Aim: This class is a model of CPreCellularGridSpaceND. It represents the cubical grid as a cell complex, whose cells are defined as an array of integers. The topology of the cells is defined by the parity of the coordinates (even: closed, odd: open). More...

#include <DGtal/topology/KhalimskyPreSpaceND.h>

Data Structures
struct	AnyCellCollection

struct	CellMap

struct	SCellMap

struct	SurfelMap

Public Types
using	Integer = TInteger
	Arithmetic ring induced by (+,-,*) and Integer numbers.

using	Cell = KhalimskyPreCell< dim, Integer >

using	SCell = SignedKhalimskyPreCell< dim, Integer >

using	Surfel = SCell

using	Sign = bool

using	DirIterator = PreCellDirectionIterator< dim, Integer >

using	Point = PointVector< dim, Integer >

using	Vector = PointVector< dim, Integer >

using	Space = SpaceND<dim, Integer>

using	PreCellularGridSpace = KhalimskyPreSpaceND<dim, Integer>

using	Cells = AnyCellCollection<Cell>

using	SCells = AnyCellCollection<SCell>

using	CellSet = std::set<Cell>
	Preferred type for defining a set of Cell(s).

using	SCellSet = std::set<SCell>
	Preferred type for defining a set of SCell(s).

using	SurfelSet = std::set<SCell>
	Preferred type for defining a set of surfels (always signed cells).

Static Public Member Functions
Pre-cell creation services (static methods)
static Cell	uCell (const Point &kp)
	From the Khalimsky coordinates of a cell, builds the corresponding unsigned pre-cell.

static Cell	uCell (Point p, const Cell &c)
	From the digital coordinates of a point in Zn and a cell type, builds the corresponding unsigned pre-cell.

static SCell	sCell (const Point &kp, Sign sign=POS)
	From the Khalimsky coordinates of a cell and a sign, builds the corresponding signed pre-cell.

static SCell	sCell (Point p, const SCell &c)
	From the digital coordinates of a point in Zn and a signed cell type, builds the corresponding signed pre-cell.

static Cell	uSpel (Point p)
	From the digital coordinates of a point in Zn, builds the corresponding pre-spel (pre-cell of maximal dimension).

static SCell	sSpel (Point p, Sign sign=POS)
	From the digital coordinates of a point in Zn, builds the corresponding pre-spel (pre-cell of maximal dimension).

static Cell	uPointel (Point p)
	From the digital coordinates of a point in Zn, builds the corresponding pre-pointel (pre-cell of dimension 0).

static SCell	sPointel (Point p, Sign sign=POS)
	From the digital coordinates of a point in Zn, builds the corresponding pre-pointel (pre-cell of dimension 0).

Read accessors to pre-cells
static Integer	uKCoord (const Cell &c, Dimension k)
	Return its Khalimsky coordinate along [k].

static Integer	uCoord (const Cell &c, Dimension k)
	Return its digital coordinate along [k].

static const Point &	uKCoords (const Cell &c)
	Return its Khalimsky coordinates.

static Point	uCoords (const Cell &c)
	Return its digital coordinates.

static Integer	sKCoord (const SCell &c, Dimension k)
	Return its Khalimsky coordinate along [k].

static Integer	sCoord (const SCell &c, Dimension k)
	Return its digital coordinate along [k].

static const Point &	sKCoords (const SCell &c)
	Return its Khalimsky coordinates.

static Point	sCoords (const SCell &c)
	Return its digital coordinates.

static Sign	sSign (const SCell &c)
	Return its sign.

Write accessors to pre-cells
static void	uSetKCoord (Cell &c, Dimension k, Integer i)
	Sets the [k]-th Khalimsky coordinate of [c] to [i].

static void	sSetKCoord (SCell &c, Dimension k, Integer i)
	Sets the [k]-th Khalimsky coordinate of [c] to [i].

static void	uSetCoord (Cell &c, Dimension k, Integer i)
	Sets the [k]-th digital coordinate of [c] to [i].

static void	sSetCoord (SCell &c, Dimension k, Integer i)
	Sets the [k]-th digital coordinate of [c] to [i].

static void	uSetKCoords (Cell &c, const Point &kp)
	Sets the Khalimsky coordinates of [c] to [kp].

static void	sSetKCoords (SCell &c, const Point &kp)
	Sets the Khalimsky coordinates of [c] to [kp].

static void	uSetCoords (Cell &c, const Point &kp)
	Sets the digital coordinates of [c] to [kp].

static void	sSetCoords (SCell &c, const Point &kp)
	Sets the digital coordinates of [c] to [kp].

static void	sSetSign (SCell &c, Sign s)
	Sets the sign of the pre-cell.

Conversion signed/unsigned
static SCell	signs (const Cell &p, Sign s)
	Creates a signed pre-cell from an unsigned one and a given sign.

static Cell	unsigns (const SCell &p)
	Creates an unsigned pre-cell from a signed one.

static SCell	sOpp (const SCell &p)
	Creates the signed pre-cell with the inverse sign of [p].

Pre-cell topology services
static Integer	uTopology (const Cell &p)
	Return the topology word of [p].

static Integer	sTopology (const SCell &p)
	Return the topology word of [p].

static Dimension	uDim (const Cell &p)
	Return the dimension of the pre-cell [p].

static Dimension	sDim (const SCell &p)
	Return the dimension of the pre-cell [p].

static bool	uIsSurfel (const Cell &b)
	Return 'true' if [b] is a surfel (spans all but one coordinate).

static bool	sIsSurfel (const SCell &b)
	Return 'true' if [b] is a surfel (spans all but one coordinate).

static bool	uIsOpen (const Cell &p, Dimension k)
	Return 'true' if [p] is open along the direction [k].

static bool	sIsOpen (const SCell &p, Dimension k)
	Return 'true' if [p] is open along the direction [k].

Iterator services for cells
static DirIterator	uDirs (const Cell &p)
	Given an unsigned pre-cell [p], returns an iterator to iterate over each coordinate the cell spans. (A spel spans all coordinates; a surfel all but one, etc).

static DirIterator	sDirs (const SCell &p)
	Given a signed pre-cell [p], returns an iterator to iterate over each coordinate the cell spans. (A spel spans all coordinates; a surfel all but one, etc).

static DirIterator	uOrthDirs (const Cell &p)
	Given an unsigned pre-cell [p], returns an iterator to iterate over each coordinate the cell does not span. (A spel spans all coordinates; a surfel all but one, etc).

static DirIterator	sOrthDirs (const SCell &p)
	Given a signed pre-cell [p], returns an iterator to iterate over each coordinate the cell does not span. (A spel spans all coordinates; a surfel all but one, etc).

static Dimension	uOrthDir (const Cell &s)
	Given an unsigned pre-surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).

static Dimension	sOrthDir (const SCell &s)
	Given a signed pre-surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).

Unsigned pre-cell geometry services
static Cell	uGetIncr (Cell p, Dimension k)
	Return the same element as [p] except for the incremented coordinate [k].

static bool	uIsMax (const Cell &p, Dimension k)
	Useful to check if you are going out of the space.

static bool	uIsInside (const Cell &p, Dimension k)
	Useful to check if you are going out of the space.

static bool	uIsInside (const Cell &p)
	Useful to check if you are going out of the space.

static Cell	uGetDecr (Cell p, Dimension k)
	Return the same element as [p] except for an decremented coordinate [k].

static bool	uIsMin (const Cell &p, Dimension k)
	Useful to check if you are going out of the space.

static Cell	uGetAdd (Cell p, Dimension k, Integer x)
	Return the same element as [p] except for a coordinate [k] incremented with x.

static Cell	uGetSub (Cell p, Dimension k, Integer x)
	Return the same element as [p] except for a coordinate [k] decremented with x.

static Cell	uTranslation (Cell p, const Vector &vec)
	Add the vector [vec] to [p].

static Cell	uProjection (Cell p, const Cell &bound, Dimension k)
	Return the projection of [p] along the [k]th direction toward [bound].

static void	uProject (Cell &p, const Cell &bound, Dimension k)
	Projects [p] along the [k]th direction toward [bound].

static bool	uNext (Cell &p, const Cell &lower, const Cell &upper)
	Increment the pre-cell [p] to its next position (as classically done in a scanning).

Signed pre-cell geometry services
static SCell	sGetIncr (SCell p, Dimension k)
	Return the same element as [p] except for the incremented coordinate [k].

static bool	sIsMax (const SCell &p, Dimension k)
	Useful to check if you are going out of the space.

static bool	sIsInside (const SCell &p, Dimension k)
	Useful to check if you are going out of the space.

static bool	sIsInside (const SCell &p)
	Useful to check if you are going out of the space.

static SCell	sGetDecr (SCell p, Dimension k)
	Return the same element as [p] except for an decremented coordinate [k].

static bool	sIsMin (const SCell &p, Dimension k)
	Useful to check if you are going out of the space.

static SCell	sGetAdd (SCell p, Dimension k, Integer x)
	Return the same element as [p] except for a coordinate [k] incremented with x.

static SCell	sGetSub (SCell p, Dimension k, Integer x)
	Return the same element as [p] except for a coordinate [k] decremented with x.

static SCell	sTranslation (SCell p, const Vector &vec)
	Add the vector [vec] to [p].

static SCell	sProjection (SCell p, const SCell &bound, Dimension k)
	Return the projection of [p] along the [k]th direction toward [bound].

static void	sProject (SCell &p, const SCell &bound, Dimension k)
	Projects [p] along the [k]th direction toward [bound].

static bool	sNext (SCell &p, const SCell &lower, const SCell &upper)
	Increment the pre-cell [p] to its next position (as classically done in a scanning).

Neighborhood services
static Cells	uNeighborhood (const Cell &cell)
	Computes the 1-neighborhood of the pre-cell [c] and returns it.

static SCells	sNeighborhood (const SCell &cell)
	Computes the 1-neighborhood of the pre-cell [c] and returns it.

static Cells	uProperNeighborhood (const Cell &cell)
	Computes the proper 1-neighborhood of the pre-cell [c] and returns it.

static SCells	sProperNeighborhood (const SCell &cell)
	Computes the proper 1-neighborhood of the pre-cell [c] and returns it.

static Cell	uAdjacent (const Cell &p, Dimension k, bool up)
	Return the adjacent element to [p] along axis [k] in the given direction and orientation.

static SCell	sAdjacent (const SCell &p, Dimension k, bool up)
	Return the adjacent element to [p] along axis [k] in the given direction and orientation.

Incidence services
static Cell	uIncident (Cell c, Dimension k, bool up)
	Return the forward or backward unsigned pre-cell incident to [c] along axis [k], depending on [up].

static SCell	sIncident (SCell c, Dimension k, bool up)
	Return the forward or backward signed pre-cell incident to [c] along axis [k], depending on [up].

static Cells	uLowerIncident (const Cell &c)
	Return the pre-cells directly low incident to c.

static Cells	uUpperIncident (const Cell &c)
	Return the pre-cells directly up incident to c.

static SCells	sLowerIncident (const SCell &c)
	Return the signed pre-cells directly low incident to c.

static SCells	sUpperIncident (const SCell &c)
	Return the signed pre-cells directly up incident to c.

static Cells	uFaces (const Cell &c)
	Return the proper faces of [c] (chain of lower incidence).

static Cells	uCoFaces (const Cell &c)
	Return the proper cofaces of [c] (chain of upper incidence).

static bool	sDirect (const SCell &p, Dimension k)
	Return 'true' if the direct orientation of [p] along [k] is in the positive coordinate direction.

static SCell	sDirectIncident (SCell p, Dimension k)
	Return the direct incident pre-cell of [p] along [k] (the incident pre-cell along [k])

static SCell	sIndirectIncident (SCell p, Dimension k)
	Return the indirect incident pre-cell of [p] along [k] (the incident cell along [k] whose sign is negative).

static Point	interiorVoxel (const SCell &c)
	For a given surfel ((n-1)-signed cell), returns its interior voxel (point in Z^d given by the direct incident n-cell to the given cell).

static Point	exteriorVoxel (const SCell &c)
	For a given surfel ((n-1)-signed cell), returns its exterior voxel (point in Z^d given by the indirect incident n-cell to the given cell).

DGtal interface
static void	selfDisplay (std::ostream &out)
	Writes/Displays the object on an output stream.

static constexpr bool	isValid ()
	Checks the validity/consistency of the object.

Static Public Attributes
static constexpr const Dimension	dimension = dim

static constexpr const Dimension	DIM = dim

static constexpr const Sign	POS = true

static constexpr const Sign	NEG = false

Private Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< TInteger >))
	Integer must be signed to characterize a ring.

Static Private Member Functions
Internals
static void	uAddFaces (Cells &faces, const Cell &c, Dimension axis)
	Used by uFaces for computing incident faces.

static void	uAddCoFaces (Cells &cofaces, const Cell &c, Dimension axis)
	Used by uCoFaces for computing incident cofaces.

Detailed Description

template<Dimension dim, typename TInteger>
class DGtal::KhalimskyPreSpaceND< dim, TInteger >

Aim: This class is a model of CPreCellularGridSpaceND. It represents the cubical grid as a cell complex, whose cells are defined as an array of integers. The topology of the cells is defined by the parity of the coordinates (even: closed, odd: open).

Description of template class 'KhalimskyPreSpaceND'

This cellular grid space has no bounds (depending on the Integer type) and thus only provides static methods.

Template Parameters

dim	the dimension of the digital space.
TInteger	the Integer class used to specify the arithmetic computations (default type = int32).

Note: Essentially a backport from ImaGene.

See also: KhalimskySpaceND

Examples: topology/khalimskySpaceScanner.cpp.

Definition at line 378 of file KhalimskyPreSpaceND.h.

Member Typedef Documentation

◆ Cell

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Cell = KhalimskyPreCell< dim, Integer >

Definition at line 388 of file KhalimskyPreSpaceND.h.

◆ Cells

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Cells = AnyCellCollection<Cell>

Definition at line 417 of file KhalimskyPreSpaceND.h.

◆ CellSet

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::CellSet = std::set<Cell>

Preferred type for defining a set of Cell(s).

Definition at line 422 of file KhalimskyPreSpaceND.h.

◆ DirIterator

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::DirIterator = PreCellDirectionIterator< dim, Integer >

Definition at line 393 of file KhalimskyPreSpaceND.h.

◆ Integer

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Integer = TInteger

Arithmetic ring induced by (+,-,*) and Integer numbers.

Definition at line 385 of file KhalimskyPreSpaceND.h.

◆ Point

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Point = PointVector< dim, Integer >

Definition at line 396 of file KhalimskyPreSpaceND.h.

◆ PreCellularGridSpace

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::PreCellularGridSpace = KhalimskyPreSpaceND<dim, Integer>

Definition at line 400 of file KhalimskyPreSpaceND.h.

◆ SCell

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::SCell = SignedKhalimskyPreCell< dim, Integer >

Definition at line 389 of file KhalimskyPreSpaceND.h.

◆ SCells

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::SCells = AnyCellCollection<SCell>

Definition at line 418 of file KhalimskyPreSpaceND.h.

◆ SCellSet

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::SCellSet = std::set<SCell>

Preferred type for defining a set of SCell(s).

Definition at line 425 of file KhalimskyPreSpaceND.h.

◆ Sign

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Sign = bool

Definition at line 392 of file KhalimskyPreSpaceND.h.

◆ Space

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Space = SpaceND<dim, Integer>

Definition at line 399 of file KhalimskyPreSpaceND.h.

◆ Surfel

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Surfel = SCell

Definition at line 391 of file KhalimskyPreSpaceND.h.

◆ SurfelSet

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::SurfelSet = std::set<SCell>

Preferred type for defining a set of surfels (always signed cells).

Definition at line 428 of file KhalimskyPreSpaceND.h.

◆ Vector

template<Dimension dim, typename TInteger >

using DGtal::KhalimskyPreSpaceND< dim, TInteger >::Vector = PointVector< dim, Integer >

Definition at line 397 of file KhalimskyPreSpaceND.h.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<Dimension dim, typename TInteger >

DGtal::KhalimskyPreSpaceND< dim, TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< TInteger >) )

private

Integer must be signed to characterize a ring.

◆ exteriorVoxel()

template<Dimension dim, typename TInteger >

static Point DGtal::KhalimskyPreSpaceND< dim, TInteger >::exteriorVoxel ( const SCell & c )

static

For a given surfel ((n-1)-signed cell), returns its exterior voxel (point in Z^d given by the indirect incident n-cell to the given cell).

Parameters

c	any signed pre-cell.

Returns: the outer voxel.

◆ interiorVoxel()

template<Dimension dim, typename TInteger >

static Point DGtal::KhalimskyPreSpaceND< dim, TInteger >::interiorVoxel ( const SCell & c )

static

For a given surfel ((n-1)-signed cell), returns its interior voxel (point in Z^d given by the direct incident n-cell to the given cell).

Parameters

c	any signed pre-cell.

Returns: the inner voxel.

◆ isValid()

template<Dimension dim, typename TInteger >

static constexpr bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::isValid ( )

staticconstexpr

Checks the validity/consistency of the object.

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

◆ sAdjacent()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sAdjacent	(	const SCell &	p,
		Dimension	k,
		bool	up )

static

Return the adjacent element to [p] along axis [k] in the given direction and orientation.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
up	if 'true' the orientation is forward along axis [k], otherwise backward.

Returns: the adjacent element to [p] along axis [k] in the given direction and orientation.

Note: It is an alias to 'up ? sGetIncr( p, k ) : sGetDecr( p, k )'.

◆ sCell() [1/2]

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sCell	(	const Point &	kp,
		Sign	sign = POS )

static

From the Khalimsky coordinates of a cell and a sign, builds the corresponding signed pre-cell.

Parameters

kp	an integer point (Khalimsky coordinates of cell).
sign	the sign of the cell (either POS or NEG).

Returns: the signed pre-cell.

◆ sCell() [2/2]

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sCell	(	Point	p,
		const SCell &	c )

static

From the digital coordinates of a point in Zn and a signed cell type, builds the corresponding signed pre-cell.

Parameters

p	an integer point (digital coordinates of cell).
c	another cell defining the topology and sign.

Returns: the pre-cell having the topology and sign of [c] and the given digital coordinates [p].

◆ sCoord()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::sCoord	(	const SCell &	c,
		Dimension	k )

static

Return its digital coordinate along [k].

Parameters

c	any signed pre-cell.
k	any valid dimension.

Returns: its digital coordinate along [k].

◆ sCoords()

template<Dimension dim, typename TInteger >

static Point DGtal::KhalimskyPreSpaceND< dim, TInteger >::sCoords ( const SCell & c )

static

Return its digital coordinates.

Parameters

c	any signed pre-cell.

Returns: its digital coordinates.

◆ sDim()

template<Dimension dim, typename TInteger >

static Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::sDim ( const SCell & p )

static

Return the dimension of the pre-cell [p].

Parameters

p	any signed pre-cell.

Returns: the dimension of the pre-cell [p].

◆ sDirect()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sDirect	(	const SCell &	p,
		Dimension	k )

static

Return 'true' if the direct orientation of [p] along [k] is in the positive coordinate direction.

The direct orientation in a direction allows to go from positive incident pre-cells to positive incident pre-cells. This means that

KPreSpace::sSign( KPreSpace::sIncident( p, k, KPreSpace::sDirect( p, k ) ) ) == KPreSpace::POS

is always true.

Parameters

p	any signed pre-cell.
k	any coordinate.

Returns: the direct orientation of [p] along [k] (true is upward, false is backward).

◆ sDirectIncident()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sDirectIncident	(	SCell	p,
		Dimension	k )

static

Return the direct incident pre-cell of [p] along [k] (the incident pre-cell along [k])

Parameters

p	any signed pre-cell.
k	any coordinate.

Returns: the direct incident pre-cell of [p] along [k] (the incident pre-cell along [k])

◆ sDirs()

template<Dimension dim, typename TInteger >

static DirIterator DGtal::KhalimskyPreSpaceND< dim, TInteger >::sDirs ( const SCell & p )

static

Given a signed pre-cell [p], returns an iterator to iterate over each coordinate the cell spans. (A spel spans all coordinates; a surfel all but one, etc).

Example:

KPreSpace::SCell p;
...
for ( auto q = KPreSpace::uDirs( p ); q != 0; ++q )
{
  Dimension dir = *q;
...
}

Parameters

p	any signed pre-cell.

Returns: an iterator that points on the first coordinate spanned by the pre-cell.

◆ selfDisplay()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::selfDisplay ( std::ostream & out )

static

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ sGetAdd()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sGetAdd	(	SCell	p,
		Dimension	k,
		Integer	x )

static

Return the same element as [p] except for a coordinate [k] incremented with x.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
x	the increment.

Returns: the same element as [p] except for a coordinate [k] incremented with x.

◆ sGetDecr()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sGetDecr	(	SCell	p,
		Dimension	k )

static

Return the same element as [p] except for an decremented coordinate [k].

Parameters

p	any pre-cell.
k	the coordinate that is changed.

Returns: the same element as [p] except for an decremented coordinate [k].

◆ sGetIncr()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sGetIncr	(	SCell	p,
		Dimension	k )

static

Return the same element as [p] except for the incremented coordinate [k].

Parameters

p	any pre-cell.
k	the coordinate that is changed.

Returns: the same element as [p] except for the incremented coordinate [k].

◆ sGetSub()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sGetSub	(	SCell	p,
		Dimension	k,
		Integer	x )

static

Return the same element as [p] except for a coordinate [k] decremented with x.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
x	the decrement.

Returns: the same element as [p] except for a coordinate [k] decremented with x.

◆ signs()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::signs	(	const Cell &	p,
		Sign	s )

static

Creates a signed pre-cell from an unsigned one and a given sign.

Parameters

p	any unsigned pre-cell.
s	a sign.

Returns: the signed version of the pre-cell [p] with sign [s].

◆ sIncident()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIncident	(	SCell	c,
		Dimension	k,
		bool	up )

static

Return the forward or backward signed pre-cell incident to [c] along axis [k], depending on [up].

Parameters

c	any signed pre-cell.
k	any coordinate.
up	if 'true' the orientation is forward along axis [k], otherwise backward.

Returns: the forward or backward signed pre-cell incident to [c] along axis [k], depending on [up]. It is worthy to note that the forward and backward pre-cell have opposite sign. Furthermore, the sign of these pre-cells is defined so as to satisfy a boundary operator.

Note: It may be a lower incident pre-cell if [c] is open along axis [k], else an upper incident pre-cell.

◆ sIndirectIncident()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIndirectIncident	(	SCell	p,
		Dimension	k )

static

Return the indirect incident pre-cell of [p] along [k] (the incident cell along [k] whose sign is negative).

Parameters

p	any signed pre-cell.
k	any coordinate.

Returns: the indirect incident pre-cell of [p] along [k] (the incident cell along [k] whose sign is negative).

◆ sIsInside() [1/2]

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsInside ( const SCell & p )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.

Returns: always true.

◆ sIsInside() [2/2]

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsInside	(	const SCell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always true.

◆ sIsMax()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsMax	(	const SCell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always false.

◆ sIsMin()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsMin	(	const SCell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always false.

◆ sIsOpen()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsOpen	(	const SCell &	p,
		Dimension	k )

static

Return 'true' if [p] is open along the direction [k].

Parameters

p	any signed pre-cell.
k	any direction.

Returns: 'true' if [p] is open along the direction [k].

◆ sIsSurfel()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sIsSurfel ( const SCell & b )

static

Return 'true' if [b] is a surfel (spans all but one coordinate).

Parameters

b	any signed pre-cell.

Returns: 'true' if [b] is a surfel (spans all but one coordinate).

◆ sKCoord()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::sKCoord	(	const SCell &	c,
		Dimension	k )

static

Return its Khalimsky coordinate along [k].

Parameters

c	any signed pre-cell.
k	any valid dimension.

Returns: its Khalimsky coordinate along [k].

◆ sKCoords()

template<Dimension dim, typename TInteger >

static const Point & DGtal::KhalimskyPreSpaceND< dim, TInteger >::sKCoords ( const SCell & c )

static

Return its Khalimsky coordinates.

Parameters

c	any signed pre-cell.

Returns: its Khalimsky coordinates.

◆ sLowerIncident()

template<Dimension dim, typename TInteger >

static SCells DGtal::KhalimskyPreSpaceND< dim, TInteger >::sLowerIncident ( const SCell & c )

static

Return the signed pre-cells directly low incident to c.

Parameters

c	any signed pre-cell.

Returns: the signed pre-cells directly low incident to c.

Note: it is the lower boundary of c expressed as a list of signed pre-cells.

◆ sNeighborhood()

template<Dimension dim, typename TInteger >

static SCells DGtal::KhalimskyPreSpaceND< dim, TInteger >::sNeighborhood ( const SCell & cell )

static

Computes the 1-neighborhood of the pre-cell [c] and returns it.

It is the set of pre-cells with same topology that are adjacent to [c].

Parameters

cell	the signed pre-cell of interest.

Returns: the pre-cells of the 1-neighborhood of [cell].

◆ sNext()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::sNext	(	SCell &	p,
		const SCell &	lower,
		const SCell &	upper )

static

Increment the pre-cell [p] to its next position (as classically done in a scanning).

Example:

Cell first, last; // lower and upper bounds
Cell p = first;
do
{ // ... whatever [p] is the current cell
}
while ( KPreSpace::uNext( p, first, last ) );

Parameters

p	any pre-cell.
lower	the lower bound.
upper	the upper bound.

Returns: true if p is still within the bounds, false if the scanning is finished.

Precondition: sTopology(p) == sTopology(lower) == sTopology(upper).

◆ sOpp()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sOpp ( const SCell & p )

static

Creates the signed pre-cell with the inverse sign of [p].

Parameters

p	any signed pre-cell.

Returns: the pre-cell [p] with opposite sign.

◆ sOrthDir()

template<Dimension dim, typename TInteger >

static Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::sOrthDir ( const SCell & s )

static

Given a signed pre-surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).

Parameters

s	a signed pre-surfel

Returns: the orthogonal direction of [s]

◆ sOrthDirs()

template<Dimension dim, typename TInteger >

static DirIterator DGtal::KhalimskyPreSpaceND< dim, TInteger >::sOrthDirs ( const SCell & p )

static

Given a signed pre-cell [p], returns an iterator to iterate over each coordinate the cell does not span. (A spel spans all coordinates; a surfel all but one, etc).

Example:

KPreSpace::SCell p;
...
for ( auto q = KPreSpace::uOrthDirs( p ); q != 0; ++q )
{
  Dimension dir = *q;
...
}

Parameters

p	any signed pre-cell.

Returns: an iterator that points on the first coordinate spanned by the cell.

◆ sPointel()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sPointel	(	Point	p,
		Sign	sign = POS )

static

From the digital coordinates of a point in Zn, builds the corresponding pre-pointel (pre-cell of dimension 0).

Parameters

p	an integer point (digital coordinates of cell).
sign	the sign of the cell (either POS or NEG).

Returns: the signed pre-pointel having the given digital coordinates [p].

◆ sProject()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sProject	(	SCell &	p,
		const SCell &	bound,
		Dimension	k )

static

Projects [p] along the [k]th direction toward [bound].

Otherwise said, p[ k ] == bound[ k ] afterwards.

Parameters

p	any pre-cell.
bound	the element acting as bound (same topology as p).
k	the concerned coordinate.

Precondition: sIsOpen(p, k) == sIsOpen(bound, k)

◆ sProjection()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sProjection	(	SCell	p,
		const SCell &	bound,
		Dimension	k )

static

Return the projection of [p] along the [k]th direction toward [bound].

Otherwise said, p[ k ] == bound[ k ] afterwards.

Parameters

p	any pre-cell.
bound	the element acting as bound (same topology as p).
k	the concerned coordinate.

Returns: the projection.

Precondition: sIsOpen(p, k) == sIsOpen(bound, k)

Postcondition: sTopology(p) == sTopology(sProjection(p, bound, k)).

◆ sProperNeighborhood()

template<Dimension dim, typename TInteger >

static SCells DGtal::KhalimskyPreSpaceND< dim, TInteger >::sProperNeighborhood ( const SCell & cell )

static

Computes the proper 1-neighborhood of the pre-cell [c] and returns it.

It is the set of pre-cells with same topology that are adjacent to [c] and different from [c].

Parameters

cell	the signed pre-cell of interest.

Returns: the pre-cells of the proper 1-neighborhood of [cell].

◆ sSetCoord()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSetCoord	(	SCell &	c,
		Dimension	k,
		Integer	i )

static

Sets the [k]-th digital coordinate of [c] to [i].

Parameters

c	any signed pre-cell.
k	any valid dimension.
i	an integer coordinate.

◆ sSetCoords()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSetCoords	(	SCell &	c,
		const Point &	kp )

static

Sets the digital coordinates of [c] to [kp].

Parameters

c	any signed pre-cell.
kp	the new digital coordinates for [c].

◆ sSetKCoord()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSetKCoord	(	SCell &	c,
		Dimension	k,
		Integer	i )

static

Sets the [k]-th Khalimsky coordinate of [c] to [i].

Parameters

c	any signed pre-cell.
k	any valid dimension.
i	an integer coordinate.

◆ sSetKCoords()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSetKCoords	(	SCell &	c,
		const Point &	kp )

static

Sets the Khalimsky coordinates of [c] to [kp].

Parameters

c	any signed pre-cell.
kp	the new Khalimsky coordinates for [c].

◆ sSetSign()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSetSign	(	SCell &	c,
		Sign	s )

static

Sets the sign of the pre-cell.

Parameters

c	(modified) any signed pre-cell.
s	any sign.

◆ sSign()

template<Dimension dim, typename TInteger >

static Sign DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSign ( const SCell & c )

static

Return its sign.

Parameters

c	any signed pre-cell.

Returns: its sign.

◆ sSpel()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sSpel	(	Point	p,
		Sign	sign = POS )

static

From the digital coordinates of a point in Zn, builds the corresponding pre-spel (pre-cell of maximal dimension).

Parameters

p	an integer point (digital coordinates of cell).
sign	the sign of the cell (either POS or NEG).

Returns: the signed pre-spel having the given digital coordinates [p].

◆ sTopology()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::sTopology ( const SCell & p )

static

Return the topology word of [p].

Parameters

p	any signed pre-cell.

Returns: the topology word of [p].

◆ sTranslation()

template<Dimension dim, typename TInteger >

static SCell DGtal::KhalimskyPreSpaceND< dim, TInteger >::sTranslation	(	SCell	p,
		const Vector &	vec )

static

Add the vector [vec] to [p].

Parameters

p	any pre-cell.
vec	any pointel.

Returns: the signed code of the cell [p] translated by [coord].

◆ sUpperIncident()

template<Dimension dim, typename TInteger >

static SCells DGtal::KhalimskyPreSpaceND< dim, TInteger >::sUpperIncident ( const SCell & c )

static

Return the signed pre-cells directly up incident to c.

Parameters

c	any signed pre-cell.

Returns: the signed pre-cells directly up incident to c.

Note: it is the upper boundary of c expressed as a list of signed pre-cells.

◆ uAddCoFaces()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uAddCoFaces	(	Cells &	cofaces,
		const Cell &	c,
		Dimension	axis )

staticprivate

Used by uCoFaces for computing incident cofaces.

◆ uAddFaces()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uAddFaces	(	Cells &	faces,
		const Cell &	c,
		Dimension	axis )

staticprivate

Used by uFaces for computing incident faces.

◆ uAdjacent()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uAdjacent	(	const Cell &	p,
		Dimension	k,
		bool	up )

static

Return the adjacent element to [p] along axis [k] in the given direction and orientation.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
up	if 'true' the orientation is forward along axis [k], otherwise backward.

Returns: the adjacent element to [p] along axis [k] in the given direction and orientation.

Note: It is an alias to 'up ? uGetIncr( p, k ) : uGetDecr( p, k )'.

◆ uCell() [1/2]

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uCell ( const Point & kp )

static

From the Khalimsky coordinates of a cell, builds the corresponding unsigned pre-cell.

Parameters

kp	an integer point (Khalimsky coordinates of cell).

Returns: the unsigned pre-cell.

Examples: topology/khalimskySpaceScanner.cpp.

◆ uCell() [2/2]

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uCell	(	Point	p,
		const Cell &	c )

static

From the digital coordinates of a point in Zn and a cell type, builds the corresponding unsigned pre-cell.

Parameters

p	an integer point (digital coordinates of cell).
c	another cell defining the topology.

Returns: the pre-cell having the topology of [c] and the given digital coordinates [p].

◆ uCoFaces()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uCoFaces ( const Cell & c )

static

Return the proper cofaces of [c] (chain of upper incidence).

Parameters

c	any unsigned ipre-cell.

Returns: the proper cofaces of [c] (chain of upper incidence).

◆ uCoord()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::uCoord	(	const Cell &	c,
		Dimension	k )

static

Return its digital coordinate along [k].

Parameters

c	any unsigned pre-cell.
k	any valid dimension.

Returns: its digital coordinate along [k].

◆ uCoords()

template<Dimension dim, typename TInteger >

static Point DGtal::KhalimskyPreSpaceND< dim, TInteger >::uCoords ( const Cell & c )

static

Return its digital coordinates.

Parameters

c	any unsigned pre-cell.

Returns: its digital coordinates.

◆ uDim()

template<Dimension dim, typename TInteger >

static Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::uDim ( const Cell & p )

static

Return the dimension of the pre-cell [p].

Parameters

p	any unsigned pre-cell.

Returns: the dimension of the pre-cell [p].

◆ uDirs()

template<Dimension dim, typename TInteger >

static DirIterator DGtal::KhalimskyPreSpaceND< dim, TInteger >::uDirs ( const Cell & p )

static

Given an unsigned pre-cell [p], returns an iterator to iterate over each coordinate the cell spans. (A spel spans all coordinates; a surfel all but one, etc).

Example:

KPreSpace::Cell p;
...
for ( auto q = KPreSpace::uDirs( p ); q != 0; ++q )
{
  Dimension dir = *q;
...
}

Parameters

p	any unsigned pre-cell.

Returns: an iterator that points on the first coordinate spanned by the pre-cell.

◆ uFaces()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uFaces ( const Cell & c )

static

Return the proper faces of [c] (chain of lower incidence).

Parameters

c	any unsigned pre-cell.

Returns: the proper faces of [c] (chain of lower incidence).

◆ uGetAdd()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uGetAdd	(	Cell	p,
		Dimension	k,
		Integer	x )

static

Return the same element as [p] except for a coordinate [k] incremented with x.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
x	the increment.

Returns: the same element as [p] except for a coordinate [k] incremented with x.

◆ uGetDecr()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uGetDecr	(	Cell	p,
		Dimension	k )

static

Return the same element as [p] except for an decremented coordinate [k].

Parameters

p	any pre-cell.
k	the coordinate that is changed.

Returns: the same element as [p] except for an decremented coordinate [k].

◆ uGetIncr()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uGetIncr	(	Cell	p,
		Dimension	k )

static

Return the same element as [p] except for the incremented coordinate [k].

Parameters

p	any pre-cell.
k	the coordinate that is changed.

Returns: the same element as [p] except for the incremented coordinate [k].

◆ uGetSub()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uGetSub	(	Cell	p,
		Dimension	k,
		Integer	x )

static

Return the same element as [p] except for a coordinate [k] decremented with x.

Parameters

p	any pre-cell.
k	the coordinate that is changed.
x	the decrement.

Returns: the same element as [p] except for a coordinate [k] decremented with x.

◆ uIncident()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIncident	(	Cell	c,
		Dimension	k,
		bool	up )

static

Return the forward or backward unsigned pre-cell incident to [c] along axis [k], depending on [up].

Parameters

c	any unsigned pre-cell.
k	any coordinate.
up	if 'true' the orientation is forward along axis [k], otherwise backward.

Returns: the forward or backward unsigned pre-cell incident to [c] along axis [k], depending on [up].

Note: It may be a lower incident pre-cell if [c] is open along axis [k], else an upper incident pre-cell.

◆ uIsInside() [1/2]

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsInside ( const Cell & p )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.

Returns: always true.

◆ uIsInside() [2/2]

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsInside	(	const Cell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always true.

◆ uIsMax()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsMax	(	const Cell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always false.

◆ uIsMin()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsMin	(	const Cell &	p,
		Dimension	k )

static

Useful to check if you are going out of the space.

Only for compatibility reasons.

Parameters

p	any pre-cell.
k	the tested coordinate.

Returns: always false.

◆ uIsOpen()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsOpen	(	const Cell &	p,
		Dimension	k )

static

Return 'true' if [p] is open along the direction [k].

Parameters

p	any pre-cell.
k	any direction.

Returns: 'true' if [p] is open along the direction [k].

◆ uIsSurfel()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uIsSurfel ( const Cell & b )

static

Return 'true' if [b] is a surfel (spans all but one coordinate).

Parameters

b	any unsigned pre-cell.

Returns: 'true' if [b] is a surfel (spans all but one coordinate).

◆ uKCoord()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::uKCoord	(	const Cell &	c,
		Dimension	k )

static

Return its Khalimsky coordinate along [k].

Parameters

c	any unsigned pre-cell.
k	any valid dimension.

Returns: its Khalimsky coordinate along [k].

◆ uKCoords()

template<Dimension dim, typename TInteger >

static const Point & DGtal::KhalimskyPreSpaceND< dim, TInteger >::uKCoords ( const Cell & c )

static

Return its Khalimsky coordinates.

Parameters

c	any unsigned pre-cell.

Returns: its Khalimsky coordinates.

◆ uLowerIncident()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uLowerIncident ( const Cell & c )

static

Return the pre-cells directly low incident to c.

Parameters

c	any unsigned pre-cell.

Returns: the pre-cells directly low incident to c.

◆ uNeighborhood()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uNeighborhood ( const Cell & cell )

static

Computes the 1-neighborhood of the pre-cell [c] and returns it.

It is the set of cells with same topology that are adjacent to [c].

Parameters

cell	the unsigned pre-cell of interest.

Returns: the pre-cells of the 1-neighborhood of [cell].

◆ uNext()

template<Dimension dim, typename TInteger >

static bool DGtal::KhalimskyPreSpaceND< dim, TInteger >::uNext	(	Cell &	p,
		const Cell &	lower,
		const Cell &	upper )

static

Increment the pre-cell [p] to its next position (as classically done in a scanning).

Example:

Cell first, last; // lower and upper bounds
Cell p = first;
do
{ // ... whatever [p] is the current cell
}
while ( KPreSpace::uNext( p, first, last ) );

Parameters

p	any pre-cell.
lower	the lower bound.
upper	the upper bound.

Returns: true if p is still within the bounds, false if the scanning is finished.

Precondition: uTopology(p) == uTopology(lower) == uTopology(upper).

◆ unsigns()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::unsigns ( const SCell & p )

static

Creates an unsigned pre-cell from a signed one.

Parameters

p	any signed pre-cell.

Returns: the unsigned version of the pre-cell [p].

◆ uOrthDir()

template<Dimension dim, typename TInteger >

static Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::uOrthDir ( const Cell & s )

static

Given an unsigned pre-surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).

Parameters

s	an unsigned pre-surfel

Returns: the orthogonal direction of [s]

◆ uOrthDirs()

template<Dimension dim, typename TInteger >

static DirIterator DGtal::KhalimskyPreSpaceND< dim, TInteger >::uOrthDirs ( const Cell & p )

static

Given an unsigned pre-cell [p], returns an iterator to iterate over each coordinate the cell does not span. (A spel spans all coordinates; a surfel all but one, etc).

Example:

KPreSpace::Cell p;
...
for ( auto q = KPreSpace::uOrthDirs( p ); q != 0; ++q )
{
  Dimension dir = *q;
...
}

Parameters

p	any unsigned pre-cell.

Returns: an iterator that points on the first coordinate spanned by the cell.

◆ uPointel()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uPointel ( Point p )

static

From the digital coordinates of a point in Zn, builds the corresponding pre-pointel (pre-cell of dimension 0).

Parameters

p	an integer point (digital coordinates of cell).

Returns: the pre-pointel having the given digital coordinates [p].

◆ uProject()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uProject	(	Cell &	p,
		const Cell &	bound,
		Dimension	k )

static

Projects [p] along the [k]th direction toward [bound].

Otherwise said, p[ k ] == bound[ k ] afterwards

Parameters

[in,out]	p	any pre-cell.
[in]	bound	the element acting as bound (same topology as p).
[in]	k	the concerned coordinate.

Precondition: uIsOpen(p, k) == uIsOpen(bound, k)

◆ uProjection()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uProjection	(	Cell	p,
		const Cell &	bound,
		Dimension	k )

static

Return the projection of [p] along the [k]th direction toward [bound].

Otherwise said, p[ k ] == bound[ k ] afterwards.

Parameters

p	any pre-cell.
bound	the element acting as bound (same topology as p).
k	the concerned coordinate.

Returns: the projection.

Precondition: uIsOpen(p, k) == uIsOpen(bound, k)

Postcondition: uTopology(p) == uTopology(uProjection(p, bound, k)).

◆ uProperNeighborhood()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uProperNeighborhood ( const Cell & cell )

static

Computes the proper 1-neighborhood of the pre-cell [c] and returns it.

It is the set of pre-cells with same topology that are adjacent to [c] and different from [c].

Parameters

cell	the unsigned pre-cell of interest.

Returns: the pre-cells of the proper 1-neighborhood of [cell].

◆ uSetCoord()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uSetCoord	(	Cell &	c,
		Dimension	k,
		Integer	i )

static

Sets the [k]-th digital coordinate of [c] to [i].

Parameters

c	any unsigned pre-cell.
k	any valid dimension.
i	an integer coordinate.

◆ uSetCoords()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uSetCoords	(	Cell &	c,
		const Point &	kp )

static

Sets the digital coordinates of [c] to [kp].

Parameters

c	any unsigned pre-cell.
kp	the new digital coordinates for [c].

◆ uSetKCoord()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uSetKCoord	(	Cell &	c,
		Dimension	k,
		Integer	i )

static

Sets the [k]-th Khalimsky coordinate of [c] to [i].

Parameters

c	any unsigned pre-cell.
k	any valid dimension.
i	an integer coordinate.

◆ uSetKCoords()

template<Dimension dim, typename TInteger >

static void DGtal::KhalimskyPreSpaceND< dim, TInteger >::uSetKCoords	(	Cell &	c,
		const Point &	kp )

static

Sets the Khalimsky coordinates of [c] to [kp].

Parameters

c	any unsigned pre-cell.
kp	the new Khalimsky coordinates for [c].

◆ uSpel()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uSpel ( Point p )

static

From the digital coordinates of a point in Zn, builds the corresponding pre-spel (pre-cell of maximal dimension).

Parameters

p	an integer point (digital coordinates of cell).

Returns: the pre-spel having the given digital coordinates [p].

◆ uTopology()

template<Dimension dim, typename TInteger >

static Integer DGtal::KhalimskyPreSpaceND< dim, TInteger >::uTopology ( const Cell & p )

static

Return the topology word of [p].

Parameters

p	any unsigned pre-cell.

Returns: the topology word of [p].

◆ uTranslation()

template<Dimension dim, typename TInteger >

static Cell DGtal::KhalimskyPreSpaceND< dim, TInteger >::uTranslation	(	Cell	p,
		const Vector &	vec )

static

Add the vector [vec] to [p].

Parameters

p	any pre-cell.
vec	any pointel.

Returns: the unsigned copy of the pre-cell [p] translated by [coord].

◆ uUpperIncident()

template<Dimension dim, typename TInteger >

static Cells DGtal::KhalimskyPreSpaceND< dim, TInteger >::uUpperIncident ( const Cell & c )

static

Return the pre-cells directly up incident to c.

Parameters

c	any unsigned pre-cell.

Returns: the pre-cells directly up incident to c.

Field Documentation

◆ DIM

template<Dimension dim, typename TInteger >

const Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::DIM = dim

staticconstexpr

Definition at line 404 of file KhalimskyPreSpaceND.h.

◆ dimension

template<Dimension dim, typename TInteger >

const Dimension DGtal::KhalimskyPreSpaceND< dim, TInteger >::dimension = dim

staticconstexpr

Definition at line 403 of file KhalimskyPreSpaceND.h.

◆ NEG

template<Dimension dim, typename TInteger >

const Sign DGtal::KhalimskyPreSpaceND< dim, TInteger >::NEG = false

staticconstexpr

Definition at line 406 of file KhalimskyPreSpaceND.h.

◆ POS

template<Dimension dim, typename TInteger >

const Sign DGtal::KhalimskyPreSpaceND< dim, TInteger >::POS = true

staticconstexpr

Definition at line 405 of file KhalimskyPreSpaceND.h.

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

KhalimskyPreSpaceND.h

Data Structures

Public Types

Static Public Member Functions

Static Public Attributes

Private Member Functions

Static Private Member Functions

Detailed Description

Member Typedef Documentation

◆ Cell

◆ Cells

◆ CellSet

◆ DirIterator

◆ Integer

◆ Point

◆ PreCellularGridSpace

◆ SCell

◆ SCells

◆ SCellSet

◆ Sign

◆ Space

◆ Surfel

◆ SurfelSet

◆ Vector

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

◆ exteriorVoxel()

◆ interiorVoxel()

◆ isValid()

◆ sAdjacent()

◆ sCell() [1/2]

◆ sCell() [2/2]

◆ sCoord()

◆ sCoords()

◆ sDim()

◆ sDirect()

◆ sDirectIncident()

◆ sDirs()

◆ selfDisplay()

◆ sGetAdd()

◆ sGetDecr()

◆ sGetIncr()

◆ sGetSub()

◆ signs()

◆ sIncident()

◆ sIndirectIncident()

◆ sIsInside() [1/2]

◆ sIsInside() [2/2]

◆ sIsMax()

◆ sIsMin()

◆ sIsOpen()

◆ sIsSurfel()

◆ sKCoord()

◆ sKCoords()

◆ sLowerIncident()

◆ sNeighborhood()

◆ sNext()

◆ sOpp()

◆ sOrthDir()

◆ sOrthDirs()

◆ sPointel()

◆ sProject()

◆ sProjection()

◆ sProperNeighborhood()

◆ sSetCoord()

◆ sSetCoords()

◆ sSetKCoord()

◆ sSetKCoords()

◆ sSetSign()

◆ sSign()

◆ sSpel()

◆ sTopology()

◆ sTranslation()

◆ sUpperIncident()

◆ uAddCoFaces()

◆ uAddFaces()

◆ uAdjacent()

◆ uCell() [1/2]

◆ uCell() [2/2]

◆ uCoFaces()

◆ uCoord()