Regina Calculation Engine
Static Public Member Functions | Static Public Attributes | List of all members
regina::detail::FaceNumberingImpl< 4, 1, true > Class Template Reference
Inheritance diagram for regina::detail::FaceNumberingImpl< 4, 1, true >:
regina::detail::FaceNumberingAPI< 4, 1 >

Static Public Member Functions

static NPerm< 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 (NPerm< 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 const int edgeNumber [5][5]
 A table that maps vertices of a pentachoron to edge numbers. More...
 
static const int edgeVertex [10][2]
 A table that maps edges of a pentachoron to vertex numbers. More...
 
static constexpr int nFaces = 10
 The total number of edges in each pentachoron. More...
 

Member Function Documentation

§ containsVertex()

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()

static unsigned regina::detail::FaceNumberingAPI< dim, subdim >::faceNumber ( NPerm< 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()

static NPerm<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.

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

Copyright © 1999-2016, 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).