Provides core functionality for combinatorial isomorphisms between dim-manifold triangulations.
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#include <triangulation/detail/isomorphism.h>
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| IsomorphismBase (unsigned nSimplices) |
| Creates a new isomorphism with no initialisation. More...
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| IsomorphismBase (const IsomorphismBase< dim > ©) |
| Creates a new copy of the given isomorphism. More...
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| ~IsomorphismBase () |
| Destroys this isomorphism. More...
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unsigned | size () const |
| Returns the number of simplices in the source triangulation associated with this isomorphism. More...
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int & | simpImage (unsigned sourceSimp) |
| Determines the image of the given source simplex under this isomorphism. More...
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int | simpImage (unsigned sourceSimp) const |
| Determines the image of the given source simplex under this isomorphism. More...
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Perm< dim+1 > & | 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...
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Perm< dim+1 > | facetPerm (unsigned sourceSimp) const |
| Determines the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism. More...
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FacetSpec< dim > | operator[] (const FacetSpec< dim > &source) const |
| Determines the image of the given source simplex facet under this isomorphism. More...
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bool | isIdentity () const |
| Determines whether or not this is an identity isomorphism. More...
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Triangulation< dim > * | apply (const Triangulation< dim > *original) const |
| Applies this isomorphism to the given triangulation, and returns the result as a new triangulation. More...
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void | applyInPlace (Triangulation< dim > *tri) const |
| Applies this isomorphism to the given triangulation, modifying the given triangulation directly. More...
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void | writeTextShort (std::ostream &out) const |
| Writes a short text representation of this object to the given output stream. More...
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void | writeTextLong (std::ostream &out) const |
| Writes a detailed text representation of this object to the given output stream. More...
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std::string | str () const |
| Returns a short text representation of this object. More...
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std::string | utf8 () const |
| Returns a short text representation of this object using unicode characters. More...
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std::string | detail () const |
| Returns a detailed text representation of this object. More...
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unsigned | nSimplices_ |
| The number of simplices in the source triangulation. More...
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int * | simpImage_ |
| Stores the simplex of the destination triangulation that each simplex of the source triangulation maps to. More...
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Perm< dim+1 > * | facetPerm_ |
| The permutation applied to the facets of each source simplex. More...
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template<int dim>
class regina::detail::IsomorphismBase< dim >
Provides core functionality for combinatorial isomorphisms between dim-manifold triangulations.
Such an isomorphism is represented by the class Isomorphism<dim>, which uses this as a base class. End users should not need to refer to IsomorphismBase directly.
See the Isomorphism class notes for further information.
- Python:
- This base class is not present, but the "end user" class Isomorphism<dim> is.
- Template Parameters
-
dim | the dimension of the triangulations that this isomorphism class works with. This must be between 2 and 15 inclusive. |
§ IsomorphismBase() [1/2]
Creates a new isomorphism with no initialisation.
The images of the simplices and their vertices must be explicitly set using simpImage() and facetPerm().
- Parameters
-
nSimplices | the number of simplices in the source triangulation associated with this isomorphism. This is allowed to be zero. |
§ IsomorphismBase() [2/2]
Creates a new copy of the given isomorphism.
- Parameters
-
copy | the isomorphism to copy. |
§ ~IsomorphismBase()
Destroys this isomorphism.
§ apply()
Applies this isomorphism to the given triangulation, and returns the result as a new triangulation.
An isomorphism represents a combinatorial map from a triangulation T to a triangulation U. This routine treats the given triangulation as the domain T, and returns the corresponding range U. The given triangulation T is not modified in any way.
In more detail: A new triangulation U is returned, so that this isomorphism represents a one-to-one, onto and boundary complete isomorphism from T to U. That is, T and U will be combinatorially identical triangulations, and this isomorphism describes the mapping from the simplices of T and their facets to the simplices of U and their facets.
The resulting triangulation U is newly created, and must be destroyed by the caller of this routine.
There are several preconditions to this routine. This routine does a small amount of sanity checking (and returns 0 if an error is detected), but it certainly does not check the full set of preconditions. It is up to the caller of this routine to verify that all of the following preconditions are met.
- Precondition
- The number of simplices in the given triangulation is precisely the number returned by size() for this isomorphism.
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The simplex images are precisely 0,1,...,size()-1 in some order (i.e., this isomorphism does not represent a mapping from a smaller triangulation into a larger triangulation).
- Parameters
-
original | the triangulation to which this isomorphism should be applied. |
- Returns
- the new isomorphic triangulation, or 0 if a problem was encountered (i.e., an unmet precondition was noticed).
§ applyInPlace()
Applies this isomorphism to the given triangulation, modifying the given triangulation directly.
This is similar to apply(), except that instead of creating a new triangulation, the simplices and vertices of the given triangulation are modified in-place.
See apply() for further details on how this operation is performed.
As with apply(), there are several preconditions to this routine. This routine does a small amount of sanity checking (and returns without changes if an error is detected), but it certainly does not check the full set of preconditions. It is up to the caller of this routine to verify that all of the following preconditions are met.
- Precondition
- The number of simplices in the given triangulation is precisely the number returned by size() for this isomorphism.
-
The simplex images are precisely 0,1,...,size()-1 in some order (i.e., this isomorphism does not represent a mapping from a smaller triangulation into a larger triangulation).
- Parameters
-
tri | the triangulation to which this isomorphism should be applied. |
§ detail()
Returns a detailed text representation of this object.
This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.
- Returns
- a detailed text representation of this object.
§ facetPerm() [1/2]
Returns a read-write reference to the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism.
Facet i of source simplex sourceSimp will be mapped to facet facetPerm(sourceSimp)[i]
of simplex simpImage(sourceSimp)
.
- Python:
- This is not available for Python users. However, the read-only version of this routine is.
- Parameters
-
sourceSimp | the index of the source simplex containing the original (dim + 1) facets; this must be between 0 and size()-1 inclusive. |
- Returns
- a read-write reference to the permutation applied to the facets of the source simplex.
§ facetPerm() [2/2]
Determines the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism.
Facet i of source simplex sourceSimp will be mapped to face facetPerm(sourceSimp)[i]
of simplex simpImage(sourceSimp)
.
- Parameters
-
sourceSimp | the index of the source simplex containing the original (dim + 1) facets; this must be between 0 and size()-1 inclusive. |
- Returns
- the permutation applied to the facets of the source simplex.
§ identity()
Returns the identity isomorphism for the given number of simplices.
This isomorphism sends every simplex and every vertex to itself.
The isomorphism will be newly constructed, and must be destroyed by the caller of this routine.
- Parameters
-
nSimplices | the number of simplices that the new isomorphism should operate upon. |
- Returns
- the newly constructed identity isomorphism.
§ isIdentity()
Determines whether or not this is an identity isomorphism.
In an identity isomorphism, each simplex image is itself, and within each simplex the facet/vertex permutation is the identity permutation.
- Returns
true
if this is an identity isomorphism, or false
otherwise.
§ operator[]()
Determines the image of the given source simplex facet under this isomorphism.
This operator returns by value: it cannot be used to alter the isomorphism.
- Parameters
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source | the given source simplex facet; this must be one of the (dim + 1) facets of one of the size() simplices in the source triangulation. |
- Returns
- the image of the source simplex facet under this isomorphism.
§ random()
Returns a random isomorphism for the given number of simplices.
This isomorphism will reorder simplices 0 to nSimplices-1
in a random fashion, and for each simplex a random permutation of its (dim + 1) vertices will be selected.
The isomorphism will be newly constructed, and must be destroyed by the caller of this routine.
Note that both the STL random number generator and the standard C function rand() are used in this routine. All possible isomorphisms for the given number of simplices are equally likely.
- Parameters
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nSimplices | the number of simplices that the new isomorphism should operate upon. |
- Returns
- the newly constructed random isomorphism.
§ simpImage() [1/2]
Determines the image of the given source simplex under this isomorphism.
- Python:
- This is not available for Python users. However, the read-only version of this routine is.
- Parameters
-
sourceSimp | the index of the source simplex; this must be between 0 and size()-1 inclusive. |
- Returns
- a reference to the index of the destination simplex that the source simplex maps to.
§ simpImage() [2/2]
Determines the image of the given source simplex under this isomorphism.
- Parameters
-
sourceSimp | the index of the source simplex; this must be between 0 and size()-1 inclusive. |
- Returns
- the index of the destination simplex that the source simplex maps to.
§ size()
Returns the number of simplices in the source triangulation associated with this isomorphism.
Note that this is always less than or equal to the number of simplices in the destination triangulation.
- Returns
- the number of simplices in the source triangulation.
§ str()
Returns a short text representation of this object.
This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
- Python:
- In addition to str(), this is also used as the Python "stringification" function
__str__()
.
- Returns
- a short text representation of this object.
§ utf8()
Returns a short text representation of this object using unicode characters.
Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.
- Returns
- a short text representation of this object.
§ writeTextLong()
Writes a detailed text representation of this object to the given output stream.
- Python:
- Not present.
- Parameters
-
out | the output stream to which to write. |
§ writeTextShort()
Writes a short text representation of this object to the given output stream.
- Python:
- Not present.
- Parameters
-
out | the output stream to which to write. |
§ facetPerm_
The permutation applied to the facets of each source simplex.
This array has size nSimplices_.
§ nSimplices_
The number of simplices in the source triangulation.
§ simpImage_
Stores the simplex of the destination triangulation that each simplex of the source triangulation maps to.
This array has size nSimplices_.
The documentation for this class was generated from the following file: