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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...
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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...
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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...
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static const int | edgeNumber [5][5] |
| A table that maps vertices of a pentachoron to edge numbers. More...
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static const int | edgeVertex [10][2] |
| A table that maps edges of a pentachoron to vertex numbers. More...
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static constexpr int | nFaces = 10 |
| The total number of edges in each pentachoron. More...
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◆ containsVertex()
Tests whether the given subdim-face of a dim-dimensional simplex contains the given vertex of the simplex.
- Parameters
-
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. |
- Returns
true
if and only if the given subdim-face contains the given vertex.
◆ faceNumber()
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
-
vertices | a 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()
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
-
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. |
- Returns
- the corresponding canonical ordering of the simplex vertices.
◆ edgeNumber
A table that maps vertices of a pentachoron to edge numbers.
Edges in a pentachoron are numbered 0,...,9. This table converts vertices to edge numbers; in particular, the edge joining vertices i and j of a pentachoron is edge number edgeNumber[i][j]
. Here i and j must be distinct, must be between 0 and 4 inclusive, and may be given in any order. The resulting edge number will be between 0 and 9 inclusive.
- Note
- Accessing
edgeNumber[i][j]
is equivalent to calling faceNumber(p)
, where p is a permutation that maps 0,1 to i,j in some order.
◆ edgeVertex
A table that maps edges of a pentachoron to vertex numbers.
Edges in a pentachoron are numbered 0,...,9. This table converts edge numbers to vertices; in particular, edge i in a pentachoron joins vertices edgeVertex[i][0]
and edgeVertex[i][1]
. Here i must be between 0 and 9 inclusive; the resulting vertex numbers will be between 0 and 4 inclusive.
It is guaranteed that edgeVertex[i][0]
will always be smaller than edgeVertex[i][1]
.
- Note
- Accessing
edgeVertex[i][j]
is equivalent to calling ordering(i)[j]
.
◆ nFaces
The total number of edges in each pentachoron.
The documentation for this class was generated from the following file: