Regina Calculation Engine
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Provides core functionality for combinatorial isomorphisms between dim-manifold triangulations.
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#include <triangulation/detail/isomorphism.h>
Public Member Functions | |
IsomorphismBase (unsigned nSimplices) | |
Creates a new isomorphism with no initialisation. More... | |
IsomorphismBase (const IsomorphismBase< dim > &src) | |
Creates a new copy of the given isomorphism. More... | |
IsomorphismBase (IsomorphismBase< dim > &&src) noexcept | |
Moves the given isomorphism into this new isomorphism. More... | |
~IsomorphismBase () | |
Destroys this isomorphism. More... | |
IsomorphismBase & | operator= (const IsomorphismBase &src) |
Copies the given isomorphism into this isomorphism. More... | |
IsomorphismBase & | operator= (IsomorphismBase &&src) noexcept |
Moves the given isomorphism into this isomorphism. More... | |
unsigned | size () 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< 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... | |
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... | |
FacetSpec< dim > | operator[] (const FacetSpec< 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< dim > * | apply (const Triangulation< dim > *original) const |
Applies this isomorphism to the given triangulation, and returns the result as a new triangulation. More... | |
void | applyInPlace (Triangulation< dim > *tri) const |
Applies this isomorphism to the given triangulation, modifying the given triangulation directly. 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 |
Writes a detailed text representation of this object to the given output stream. 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... | |
Static Public Member Functions | |
static Isomorphism< dim > | identity (unsigned nSimplices) |
Returns the identity isomorphism for the given number of simplices. More... | |
static Isomorphism< dim > | random (unsigned nSimplices, bool even=false) |
Returns a random isomorphism for the given number of simplices. More... | |
Protected Attributes | |
unsigned | nSimplices_ |
The number of simplices in the source triangulation. More... | |
int * | simpImage_ |
Stores the simplex of the destination triangulation that each simplex of the source triangulation maps to. More... | |
Perm< dim+1 > * | facetPerm_ |
The permutation applied to the facets of each source simplex. More... | |
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.
dim | the dimension of the triangulations that this isomorphism class works with. This must be between 2 and 15 inclusive. |
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inline |
Creates a new isomorphism with no initialisation.
The images of the simplices and their vertices must be explicitly set using simpImage() and facetPerm().
nSimplices | the number of simplices in the source triangulation associated with this isomorphism. This is allowed to be zero. |
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inline |
Creates a new copy of the given isomorphism.
This constructor induces a deep copy of src.
src | the isomorphism to copy. |
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inlinenoexcept |
Moves the given isomorphism into this new isomorphism.
This is a fast (constant time) operation.
The isomorphism that is passed (src) will no longer be usable.
src | the isomorphism to move. |
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inline |
Destroys this isomorphism.
Triangulation< dim > * regina::detail::IsomorphismBase< dim >::apply | ( | const Triangulation< dim > * | original | ) | const |
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.
original | the triangulation to which this isomorphism should be applied. |
void regina::detail::IsomorphismBase< dim >::applyInPlace | ( | Triangulation< dim > * | tri | ) | const |
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.
tri | the triangulation to which this isomorphism should be applied. |
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inherited |
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.
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inline |
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)
.
sourceSimp | the index of the source simplex containing the original (dim + 1) facets; this must be between 0 and size()-1 inclusive. |
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inline |
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)
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sourceSimp | the index of the source simplex containing the original (dim + 1) facets; this must be between 0 and size()-1 inclusive. |
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inlinestatic |
Returns the identity isomorphism for the given number of simplices.
This isomorphism sends every simplex and every vertex to itself.
nSimplices | the number of simplices that the new isomorphism should operate upon. |
bool regina::detail::IsomorphismBase< dim >::isIdentity | ( | ) | const |
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.
true
if this is an identity isomorphism, or false
otherwise. IsomorphismBase< dim > & regina::detail::IsomorphismBase< dim >::operator= | ( | const IsomorphismBase< dim > & | src | ) |
Copies the given isomorphism into this isomorphism.
It does not matter if this and the given isomorphism use different numbers of simplices; if they do then this isomorphism will be resized as a result.
This operator induces a deep copy of src.
src | the isomorphism to copy. |
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noexcept |
Moves the given isomorphism into this isomorphism.
This is a fast (constant time) operation.
It does not matter if this and the given isomorphism use different numbers of simplices; if they do then this isomorphism will be resized as a result.
The isomorphism that is passed (src) will no longer be usable.
src | the isomorphism to move. |
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inline |
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.
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. |
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static |
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.
All possible isomorphisms for the given number of simplices are equally likely.
This routine is thread-safe, and uses RandomEngine for its random number generation.
nSimplices | the number of simplices that the new isomorphism should operate upon. |
even | if true , then every simplex will have its vertices permuted with an even permutation. This means that, if the random isomorphism is applied to an oriented triangulation, it will preserve the orientation. |
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inline |
Determines the image of the given source simplex under this isomorphism.
sourceSimp | the index of the source simplex; this must be between 0 and size()-1 inclusive. |
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inline |
Determines the image of the given source simplex under this isomorphism.
sourceSimp | the index of the source simplex; this must be between 0 and size()-1 inclusive. |
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inline |
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.
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inherited |
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.
__str__()
.
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inherited |
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.
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inline |
Writes a detailed text representation of this object to the given output stream.
out | the output stream to which to write. |
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inline |
Writes a short text representation of this object to the given output stream.
out | the output stream to which to write. |
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protected |
The permutation applied to the facets of each source simplex.
This array has size nSimplices_.
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protected |
The number of simplices in the source triangulation.
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protected |
Stores the simplex of the destination triangulation that each simplex of the source triangulation maps to.
This array has size nSimplices_.