Regina Calculation Engine
|
Represents a combinatorial isomorphism from one triangulation into another. More...
#include <triangulation/nisomorphism.h>
Public Member Functions | |
NIsomorphism (unsigned sourceTetrahedra) | |
Creates a new isomorphism with no initialisation. More... | |
NIsomorphism (const NIsomorphism &cloneMe) | |
Creates a new isomorphism identical to the given isomorphism. More... | |
unsigned | getSourceTetrahedra () const |
Returns the number of tetrahedra in the source triangulation associated with this isomorphism. More... | |
int & | tetImage (unsigned sourceTet) |
Determines the image of the given source tetrahedron under this isomorphism. More... | |
int | tetImage (unsigned sourceTet) const |
Determines the image of the given source tetrahedron under this isomorphism. More... | |
NPerm4 & | facePerm (unsigned sourceTet) |
Returns a read-write reference to the permutation that is applied to the four faces of the given source tetrahedron under this isomorphism. More... | |
NPerm4 | facePerm (unsigned sourceTet) const |
Determines the permutation that is applied to the four faces of the given source tetrahedron under this isomorphism. More... | |
![]() | |
NGenericIsomorphism (unsigned nSimplices) | |
Creates a new isomorphism with no initialisation. More... | |
NGenericIsomorphism (const NGenericIsomorphism &cloneMe) | |
Creates a new isomorphism identical to the given isomorphism. More... | |
~NGenericIsomorphism () | |
Destroys this isomorphism. More... | |
unsigned | getSourceSimplices () const |
Returns the number of simplices in the source triangulation associated with this isomorphism. More... | |
int & | simpImage (unsigned sourceSimp) |
Determines the image of the given source simplex under this isomorphism. More... | |
int | simpImage (unsigned sourceSimp) const |
Determines the image of the given source simplex under this isomorphism. More... | |
Perm & | facetPerm (unsigned sourceSimp) |
Returns a read-write reference to the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism. More... | |
Perm | facetPerm (unsigned sourceSimp) const |
Determines the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism. More... | |
NFacetSpec< dim > | operator[] (const NFacetSpec< dim > &source) const |
Determines the image of the given source simplex facet under this isomorphism. More... | |
bool | isIdentity () const |
Determines whether or not this is an identity isomorphism. More... | |
Triangulation * | apply (const Triangulation *original) const |
This NGenericIsomorphism object represents a combinatorial identification from a triangulation T to a triangulation U. More... | |
void | applyInPlace (Triangulation *tri) const |
Applies this isomorphism to the given triangulation, modifying the given triangulation directly. More... | |
void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
![]() | |
ShareableObject () | |
Default constructor that does nothing. More... | |
virtual | ~ShareableObject () |
Default destructor that does nothing. More... | |
std::string | str () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toString () const |
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More... | |
std::string | detail () const |
Returns the output from writeTextLong() as a string. More... | |
std::string | toStringLong () const |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More... | |
Additional Inherited Members | |
![]() | |
typedef DimTraits< dim > ::Isomorphism | Isomorphism |
The isomorphism class used by triangulations of this specific dimension. More... | |
typedef DimTraits< dim >::Perm | Perm |
The permutation class used to glue together facets of simplices when building triangulations in this dimension. More... | |
typedef DimTraits< dim >::Simplex | Simplex |
The class that represents a top-level simplex of a triangulation in this dimension. More... | |
typedef DimTraits< dim > ::Triangulation | Triangulation |
The triangulation class specific to this dimension. More... | |
![]() | |
static Isomorphism * | random (unsigned nSimplices) |
Returns a random isomorphism for the given number of simplices. More... | |
![]() | |
noncopyable () | |
A constructor which does nothing. More... | |
~noncopyable () | |
A destructor which does nothing. More... | |
![]() | |
unsigned | nSimplices_ |
The number of simplices in the source triangulation. More... | |
int * | simpImage_ |
The simplex of the destination triangulation that each simplex of the source triangulation maps to. More... | |
Perm * | facetPerm_ |
The permutation applied to the facets of each source simplex. More... | |
Represents a combinatorial isomorphism from one triangulation into another.
In essence, a combinatorial isomorphism from triangulation T to triangulation U is a one-to-one map from the tetrahedra of T to the tetrahedra of U that allows relabelling of both the tetrahedra and their faces (or equivalently, their vertices), and that preserves gluings across adjacent tetrahedra.
More precisely: An isomorphism consists of (i) a one-to-one map f from the tetrahedra of T to the tetrahedra of U, and (ii) for each tetrahedron S of T, a permutation f_S of the faces (0,1,2,3) of S, for which the following condition holds:
Isomorphisms can be boundary complete or boundary incomplete. A boundary complete isomorphism satisfies the additional condition:
A boundary complete isomorphism thus indicates that a copy of triangulation T is present as an entire component (or components) of U, whereas a boundary incomplete isomorphism represents an embedding of a copy of triangulation T as a subcomplex of some possibly larger component (or components) of U.
Note that in all cases triangulation U may contain more tetrahedra than triangulation T.
|
inline |
Creates a new isomorphism with no initialisation.
sourceTetrahedra | the number of tetrahedra in the source triangulation associated with this isomorphism; this may be zero. |
|
inline |
Creates a new isomorphism identical to the given isomorphism.
cloneMe | the isomorphism upon which to base the new isomorphism. |
|
inline |
Returns a read-write reference to the permutation that is applied to the four faces of the given source tetrahedron under this isomorphism.
Face i of source tetrahedron sourceTet will be mapped to face facePerm(sourceTet)[i]
of tetrahedron tetImage(sourceTet)
.
This is a convenience routine specific to three dimensions, and is identical to the dimension-agnostic routine facetPerm().
sourceTet | the index of the source tetrahedron containing the original four faces; this must be between 0 and getSourceSimplices()-1 inclusive. |
|
inline |
Determines the permutation that is applied to the four faces of the given source tetrahedron under this isomorphism.
Face i of source tetrahedron sourceTet will be mapped to face facePerm(sourceTet)[i]
of tetrahedron tetImage(sourceTet)
.
This is a convenience routine specific to three dimensions, and is identical to the dimension-agnostic routine facetPerm().
sourceTet | the index of the source tetrahedron containing the original four faces; this must be between 0 and getSourceSimplices()-1 inclusive. |
|
inline |
Returns the number of tetrahedra in the source triangulation associated with this isomorphism.
Note that this is always less than or equal to the number of tetrahedra in the destination triangulation.
This is a convenience routine specific to three dimensions, and is identical to the dimension-agnostic routine getSourceSimplices().
|
inline |
Determines the image of the given source tetrahedron under this isomorphism.
This is a convenience routine specific to three dimensions, and is identical to the dimension-agnostic routine simpImage().
sourceTet | the index of the source tetrahedron; this must be between 0 and getSourceSimplices()-1 inclusive. |
|
inline |
Determines the image of the given source tetrahedron under this isomorphism.
This is a convenience routine specific to three dimensions, and is identical to the dimension-agnostic routine simpImage().
sourceTet | the index of the source tetrahedron; this must be between 0 and getSourceSimplices()-1 inclusive. |