Regina Calculation Engine
Static Public Member Functions | Static Public Attributes | List of all members
regina::FaceNumbering< dim, subdim > Class Template Reference


Specifies how subdim-faces are numbered within a dim-dimensional simplex. More...

#include <triangulation/facenumbering.h>

Inheritance diagram for regina::FaceNumbering< dim, subdim >:
regina::detail::FaceNumberingImpl< dim, subdim,((dim+1) >=2 *(subdim+1))> regina::detail::FaceNumberingAPI< dim, subdim > regina::detail::FaceBase< 3, 0 > regina::detail::FaceBase< 3, 2 > regina::detail::FaceBase< 4, 0 > regina::detail::FaceBase< 4, 1 > regina::detail::FaceBase< dim, subdim > regina::Face< 3, 0 > regina::Face< 3, 2 > regina::Face< 4, 0 > regina::Face< 4, 1 > regina::Face< 3 > regina::Face< dim, dim-1 > regina::Face< tridim, subdim > regina::Face< dim, subdim >

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...
 

Detailed Description

template<int dim, int subdim>
class regina::FaceNumbering< dim, subdim >


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.

Python
This class is not available in Python. However, all of its routines can be accessed through Face<dim, subdim> (which in Python becomes Facedim_subdim, or one of the type aliases such as Vertex3, Edge2 and so on).
Template Parameters
dimthe dimension of the simplex whose faces we are numbering. This must be between 1 and 15 inclusive.
subdimthe dimension of the faces that we are numbering. This must be between 0 and dim-1 inclusive.

Member Function Documentation

◆ containsVertex()

template<int dim, int subdim>
static bool regina::detail::FaceNumberingAPI< dim, subdim >::containsVertex ( unsigned  face,
unsigned  vertex 
)
staticinherited

Tests whether the given subdim-face of a dim-dimensional simplex contains the given vertex of the simplex.

Parameters
facea subdim-face number in a dim-simplex; this must be between 0 and (dim+1 choose subdim+1)-1 inclusive.
vertexa vertex number in a dim-simplex; this must be between 0 and dim inclusive.
Returns
true if and only if the given subdim-face contains the given vertex.

◆ faceNumber()

template<int dim, int subdim>
static unsigned regina::detail::FaceNumberingAPI< dim, subdim >::faceNumber ( Perm< dim+1 >  vertices)
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].

Parameters
verticesa permutation whose first (subdim + 1) elements represent some vertex numbers in a dim-simplex.
Returns
the corresponding subdim-face number in the dim-simplex. This will be between 0 and (dim+1 choose subdim+1)-1 inclusive.

◆ ordering()

template<int dim, int subdim>
static Perm<dim + 1> regina::detail::FaceNumberingAPI< dim, subdim >::ordering ( unsigned  face)
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>():

  • ordering() is a static function, which returns the same permutation for the same face number, regardless of which dim-simplex we are looking at. The images of 0,...,subdim will always appear in increasing order, and the images of (subdim + 1),...,dim will be arbitrary.
  • faceMapping() examines the underlying face F of the triangulation and, across all appearances of F in different dim-simplices: (i) chooses the images of 0,...,subdim to map to the same respective vertices of F; and (ii) chooses the images of (subdim + 1),...,dim to maintain a "consistent orientation" constraint.
Parameters
faceidentifies which subdim-face of a dim-dimensional simplex to query. This must be between 0 and (dim+1 choose subdim+1)-1 inclusive.
Returns
the corresponding canonical ordering of the simplex vertices.

Member Data Documentation

◆ nFaces

constexpr int regina::detail::FaceNumberingImpl< dim, subdim, lex >::nFaces
staticinherited

The total number of subdim-dimensional faces in each dim-dimensional simplex.


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

Copyright © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).