Regina Calculation Engine
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Details for implementing triangulations in arbitrary dimensions. More...
Classes | |
class | regina::BoundaryComponent< dim > |
A component of the boundary of a dim-manifold triangulation. More... | |
class | regina::Component< dim > |
A connected component of a dim-manifold triangulation. More... | |
class | regina::FaceEmbedding< dim, subdim > |
Details how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
class | regina::Face< dim, subdim > |
Represents a subdim-face in the skeleton of a dim-dimensional triangulation. More... | |
class | regina::FacetPairing< dim > |
Represents the dual graph of a dim-manifold triangulation; that is, the pairwise matching of facets of dim-dimensional simplices. More... | |
class | regina::Isomorphism< dim > |
Represents a combinatorial isomorphism from one dim-manifold triangulation into another. More... | |
class | regina::Face< dim, dim > |
Represents a top-dimensional simplex in a dim-manifold triangulation. More... | |
class | regina::FaceList< dim, subdim > |
Stores the list of all subdim-faces of a dim-dimensional triangulation. More... | |
class | regina::Triangulation< dim > |
A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets. More... | |
class | regina::DegreeLessThan< dim, subdim > |
A function object used for sorting faces of triangulations by increasing degree. More... | |
class | regina::DegreeGreaterThan< dim, subdim > |
A function object used for sorting faces of triangulations by decreasing degree. More... | |
Typedefs | |
template<int dim> | |
using | regina::VertexEmbedding = FaceEmbedding< dim, 0 > |
Details how a vertex of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
template<int dim> | |
using | regina::EdgeEmbedding = FaceEmbedding< dim, 1 > |
Details how a edge of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
template<int dim> | |
using | regina::TriangleEmbedding = FaceEmbedding< dim, 2 > |
Details how a triangular face of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
template<int dim> | |
using | regina::TetrahedronEmbedding = FaceEmbedding< dim, 3 > |
Details how a tetrahedral face of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
template<int dim> | |
using | regina::PentachoronEmbedding = FaceEmbedding< dim, 4 > |
Details how a pentachoron face of a dim-dimensional triangulation appears within each top-dimensional simplex. More... | |
template<int dim> | |
using | regina::Vertex = Face< dim, 0 > |
Refers to a vertex of a dim-dimensional triangulation. More... | |
template<int dim> | |
using | regina::Edge = Face< dim, 1 > |
Refers to an edge of a dim-dimensional triangulation. More... | |
template<int dim> | |
using | regina::Triangle = Face< dim, 2 > |
Refers to a triangular face of a dim-dimensional triangulation. More... | |
template<int dim> | |
using | regina::Tetrahedron = Face< dim, 3 > |
Refers to a tetrahedral face of a dim-dimensional triangulation. More... | |
template<int dim> | |
using | regina::Pentachoron = Face< dim, 4 > |
Refers to a pentachoron face of a dim-dimensional triangulation. More... | |
template<int dim> | |
using | regina::Simplex = Face< dim, dim > |
Refers to a top-dimensional simplex in a dim-dimensional triangulation. More... | |
typedef std::vector< Face< dim, subdim > * >::const_iterator | regina::FaceList< dim, subdim >::Iterator |
An iterator type for iterating through this list of faces. More... | |
Functions | |
size_t | regina::FaceList< dim, subdim >::size () const |
Returns the number of subdim-faces in the triangulation. More... | |
Face< dim, subdim > * | regina::FaceList< dim, subdim >::operator[] (size_t index) const |
Returns the requested subdim-face. More... | |
Iterator | regina::FaceList< dim, subdim >::begin () const |
Returns an iterator pointing to the first subdim-face. More... | |
Iterator | regina::FaceList< dim, subdim >::end () const |
Returns an iterator pointing beyond the last subdim-face. More... | |
regina::FaceList< dim, subdim >::FaceList (const FaceList &)=delete | |
FaceList & | regina::FaceList< dim, subdim >::operator= (const FaceList &)=delete |
regina::FaceList< dim, subdim >::FaceList ()=default | |
Creates an empty list of subdim-faces. More... | |
void | regina::FaceList< dim, subdim >::push_back (Face< dim, subdim > *face) |
Pushes the given face onto the end of this list. More... | |
void | regina::FaceList< dim, subdim >::destroy () |
Destroys all faces in this list, and clears the list itself. More... | |
void | regina::FaceList< dim, subdim >::swap (FaceList< dim, subdim > &other) |
Swaps all faces in this list with those in the given list. More... | |
bool | regina::FaceList< dim, subdim >::sameDegrees (const FaceList< dim, subdim > &other) const |
Tests whether this and the given triangulation have the same subdim-face degree sequences. More... | |
template<typename Iterator > | |
void | regina::FaceList< dim, subdim >::reorderFaces (Iterator begin, Iterator end) |
Reorders this list of faces. More... | |
Details for implementing triangulations in arbitrary dimensions.
using regina::Edge = typedef Face<dim, 1> |
Refers to an edge of a dim-dimensional triangulation.
This is the preferred way to refer to an edge of a triangulation (as opposed to the more clumsy notation Face<dim, 1>).
Edge5
).dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
using regina::EdgeEmbedding = typedef FaceEmbedding<dim, 1> |
Details how a edge of a dim-dimensional triangulation appears within each top-dimensional simplex.
This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 1>).
EdgeEmbedding5
).dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
typedef std::vector<Face<dim, subdim>*>::const_iterator regina::FaceList< dim, subdim >::Iterator |
An iterator type for iterating through this list of faces.
Dereferencing such an iterator will return a pointer of type Face<dim, subdim>*
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using regina::Pentachoron = typedef Face<dim, 4> |
Refers to a pentachoron face of a dim-dimensional triangulation.
This alias is also valid for the case dim = 4, where it refers to a top-dimensional simplex of a 4-dimensional triangulation.
This is the preferred way to refer to a 4-face of a triangulation (as opposed to the more clumsy notation Face<dim, 4>).
Pentachoron9
).dim | the dimension of the underlying triangulation. This must be between 4 and 15 inclusive. |
using regina::PentachoronEmbedding = typedef FaceEmbedding<dim, 4> |
Details how a pentachoron face of a dim-dimensional triangulation appears within each top-dimensional simplex.
This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 4>).
PentachoronEmbedding14
).dim | the dimension of the underlying triangulation. This must be between 5 and 15 inclusive. |
using regina::Simplex = typedef Face<dim, dim> |
Refers to a top-dimensional simplex in a dim-dimensional triangulation.
This is the preferred way to refer to a top-dimensional simplex (as opposed to the more clumsy notation Face<dim, dim>).
dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
using regina::Tetrahedron = typedef Face<dim, 3> |
Refers to a tetrahedral face of a dim-dimensional triangulation.
This alias is also valid for the case dim = 3, where it refers to a top-dimensional simplex of a 3-dimensional triangulation.
This is the preferred way to refer to a 3-face of a triangulation (as opposed to the more clumsy notation Face<dim, 3>).
Tetrahedron7
).dim | the dimension of the underlying triangulation. This must be between 3 and 15 inclusive. |
using regina::TetrahedronEmbedding = typedef FaceEmbedding<dim, 3> |
Details how a tetrahedral face of a dim-dimensional triangulation appears within each top-dimensional simplex.
This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 3>).
TetrahedronEmbedding7
).dim | the dimension of the underlying triangulation. This must be between 4 and 15 inclusive. |
using regina::Triangle = typedef Face<dim, 2> |
Refers to a triangular face of a dim-dimensional triangulation.
This alias is also valid for the case dim = 2, where it refers to a top-dimensional simplex of a 2-dimensional triangulation.
This is the preferred way to refer to a 2-face of a triangulation (as opposed to the more clumsy notation Face<dim, 2>).
Triangle4
).dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
using regina::TriangleEmbedding = typedef FaceEmbedding<dim, 2> |
Details how a triangular face of a dim-dimensional triangulation appears within each top-dimensional simplex.
This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 2>).
TriangleEmbedding12
).dim | the dimension of the underlying triangulation. This must be between 3 and 15 inclusive. |
using regina::Vertex = typedef Face<dim, 0> |
Refers to a vertex of a dim-dimensional triangulation.
This is the preferred way to refer to a vertex of a triangulation (as opposed to the more clumsy notation Face<dim, 0>).
Vertex8
).dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
using regina::VertexEmbedding = typedef FaceEmbedding<dim, 0> |
Details how a vertex of a dim-dimensional triangulation appears within each top-dimensional simplex.
This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 0>).
VertexEmbedding3
).dim | the dimension of the underlying triangulation. This must be between 2 and 15 inclusive. |
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Returns an iterator pointing to the first subdim-face.
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Destroys all faces in this list, and clears the list itself.
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Returns an iterator pointing beyond the last subdim-face.
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protecteddefault |
Creates an empty list of subdim-faces.
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inlineprotected |
Pushes the given face onto the end of this list.
This object will take ownership of the given face.
face | the face to push. |
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Reorders this list of faces.
The given range should contain exactly the faces in this list but in a (possibly) different order. This routine will then replace the items in this list with the given range, which will therefore just reorder them.
Note that the indices returned by Face<dim, subdim>::index() will change as a result.
Iterator | an input iterator type, whose dereference operator returns a pointer of type Face<dim, subdim>* . |
begin | an iterator that points to the beginning of the range of reordered faces. |
end | an iterator that points past the end of the range of reordered faces. |
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protected |
Tests whether this and the given triangulation have the same subdim-face degree sequences.
For the purposes of this routine, degree sequences are considered to be unordered.
other | the triangulation to compare against this. |
true
if and only if the degree sequences are equal.
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inline |
Returns the number of subdim-faces in the triangulation.
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inlineprotected |
Swaps all faces in this list with those in the given list.
other | the list of faces to swap with this. |