Aim: This class is a model of CCellularGridSpaceND. 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/KhalimskySpaceND.h>
Data Structures | |
| struct | CellMap |
| struct | SCellMap |
| struct | SurfelMap |
Public Types | |
| enum | Closure { CLOSED , OPEN , PERIODIC } |
| Boundaries closure type. More... | |
| typedef TInteger | Integer |
| Arithmetic ring induced by (+,-,*) and Integer numbers. More... | |
| typedef NumberTraits< Integer >::UnsignedVersion | Size |
| Type used to represent sizes in the digital space. More... | |
| typedef SpaceND< dim, Integer > | Space |
| typedef KhalimskySpaceND< dim, Integer > | CellularGridSpace |
| typedef KhalimskyPreSpaceND< dim, Integer > | PreCellularGridSpace |
| typedef KhalimskyCell< dim, Integer > | Cell |
| typedef KhalimskyPreCell< dim, Integer > | PreCell |
| typedef SignedKhalimskyCell< dim, Integer > | SCell |
| typedef SignedKhalimskyPreCell< dim, Integer > | SPreCell |
| typedef SCell | Surfel |
| typedef bool | Sign |
| using | DirIterator = typename PreCellularGridSpace::DirIterator |
| typedef PointVector< dim, Integer > | Point |
| typedef PointVector< dim, Integer > | Vector |
| template<typename CellType > | |
| using | AnyCellCollection = typename PreCellularGridSpace::template AnyCellCollection< CellType > |
| typedef AnyCellCollection< Cell > | Cells |
| typedef AnyCellCollection< SCell > | SCells |
| typedef std::set< Cell > | CellSet |
| Preferred type for defining a set of Cell(s). More... | |
| typedef std::set< SCell > | SCellSet |
| Preferred type for defining a set of SCell(s). More... | |
| typedef std::set< SCell > | SurfelSet |
| Preferred type for defining a set of surfels (always signed cells). More... | |
Public Member Functions | |
Standard services | |
| ~KhalimskySpaceND () | |
| Destructor. More... | |
| KhalimskySpaceND () | |
| Default constructor. More... | |
| KhalimskySpaceND (const KhalimskySpaceND &other)=default | |
| Copy constructor. More... | |
| KhalimskySpaceND & | operator= (const KhalimskySpaceND &other)=default |
| Copy operator. More... | |
| KhalimskySpaceND (KhalimskySpaceND &&other)=default | |
| Move constructor. More... | |
| KhalimskySpaceND & | operator= (KhalimskySpaceND &&other)=default |
| Move operator. More... | |
| bool | init (const Point &lower, const Point &upper, bool isClosed) |
| Specifies the upper and lower bounds for the maximal cells in this space. More... | |
| bool | init (const Point &lower, const Point &upper, Closure closure) |
| Specifies the upper and lower bounds for the maximal cells in this space. More... | |
| bool | init (const Point &lower, const Point &upper, const std::array< Closure, dim > &closure) |
| Specifies the upper and lower bounds for the maximal cells in this space. More... | |
Basic services | |
| Size | size (Dimension k) const |
| Return the width of the space in the k-dimension. More... | |
| Integer | min (Dimension k) const |
| Return the minimal digital coordinate in the k-dimension. More... | |
| Integer | max (Dimension k) const |
| Return the maximal digital coordinate in the k-dimension. More... | |
| const Point & | lowerBound () const |
| Return the lower bound for digital points in this space. More... | |
| const Point & | upperBound () const |
| Return the upper bound for digital points in this space. More... | |
| const Cell & | lowerCell () const |
| Return the lower bound for cells in this space. More... | |
| const Cell & | upperCell () const |
| Return the upper bound for cells in this space. More... | |
| bool | uIsValid (const PreCell &c, Dimension k) const |
Returns true if the given unsigned cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell. More... | |
| bool | uIsValid (const PreCell &c) const |
Returns true if the given unsigned cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell. More... | |
| bool | sIsValid (const SPreCell &c, Dimension k) const |
Returns true if the given signed cell his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell. More... | |
| bool | sIsValid (const SPreCell &c) const |
Returns true if the given signed cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell. More... | |
| bool | cIsValid (const Point &p, Dimension k) const |
Returns true if the given cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell. More... | |
| bool | cIsValid (const Point &p) const |
Returns true if the given cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell. More... | |
Closure type query | |
| bool | isSpaceClosed () const |
| Return 'true' iff the space is closed or periodic along every dimension. More... | |
| bool | isSpaceClosed (Dimension k) const |
| Return 'true' iff the space is closed or periodic along the specified dimension. More... | |
| bool | isSpacePeriodic () const |
| Return 'true' iff the space is periodic along every dimension. More... | |
| bool | isSpacePeriodic (Dimension k) const |
| Return 'true' iff the space is periodic along the specified dimension. More... | |
| bool | isAnyDimensionPeriodic () const |
| Return 'true' iff the space is periodic along at least one dimension. More... | |
| Closure | getClosure (Dimension k) const |
| Gets closure type. More... | |
Cell creation services | |
| Cell | uCell (const PreCell &c) const |
| From an unsigned cell, returns an unsigned cell lying into this Khalismky space. More... | |
| Cell | uCell (const Point &kp) const |
| From the Khalimsky coordinates of a cell, builds the corresponding unsigned cell lying into this Khalismky space. More... | |
| Cell | uCell (Point p, const PreCell &c) const |
| From the digital coordinates of a point in Zn and a cell type, builds the corresponding unsigned cell lying into this Khalismky space. More... | |
| SCell | sCell (const SPreCell &c) const |
| From a signed cell, returns a signed cell lying into this Khalismky space. More... | |
| SCell | sCell (const Point &kp, Sign sign=POS) const |
| From the Khalimsky coordinates of a cell and a sign, builds the corresponding signed cell lying into this Khalismky space. More... | |
| SCell | sCell (Point p, const SPreCell &c) const |
| From the digital coordinates of a point in Zn and a signed cell type, builds the corresponding signed cell lying into this Khalismky space. More... | |
| Cell | uSpel (Point p) const |
| From the digital coordinates of a point in Zn, builds the corresponding spel (cell of maximal dimension) lying into this Khalismky space. More... | |
| SCell | sSpel (Point p, Sign sign=POS) const |
| From the digital coordinates of a point in Zn, builds the corresponding spel (cell of maximal dimension) lying into this Khalismky space. More... | |
| Cell | uPointel (Point p) const |
| From the digital coordinates of a point in Zn, builds the corresponding pointel (cell of dimension 0) lying into this Khalismky space. More... | |
| SCell | sPointel (Point p, Sign sign=POS) const |
| From the digital coordinates of a point in Zn, builds the corresponding pointel (cell of dimension 0) lying into this Khalismky space. More... | |
Read accessors to cells | |
| Integer | uKCoord (const Cell &c, Dimension k) const |
| Return its Khalimsky coordinate along [k]. More... | |
| Integer | uCoord (const Cell &c, Dimension k) const |
| Return its digital coordinate along [k]. More... | |
| const Point & | uKCoords (const Cell &c) const |
| Return its Khalimsky coordinates. More... | |
| Point | uCoords (const Cell &c) const |
| Return its digital coordinates. More... | |
| Integer | sKCoord (const SCell &c, Dimension k) const |
| Return its Khalimsky coordinate along [k]. More... | |
| Integer | sCoord (const SCell &c, Dimension k) const |
| Return its digital coordinate along [k]. More... | |
| const Point & | sKCoords (const SCell &c) const |
| Return its Khalimsky coordinates. More... | |
| Point | sCoords (const SCell &c) const |
| Return its digital coordinates. More... | |
| Sign | sSign (const SCell &c) const |
| Return its sign. More... | |
Write accessors to cells | |
| void | uSetKCoord (Cell &c, Dimension k, Integer i) const |
| Sets the [k]-th Khalimsky coordinate of [c] to [i]. More... | |
| void | sSetKCoord (SCell &c, Dimension k, Integer i) const |
| Sets the [k]-th Khalimsky coordinate of [c] to [i]. More... | |
| void | uSetCoord (Cell &c, Dimension k, Integer i) const |
| Sets the [k]-th digital coordinate of [c] to [i]. More... | |
| void | sSetCoord (SCell &c, Dimension k, Integer i) const |
| Sets the [k]-th digital coordinate of [c] to [i]. More... | |
| void | uSetKCoords (Cell &c, const Point &kp) const |
| Sets the Khalimsky coordinates of [c] to [kp]. More... | |
| void | sSetKCoords (SCell &c, const Point &kp) const |
| Sets the Khalimsky coordinates of [c] to [kp]. More... | |
| void | uSetCoords (Cell &c, const Point &kp) const |
| Sets the digital coordinates of [c] to [kp]. More... | |
| void | sSetCoords (SCell &c, const Point &kp) const |
| Sets the digital coordinates of [c] to [kp]. More... | |
| void | sSetSign (SCell &c, Sign s) const |
| Sets the sign of the cell. More... | |
Conversion signed/unsigned | |
| SCell | signs (const Cell &p, Sign s) const |
| Creates a signed cell from an unsigned one and a given sign. More... | |
| Cell | unsigns (const SCell &p) const |
| Creates an unsigned cell from a signed one. More... | |
| SCell | sOpp (const SCell &p) const |
| Creates the signed cell with the inverse sign of [p]. More... | |
Cell topology services | |
| Integer | uTopology (const Cell &p) const |
| Return the topology word of [p]. More... | |
| Integer | sTopology (const SCell &p) const |
| Return the topology word of [p]. More... | |
| Dimension | uDim (const Cell &p) const |
| Return the dimension of the cell [p]. More... | |
| Dimension | sDim (const SCell &p) const |
| Return the dimension of the cell [p]. More... | |
| bool | uIsSurfel (const Cell &b) const |
| Return 'true' if [b] is a surfel (spans all but one coordinate). More... | |
| bool | sIsSurfel (const SCell &b) const |
| Return 'true' if [b] is a surfel (spans all but one coordinate). More... | |
| bool | uIsOpen (const Cell &p, Dimension k) const |
| Return 'true' if [p] is open along the direction [k]. More... | |
| bool | sIsOpen (const SCell &p, Dimension k) const |
| Return 'true' if [p] is open along the direction [k]. More... | |
Iterator services for cells | |
| DirIterator | uDirs (const Cell &p) const |
| Given an unsigned cell [p], returns an iterator to iterate over each coordinate the cell spans. More... | |
| DirIterator | sDirs (const SCell &p) const |
| Given a signed cell [p], returns an iterator to iterate over each coordinate the cell spans. More... | |
| DirIterator | uOrthDirs (const Cell &p) const |
| Given an unsigned cell [p], returns an iterator to iterate over each coordinate the cell does not span. More... | |
| DirIterator | sOrthDirs (const SCell &p) const |
| Given a signed cell [p], returns an iterator to iterate over each coordinate the cell does not span. More... | |
| Dimension | uOrthDir (const Cell &s) const |
| Given an unsigned surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed). More... | |
| Dimension | sOrthDir (const SCell &s) const |
| Given a signed surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed). More... | |
Unsigned cell geometry services | |
| Integer | uFirst (const PreCell &p, Dimension k) const |
| Return the k-th Khalimsky coordinate of the first cell of the space with the same type as [p]. More... | |
| Cell | uFirst (const PreCell &p) const |
| Return the first cell of the space with the same type as [p]. More... | |
| Integer | uLast (const PreCell &p, Dimension k) const |
| Return the k-th Khalimsky coordinate of the last cell of the space with the same type as [p]. More... | |
| Cell | uLast (const PreCell &p) const |
| Return the last cell of the space with the same type as [p]. More... | |
| Cell | uGetIncr (const Cell &p, Dimension k) const |
| Return the same element as [p] except for the incremented coordinate [k]. More... | |
| bool | uIsMax (const Cell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| bool | uIsInside (const PreCell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| bool | uIsInside (const PreCell &p) const |
| Useful to check if you are going out of the space. More... | |
| bool | cIsInside (const Point &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| bool | cIsInside (const Point &p) const |
| Useful to check if you are going out of the space. More... | |
| Cell | uGetMax (Cell p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| Cell | uGetDecr (const Cell &p, Dimension k) const |
| Return the same element as [p] except for an decremented coordinate [k]. More... | |
| bool | uIsMin (const Cell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| Cell | uGetMin (Cell p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| Cell | uGetAdd (const Cell &p, Dimension k, Integer x) const |
| Return the same element as [p] except for a coordinate [k] incremented with x. More... | |
| Cell | uGetSub (const Cell &p, Dimension k, Integer x) const |
| Return the same element as [p] except for a coordinate [k] decremented with x. More... | |
| Integer | uDistanceToMax (const Cell &p, Dimension k) const |
| Useful to check if you are going out of the space (for non-periodic dimensions). More... | |
| Integer | uDistanceToMin (const Cell &p, Dimension k) const |
| Useful to check if you are going out of the space (for non-periodic dimensions). More... | |
| Cell | uTranslation (const Cell &p, const Vector &vec) const |
| Add the vector [vec] to [p]. More... | |
| Cell | uProjection (const Cell &p, const Cell &bound, Dimension k) const |
| Return the projection of [p] along the [k]th direction toward [bound]. More... | |
| void | uProject (Cell &p, const Cell &bound, Dimension k) const |
| Projects [p] along the [k]th direction toward [bound]. More... | |
| bool | uNext (Cell &p, const Cell &lower, const Cell &upper) const |
| Increment the cell [p] to its next position (as classically done in a scanning). More... | |
Signed cell geometry services | |
| Integer | sFirst (const SPreCell &p, Dimension k) const |
| Return the k-th coordinate of the first cell of the space with the same type as [p]. More... | |
| SCell | sFirst (const SPreCell &p) const |
| Return the first cell of the space with the same type as [p]. More... | |
| Integer | sLast (const SPreCell &p, Dimension k) const |
| Return the k-th Khalimsky coordinate of the last cell of the space with the same type as [p]. More... | |
| SCell | sLast (const SPreCell &p) const |
| Return the last cell of the space with the same type as [p]. More... | |
| SCell | sGetIncr (const SCell &p, Dimension k) const |
| Return the same element as [p] except for the incremented coordinate [k]. More... | |
| bool | sIsMax (const SCell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| bool | sIsInside (const SPreCell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| bool | sIsInside (const SPreCell &p) const |
| Useful to check if you are going out of the space. More... | |
| SCell | sGetMax (SCell p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| SCell | sGetDecr (const SCell &p, Dimension k) const |
| Return the same element as [p] except for an decremented coordinate [k]. More... | |
| bool | sIsMin (const SCell &p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| SCell | sGetMin (SCell p, Dimension k) const |
| Useful to check if you are going out of the space. More... | |
| SCell | sGetAdd (const SCell &p, Dimension k, Integer x) const |
| Return the same element as [p] except for a coordinate [k] incremented with x. More... | |
| SCell | sGetSub (const SCell &p, Dimension k, Integer x) const |
| Return the same element as [p] except for a coordinate [k] decremented with x. More... | |
| Integer | sDistanceToMax (const SCell &p, Dimension k) const |
| Useful to check if you are going out of the space (for non-periodic dimensions). More... | |
| Integer | sDistanceToMin (const SCell &p, Dimension k) const |
| Useful to check if you are going out of the space (for non-periodic dimensions). More... | |
| SCell | sTranslation (const SCell &p, const Vector &vec) const |
| Add the vector [vec] to [p]. More... | |
| SCell | sProjection (const SCell &p, const SCell &bound, Dimension k) const |
| Return the projection of [p] along the [k]th direction toward [bound]. More... | |
| void | sProject (SCell &p, const SCell &bound, Dimension k) const |
| Projects [p] along the [k]th direction toward [bound]. More... | |
| bool | sNext (SCell &p, const SCell &lower, const SCell &upper) const |
| Increment the cell [p] to its next position (as classically done in a scanning). More... | |
Neighborhood services | |
| Cells | uNeighborhood (const Cell &cell) const |
| Computes the 1-neighborhood of the cell [c] and returns it. More... | |
| SCells | sNeighborhood (const SCell &cell) const |
| Computes the 1-neighborhood of the cell [c] and returns it. More... | |
| Cells | uProperNeighborhood (const Cell &cell) const |
| Computes the proper 1-neighborhood of the cell [c] and returns it. More... | |
| SCells | sProperNeighborhood (const SCell &cell) const |
| Computes the proper 1-neighborhood of the cell [c] and returns it. More... | |
| Cell | uAdjacent (const Cell &p, Dimension k, bool up) const |
| Return the adjacent element to [p] along axis [k] in the given direction and orientation. More... | |
| SCell | sAdjacent (const SCell &p, Dimension k, bool up) const |
| Return the adjacent element to [p] along axis [k] in the given direction and orientation. More... | |
Incidence services | |
| Cell | uIncident (const Cell &c, Dimension k, bool up) const |
| Return the forward or backward unsigned cell incident to [c] along axis [k], depending on [up]. More... | |
| SCell | sIncident (const SCell &c, Dimension k, bool up) const |
| Return the forward or backward signed cell incident to [c] along axis [k], depending on [up]. More... | |
| Cells | uLowerIncident (const Cell &c) const |
| Return the cells directly low incident to c in this space. More... | |
| Cells | uUpperIncident (const Cell &c) const |
| Return the cells directly up incident to c in this space. More... | |
| SCells | sLowerIncident (const SCell &c) const |
| Return the signed cells directly low incident to c in this space. More... | |
| SCells | sUpperIncident (const SCell &c) const |
| Return the signed cells directly up incident to c in this space. More... | |
| Cells | uFaces (const Cell &c) const |
| Return the proper faces of [c] (chain of lower incidence) that belong to the space. More... | |
| Cells | uCoFaces (const Cell &c) const |
| Return the proper cofaces of [c] (chain of upper incidence) that belong to the space. More... | |
| bool | sDirect (const SCell &p, Dimension k) const |
| Return 'true' if the direct orientation of [p] along [k] is in the positive coordinate direction. More... | |
| SCell | sDirectIncident (const SCell &p, Dimension k) const |
| Return the direct incident cell of [p] along [k] (the incident cell along [k]) More... | |
| SCell | sIndirectIncident (const SCell &p, Dimension k) const |
| Return the indirect incident cell of [p] along [k] (the incident cell along [k] whose sign is negative). More... | |
| Point | interiorVoxel (const SCell &c) const |
| 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). More... | |
| Point | exteriorVoxel (const SCell &c) const |
| 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). More... | |
DGtal interface | |
| void | selfDisplay (std::ostream &out) const |
| Writes/Displays the object on an output stream. More... | |
| bool | isValid () const |
| Checks the validity/consistency of the object. More... | |
Static Public Attributes | |
| static const constexpr Dimension | dimension = dim |
| static const constexpr Dimension | DIM = dim |
| static const constexpr Sign | POS = true |
| static const constexpr Sign | NEG = false |
Private Types | |
| typedef KhalimskySpaceNDHelper< KhalimskySpaceND< dim, TInteger > > | Helper |
| Features basic operations on coordinates, especially for periodic dimensions. More... | |
Private Member Functions | |
| BOOST_CONCEPT_ASSERT ((concepts::CInteger< TInteger >)) | |
| Integer must be signed to characterize a ring. More... | |
Internals | |
| void | uAddFaces (Cells &faces, const Cell &c, Dimension axis) const |
| Used by uFaces for computing incident faces. More... | |
| void | uAddCoFaces (Cells &cofaces, const Cell &c, Dimension axis) const |
| Used by uCoFaces for computing incident cofaces. More... | |
Private Attributes | |
| Point | myLower |
| Point | myUpper |
| Cell | myCellLower |
| Cell | myCellUpper |
| std::array< Closure, dimension > | myClosure |
Friends | |
| class | KhalimskySpaceNDHelper< KhalimskySpaceND< dim, TInteger > > |
Detailed Description
class DGtal::KhalimskySpaceND< dim, TInteger >
Aim: This class is a model of CCellularGridSpaceND. 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 'KhalimskySpaceND'
When initializing the space using init(), the user should choose, for each dimension spanned by the space, between a closed and non-periodic (default) cell dimension, an open cell dimension or a periodic cell dimension. The space is generally finite, except for arbitrary size integers and when the space has a periodic dimension.
Supposing that the space has been initialized with digital bounds lower and upper, the methods lowerBound() and upperBound() will always return, respectively, lower and upper. It as also true for periodic dimension, in order to span over the unique digital points of the space.
In the same way, lowerCell() and upperCell() respect the following rules:
- the k-th Khalimsky coordinate of lowerCell() is equal to:
2*lower[k]if the k-th dimension is closed or periodic,2*lower[k]+1if the k-th dimension is open;
- the k-th Khalimsky coordinate of upperCell() is equal to:
2*upper[k]+2if the k-th dimension is closed,2*upper[k]+1if the k-th dimension is open or periodic.
The special behavior for periodic dimensions guarantees that each cell has unique Khalimsky coordinates in this range. It is useful to span the space and also for cell-based containers (see e.g. CubicalComplex). Uniqueness also gives meaning to equality tests between cells.
Following this concept, the related methods size(), min(), max(), uFirst(), uLast(), uGetMin(), uGetMax(), uDistanceToMin(), uDistanceToMax(), sFirst(), sLast(), sGetMin(), sGetMax(), sDistanceToMin() and sDistanceToMax() behave for periodic dimensions like for finite dimensions, using the bounds described above.
Thus, if a cell needs to be compared to the bounds, prefer using dedicated tests like uIsMin(), uIsMax(), sIsMin() and sIsMax() that return always false for a periodic dimension, and uIsInside() and sIsInside() that return always true for a periodic dimension.
To be consistent with those choices, each cell returned or modified by a KhalimskySpaceND method will have his Khalimsky coordinates along periodic dimensions between the corresponding coordinates of lowerCell() and upperCell(). But, in order to keep low computational cost, each cell passed by parameter to a KhalimskySpaceND method must follow the same conditions. This validity can be tested with the dedicated methods uIsValid() and sIsValid().
Exceptions exist for uCell(const PreCell &) const and sCell(const SPreCell &) const that are specially featured to correct Khalimsky coordinates of a given cell. In addition, when a method accepts a coordinate as parameter, it is always corrected along periodic dimensions.
- 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.
- Warning
- Periodic Khalimsky space and per-dimension closure specification are new features. Therefore, there is no guarantee that it is compatible with the whole DGtal library.
- Examples
- dec/exampleDECSurface.cpp, dec/exampleHeatLaplace.cpp, geometry/surfaces/dvcm-2d-curvature.cpp, geometry/surfaces/dvcm-3d.cpp, geometry/tools/exampleAlphaShape.cpp, geometry/volumes/checkFullConvexityTheorems.cpp, geometry/volumes/digitalPolyhedronBuilder3D.cpp, geometry/volumes/fullConvexityShortestPaths3D.cpp, geometry/volumes/fullConvexitySphereGeodesics.cpp, geometry/volumes/standardDigitalPolyhedronBuilder3D.cpp, topology/ctopo-2-3d.cpp, topology/ctopo-2.cpp, topology/ctopo-fillContours.cpp, topology/khalimskySpaceScanner.cpp, tutorial-examples/AreaSurfaceEstimation-final.cpp, and tutorial-examples/freemanChainFromImage.cpp.
Definition at line 392 of file KhalimskySpaceND.h.
Member Typedef Documentation
◆ AnyCellCollection
| using DGtal::KhalimskySpaceND< dim, TInteger >::AnyCellCollection = typename PreCellularGridSpace::template AnyCellCollection< CellType > |
Definition at line 436 of file KhalimskySpaceND.h.
◆ Cell
| typedef KhalimskyCell< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::Cell |
Definition at line 415 of file KhalimskySpaceND.h.
◆ Cells
| typedef AnyCellCollection<Cell> DGtal::KhalimskySpaceND< dim, TInteger >::Cells |
Definition at line 439 of file KhalimskySpaceND.h.
◆ CellSet
| typedef std::set<Cell> DGtal::KhalimskySpaceND< dim, TInteger >::CellSet |
Preferred type for defining a set of Cell(s).
Definition at line 444 of file KhalimskySpaceND.h.
◆ CellularGridSpace
| typedef KhalimskySpaceND<dim, Integer> DGtal::KhalimskySpaceND< dim, TInteger >::CellularGridSpace |
Definition at line 411 of file KhalimskySpaceND.h.
◆ DirIterator
| using DGtal::KhalimskySpaceND< dim, TInteger >::DirIterator = typename PreCellularGridSpace::DirIterator |
Definition at line 422 of file KhalimskySpaceND.h.
◆ Helper
|
private |
Features basic operations on coordinates, especially for periodic dimensions.
Definition at line 396 of file KhalimskySpaceND.h.
◆ Integer
| typedef TInteger DGtal::KhalimskySpaceND< dim, TInteger >::Integer |
Arithmetic ring induced by (+,-,*) and Integer numbers.
Definition at line 404 of file KhalimskySpaceND.h.
◆ Point
| typedef PointVector< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::Point |
Definition at line 425 of file KhalimskySpaceND.h.
◆ PreCell
| typedef KhalimskyPreCell< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::PreCell |
Definition at line 416 of file KhalimskySpaceND.h.
◆ PreCellularGridSpace
| typedef KhalimskyPreSpaceND<dim, Integer> DGtal::KhalimskySpaceND< dim, TInteger >::PreCellularGridSpace |
Definition at line 412 of file KhalimskySpaceND.h.
◆ SCell
| typedef SignedKhalimskyCell< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::SCell |
Definition at line 417 of file KhalimskySpaceND.h.
◆ SCells
| typedef AnyCellCollection<SCell> DGtal::KhalimskySpaceND< dim, TInteger >::SCells |
Definition at line 440 of file KhalimskySpaceND.h.
◆ SCellSet
| typedef std::set<SCell> DGtal::KhalimskySpaceND< dim, TInteger >::SCellSet |
Preferred type for defining a set of SCell(s).
Definition at line 447 of file KhalimskySpaceND.h.
◆ Sign
| typedef bool DGtal::KhalimskySpaceND< dim, TInteger >::Sign |
Definition at line 421 of file KhalimskySpaceND.h.
◆ Size
| typedef NumberTraits<Integer>::UnsignedVersion DGtal::KhalimskySpaceND< dim, TInteger >::Size |
Type used to represent sizes in the digital space.
Definition at line 407 of file KhalimskySpaceND.h.
◆ Space
| typedef SpaceND<dim, Integer> DGtal::KhalimskySpaceND< dim, TInteger >::Space |
Definition at line 410 of file KhalimskySpaceND.h.
◆ SPreCell
| typedef SignedKhalimskyPreCell< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::SPreCell |
Definition at line 418 of file KhalimskySpaceND.h.
◆ Surfel
| typedef SCell DGtal::KhalimskySpaceND< dim, TInteger >::Surfel |
Definition at line 420 of file KhalimskySpaceND.h.
◆ SurfelSet
| typedef std::set<SCell> DGtal::KhalimskySpaceND< dim, TInteger >::SurfelSet |
Preferred type for defining a set of surfels (always signed cells).
Definition at line 450 of file KhalimskySpaceND.h.
◆ Vector
| typedef PointVector< dim, Integer > DGtal::KhalimskySpaceND< dim, TInteger >::Vector |
Definition at line 426 of file KhalimskySpaceND.h.
Member Enumeration Documentation
◆ Closure
| enum DGtal::KhalimskySpaceND::Closure |
Boundaries closure type.
| Enumerator | |
|---|---|
| CLOSED | The dimension is closed and non-periodic. |
| OPEN | The dimension is open. |
| PERIODIC | The dimension is periodic. |
Definition at line 471 of file KhalimskySpaceND.h.
Constructor & Destructor Documentation
◆ ~KhalimskySpaceND()
| DGtal::KhalimskySpaceND< dim, TInteger >::~KhalimskySpaceND | ( | ) |
Destructor.
◆ KhalimskySpaceND() [1/3]
| DGtal::KhalimskySpaceND< dim, TInteger >::KhalimskySpaceND | ( | ) |
Default constructor.
◆ KhalimskySpaceND() [2/3]
|
default |
Copy constructor.
- Parameters
-
other the object to clone.
◆ KhalimskySpaceND() [3/3]
|
default |
Move constructor.
- Parameters
-
other the object to clone.
Member Function Documentation
◆ BOOST_CONCEPT_ASSERT()
|
private |
Integer must be signed to characterize a ring.
◆ cIsInside() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::cIsInside | ( | const Point & | p | ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any integer point (Khalimsky coordinates).
- Returns
- true if [p] has its coordinates within the allowed bounds.
- Note
- Only the non-periodic dimensions are checked.
◆ cIsInside() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::cIsInside | ( | const Point & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any integer point (Khalimsky coordinates). k the tested coordinate.
- Returns
- true if [p] has its [k]-coordinate within the allowed bounds.
- Note
- It returns always true for periodic dimension.
◆ cIsValid() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::cIsValid | ( | const Point & | p | ) | const |
Returns true if the given cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Parameters
-
p an integer point (Khalimsky coordinates of cell).
- Returns
trueif the given cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
◆ cIsValid() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::cIsValid | ( | const Point & | p, |
| Dimension | k | ||
| ) | const |
Returns true if the given cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Parameters
-
p an integer point (Khalimsky coordinates of cell). k a dimension.
- Returns
trueif the given cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
◆ exteriorVoxel()
| Point DGtal::KhalimskySpaceND< dim, TInteger >::exteriorVoxel | ( | const SCell & | c | ) | const |
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.
Referenced by TEST_CASE().
◆ getClosure()
| Closure DGtal::KhalimskySpaceND< dim, TInteger >::getClosure | ( | Dimension | k | ) | const |
Gets closure type.
- Parameters
-
k the dimension.
- Returns
- closure type along the specified dimension.
◆ init() [1/3]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::init | ( | const Point & | lower, |
| const Point & | upper, | ||
| bool | isClosed | ||
| ) |
Specifies the upper and lower bounds for the maximal cells in this space.
- Parameters
-
lower the lowest point in this space (digital coords) upper the upper point in this space (digital coords) isClosed 'true' if this space is closed and non-periodic in every dimension, 'false' if open.
- Returns
- true if the initialization was valid (ie, such bounds are representable with these integers).
- Examples
- dec/exampleDECSurface.cpp, dec/exampleHeatLaplace.cpp, geometry/curves/exampleGridCurve2d.cpp, geometry/curves/exampleGridCurve3d.cpp, geometry/tools/exampleAlphaShape.cpp, topology/ctopo-2-3d.cpp, topology/ctopo-2.cpp, tutorial-examples/AreaSurfaceEstimation-final.cpp, and tutorial-examples/freemanChainFromImage.cpp.
Referenced by accuracyTest(), alphaShape(), ballGenerator(), digitize(), estimatorOnShapeDigitization(), DGtal::functions::generateVoxelComplexTable(), getComplex(), laplace_sphere(), laplacian(), main(), Object3D(), SCENARIO(), test3dSurfaceHelper(), TEST_CASE(), testBallQuad(), testCombinatorialSurface(), testCompareEstimator(), testComputeInterior(), testCube(), testCurvature2d(), testDigitalSetBoundary(), testDigitalSurface(), testDigitalSurfaceBoostGraphInterface(), testDigitization(), testEmbedder(), testEstimatorCache(), testExplicitDigitalSurface(), testFindABel(), testFitting(), testGaussianCurvature3d(), testImplicitDigitalSurface(), testLightExplicitDigitalSurface(), testLightImplicitDigitalSurface(), testLocalConvolutionNormalVectorEstimator(), testLocalEstimatorFromFunctorAdapter(), testMeanCurvature3d(), testNormaliation(), testObjectGraph(), testOrderingDigitalSurfaceFacesAroundVertex(), testPrincipalCurvatures3d(), testQuadNorm(), testRaySurface(), testRaySurfelIntersection(), testTrueLocalEstimatorOnShapeDigitization(), and testUmbrellaComputer().
◆ init() [2/3]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::init | ( | const Point & | lower, |
| const Point & | upper, | ||
| Closure | closure | ||
| ) |
Specifies the upper and lower bounds for the maximal cells in this space.
- Parameters
-
lower the lowest point in this space (digital coords) upper the upper point in this space (digital coords) closure CLOSED, OPEN or PERIODIC if this space is resp. closed (and non-periodic), open or periodic in every dimension.
- Returns
- true if the initialization was valid (ie, such bounds are representable with these integers).
