPT_ASSERT ((boost::SimpleAssociativeContainer< SCellSet >))

	BOOST_CONCEPT_ASSERT ((boost::SimpleAssociativeContainer< SurfelSet >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< CellMap >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< SCellMap >))

	BOOST_CONCEPT_ASSERT ((boost::UniqueAssociativeContainer< SurfelMap >))

	BOOST_CONCEPT_ASSERT ((boost::PairAssociativeContainer< CellMap >))

	BOOST_CONCEPT_ASSERT ((boost::PairAssociativeContainer< SCellMap >))

	BOOST_CONCEPT_ASSERT ((boost::PairAssociativeContainer< SurfelMap >))

	BOOST_CONCEPT_USAGE (CPreCellularGridSpaceND)

void	checkConstConstraints () const

Private Attributes
T	myX

CPreCellularGridSpaceND< T >::Integer	myInteger

Size	mySize

Dimension	myDim

CPreCellularGridSpaceND< T >::Point	myP1

CPreCellularGridSpaceND< T >::Point	myP2

CPreCellularGridSpaceND< T >::Cell	myCell

CPreCellularGridSpaceND< T >::SCell	mySCell

bool	myBool

Detailed Description

template<typename T>
struct DGtal::concepts::CCellularGridSpaceND< T >

Aim: This concept describes a cellular grid space in nD. In these spaces obtained by cartesian product, cells have a cubic shape that depends on the dimension: 0-cells are points, 1-cells are unit segments, 2-cells are squares, 3-cells are cubes, and so on.

Description of concept 'CCellularGridSpaceND'

Refinement of CPreCellularGridSpaceND

In addition of CPreCellularGridSpaceND, CCellularGridSpaceND add bounds and related methods.

Models of CCellularGridSpaceND are used whenever you need to define a topology on your subsets of the digital space, especially boundaries of objects, curves and digital surfaces.

The space is generally finite (except for arbitrary size integers). The user should choose between a closed (default) cell space or an open cell space.

We refer the reader to Cellular grid space and topology, unoriented and oriented cells, incidence for further details.

Associated types

Size: the integral unsigned type for representing sizes in the space (model of CUnsignedNumber and CIntegralNumber).

Notation

X : A type that is a model of CCellularGridSpaceND
x : object of type X
k : object of type Dimension
i : object of type Integer
c : object of type Cell
sc : object of type SCell
s : object of type Surfel
p, p1, p2 : object of type Point
v : object of type Vector
sign: object of type Sign

Definitions

a model of CCellularGridSpaceND is said closed if it includes the cells of lower dimension along its bounds. It is indeed closed in the sense of the star-topology.
a model of CCellularGridSpaceND is said open if it does not include the cells of lower dimension along its bounds. It is indeed open in the sense of the star-topology.
when it is initialized with points p1 and p2, the cellular space has a parallelepipedic shape bounded by the given coordinates. Any valid cell has then digital coordinates in-between p1 and p2 (included).
when it is default constructed, it is bounded by points -p and p (p is model dependant)
adjacent cells to some cell c are cells, lying within the space bounds, with the same topology as c but whose one of their digital coordinates differs by one. They are often called 1-adjacent.
incident cells to some cell c are cells, lying within the space bounds, that are either a face of c or such that c is one of their faces.

Valid expressions and semantics

Name	Expression	Type requirements	Return type	Semantics
initialization	x.init(p1, p2, b)	b is `bool`	`bool`	initializes the space so that cells are within the bounds p1 and p2, returns true iff the initialization was valid (ie, such bounds are representable with these integers).
Size or width	x.size( k )		Integer	returns the size/width of the space along the axis k
Minimal coordinate	x.min( k )		Integer	returns the minimal possible digital coordinate along the axis k
Maximal coordinate	x.max( k )		Integer	returns the maximal possible digital coordinate along the axis k
Lower bound	x.lowerBound()		Point	returns the lowest point in the space, i.e. p1
Upper bound	x.upperBound()		Point	returns the uppermost point in the space, i.e. p1
Lower cell	x.lowerCell()		Cell	returns the lowest cell in the space
Upper cell	x.upperCell()		Cell	returns the uppermost cell in the space
Closedness	x.isSpaceClosed()		`bool`	returns 'true' iff the cellular space is closed

Get first cell	x.uFirst(c)		Cell	returns the first cell of the space with same topology as c
Get last cell	x.uLast(c)		Cell	returns the last cell of the space with same topology as c
Get maximal cell along some axis	x.uGetMax(c,k)		Cell	returns the same cell as c except the k-th coordinate that is the maximal possible
Get minimal cell along some axis	x.uGetMin(c,k)		Cell	returns the same cell as c except the k-th coordinate that is the minimal possible
Distance to upper bound	x.uDistanceToMax(c,k)		Integer	returns the number of increments to do along the k-th axis to reach the upper bound
Distance to lower bound	x.uDistanceToMin(c,k)		Integer	returns the number of decrements to do along the k-th axis to reach the lower bound

