Regina Calculation Engine
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Specifies how subdim-faces are numbered within a dim-dimensional simplex.
More...
#include <triangulation/facenumbering.h>
Static Public Member Functions | |
static Perm< dim+1 > | ordering (unsigned face) |
Given a subdim-face number within a dim-dimensional simplex, returns the corresponding canonical ordering of the simplex vertices. More... | |
static unsigned | faceNumber (Perm< dim+1 > vertices) |
Identifies which subdim-face in a dim-dimensional simplex is represented by the first (subdim + 1) elements of the given permutation. More... | |
static bool | containsVertex (unsigned face, unsigned vertex) |
Tests whether the given subdim-face of a dim-dimensional simplex contains the given vertex of the simplex. More... | |
Static Public Attributes | |
static constexpr int | nFaces |
The total number of subdim-dimensional faces in each dim-dimensional simplex. More... | |
Specifies how subdim-faces are numbered within a dim-dimensional simplex.
Regina uses the following general scheme for numbering faces:
Every class Face<dim, subdim> inherits from this class, which means you can access these routines as Face<dim, subdim>::ordering(), Face<dim, subdim>::faceNumber(), and so on.
An advantage of referring to FaceNumbering<dim, subdim> directly (as opposed to Face<dim, subdim>) is that its header is lightweight: it does not pull in the large and complex headers required by Face<dim, subdim>.
This class is specialised (and optimised) in Regina's standard dimensions.
dim | the dimension of the simplex whose faces we are numbering. This must be between 1 and 15 inclusive. |
subdim | the dimension of the faces that we are numbering. This must be between 0 and dim-1 inclusive. |
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staticinherited |
Tests whether the given subdim-face of a dim-dimensional simplex contains the given vertex of the simplex.
face | a subdim-face number in a dim-simplex; this must be between 0 and (dim+1 choose subdim+1)-1 inclusive. |
vertex | a vertex number in a dim-simplex; this must be between 0 and dim inclusive. |
true
if and only if the given subdim-face contains the given vertex.
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staticinherited |
Identifies which subdim-face in a dim-dimensional simplex is represented by the first (subdim + 1) elements of the given permutation.
In other words, this routine identifies which subdim-face number within a dim-dimensional simplex spans vertices vertices[0, ..., subdim]
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vertices | a permutation whose first (subdim + 1) elements represent some vertex numbers in a dim-simplex. |
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staticinherited |
Given a subdim-face number within a dim-dimensional simplex, returns the corresponding canonical ordering of the simplex vertices.
If this canonical ordering is c, then c[0,...,subdim] will be the vertices of the given face in increasing numerical order. That is, c[0] < ... < c[subdim]. The remaining images c[(subdim + 1),...,dim] will be ordered arbitrarily.
Note that this is not the same permutation as returned by Simplex<dim>::faceMapping<subdim>():
face | identifies which subdim-face of a dim-dimensional simplex to query. This must be between 0 and (dim+1 choose subdim+1)-1 inclusive. |
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staticinherited |
The total number of subdim-dimensional faces in each dim-dimensional simplex.