◆ init() [3/3]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::init | ( | const Point & | lower, |
| const Point & | upper, | ||
| const std::array< Closure, dim > & | closure | ||
| ) |
Specifies the upper and lower bounds for the maximal cells in this space.
- Parameters
-
lower the lowest point in this space (digital coords) upper the upper point in this space (digital coords) closure an array of CLOSED, OPEN or PERIODIC if this space is resp. closed (and non-periodic), open or periodic in the corresponding dimension.
- Returns
- true if the initialization was valid (ie, such bounds are representable with these integers).
◆ interiorVoxel()
| Point DGtal::KhalimskySpaceND< dim, TInteger >::interiorVoxel | ( | const SCell & | c | ) | const |
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.
Referenced by TEST_CASE().
◆ isAnyDimensionPeriodic()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isAnyDimensionPeriodic | ( | ) | const |
Return 'true' iff the space is periodic along at least one dimension.
- Returns
- 'true' iff the space is periodic along at least one dimension.
◆ isSpaceClosed() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isSpaceClosed | ( | ) | const |
Return 'true' iff the space is closed or periodic along every dimension.
- Returns
- 'true' iff the space is closed or periodic along every dimension.
◆ isSpaceClosed() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isSpaceClosed | ( | Dimension | k | ) | const |
Return 'true' iff the space is closed or periodic along the specified dimension.
- Parameters
-
k the dimension.
- Returns
- 'true' iff the space is closed or periodic along the specified dimension.
◆ isSpacePeriodic() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isSpacePeriodic | ( | ) | const |
Return 'true' iff the space is periodic along every dimension.
- Returns
- 'true' iff the space is periodic along every dimension.
◆ isSpacePeriodic() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isSpacePeriodic | ( | Dimension | k | ) | const |
Return 'true' iff the space is periodic along the specified dimension.
- Parameters
-
k the dimension.
- Returns
- 'true' iff the space is periodic along the specified dimension.
◆ isValid()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::isValid | ( | ) | const |
Checks the validity/consistency of the object.
- Returns
- 'true' if the object is valid, 'false' otherwise.
◆ lowerBound()
| const Point & DGtal::KhalimskySpaceND< dim, TInteger >::lowerBound | ( | ) | const |
Return the lower bound for digital points in this space.
- Returns
- the lower bound for digital points in this space.
- Note
- For periodic dimension, it returns the lower digital point with unique coordinates. See also the class documentation.
- Examples
- topology/ctopo-2.cpp.
Referenced by main(), SCENARIO(), and TEST_CASE_METHOD().
◆ lowerCell()
| const Cell & DGtal::KhalimskySpaceND< dim, TInteger >::lowerCell | ( | ) | const |
Return the lower bound for cells in this space.
- Returns
- the lower bound for cells in this space.
- Note
- For periodic dimension, it returns the upper cell with unique coordinates. See also the class documentation.
Referenced by main().
◆ max()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::max | ( | Dimension | k | ) | const |
Return the maximal digital coordinate in the k-dimension.
- Parameters
-
k a coordinate.
- Returns
- the maximal digital coordinate in the k-dimension.
- Note
- For periodic dimension, it returns the maximal unique digital coordinate along that dimension.
◆ min()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::min | ( | Dimension | k | ) | const |
Return the minimal digital coordinate in the k-dimension.
- Parameters
-
k a dimension.
- Returns
- the minimal digital coordinate in the k-dimension.
- Note
- For periodic dimension, it returns the minimal unique digital coordinate along that dimension.
◆ operator=() [1/2]
|
default |
Copy operator.
- Parameters
-
other the object to copy.
- Returns
- a reference on 'this'.
◆ operator=() [2/2]
|
default |
Move operator.
- Parameters
-
other the object to copy.
- Returns
- a reference on 'this'.
◆ sAdjacent()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sAdjacent | ( | const SCell & | p, |
| Dimension | k, | ||
| bool | up | ||
| ) | const |
Return the adjacent element to [p] along axis [k] in the given direction and orientation.
- Parameters
-
p any 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 )'.
- Precondition
sIsValid(p)and notsIs(Min|Max)(p, k)depending on up value.
- Postcondition
- `sIsValid(sAdjacent(p, k, up)) is true.
◆ sCell() [1/3]
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sCell | ( | const Point & | kp, |
| Sign | sign = POS |
||
| ) | const |
From the Khalimsky coordinates of a cell and a sign, builds the corresponding signed cell lying into this Khalismky space.
Along a non-periodic dimension, if the given Khalimsky coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the Khalimsky coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
kp an integer point (Khalimsky coordinates of cell). sign the sign of the cell (either POS or NEG).
- Returns
- the signed cell.
- Postcondition
sIsValid(sCell(kp, sign))is true.
◆ sCell() [2/3]
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sCell | ( | const SPreCell & | c | ) | const |
From a signed cell, returns a signed cell lying into this Khalismky space.
Along a non-periodic dimension, if the given Khalimsky coordinate lies outside the space, it replaces it by the nearest valid coordinate.
Along a periodic dimension, the Khalimsky coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
c a signed cell.
- Returns
- the same signed cell with appropriate Khalimsky coordinates along periodic dimensions.
- Postcondition
sIsValid(sCell(c))is true.-
sCell(c) == cifsIsValid(c).
Referenced by cmpSCellsIfInside(), digitize(), main(), testCellDrawOnBoard(), testFaces(), testFindABel(), testNeighborhood(), testRaySurfelIntersection(), testScan(), and testSurfelAdjacency().
◆ sCell() [3/3]
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sCell | ( | Point | p, |
| const SPreCell & | c | ||
| ) | const |
From the digital coordinates of a point in Zn and a signed cell type, builds the corresponding signed cell lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell). c another cell defining the topology and sign.
- Returns
- the cell having the topology and sign of [c] and the given digital coordinates [p].
- Postcondition
sIsValid(sCell(p, c))is true.
◆ sCoord()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sCoord | ( | const SCell & | c, |
| Dimension | k | ||
| ) | const |
Return its digital coordinate along [k].
- Parameters
-
c any signed cell. k any valid dimension.
- Returns
- its digital coordinate along [k].
- Precondition
uIsValid(c)is true.
◆ sCoords()
| Point DGtal::KhalimskySpaceND< dim, TInteger >::sCoords | ( | const SCell & | c | ) | const |
Return its digital coordinates.
- Parameters
-
c any signed cell.
- Returns
- its digital coordinates.
- Precondition
uIsValid(c)is true.
Referenced by main(), DGtal::functors::SCellToPoint< KSpace >::operator()(), DGtal::functors::SCellToArrow< KSpace >::operator()(), DGtal::functors::SCellToInnerPoint< KSpace >::operator()(), DGtal::functors::SCellToOuterPoint< KSpace >::operator()(), DGtal::functors::SCellToIncidentPoints< KSpace >::operator()(), DGtal::functors::SCellToCode< KSpace >::operator()(), TEST_CASE(), testFindABel(), testLocalConvolutionNormalVectorEstimator(), and testOrderingDigitalSurfaceFacesAroundVertex().
◆ sDim()
| Dimension DGtal::KhalimskySpaceND< dim, TInteger >::sDim | ( | const SCell & | p | ) | const |
Return the dimension of the cell [p].
- Parameters
-
p any signed cell.
- Returns
- the dimension of the cell [p].
Referenced by DGtal::functors::SCellToPoint< KSpace >::operator()(), SCENARIO(), and testFindABel().
◆ sDirect()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sDirect | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
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 cells to positive incident cells. This means that
is always true.
- Parameters
-
p any signed cell. k any coordinate.
- Returns
- the direct orientation of [p] along [k] (true is upward, false is backward).
Referenced by main(), testCellDrawOnBoard(), testDirectIncidence(), and testSurfelAdjacency().
◆ sDirectIncident()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sDirectIncident | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Return the direct incident cell of [p] along [k] (the incident cell along [k])
- Parameters
-
p any signed cell. k any coordinate.
- Returns
- the direct incident cell of [p] along [k] (the incident cell along [k])
- Precondition
sIsValid(p)and the cell should have a direct incident cell in this direction.
- Postcondition
sIsValid(c)is true for every returned cell c. ose sign is positive).
Referenced by main(), DGtal::functors::SCellToInnerPoint< KSpace >::operator()(), DGtal::functors::SCellToIncidentPoints< KSpace >::operator()(), testDirectIncidence(), testFindABel(), and testSurfelAdjacency().
◆ sDirs()
| DirIterator DGtal::KhalimskySpaceND< dim, TInteger >::sDirs | ( | const SCell & | p | ) | const |
Given a signed 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:
- Parameters
-
p any signed cell.
- Returns
- an iterator that points on the first coordinate spanned by the cell.
- Examples
- topology/ctopo-2-3d.cpp.
Referenced by main(), DGtal::functors::SCellToPoint< KSpace >::operator()(), DGtal::functors::SCellToArrow< KSpace >::operator()(), DGtal::functors::SCellToCode< KSpace >::operator()(), testDigitalSetBoundary(), testDirectIncidence(), testImplicitDigitalSurface(), testIncidence(), testLightImplicitDigitalSurface(), and testUmbrellaComputer().
◆ sDistanceToMax()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sDistanceToMax | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space (for non-periodic dimensions).
- Parameters
-
p any cell. k the coordinate that is tested.
- Returns
- the number of increment to do to reach the maximum value.
- Precondition
sIsValid(p)is true.
◆ sDistanceToMin()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sDistanceToMin | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space (for non-periodic dimensions).
- Parameters
-
p any cell. k the coordinate that is tested.
- Returns
- the number of decrement to do to reach the minimum value.
- Precondition
sIsValid(p)is true.
◆ selfDisplay()
| void DGtal::KhalimskySpaceND< dim, TInteger >::selfDisplay | ( | std::ostream & | out | ) | const |
Writes/Displays the object on an output stream.
- Parameters
-
out the output stream where the object is written.
◆ sFirst() [1/2]
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sFirst | ( | const SPreCell & | p | ) | const |
Return the first cell of the space with the same type as [p].
- Returns
- the first cell of the space with the same type as [p].
- Note
- Along periodic dimensions, it returns the first unique coordinate of a cell of same type as p.
- Postcondition
sIsValid(sFirst(p))is true.
◆ sFirst() [2/2]
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sFirst | ( | const SPreCell & | p, |
| Dimension | k | ||
| ) | const |
Return the k-th coordinate of the first cell of the space with the same type as [p].
- Returns
- the k-th coordinate of the first cell of the space with the same type as [p].
- Note
- For periodic dimension, it returns the first unique coordinate of a cell of same type as p.
- Postcondition
- The returned coordinate is between
lowerCell()[k]andupperCell()[k].
◆ sGetAdd()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetAdd | ( | const SCell & | p, |
| Dimension | k, | ||
| Integer | x | ||
| ) | const |
Return the same element as [p] except for a coordinate [k] incremented with x.
- Parameters
-
p any cell. k the coordinate that is changed. x the increment.
- Returns
- the same element as [p] except for a coordinate [k] incremented with x.
- Precondition
sIsValid(p)and (x <= sDistanceToMax(p, k)orisSpacePeriodic(k)).
- Postcondition
sIsValid(sGetAdd(p, k, x))is true.
◆ sGetDecr()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetDecr | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Return the same element as [p] except for an decremented coordinate [k].
- Parameters
-
p any cell. k the coordinate that is changed.
- Returns
- the same element as [p] except for an decremented coordinate [k].
- Precondition
sIsValid(p)and notsIsMin(p).
- Postcondition
sIsValid(sGetDecr(p, k))is true.
◆ sGetIncr()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetIncr | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Return the same element as [p] except for the incremented coordinate [k].
- Parameters
-
p any cell. k the coordinate that is changed.
- Returns
- the same element as [p] except for the incremented coordinate [k].
- Precondition
sIsValid(p)and notsIsMax(p).
- Postcondition
sIsValid(sGetIncr(p, k))is true.
◆ sGetMax()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetMax | ( | SCell | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the concerned coordinate.
- Returns
- the cell similar to [p] but with the maximum allowed [k]-coordinate.
- Precondition
sIsValid(p, d)is true for each dimension d different than k.
- Postcondition
sIsValid(sGetMax(p, k))is true.
◆ sGetMin()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetMin | ( | SCell | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the concerned coordinate.
- Returns
- the cell similar to [p] but with the minimum allowed [k]-coordinate.
- Precondition
sIsValid(p, d)is true for each dimension d different than k.
- Postcondition
sIsValid(sGetMin(p, k))is true.
◆ sGetSub()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sGetSub | ( | const SCell & | p, |
| Dimension | k, | ||
| Integer | x | ||
| ) | const |
Return the same element as [p] except for a coordinate [k] decremented with x.
- Parameters
-
p any cell. k the coordinate that is changed. x the decrement.
- Returns
- the same element as [p] except for a coordinate [k] decremented with x.
- Precondition
- suIsValid(p)
and (x <= sDistanceToMin(p, k)orisSpacePeriodic(k)). @postsIsValid(sGetSub(p, k, x))` is true.
◆ signs()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::signs | ( | const Cell & | p, |
| Sign | s | ||
| ) | const |
Creates a signed cell from an unsigned one and a given sign.
- Parameters
-
p any unsigned cell. s a sign.
- Returns
- the signed version of the cell [p] with sign [s].
- Precondition
uIsValid(p)is true.
- Postcondition
sIsValid(signs(p, s))is true.
◆ sIncident()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sIncident | ( | const SCell & | c, |
| Dimension | k, | ||
| bool | up | ||
| ) | const |
Return the forward or backward signed cell incident to [c] along axis [k], depending on [up].
- Parameters
-
c any signed cell. k any coordinate. up if 'true' the orientation is forward along axis [k], otherwise backward.
- Returns
- the forward or backward signed cell incident to [c] along axis [k], depending on [up]. It is worthy to note that the forward and backward cell have opposite sign. Furthermore, the sign of these cells is defined so as to satisfy a boundary operator.
- Note
- It may be a lower incident cell if [c] is open along axis [k], else an upper incident cell.
- Precondition
sIsValid(c)and the cell should have an incident cell in this direction/orientation.
- Postcondition
sIsValid(sIncident(c, k, up))is true.
Referenced by main(), testCellDrawOnBoard(), testDirectIncidence(), testExplicitDigitalSurface(), testIncidence(), testLightExplicitDigitalSurface(), and testSurfelAdjacency().
◆ sIndirectIncident()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sIndirectIncident | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Return the indirect incident cell of [p] along [k] (the incident cell along [k] whose sign is negative).
- Parameters
-
p any signed cell. k any coordinate.
- Returns
- the indirect incident cell of [p] along [k] (the incident cell along [k] whose sign is negative).
- Precondition
sIsValid(p)and the cell should have an indirect incident cell in this direction.
- Postcondition
sIsValid(c)is true for every returned cell c. ose sign is positive).
Referenced by main(), DGtal::functors::SCellToPoint< KSpace >::operator()(), DGtal::functors::SCellToArrow< KSpace >::operator()(), DGtal::functors::SCellToOuterPoint< KSpace >::operator()(), DGtal::functors::SCellToIncidentPoints< KSpace >::operator()(), DGtal::functors::SCellToCode< KSpace >::operator()(), and testFindABel().
◆ sIsInside() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsInside | ( | const SPreCell & | p | ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell.
- Returns
- true if [p] has its coordinates within the allowed bounds.
- Note
- Only the non-periodic dimensions are checked.
◆ sIsInside() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsInside | ( | const SPreCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] has its [k]-coordinate within the allowed bounds.
- Note
- It returns always true for periodic dimension.
Referenced by cmpSCellsIfInside().
◆ sIsMax()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsMax | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] cannot have its [k]-coordinate augmented without leaving the space.
- Note
- It returns always false for periodic dimension.
- Precondition
sIsInside(p)is true.
◆ sIsMin()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsMin | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] cannot have its [k]-coordinate decreased without leaving the space.
- Note
- It returns always false for periodic dimension.
- Precondition
sIsInside(p)is true.
◆ sIsOpen()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsOpen | ( | const SCell & | p, |
| Dimension | k | ||
| ) | const |
Return 'true' if [p] is open along the direction [k].
- Parameters
-
p any signed cell. k any direction.
- Returns
- 'true' if [p] is open along the direction [k].
◆ sIsSurfel()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsSurfel | ( | const SCell & | b | ) | const |
Return 'true' if [b] is a surfel (spans all but one coordinate).
- Parameters
-
b any signed cell.
- Returns
- 'true' if [b] is a surfel (spans all but one coordinate).
◆ sIsValid() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsValid | ( | const SPreCell & | c | ) | const |
Returns true if the given signed cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Parameters
-
c a signed cell.
- Returns
trueif the given signed cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
- See also
- sCell(const SCell &) const to correct Khalimsky coordinates along periodic dimensions.
◆ sIsValid() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sIsValid | ( | const SPreCell & | c, |
| Dimension | k | ||
| ) | const |
Returns true if the given signed cell his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Parameters
-
c a signed cell. k a dimension.
- Returns
trueif the given signed cell his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
- See also
- sCell(const SCell &) const to correct Khalimsky coordinates along periodic dimensions.
◆ size()
| Size DGtal::KhalimskySpaceND< dim, TInteger >::size | ( | Dimension | k | ) | const |
Return the width of the space in the k-dimension.
- Parameters
-
k a dimension.
- Returns
- the width of the space in the k-dimension.
- Note
- For periodic dimension, it returns the number of unique coordinates along that dimension.
◆ sKCoord()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sKCoord | ( | const SCell & | c, |
| Dimension | k | ||
| ) | const |
Return its Khalimsky coordinate along [k].
- Parameters
-
c any signed cell. k any valid dimension.
- Returns
- its Khalimsky coordinate along [k].
- Precondition
uIsValid(c)is true.
Referenced by testDigitalSurfaceBoostGraphInterface().
◆ sKCoords()
| const Point & DGtal::KhalimskySpaceND< dim, TInteger >::sKCoords | ( | const SCell & | c | ) | const |
Return its Khalimsky coordinates.
- Parameters
-
c any signed cell.
- Returns
- its Khalimsky coordinates.
- Precondition
uIsValid(c)is true.
Referenced by main(), DGtal::functors::deprecated::SCellToMidPoint< KSpace >::operator()(), DGtal::functors::SCellToArrow< KSpace >::operator()(), DGtal::functors::SCellToCode< KSpace >::operator()(), testCombinatorialSurface(), testCube(), and testUmbrellaComputer().
◆ sLast() [1/2]
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sLast | ( | const SPreCell & | p | ) | const |
Return the last cell of the space with the same type as [p].
- Returns
- the last cell of the space with the same type as [p].
- Note
- Along periodic dimensions, it returns the last unique coordinate of a cell of same type as p.
- Postcondition
sIsValid(sLast(p))is true.
◆ sLast() [2/2]
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sLast | ( | const SPreCell & | p, |
| Dimension | k | ||
| ) | const |
Return the k-th Khalimsky coordinate of the last cell of the space with the same type as [p].
- Returns
- the k-th Khalimsky coordinate of the last cell of the space with the same type as [p].
- Note
- For periodic dimension, it returns the last unique coordinate of a cell of same type as p.
- Postcondition
- The returned coordinate is between
lowerCell()[k]andupperCell()[k].
◆ sLowerIncident()
| SCells DGtal::KhalimskySpaceND< dim, TInteger >::sLowerIncident | ( | const SCell & | c | ) | const |
Return the signed cells directly low incident to c in this space.
- Parameters
-
c any signed cell.
- Returns
- the signed cells directly low incident to c in this space.
- Note
- it is the lower boundary of c expressed as a list of signed cells.
- Precondition
sIsValid(c)is true.
- Postcondition
sIsValid(b)is true for every returned cell b.
◆ sNeighborhood()
| SCells DGtal::KhalimskySpaceND< dim, TInteger >::sNeighborhood | ( | const SCell & | cell | ) | const |
Computes the 1-neighborhood of the cell [c] and returns it.
It is the set of cells with same topology that are adjacent to [c] and which are within the bounds of this space.
- Parameters
-
cell the signed cell of interest.
- Returns
- the cells of the 1-neighborhood of [cell].
- Precondition
sIsValid(cell)is true.
- Postcondition
sIsValid(c)is true for every returned cell c.
Referenced by testNeighborhood().
◆ sNext()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::sNext | ( | SCell & | p, |
| const SCell & | lower, | ||
| const SCell & | upper | ||
| ) | const |
Increment the cell [p] to its next position (as classically done in a scanning).
Example:
- Parameters
-
p any 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
sIsValid(p)andsIsValid(lower)andsIsValid(upper)andsTopology(p) == sTopology(lower) == sTopology(upper).
- Postcondition
sIsValid(p)is true.
Referenced by testScan().
◆ sOpp()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sOpp | ( | const SCell & | p | ) | const |
Creates the signed cell with the inverse sign of [p].
- Parameters
-
p any signed cell.
- Returns
- the cell [p] with opposite sign.
- Precondition
sIsValid(p)is true.
- Postcondition
sIsValid(sOpp(p))is true.
Referenced by SCENARIO(), and testIncidence().
◆ sOrthDir()
| Dimension DGtal::KhalimskySpaceND< dim, TInteger >::sOrthDir | ( | const SCell & | s | ) | const |
Given a signed surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).
- Parameters
-
s a signed surfel
- Returns
- the orthogonal direction of [s]
Referenced by main(), testFindABel(), and testSurfelAdjacency().
◆ sOrthDirs()
| DirIterator DGtal::KhalimskySpaceND< dim, TInteger >::sOrthDirs | ( | const SCell & | p | ) | const |
Given a signed 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:
- Parameters
-
p any signed cell.
- Returns
- an iterator that points on the first coordinate spanned by the cell.
