3-Manifold Triangulations

Details for implementing triangulations of 3-manifolds. More...

## Classes

class | regina::BoundaryComponent< 3 >
| A component of the boundary of a 3-manifold triangulation. More...
class | regina::Component< 3 >
| Represents a connected component of a 3-manifold triangulation. More...
class | regina::Face< 3, 3 >
| Represents a tetrahedron within a 3-manifold triangulation. More...
class | regina::Face< 3, 2 >
| Represents a triangle in the skeleton of a 3-manifold triangulation. More...
class | regina::Triangulation< 3 >
| Represents a 3-dimensional triangulation, typically of a 3-manifold. More...
class | regina::Face< 3, 0 >
| Represents a vertex in the skeleton of a 3-manifold triangulation. More...

## Typedefs

typedef BoundaryComponent< 3 > | regina::NBoundaryComponent
| Deprecated typedef for backward compatibility. More...
typedef Component< 3 > | regina::NComponent
| Deprecated typedef for backward compatibility. More...
typedef Simplex< 3 > | regina::NTetrahedron
| Deprecated typedef for backward compatibility. More...
typedef FaceEmbedding< 3, 2 > | regina::NTriangleEmbedding
| Deprecated typedef for backward compatibility. More...
typedef Face< 3, 2 > | regina::NTriangle
| Deprecated typedef for backward compatibility. More...
typedef Triangulation< 3 > | regina::NTriangulation
| Deprecated typedef for backward compatibility. More...
typedef FaceEmbedding< 3, 1 > | regina::NEdgeEmbedding
| Deprecated typedef for backward compatibility. More...
typedef Face< 3, 1 > | regina::NEdge
| Deprecated typedef for backward compatibility. More...
typedef FaceEmbedding< 3, 0 > | regina::NVertexEmbedding
| Deprecated typedef for backward compatibility. More...
typedef Face< 3, 0 > | regina::NVertex
| Deprecated typedef for backward compatibility. More...

## Enumerations

enum | regina::TuraevViroAlg { regina::TV_DEFAULT = 0, regina::TV_BACKTRACK = 1, regina::TV_TREEWIDTH = 2, regina::TV_NAIVE = 3 }
| Represents the various algorithms available for computing Turaev-Viro invariants. More...

## Detailed Description

Details for implementing triangulations of 3-manifolds.

## Typedef Documentation

## NBoundaryComponent

typedef BoundaryComponent<3> regina::NBoundaryComponent

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NBoundaryComponent, you should use the real class name BoundaryComponent<3>.

## NComponent

typedef Component<3> regina::NComponent

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NComponent, you should use the real class name Component<3>.

## NEdge

typedef Face<3, 1> regina::NEdge

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NEdge, you should use either the new alias Edge<3>, or the full class name Face<3, 1>.

## NEdgeEmbedding

typedef FaceEmbedding<3, 1> regina::NEdgeEmbedding

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NEdgeEmbedding, you should use either the new alias EdgeEmbedding<3>, or the full class name FaceEmbedding<3, 1>.

## NTetrahedron

typedef Simplex<3> regina::NTetrahedron

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NTetrahedron, you should use the new alias Simplex<3> (or, if you prefer, the full class name Face<3, 3>).

## NTriangle

typedef Face<3, 2> regina::NTriangle

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NTriangle, you should use either the new alias Triangle<3>, or the full class name Face<3, 2>.

## NTriangleEmbedding

typedef FaceEmbedding<3, 2> regina::NTriangleEmbedding

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NTriangleEmbedding, you should use either the new alias TriangleEmbedding<3>, or the full class name FaceEmbedding<3, 2>.

## NTriangulation

typedef Triangulation<3> regina::NTriangulation

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NTriangulation, you should use the templated class name Triangulation<3>.

## NVertex

typedef Face<3, 0> regina::NVertex

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NVertex, you should use either the new alias Vertex<3>, or the full class name Face<3, 0>.

## NVertexEmbedding

typedef FaceEmbedding<3, 0> regina::NVertexEmbedding

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
  Instead of the old typedef NVertexEmbedding, you should use either the new alias VertexEmbedding<3>, or the full class name FaceEmbedding<3, 0>.

## Enumeration Type Documentation

## TuraevViroAlg

enum regina::TuraevViroAlg

Represents the various algorithms available for computing Turaev-Viro invariants.

Enumerator
TV_DEFAULT | The default algorithm. Here Regina will choose whichever algorithm it thinks (rightly or wrongly) is most appropriate.
TV_BACKTRACK | An optimised backtracking algorithm. This enumerates edge colourings and sums their corresponding weights. This can be slow in general (since there could be exponentially many edge colourings), but it has very small memory usage.
TV_TREEWIDTH | A treewidth-based algorithm. This uses dynamic programming over a tree decomposition of the face pairing graph. This can be fast for triangulations whose face pairing graphs have small treewidth, but it may require extremely large amounts of memory.

TV_NAIVE

An unoptimised backtracking algorithm.

Like TV_BACKTRACK, this enumerates edge colourings and sums weights. However, the implementation is more naive.

Warning
  This algorithm should only be used for comparison and experimentation. Due to its slow performance, it is not suitable for "real" applications.

Copyright © 1999-2016, 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@maths.uq.edu.au).