Get first cell	x.sFirst(sc)		SCell	returns the first cell of the space with same topology as sc
Get last cell	x.sLast(sc)		SCell	returns the last cell of the space with same topology as sc
Get maximal cell along some axis	x.sGetMax(sc,k)		SCell	returns the same cell as sc except the k-th coordinate that is the maximal possible
Get minimal cell along some axis	x.sGetMin(sc,k)		SCell	returns the same cell as sc except the k-th coordinate that is the minimal possible
Distance to upper bound	x.sDistanceToMax(sc,k)		Integer	returns the number of increments to do along the k-th axis to reach the upper bound
Distance to lower bound	x.sDistanceToMin(sc,k)		Integer	returns the number of decrements to do along the k-th axis to reach the lower bound

Invariants

Models

KhalimskySpaceND

Notes

Template Parameters

T	the type that should be a model of CCellularGridSpaceND.

Definition at line 162 of file CCellularGridSpaceND.h.

Member Typedef Documentation

◆ Size

template<typename T >

typedef T::Size DGtal::concepts::CCellularGridSpaceND< T >::Size

Definition at line 167 of file CCellularGridSpaceND.h.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename T >

DGtal::concepts::CCellularGridSpaceND< T >::BOOST_CONCEPT_ASSERT ( (CIntegralNumber< Size >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename T >

DGtal::concepts::CCellularGridSpaceND< T >::BOOST_CONCEPT_ASSERT ( (CUnsignedNumber< Size >) )

◆ BOOST_CONCEPT_USAGE()

template<typename T >

DGtal::concepts::CCellularGridSpaceND< T >::BOOST_CONCEPT_USAGE ( CCellularGridSpaceND< T > )

inline

Definition at line 172 of file CCellularGridSpaceND.h.

  {
    ConceptUtils::sameType( myBool, myX.init( myP1, myP2, myBool ) );
    checkConstConstraints();
  }

References DGtal::concepts::CCellularGridSpaceND< T >::checkConstConstraints(), DGtal::concepts::CCellularGridSpaceND< T >::myBool, DGtal::concepts::CCellularGridSpaceND< T >::myP1, DGtal::concepts::CCellularGridSpaceND< T >::myP2, DGtal::concepts::CCellularGridSpaceND< T >::myX, and DGtal::concepts::ConceptUtils::sameType().

◆ checkConstConstraints()

template<typename T >

void DGtal::concepts::CCellularGridSpaceND< T >::checkConstConstraints ( ) const

inline

Definition at line 177 of file CCellularGridSpaceND.h.

  {
    ConceptUtils::sameType( mySize, myX.size( myDim ) );
    ConceptUtils::sameType( myInteger, myX.min( myDim ) );
    ConceptUtils::sameType( myInteger, myX.max( myDim ) );
    ConceptUtils::sameType( myP1, myX.lowerBound() );
    ConceptUtils::sameType( myP2, myX.upperBound() );
    ConceptUtils::sameType( myCell, myX.lowerCell() );
    ConceptUtils::sameType( myCell, myX.upperCell() );
    ConceptUtils::sameType( myBool, myX.isSpaceClosed() );
    // -------------------- Unsigned cell geometry services --------------------
    ConceptUtils::sameType( myCell, myX.uFirst( myCell ) );
    ConceptUtils::sameType( myCell, myX.uLast( myCell ) );
    ConceptUtils::sameType( myCell, myX.uGetMax( myCell, myDim ) );
    ConceptUtils::sameType( myCell, myX.uGetMin( myCell, myDim ) );
    ConceptUtils::sameType( myInteger, myX.uDistanceToMax( myCell, myDim ) );
    ConceptUtils::sameType( myInteger, myX.uDistanceToMin( myCell, myDim ) );
    // -------------------- Signed cell geometry services --------------------
    ConceptUtils::sameType( mySCell, myX.sFirst( mySCell ) );
    ConceptUtils::sameType( mySCell, myX.sLast( mySCell ) );
    ConceptUtils::sameType( mySCell, myX.sGetMax( mySCell, myDim ) );
    ConceptUtils::sameType( mySCell, myX.sGetMin( mySCell, myDim ) );
    ConceptUtils::sameType( myInteger, myX.sDistanceToMax( mySCell, myDim ) );
    ConceptUtils::sameType( myInteger, myX.sDistanceToMin( mySCell, myDim ) );
 
}