Referenced by main(), DGtal::functors::SCellToInnerPoint< KSpace >::operator()(), DGtal::functors::SCellToOuterPoint< KSpace >::operator()(), and DGtal::functors::SCellToIncidentPoints< KSpace >::operator()().
◆ sPointel()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sPointel | ( | Point | p, |
| Sign | sign = POS |
||
| ) | const |
From the digital coordinates of a point in Zn, builds the corresponding pointel (cell of dimension 0) lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell). sign the sign of the cell (either POS or NEG).
- Returns
- the signed pointel having the given digital coordinates [p].
- Postcondition
uIsValid(uSpel(p))is true.
Referenced by main().
◆ sProject()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sProject | ( | SCell & | p, |
| const SCell & | bound, | ||
| Dimension | k | ||
| ) | const |
Projects [p] along the [k]th direction toward [bound].
Otherwise said, p[ k ] == bound[ k ] afterwards.
- Parameters
-
p any cell. bound the element acting as bound (same topology as p). k the concerned coordinate.
- Precondition
sIsValid(p)andsIsValid(bound)andsIsOpen(p, k) == sIsOpen(bound, k)
- Postcondition
sIsValid(p).
◆ sProjection()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sProjection | ( | const SCell & | p, |
| const SCell & | bound, | ||
| Dimension | k | ||
| ) | const |
Return the projection of [p] along the [k]th direction toward [bound].
Otherwise said, p[ k ] == bound[ k ] afterwards.
- Parameters
-
p any cell. bound the element acting as bound (same topology as p). k the concerned coordinate.
- Returns
- the projection.
- Precondition
sIsValid(p)andsIsValid(bound)andsIsOpen(p, k) == sIsOpen(bound, k)
- Postcondition
sIsValid(sProjection(p, bound, k))andsTopology(p) == sTopology(sProjection(p, bound, k)).
◆ sProperNeighborhood()
| SCells DGtal::KhalimskySpaceND< dim, TInteger >::sProperNeighborhood | ( | const SCell & | cell | ) | const |
Computes the proper 1-neighborhood of the cell [c] and returns it.
It is the set of cells with same topology that are adjacent to [c], different from [c] and which are within the bounds of this space.
- Parameters
-
cell the signed cell of interest.
- Returns
- the cells of the proper 1-neighborhood of [cell].
- Precondition
sIsValid(cell)is true.
- Postcondition
sIsValid(c)is true for every returned cell c.
Referenced by testNeighborhood().
◆ sSetCoord()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sSetCoord | ( | SCell & | c, |
| Dimension | k, | ||
| Integer | i | ||
| ) | const |
Sets the [k]-th digital coordinate of [c] to [i].
- Parameters
-
c any signed cell. k any valid dimension. i an integer coordinate within the space.
- Note
- The coordinate i will be corrected if k is a periodic dimension.
- Precondition
sIsValid(c)is true and i is within the space bounds if k is a non-periodic dimension.
- Postcondition
sIsValid(c)is true.
◆ sSetCoords()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sSetCoords | ( | SCell & | c, |
| const Point & | kp | ||
| ) | const |
Sets the digital coordinates of [c] to [kp].
- Parameters
-
c any signed cell. kp the new Khalimsky coordinates for [c].
- Note
- The coordinates kp will be corrected for periodic dimensions.
- Precondition
- kp is within the space bounds for non-periodic dimensions.
- Postcondition
sIsValid(c)is true.
◆ sSetKCoord()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sSetKCoord | ( | SCell & | c, |
| Dimension | k, | ||
| Integer | i | ||
| ) | const |
Sets the [k]-th Khalimsky coordinate of [c] to [i].
- Parameters
-
c any signed cell. k any valid dimension. i an integer coordinate within the space.
- Note
- The coordinate i will be corrected if k is a periodic dimension.
- Precondition
sIsValid(c)is true and i is within the space bounds if k is a non-periodic dimension.
- Postcondition
sIsValid(c)is true.
◆ sSetKCoords()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sSetKCoords | ( | SCell & | c, |
| const Point & | kp | ||
| ) | const |
Sets the Khalimsky coordinates of [c] to [kp].
- Parameters
-
c any signed cell. kp the new Khalimsky coordinates for [c].
- Note
- The coordinates kp will be corrected for periodic dimensions.
- Precondition
- kp is within the space bounds for non-periodic dimensions.
- Postcondition
sIsValid(c)is true.
◆ sSetSign()
| void DGtal::KhalimskySpaceND< dim, TInteger >::sSetSign | ( | SCell & | c, |
| Sign | s | ||
| ) | const |
Sets the sign of the cell.
- Parameters
-
c (modified) any signed cell. s any sign.
◆ sSign()
| Sign DGtal::KhalimskySpaceND< dim, TInteger >::sSign | ( | const SCell & | c | ) | const |
Return its sign.
- Parameters
-
c any signed cell.
- Returns
- its sign.
- Precondition
uIsValid(c)is true.
Referenced by testDirectIncidence().
◆ sSpel()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sSpel | ( | Point | p, |
| Sign | sign = POS |
||
| ) | const |
From the digital coordinates of a point in Zn, builds the corresponding spel (cell of maximal dimension) lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell). sign the sign of the cell (either POS or NEG).
- Returns
- the signed spel having the given digital coordinates [p].
- Postcondition
sIsValid(sSpel(p, sign))is true.
Referenced by main(), testDirectIncidence(), testExplicitDigitalSurface(), testIncidence(), and testLightExplicitDigitalSurface().
◆ sTopology()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::sTopology | ( | const SCell & | p | ) | const |
Return the topology word of [p].
- Parameters
-
p any signed cell.
- Returns
- the topology word of [p].
Referenced by testFaces(), testNeighborhood(), and testScan().
◆ sTranslation()
| SCell DGtal::KhalimskySpaceND< dim, TInteger >::sTranslation | ( | const SCell & | p, |
| const Vector & | vec | ||
| ) | const |
Add the vector [vec] to [p].
- Parameters
-
p any cell. vec any pointel.
- Returns
- the signed code of the cell [p] translated by [coord].
- Precondition
sIsValid(p, k)and (sDistanceToMin(p, k) <= vec[k] <= sDistanceToMax(p, k) or isPeriodicSpace(k) )for each dimension k.
- Postcondition
sIsValid(sTranslation(p, vec))is true.
Referenced by main().
◆ sUpperIncident()
| SCells DGtal::KhalimskySpaceND< dim, TInteger >::sUpperIncident | ( | const SCell & | c | ) | const |
Return the signed cells directly up incident to c in this space.
- Parameters
-
c any signed cell.
- Returns
- the signed cells directly up incident to c in this space.
- Note
- it is the upper boundary of c expressed as a list of signed cells.
- Precondition
sIsValid(c)is true.
- Postcondition
sIsValid(b)is true for every returned cell b.
◆ uAddCoFaces()
|
private |
Used by uCoFaces for computing incident cofaces.
◆ uAddFaces()
|
private |
Used by uFaces for computing incident faces.
◆ uAdjacent()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uAdjacent | ( | const Cell & | p, |
| Dimension | k, | ||
| bool | up | ||
| ) | const |
Return the adjacent element to [p] along axis [k] in the given direction and orientation.
- Parameters
-
p any 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 )'.
- Precondition
uIsValid(p)and notuIs(Min|Max)(p, k)depending on up value.
- Postcondition
- `uIsValid(uAdjacent(p, k, up)) is true.
◆ uCell() [1/3]
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uCell | ( | const Point & | kp | ) | const |
From the Khalimsky coordinates of a cell, builds the corresponding unsigned cell lying into this Khalismky space.
Along a non-periodic dimension, if the given Khalimsky coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the Khalimsky coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
kp an integer point (Khalimsky coordinates of cell).
- Returns
- the unsigned cell.
- Postcondition
uIsValid(uCell(kp))is true.
◆ uCell() [2/3]
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uCell | ( | const PreCell & | c | ) | const |
From an unsigned cell, returns an unsigned cell lying into this Khalismky space.
Along a non-periodic dimension, if the given Khalimsky coordinate lies outside the space, it replaces it by the nearest valid coordinate.
Along a periodic dimension, the Khalimsky coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
c a cell.
- Returns
- the same cell with appropriate Khalimsky coordinates along periodic dimensions.
- Postcondition
uIsValid(uCell(c))is true.-
uCell(c) == cifuIsValid(c).
Referenced by DGtal::dec_helper::averageOperator20(), cmpUCellsIfInside(), GIVEN(), main(), SCENARIO(), testCellDrawOnBoard(), testFaces(), testNeighborhood(), testQuadNorm(), and testScan().
◆ uCell() [3/3]
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uCell | ( | Point | p, |
| const PreCell & | c | ||
| ) | const |
From the digital coordinates of a point in Zn and a cell type, builds the corresponding unsigned cell lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell). c another cell defining the topology.
- Returns
- the cell having the topology of [c] and the given digital coordinates [p].
- Postcondition
uIsValid(uCell(p, c))is true.
◆ uCoFaces()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uCoFaces | ( | const Cell & | c | ) | const |
Return the proper cofaces of [c] (chain of upper incidence) that belong to the space.
- Parameters
-
c any unsigned cell.
- Returns
- the proper cofaces of [c] (chain of upper incidence) that belong to the space.
- Precondition
uIsValid(c)is true.
- Postcondition
uIsValid(b)is true for every returned cell b.
Referenced by testCellularGridSpaceNDCoFaces(), and testFaces().
◆ uCoord()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uCoord | ( | const Cell & | c, |
| Dimension | k | ||
| ) | const |
Return its digital coordinate along [k].
- Parameters
-
c any unsigned cell. k any valid dimension.
- Returns
- its digital coordinate along [k].
- Precondition
uIsValid(c)is true.
◆ uCoords()
| Point DGtal::KhalimskySpaceND< dim, TInteger >::uCoords | ( | const Cell & | c | ) | const |
Return its digital coordinates.
- Parameters
-
c any unsigned cell.
- Returns
- its digital coordinates
- Precondition
uIsValid(c)is true.
Referenced by centerSurfel(), main(), and SCENARIO().
◆ uDim()
| Dimension DGtal::KhalimskySpaceND< dim, TInteger >::uDim | ( | const Cell & | p | ) | const |
Return the dimension of the cell [p].
- Parameters
-
p any unsigned cell.
- Returns
- the dimension of the cell [p].
Referenced by DGtal::dec_helper::averageOperator20(), testCellularGridSpaceNDCoFaces(), testCellularGridSpaceNDFaces(), and testFaces().
◆ uDirs()
| DirIterator DGtal::KhalimskySpaceND< dim, TInteger >::uDirs | ( | const Cell & | p | ) | const |
Given an unsigned 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:
- Parameters
-
p any unsigned cell.
- Returns
- an iterator that points on the first coordinate spanned by the cell.
Referenced by main().
◆ uDistanceToMax()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uDistanceToMax | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space (for non-periodic dimensions).
- Parameters
-
p any cell. k the coordinate that is tested.
- Returns
- the number of increment to do to reach the maximum value.
- Precondition
uIsValid(p)is true.
◆ uDistanceToMin()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uDistanceToMin | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space (for non-periodic dimensions).
- Parameters
-
p any cell. k the coordinate that is tested.
- Returns
- the number of decrement to do to reach the minimum value.
- Precondition
uIsValid(p)is true.
◆ uFaces()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uFaces | ( | const Cell & | c | ) | const |
Return the proper faces of [c] (chain of lower incidence) that belong to the space.
- Parameters
-
c any unsigned cell.
- Returns
- the proper faces of [c] (chain of lower incidence) that belong to the space.
- Precondition
uIsValid(c)is true.
- Postcondition
uIsValid(b)is true for every returned cell b.
Referenced by testCellularGridSpaceNDFaces(), and testFaces().
◆ uFirst() [1/2]
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uFirst | ( | const PreCell & | p | ) | const |
Return the first cell of the space with the same type as [p].
- Returns
- the first cell of the space with the same type as [p].
- Note
- Along periodic dimensions, it returns the first unique coordinate of a cell of same type as p.
- Postcondition
uIsValid(uFirst(p))is true.
◆ uFirst() [2/2]
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uFirst | ( | const PreCell & | p, |
| Dimension | k | ||
| ) | const |
Return the k-th Khalimsky coordinate of the first cell of the space with the same type as [p].
- Returns
- the k-th Khalimsky coordinate of the first cell of the space with the same type as [p].
- Note
- For periodic dimension, it returns the first unique coordinate of a cell of same type as p.
- Postcondition
- The returned coordinate is between
lowerCell()[k]andupperCell()[k].
Referenced by main().
◆ uGetAdd()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetAdd | ( | const Cell & | p, |
| Dimension | k, | ||
| Integer | x | ||
| ) | const |
Return the same element as [p] except for a coordinate [k] incremented with x.
- Parameters
-
p any cell. k the coordinate that is changed. x the increment.
- Returns
- the same element as [p] except for a coordinate [k] incremented with x.
- Precondition
uIsValid(p)and (x <= uDistanceToMax(p, k)orisSpacePeriodic(k)).
- Postcondition
uIsValid(uGetAdd(p, k, x))is true.
◆ uGetDecr()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetDecr | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Return the same element as [p] except for an decremented coordinate [k].
- Parameters
-
p any cell. k the coordinate that is changed.
- Returns
- the same element as [p] except for an decremented coordinate [k].
- Precondition
uIsValid(p)and notuIsMin(p).
- Postcondition
uIsValid(uGetDecr(p, k))is true.
◆ uGetIncr()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetIncr | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Return the same element as [p] except for the incremented coordinate [k].
- Parameters
-
p any cell. k the coordinate that is changed.
- Returns
- the same element as [p] except for the incremented coordinate [k].
- Precondition
uIsValid(p)and notuIsMax(p).
- Postcondition
uIsValid(uGetIncr(p, k))is true.
◆ uGetMax()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetMax | ( | Cell | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the concerned coordinate.
- Returns
- the cell similar to [p] but with the maximum allowed [k]-coordinate.
- Precondition
uIsValid(p, d)is true for each dimension d different than k.
- Postcondition
uIsValid(uGetMax(p, k))is true.
Referenced by main().
◆ uGetMin()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetMin | ( | Cell | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the concerned coordinate.
- Returns
- the cell similar to [p] but with the minimum allowed [k]-coordinate.
- Precondition
uIsValid(p, d)is true for each dimension d different than k.
- Postcondition
uIsValid(uGetMin(p, k))is true.
◆ uGetSub()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uGetSub | ( | const Cell & | p, |
| Dimension | k, | ||
| Integer | x | ||
| ) | const |
Return the same element as [p] except for a coordinate [k] decremented with x.
- Parameters
-
p any cell. k the coordinate that is changed. x the decrement.
- Returns
- the same element as [p] except for a coordinate [k] decremented with x.
- Precondition
uIsValid(p)and (x <= uDistanceToMin(p, k)orisSpacePeriodic(k)).
- Postcondition
uIsValid(uGetSub(p, k, x))is true.
◆ uIncident()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uIncident | ( | const Cell & | c, |
| Dimension | k, | ||
| bool | up | ||
| ) | const |
Return the forward or backward unsigned cell incident to [c] along axis [k], depending on [up].
- Parameters
-
c any unsigned cell. k any coordinate. up if 'true' the orientation is forward along axis [k], otherwise backward.
- Returns
- the forward or backward unsigned cell incident to [c] along axis [k], depending on [up].
- Note
- It may be a lower incident cell if [c] is open along axis [k], else an upper incident cell.
- Precondition
uIsValid(c)and the cell should have an incident cell in this direction/orientation.
- Postcondition
uIsValid(uIncident(c, k, up))is true.
Referenced by main(), and testCellDrawOnBoard().
◆ uIsInside() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsInside | ( | const PreCell & | p | ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell.
- Returns
- true if [p] has its coordinates within the allowed bounds.
- Note
- Only the non-periodic dimensions are checked.
◆ uIsInside() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsInside | ( | const PreCell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] has its [k]-coordinate within the allowed bounds.
- Note
- It returns always true for periodic dimension.
Referenced by cmpUCellsIfInside(), main(), testCellularGridSpaceNDCoFaces(), testCellularGridSpaceNDFaces(), testFaces(), testFindABel(), testNeighborhood(), and testSurfelAdjacency().
◆ uIsMax()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsMax | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] cannot have its [k]-coordinate augmented without leaving the space.
- Note
- It returns always false for periodic dimension.
- Precondition
uIsInside(p)is true.
◆ uIsMin()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsMin | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Useful to check if you are going out of the space.
- Parameters
-
p any cell. k the tested coordinate.
- Returns
- true if [p] cannot have its [k]-coordinate decreased without leaving the space.
- Note
- It returns always false for periodic dimension.
- Precondition
uIsInside(p)is true.
◆ uIsOpen()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsOpen | ( | const Cell & | p, |
| Dimension | k | ||
| ) | const |
Return 'true' if [p] is open along the direction [k].
- Parameters
-
p any cell. k any direction.
- Returns
- 'true' if [p] is open along the direction [k].
◆ uIsSurfel()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsSurfel | ( | const Cell & | b | ) | const |
Return 'true' if [b] is a surfel (spans all but one coordinate).
- Parameters
-
b any unsigned cell.
- Returns
- 'true' if [b] is a surfel (spans all but one coordinate).
◆ uIsValid() [1/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsValid | ( | const PreCell & | c | ) | const |
Returns true if the given unsigned cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Parameters
-
c a unsigned cell.
- Returns
trueif the given unsigned cell has Khalimsky coordinates between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
- See also
- uCell(const Cell &) const to correct Khalimsky coordinates along periodic dimensions.
◆ uIsValid() [2/2]
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uIsValid | ( | const PreCell & | c, |
| Dimension | k | ||
| ) | const |
Returns true if the given unsigned cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Parameters
-
c an unsigned cell. k a dimension.
- Returns
trueif the given unsigned cell has his k-th Khalimsky coordinate between those of the cells returned by lowerCell and upperCell.
- Note
- For periodic dimension, even if there is no bounds, it guarantees that each cell has unique coordinates.
- See also
- uCell(const Cell &) const to correct Khalimsky coordinates along periodic dimensions.
◆ uKCoord()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uKCoord | ( | const Cell & | c, |
| Dimension | k | ||
| ) | const |
Return its Khalimsky coordinate along [k].
- Parameters
-
c any unsigned cell. k any valid dimension.
- Returns
- its Khalimsky coordinate along [k].
- Precondition
uIsValid(c)is true.
◆ uKCoords()
| const Point & DGtal::KhalimskySpaceND< dim, TInteger >::uKCoords | ( | const Cell & | c | ) | const |
Return its Khalimsky coordinates.
- Parameters
-
c any unsigned cell.
- Returns
- its Khalimsky coordinates.
- Precondition
uIsValid(c)is true.
Referenced by DGtal::dec_helper::averageOperator20().
◆ uLast() [1/2]
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uLast | ( | const PreCell & | p | ) | const |
Return the last cell of the space with the same type as [p].
- Returns
- the last cell of the space with the same type as [p].
- Note
- Along periodic dimensions, it returns the last unique coordinate of a cell of same type as p.
- Postcondition
uIsValid(uLast(p))is true.
◆ uLast() [2/2]
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uLast | ( | const PreCell & | p, |
| Dimension | k | ||
| ) | const |
Return the k-th Khalimsky coordinate of the last cell of the space with the same type as [p].
- Returns
- the k-th Khalimsky coordinate of the last cell of the space with the same type as [p].
- Note
- For periodic dimension, it returns the last unique coordinate of a cell of same type as p.
- Postcondition
- The returned coordinate is between
lowerCell()[k]andupperCell()[k].
Referenced by main().
◆ uLowerIncident()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uLowerIncident | ( | const Cell & | c | ) | const |
Return the cells directly low incident to c in this space.
- Parameters
-
c any unsigned cell.
- Returns
- the cells directly low incident to c in this space.
- Precondition
uIsValid(c)is true.
- Postcondition
uIsValid(b)is true for every returned cell b.
◆ uNeighborhood()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uNeighborhood | ( | const Cell & | cell | ) | const |
Computes the 1-neighborhood of the cell [c] and returns it.
It is the set of cells with same topology that are adjacent to [c] and which are within the bounds of this space.
- Parameters
-
cell the unsigned cell of interest.
- Returns
- the cells of the 1-neighborhood of [cell].
- Precondition
uIsValid(cell)is true.
- Postcondition
uIsValid(c)is true for every returned cell c.
Referenced by testNeighborhood().
◆ uNext()
| bool DGtal::KhalimskySpaceND< dim, TInteger >::uNext | ( | Cell & | p, |
| const Cell & | lower, | ||
| const Cell & | upper | ||
| ) | const |
Increment the cell [p] to its next position (as classically done in a scanning).
Example:
- Parameters
-
p any 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
uIsValid(p)anduIsValid(lower)anduIsValid(upper)anduTopology(p) == uTopology(lower) == uTopology(upper).
- Postcondition
uIsValid(p)is true.
Referenced by main(), and testScan().
◆ unsigns()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::unsigns | ( | const SCell & | p | ) | const |
Creates an unsigned cell from a signed one.
- Parameters
-
p any signed cell.
- Returns
- the unsigned version of the cell [p].
- Precondition
sIsValid(p)is true.
- Postcondition
uIsValid(unsigns(p))is true.
- Examples
- dec/exampleHeatLaplace.cpp.
Referenced by DGtal::dec_helper::averageOperator20(), main(), TEST_CASE(), and testLocalConvolutionNormalVectorEstimator().
◆ uOrthDir()
| Dimension DGtal::KhalimskySpaceND< dim, TInteger >::uOrthDir | ( | const Cell & | s | ) | const |
Given an unsigned surfel [s], returns its orthogonal direction (ie, the coordinate where the surfel is closed).
