Regina Calculation Engine
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Details how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
#include <triangulation/generic.h>
Public Member Functions | |
FaceEmbedding ()=default | |
Default constructor. More... | |
FaceEmbedding (Simplex< dim > *simplex, int face) | |
Creates a new object containing the given data. More... | |
FaceEmbedding (const FaceEmbedding &cloneMe)=default | |
Creates a new copy of the given object. More... | |
FaceEmbedding & | operator= (const FaceEmbedding &cloneMe)=default |
Sets this to be a copy of the given object. More... | |
Simplex< dim > * | simplex () const |
Returns the top-dimensional simplex in which the underlying subdim-face of the triangulation is contained. More... | |
int | face () const |
Returns the corresponding face number of simplex(). More... | |
Perm< dim+1 > | vertices () const |
Maps vertices (0,...,subdim) of the underlying subdim-face of the triangulation to the corresponding vertex numbers of simplex(). More... | |
bool | operator== (const FaceEmbeddingBase &rhs) const |
Tests whether this and the given object are identical. More... | |
bool | operator!= (const FaceEmbeddingBase &rhs) const |
Tests whether this and the given object are different. More... | |
void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const |
A default implementation for detailed output. More... | |
std::string | str () const |
Returns a short text representation of this object. More... | |
std::string | utf8 () const |
Returns a short text representation of this object using unicode characters. More... | |
std::string | detail () const |
Returns a detailed text representation of this object. More... | |
Details how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex.
For small-dimensional faces, this class is typically described using dimension-specific type aliases: VertexEmbedding<dim>, EdgeEmbedding<dim>, TriangleEmbedding<dim>, TetrahedronEmbedding<dim> and PentachoronEmbedding<dim> refer to the cases subdim = 0, 1, 2, 3 and 4 respectively.
For a dim-dimensional triangulation T, each subdim-face F typically belongs to many top-dimensional simplices of T, and therefore has many associated FaceEmbedding objects. These individual FaceEmbedding objects correspond to the top-dimensional simplices of the link of F (which is a (dim - subdim - 1)-dimensional triangulation).
If dim is one of Regina's standard dimensions, then this template is specialised to offer additional dimension-specific aliases. In order to use these specialised classes, you will need to include the corresponding triangulation headers (e.g., triangulation/dim2.h for dim = 2, or triangulation/dim3.h for dim = 3).
dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
subdim | the dimension of the faces of the underlying triangulation. This must be between 0 and dim-1 inclusive. |
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inlineinherited |
A default implementation for detailed output.
This routine simply calls T::writeTextShort() and appends a final newline.
out | the output stream to which to write. |