Regina Calculation Engine
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regina::NIsomorphism Class Reference

Represents a combinatorial isomorphism from one triangulation into another. More...

#include <triangulation/nisomorphism.h>

Inheritance diagram for regina::NIsomorphism:
regina::NGenericIsomorphism< 3 > regina::ShareableObject regina::boost::noncopyable regina::NIsomorphismDirect

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...
 
NPerm4facePerm (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...
 
- Public Member Functions inherited from regina::NGenericIsomorphism< 3 >
 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...
 
PermfacetPerm (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...
 
Triangulationapply (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...
 
- Public Member Functions inherited from regina::ShareableObject
 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

- Public Types inherited from regina::NGenericIsomorphism< 3 >
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 Public Member Functions inherited from regina::NGenericIsomorphism< 3 >
static Isomorphismrandom (unsigned nSimplices)
 Returns a random isomorphism for the given number of simplices. More...
 
- Protected Member Functions inherited from regina::boost::noncopyable
 noncopyable ()
 A constructor which does nothing. More...
 
 ~noncopyable ()
 A destructor which does nothing. More...
 
- Protected Attributes inherited from regina::NGenericIsomorphism< 3 >
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...
 
PermfacetPerm_
 The permutation applied to the facets of each source simplex. More...
 

Detailed Description

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.

Test:
Included in the test suite.
Todo:
Feature: Composition of isomorphisms.

Constructor & Destructor Documentation

regina::NIsomorphism::NIsomorphism ( unsigned  sourceTetrahedra)
inline

Creates a new isomorphism with no initialisation.

Python:
Not present.
Parameters
sourceTetrahedrathe number of tetrahedra in the source triangulation associated with this isomorphism; this may be zero.
regina::NIsomorphism::NIsomorphism ( const NIsomorphism cloneMe)
inline

Creates a new isomorphism identical to the given isomorphism.

Parameters
cloneMethe isomorphism upon which to base the new isomorphism.

Member Function Documentation

NPerm4 & regina::NIsomorphism::facePerm ( unsigned  sourceTet)
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().

Python:
Not present, though the read-only version of this routine is.
Parameters
sourceTetthe index of the source tetrahedron containing the original four faces; this must be between 0 and getSourceSimplices()-1 inclusive.
Returns
a read-write reference to the permutation applied to the four faces of the source tetrahedron.
NPerm4 regina::NIsomorphism::facePerm ( unsigned  sourceTet) const
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().

Parameters
sourceTetthe index of the source tetrahedron containing the original four faces; this must be between 0 and getSourceSimplices()-1 inclusive.
Returns
the permutation applied to the four faces of the source tetrahedron.
unsigned regina::NIsomorphism::getSourceTetrahedra ( ) const
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().

Returns
the number of tetrahedra in the source triangulation.
int & regina::NIsomorphism::tetImage ( unsigned  sourceTet)
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().

Python:
Not present, though the read-only version of this routine is.
Parameters
sourceTetthe index of the source tetrahedron; this must be between 0 and getSourceSimplices()-1 inclusive.
Returns
a reference to the index of the destination tetrahedron that the source tetrahedron maps to.
int regina::NIsomorphism::tetImage ( unsigned  sourceTet) const
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().

Parameters
sourceTetthe index of the source tetrahedron; this must be between 0 and getSourceSimplices()-1 inclusive.
Returns
the index of the destination tetrahedron that the source tetrahedron maps to.

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

Copyright © 1999-2013, 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@debian.org).