- Parameters
-
s an unsigned surfel
- Returns
- the orthogonal direction of [s]
◆ uOrthDirs()
| DirIterator DGtal::KhalimskySpaceND< dim, TInteger >::uOrthDirs | ( | const Cell & | p | ) | const |
Given an unsigned 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:
- Parameters
-
p any unsigned cell.
- Returns
- an iterator that points on the first coordinate spanned by the cell.
◆ uPointel()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uPointel | ( | Point | p | ) | const |
From the digital coordinates of a point in Zn, builds the corresponding pointel (cell of dimension 0) lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell).
- Returns
- the pointel having the given digital coordinates [p].
- Postcondition
uIsValid(uSpel(p))is true.
Referenced by main(), SCENARIO(), and testCellularGridSpaceNDCoFaces().
◆ upperBound()
| const Point & DGtal::KhalimskySpaceND< dim, TInteger >::upperBound | ( | ) | const |
Return the upper bound for digital points in this space.
- Returns
- the upper bound for digital points in this space.
- Note
- For periodic dimension, it returns the upper digital point with unique coordinates. See also the class documentation.
- Examples
- topology/ctopo-2.cpp.
Referenced by main(), SCENARIO(), and TEST_CASE_METHOD().
◆ upperCell()
| const Cell & DGtal::KhalimskySpaceND< dim, TInteger >::upperCell | ( | ) | const |
Return the upper bound for cells in this space.
- Returns
- the upper bound for cells in this space.
- Note
- For periodic dimension, it returns the upper cell with unique coordinates. See also the class documentation.
◆ uProject()
| void DGtal::KhalimskySpaceND< dim, TInteger >::uProject | ( | Cell & | p, |
| const Cell & | bound, | ||
| Dimension | k | ||
| ) | const |
Projects [p] along the [k]th direction toward [bound].
Otherwise said, p[ k ] == bound[ k ] afterwards
- Parameters
-
[in,out] p any cell. [in] bound the element acting as bound (same topology as p). [in] k the concerned coordinate.
- Precondition
uIsValid(p)anduIsValid(bound)anduIsOpen(p, k) == uIsOpen(bound, k)
- Postcondition
uIsValid(p).
◆ uProjection()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uProjection | ( | const Cell & | p, |
| const Cell & | bound, | ||
| Dimension | k | ||
| ) | const |
Return the projection of [p] along the [k]th direction toward [bound].
Otherwise said, p[ k ] == bound[ k ] afterwards.
- Parameters
-
p any cell. bound the element acting as bound (same topology as p). k the concerned coordinate.
- Returns
- the projection.
- Precondition
uIsValid(p)anduIsValid(bound)anduIsOpen(p, k) == uIsOpen(bound, k)
- Postcondition
uIsValid(uProjection(p, bound, k))anduTopology(p) == uTopology(uProjection(p, bound, k)).
◆ uProperNeighborhood()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uProperNeighborhood | ( | const Cell & | cell | ) | const |
Computes the proper 1-neighborhood of the cell [c] and returns it.
It is the set of cells with same topology that are adjacent to [c], different from [c] and which are within the bounds of this space.
- Parameters
-
cell the unsigned cell of interest.
- Returns
- the cells of the proper 1-neighborhood of [cell].
- Precondition
uIsValid(cell)is true.
- Postcondition
uIsValid(c)is true for every returned cell c.
Referenced by testNeighborhood().
◆ uSetCoord()
| void DGtal::KhalimskySpaceND< dim, TInteger >::uSetCoord | ( | Cell & | c, |
| Dimension | k, | ||
| Integer | i | ||
| ) | const |
Sets the [k]-th digital coordinate of [c] to [i].
- Parameters
-
c any unsigned cell. k any valid dimension. i an integer coordinate within the space.
- Note
- The coordinate i will be corrected if k is a periodic dimension.
- Precondition
uIsValid(c)is true and i is within the space bounds if k is a non-periodic dimension.
- Postcondition
uIsValid(c)is true.
◆ uSetCoords()
| void DGtal::KhalimskySpaceND< dim, TInteger >::uSetCoords | ( | Cell & | c, |
| const Point & | kp | ||
| ) | const |
Sets the digital coordinates of [c] to [kp].
- Parameters
-
c any unsigned cell. kp the new Khalimsky coordinates for [c].
- Note
- The coordinates kp will be corrected for periodic dimensions.
- Precondition
- kp is within the space bounds for non-periodic dimensions.
- Postcondition
uIsValid(c)is true.
◆ uSetKCoord()
| void DGtal::KhalimskySpaceND< dim, TInteger >::uSetKCoord | ( | Cell & | c, |
| Dimension | k, | ||
| Integer | i | ||
| ) | const |
Sets the [k]-th Khalimsky coordinate of [c] to [i].
- Parameters
-
c any unsigned cell. k any valid dimension. i an integer coordinate within the space.
- Note
- The coordinate i will be corrected if k is a periodic dimension.
- Precondition
uIsValid(c)is true and i is within the space bounds if k is a non-periodic dimension.
- Postcondition
uIsValid(c)is true.
◆ uSetKCoords()
| void DGtal::KhalimskySpaceND< dim, TInteger >::uSetKCoords | ( | Cell & | c, |
| const Point & | kp | ||
| ) | const |
Sets the Khalimsky coordinates of [c] to [kp].
- Parameters
-
c any unsigned cell. kp the new Khalimsky coordinates for [c].
- Note
- The coordinates kp will be corrected for periodic dimensions.
- Precondition
- kp is within the space bounds for non-periodic dimensions.
- Postcondition
uIsValid(c)is true.
◆ uSpel()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uSpel | ( | Point | p | ) | const |
From the digital coordinates of a point in Zn, builds the corresponding spel (cell of maximal dimension) lying into this Khalismky space.
Along a non-periodic dimension, if the given digital coordinate lies outside the space, it is replaced by the nearest valid coordinate.
Along a periodic dimension, the digital coordinate is corrected (by periodicity) to lie between the coordinates of lowerCell() and upperCell().
- Parameters
-
p an integer point (digital coordinates of cell).
- Returns
- the spel having the given digital coordinates [p].
- Postcondition
uIsValid(uSpel(p))is true.
Referenced by main(), SCENARIO(), testCellularGridSpaceNDCoFaces(), testCellularGridSpaceNDFaces(), testFindABel(), and testSurfelAdjacency().
◆ uTopology()
| Integer DGtal::KhalimskySpaceND< dim, TInteger >::uTopology | ( | const Cell & | p | ) | const |
Return the topology word of [p].
- Parameters
-
p any unsigned cell.
- Returns
- the topology word of [p].
Referenced by testFaces(), testNeighborhood(), and testScan().
◆ uTranslation()
| Cell DGtal::KhalimskySpaceND< dim, TInteger >::uTranslation | ( | const Cell & | p, |
| const Vector & | vec | ||
| ) | const |
Add the vector [vec] to [p].
- Parameters
-
p any cell. vec any pointel.
- Returns
- the unsigned copy of the cell [p] translated by [coord].
- Precondition
uIsValid(p, k)and (uDistanceToMin(p, k) <= vec[k] <= uDistanceToMax(p, k) or isPeriodicSpace(k) )for each dimension k.
- Postcondition
uIsValid(uTranslation(p, vec))is true.
Referenced by main().
◆ uUpperIncident()
| Cells DGtal::KhalimskySpaceND< dim, TInteger >::uUpperIncident | ( | const Cell & | c | ) | const |
Return the cells directly up incident to c in this space.
- Parameters
-
c any unsigned cell.
- Returns
- the cells directly up incident to c in this space.
- Precondition
uIsValid(c)is true.
- Postcondition
uIsValid(b)is true for every returned cell b.
Friends And Related Function Documentation
◆ KhalimskySpaceNDHelper< KhalimskySpaceND< dim, TInteger > >
|
friend |
Definition at line 396 of file KhalimskySpaceND.h.
Field Documentation
◆ DIM
|
staticconstexpr |
Definition at line 431 of file KhalimskySpaceND.h.
◆ dimension
|
staticconstexpr |
Definition at line 430 of file KhalimskySpaceND.h.
Referenced by DGtal::Shortcuts< TKSpace >::getPointelRange(), DGtal::Shortcuts< TKSpace >::getPrimalVertices(), main(), DGtal::Shortcuts< TKSpace >::makeDualPolygonalSurface(), DGtal::Shortcuts< TKSpace >::makePrimalPolygonalSurface(), DGtal::Shortcuts< TKSpace >::makePrimalSurfaceMesh(), DGtal::Shortcuts< TKSpace >::CellReader::operator()(), DGtal::Shortcuts< TKSpace >::SCellReader::operator()(), DGtal::Shortcuts< TKSpace >::CellWriter::operator()(), DGtal::Shortcuts< TKSpace >::outputDualDigitalSurfaceAsObj(), DGtal::Shortcuts< TKSpace >::outputSurfelsAsObj(), DGtal::Shortcuts< TKSpace >::saveOBJ(), DGtal::Shortcuts< TKSpace >::saveOFF(), DGtal::Shortcuts< TKSpace >::saveVectorFieldOBJ(), testCellDrawOnBoard(), testCellularGridSpaceNDCoFaces(), testCellularGridSpaceNDFaces(), testDigitalSurface(), testFaces(), testFindABel(), testNeighborhood(), testScan(), testSurfelAdjacency(), DGtal::functors::VCMAbsoluteCurvatureFunctor< TVCMOnDigitalSurface >::VCMAbsoluteCurvatureFunctor(), DGtal::functors::VCMFirstPrincipalAbsoluteCurvatureFunctor< TVCMOnDigitalSurface >::VCMFirstPrincipalAbsoluteCurvatureFunctor(), DGtal::functors::VCMMeanAbsoluteCurvatures3DFunctor< TVCMOnDigitalSurface >::VCMMeanAbsoluteCurvatures3DFunctor(), and DGtal::functors::VCMSecondPrincipalAbsoluteCurvatureFunctor< TVCMOnDigitalSurface >::VCMSecondPrincipalAbsoluteCurvatureFunctor().
◆ myCellLower
|
private |
Definition at line 2067 of file KhalimskySpaceND.h.
◆ myCellUpper
|
private |
Definition at line 2068 of file KhalimskySpaceND.h.
◆ myClosure
|
private |
Definition at line 2069 of file KhalimskySpaceND.h.
◆ myLower
|
private |
Definition at line 2065 of file KhalimskySpaceND.h.
◆ myUpper
|
private |
Definition at line 2066 of file KhalimskySpaceND.h.
◆ NEG
|
staticconstexpr |
Definition at line 433 of file KhalimskySpaceND.h.
Referenced by main().
◆ POS
|
staticconstexpr |
Definition at line 432 of file KhalimskySpaceND.h.
Referenced by main(), testCellDrawOnBoard(), testDirectIncidence(), testExplicitDigitalSurface(), testIncidence(), testLightExplicitDigitalSurface(), and testSurfelAdjacency().
The documentation for this class was generated from the following file:
