Aim: A helper class to build polytopes from digital sets and to check digital k-convexity.
More...
#include <DGtal/geometry/volumes/DigitalConvexity.h>
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| | ~DigitalConvexity ()=default |
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| | DigitalConvexity ()=default |
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| | DigitalConvexity (const Self &other)=default |
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| | DigitalConvexity (Clone< KSpace > K) |
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| | DigitalConvexity (Point lo, Point hi) |
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| Self & | operator= (const Self &other)=default |
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| const KSpace & | space () const |
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| template<typename PointIterator > |
| CellGeometry | makeCellCover (PointIterator itB, PointIterator itE, Dimension i=0, Dimension k=KSpace::dimension) const |
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| CellGeometry | makeCellCover (const LatticePolytope &P, Dimension i=0, Dimension k=KSpace::dimension) const |
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| CellGeometry | makeCellCover (const RationalPolytope &P, Dimension i=0, Dimension k=KSpace::dimension) const |
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| bool | isKConvex (const LatticePolytope &P, const Dimension k) const |
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| bool | isFullyConvex (const LatticePolytope &P) const |
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| bool | isKSubconvex (const LatticePolytope &P, const CellGeometry &C, const Dimension k) const |
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| bool | isFullySubconvex (const LatticePolytope &P, const CellGeometry &C) const |
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| bool | isKConvex (const RationalPolytope &P, const Dimension k) const |
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| bool | isFullyConvex (const RationalPolytope &P) const |
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| bool | isKSubconvex (const RationalPolytope &P, const CellGeometry &C, const Dimension k) const |
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| bool | isFullySubconvex (const RationalPolytope &P, const CellGeometry &C) const |
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| void | selfDisplay (std::ostream &out) const |
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| bool | isValid () const |
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| enum class | SimplexType { INVALID
, DEGENERATED
, UNITARY
, COMMON
} |
| | The possible types for simplices. More...
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| template<typename PointIterator > |
| static LatticePolytope | makeSimplex (PointIterator itB, PointIterator itE) |
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| static LatticePolytope | makeSimplex (std::initializer_list< Point > l) |
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| template<typename PointIterator > |
| static RationalPolytope | makeRationalSimplex (Integer d, PointIterator itB, PointIterator itE) |
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| static RationalPolytope | makeRationalSimplex (std::initializer_list< Point > l) |
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| template<typename PointIterator > |
| static bool | isSimplexFullDimensional (PointIterator itB, PointIterator itE) |
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| static bool | isSimplexFullDimensional (std::initializer_list< Point > l) |
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| template<typename PointIterator > |
| static SimplexType | simplexType (PointIterator itB, PointIterator itE) |
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| static SimplexType | simplexType (std::initializer_list< Point > l) |
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| template<typename PointIterator > |
| static void | displaySimplex (std::ostream &out, PointIterator itB, PointIterator itE) |
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| static void | displaySimplex (std::ostream &out, std::initializer_list< Point > l) |
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template<typename TKSpace>
class DGtal::DigitalConvexity< TKSpace >
Aim: A helper class to build polytopes from digital sets and to check digital k-convexity.
Description of template class 'DigitalConvexity'
It is a model of boost::CopyConstructible, boost::DefaultConstructible, boost::Assignable.
- Template Parameters
-
| TKSpace | an arbitrary model of CCellularGridSpaceND. |
Definition at line 73 of file DigitalConvexity.h.
◆ Cell
template<typename TKSpace >
◆ CellGeometry
template<typename TKSpace >
◆ Integer
template<typename TKSpace >
◆ KSpace
template<typename TKSpace >
◆ LatticePolytope
template<typename TKSpace >
◆ Point
template<typename TKSpace >
◆ PointRange
template<typename TKSpace >
◆ Polytope
template<typename TKSpace >
◆ RationalPolytope
template<typename TKSpace >
◆ Self
template<typename TKSpace >
◆ Space
template<typename TKSpace >
◆ Vector
template<typename TKSpace >
◆ SimplexType
template<typename TKSpace >
The possible types for simplices.
| Enumerator |
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| INVALID | When there are not the right number of vertices.
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| DEGENERATED | When the points of the simplex are not in general position.
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| UNITARY | When its edges form a unit parallelotope (det = +/- 1)
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| COMMON | Common simplex.
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Definition at line 222 of file DigitalConvexity.h.
◆ ~DigitalConvexity()
template<typename TKSpace >
◆ DigitalConvexity() [1/4]
template<typename TKSpace >
◆ DigitalConvexity() [2/4]
template<typename TKSpace >
Copy constructor.
- Parameters
-
| other | the object to clone. |
◆ DigitalConvexity() [3/4]
template<typename TKSpace >
Constructor from cellular space.
- Parameters
-
| K | any cellular grid space. |
◆ DigitalConvexity() [4/4]
template<typename TKSpace >
Constructor from lower and upper points.
- Parameters
-
| lo | the lowest point of the domain (bounding box for computations). |
| hi | the highest point of the domain (bounding box for computations). |
◆ BOOST_CONCEPT_ASSERT()
template<typename TKSpace >
◆ displaySimplex() [1/2]
template<typename TKSpace >
template<typename PointIterator >
| static void DGtal::DigitalConvexity< TKSpace >::displaySimplex |
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std::ostream & |
out, |
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PointIterator |
itB, |
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PointIterator |
itE |
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) |
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static |
Displays information about the simplex formed by the given range [itB,itE) of lattice points.
- Template Parameters
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| PointIterator | any model of forward iterator on Point. |
- Parameters
-
| [in,out] | out | the output stream where information is outputed. |
| itB | the start of the range of n+1 points defining the simplex. |
| itE | past the end the range of n+1 points defining the simplex. |
◆ displaySimplex() [2/2]
template<typename TKSpace >
Displays information about simplex formed by the given list l of lattice points.
- Parameters
-
| [in,out] | out | the output stream where information is outputed. |
| l | any list of lattice points. |
◆ insidePoints() [1/2]
template<typename TKSpace >
- Parameters
-
| polytope | any lattice polytope. |
- Returns
- the range of digital points that belongs to the polytope.
◆ insidePoints() [2/2]
template<typename TKSpace >
- Parameters
-
| polytope | any rational polytope. |
- Returns
- the range of digital points that belongs to the polytope.
◆ interiorPoints() [1/2]
template<typename TKSpace >
- Parameters
-
| polytope | any lattice polytope. |
- Returns
- the range of digital points that belongs to the interior of the polytope.
◆ interiorPoints() [2/2]
template<typename TKSpace >
- Parameters
-
| polytope | any rational polytope. |
- Returns
- the range of digital points that belongs to the interior of the polytope.
◆ isFullyConvex() [1/2]
template<typename TKSpace >
Tells if a given polytope P is fully digitally convex. The digital 0-convexity is the usual property \( Conv( P \cap Z^d ) = P \cap Z^d) \). Otherwise the property asks that the points inside P touch as many k-cells that the convex hull of P, for any valid dimension k.
- Parameters
-
| P | any lattice polytope such that P.canBeSummed() == true. |
- Returns
- 'true' iff the polytope P is fully digitally convex.
- Note
- A polytope is always digitally 0-convex. Furthermore, if it is not digitally d-1-convex then it is digitally d-convex (d := KSpace::dimension). Hence, we only check k-convexity for 1 <= k <= d-1.
◆ isFullyConvex() [2/2]
template<typename TKSpace >
Tells if a given polytope P is fully digitally convex. The digital 0-convexity is the usual property \( Conv( P \cap Z^d ) = P \cap Z^d) \). Otherwise the property asks that the points inside P touch as many k-cells that the convex hull of P, for any valid dimension k.
- Parameters
-
| P | any rational polytope such that P.canBeSummed() == true. |
- Returns
- 'true' iff the polytope P is fully digitally convex.
- Note
- A polytope is always digitally 0-convex. Furthermore, if it is not digitally d-1-convex then it is digitally d-convex (d := KSpace::dimension). Hence, we only check k-convexity for 1 <= k <= d-1.
◆ isFullySubconvex() [1/2]
template<typename TKSpace >
Tells if a given polytope P is digitally fully subconvex to some cell cover C. The digital 0-subconvexity is the usual property \( Conv( P \cap Z^d ) \subset C \cap Z^d) \). Otherwise the property asks that the k-cells intersected by the convex hull of P is a subset of the k-cells of C.
- Parameters
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| P | any lattice polytope such that P.canBeSummed() == true. |
| C | any cell cover geometry (i.e. a cubical complex). |
- Returns
- 'true' iff the polytope P is digitally fully subconvex to C.
- Note
- This method only checks the k-subconvexity for valid dimensions stored in C.
Referenced by main().
◆ isFullySubconvex() [2/2]
template<typename TKSpace >
Tells if a given polytope P is digitally fully subconvex to some cell cover C. The digital 0-subconvexity is the usual property \( Conv( P \cap Z^d ) \subset C \cap Z^d) \). Otherwise the property asks that the k-cells intersected by the convex hull of P is a subset of the k-cells of C.
- Parameters
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| P | any rational polytope such that P.canBeSummed() == true. |
| C | any cell cover geometry (i.e. a cubical complex). |
- Returns
- 'true' iff the polytope P is digitally fully subconvex to C.
- Note
- This method only checks the k-subconvexity for valid dimensions stored in C.
◆ isKConvex() [1/2]
template<typename TKSpace >
Tells if a given polytope P is digitally k-convex. The digital 0-convexity is the usual property \( Conv( P \cap Z^d ) = P \cap Z^d) \). Otherwise the property asks that the points inside P touch as many k-cells that the convex hull of P.
- Parameters
-
| P | any lattice polytope such that P.canBeSummed() == true. |
| k | the dimension for which the digital k-convexity is checked, 0 <= k <= KSpace::dimension. |
- Returns
- 'true' iff the polytope P is digitally k-convex.
- Note
- A polytope is always digitally 0-convex. Furthermore, if it is not digitally d-1-convex then it is digitally not d-convex (d := KSpace::dimension).
◆ isKConvex() [2/2]
template<typename TKSpace >
Tells if a given polytope P is digitally k-convex. The digital 0-convexity is the usual property \( Conv( P \cap Z^d ) = P \cap Z^d) \). Otherwise the property asks that the points inside P touch as many k-cells that the convex hull of P.
- Parameters
-
| P | any rational polytope such that P.canBeSummed() == true. |
| k | the dimension for which the digital k-convexity is checked, 0 <= k <= KSpace::dimension. |
- Returns
- 'true' iff the polytope P is digitally k-convex.
- Note
- A polytope is always digitally 0-convex. Furthermore, if it is not digitally d-1-convex then it is digitally not d-convex (d := KSpace::dimension).
◆ isKSubconvex() [1/2]
template<typename TKSpace >
Tells if a given polytope P is digitally k-subconvex of some cell cover C. The digital 0-subconvexity is the usual property \( Conv( P \cap Z^d ) \subset C \cap Z^d) \). Otherwise the property asks that the k-cells intersected by the convex hull of P is a subset of the k-cells of C.
- Parameters
-
| P | any lattice polytope such that P.canBeSummed() == true. |
| C | any cell cover geometry (i.e. a cubical complex). |
| k | the dimension for which the digital k-convexity is checked, 0 <= k <= KSpace::dimension. |
- Returns
- 'true' iff the polytope P is a digitally k-subconvex of C.
◆ isKSubconvex() [2/2]
template<typename TKSpace >
Tells if a given polytope P is digitally k-subconvex of some cell cover C. The digital 0-subconvexity is the usual property \( Conv( P \cap Z^d ) \subset C \cap Z^d) \). Otherwise the property asks that the k-cells intersected by the convex hull of P is a subset of the k-cells of C.
- Parameters
-
| P | any rational polytope such that P.canBeSummed() == true. |
| C | any cell cover geometry (i.e. a cubical complex). |
| k | the dimension for which the digital k-convexity is checked, 0 <= k <= KSpace::dimension. |
- Returns
- 'true' iff the polytope P is a digitally k-subconvex of C.
◆ isSimplexFullDimensional() [1/2]
template<typename TKSpace >
template<typename PointIterator >
Checks if the given range [itB,itE) of lattice points form a full dimensional simplex, i.e. it must contain Space::dimension+1 points in general position.
- Template Parameters
-
| PointIterator | any model of forward iterator on Point. |
- Parameters
-
| itB | the start of the range of n+1 points defining the simplex. |
| itE | past the end the range of n+1 points defining the simplex. |
Referenced by main().
◆ isSimplexFullDimensional() [2/2]
template<typename TKSpace >
Checks if the given list of lattice points l form a full dimensional simplex, i.e. it must contain Space::dimension+1 points in general position.
- Parameters
-
| l | any list of d+1 points in general positions. |
◆ isValid()
template<typename TKSpace >
Checks the validity/consistency of the object. If the polytope has been default constructed, it is invalid.
- Returns
- 'true' if the object is valid, 'false' otherwise.
◆ makeCellCover() [1/3]
template<typename TKSpace >
Builds the cell geometry containing all the j-cells touching the lattice polytope P, for i <= j <= k. It conbains thus all the j-cells intersecting the convex enveloppe of P.
- Parameters
-
| P | any lattice polytope such that P.canBeSummed() == true. |
| i | the first dimension for which the cell cover is computed. |
| k | the last dimension for which the cell cover is computed. |
◆ makeCellCover() [2/3]
template<typename TKSpace >
Builds the cell geometry containing all the j-cells touching the rational polytope P, for i <= j <= k. It conbains thus all the j-cells intersecting the convex enveloppe of P.
- Parameters
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| P | any rational polytope such that P.canBeSummed() == true. |
| i | the first dimension for which the cell cover is computed. |
| k | the last dimension for which the cell cover is computed. |
◆ makeCellCover() [3/3]
template<typename TKSpace >
template<typename PointIterator >
Builds the cell geometry containing all the j-cells touching a point of [itB,itE), for i <= j <= k.
- Template Parameters
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| PointIterator | any model of input iterator on Points. |
- Parameters
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| itB | start of a range of arbitrary points. |
| itE | past the end of a range of arbitrary points. |
| i | the first dimension for which the cell cover is computed. |
| k | the last dimension for which the cell cover is computed. |
Referenced by main().
◆ makeRationalSimplex() [1/2]
template<typename TKSpace >
template<typename PointIterator >
Constructs a rational polytope from a rational simplex given as a range [itB,itE) of lattice points. Note that the range must contain Space::dimension+1 points or less in general position.
- Template Parameters
-
| PointIterator | any model of forward iterator on Point. |
- Parameters
-
| d | the common denominator of all given lattice point coordinates. |
| itB | the start of the range of no more than n+1 points defining the simplex. |
| itE | past the end the range of no more than n+1 points defining the simplex. |
- Note
- If your range is
[itB,itE) = { (3,2), (1,7), (6,6) } and the denominator d = 4, then your polytope has vertices { (3/4,2/4), (1/4,7/4), (6/4,6/4) }.
◆ makeRationalSimplex() [2/2]
template<typename TKSpace >
Constructs a rational polytope from a simplex given as an initializer_list.
- Parameters
-
| l | any list where the first point give the denominator and then no more than d+1 points in general positions. |
- Note
- If your list is
l = { (4,x), (3,2), (1,7), (6,6) }, then the denominator is d = 4 and your polytope has vertices { (3/4,2/4), (1/4,7/4), (6/4,6/4) }.
◆ makeSimplex() [1/2]
template<typename TKSpace >
template<typename PointIterator >
Constructs a lattice polytope from a simplex given as a range [itB,itE) of lattice points. Note that the range must contain Space::dimension+1 points or less in general position.
- Template Parameters
-
| PointIterator | any model of forward iterator on Point. |
- Parameters
-
| itB | the start of the range of no more than n+1 points defining the simplex. |
| itE | past the end the range of no more than n+1 points defining the simplex. |
Referenced by main().
◆ makeSimplex() [2/2]
template<typename TKSpace >
Constructs a lattice polytope from a simplex given as an initializer_list.
- Parameters
-
| l | any list of no more than d+1 points in general positions. |
- Precondition
- Note that the list must contain no more than Space::dimension+1 points in general position.
◆ operator=()
template<typename TKSpace >
Assignment.
- Parameters
-
- Returns
- a reference on 'this'.
◆ selfDisplay()
template<typename TKSpace >
Writes/Displays the object on an output stream.
- Parameters
-
| out | the output stream where the object is written. |
◆ simplexType() [1/2]
template<typename TKSpace >
template<typename PointIterator >
Returns the type of simplex formed by the given range [itB,itE) of lattice points.
- Template Parameters
-
| PointIterator | any model of forward iterator on Point. |
- Parameters
-
| itB | the start of the range of n+1 points defining the simplex. |
| itE | past the end the range of n+1 points defining the simplex. |
- Returns
- the type of simplex formed by the given range [itB,itE) of lattice points.
◆ simplexType() [2/2]
template<typename TKSpace >
Returns the type of simplex formed by the given list l of lattice points.
- Parameters
-
| l | any list of lattice points. |
- Returns
- the type of simplex formed by the given list of lattice points.
◆ space()
template<typename TKSpace >
- Returns
- a const reference to the cellular grid space used by this object.
◆ dimension
template<typename TKSpace >
◆ myK
template<typename TKSpace >
The documentation for this class was generated from the following file:
