Regina Calculation Engine
Static Public Member Functions | List of all members
regina::Example< 2 > Class Reference

Offers routines for constructing a variety of sample 2-dimensional triangulations. More...

#include <triangulation/example2.h>

Inheritance diagram for regina::Example< 2 >:
regina::detail::ExampleBase< 2 >

Static Public Member Functions

static Triangulation< 2 > * orientable (unsigned genus, unsigned punctures)
 Returns a triangulation of the given orientable surface. More...
 
static Triangulation< 2 > * nonOrientable (unsigned genus, unsigned punctures)
 Returns a triangulation of the given non-orientable surface. More...
 
static Triangulation< 2 > * sphereTetrahedron ()
 Returns the four-triangle 2-sphere formed from the boundary of a tetrahedron. More...
 
static Triangulation< 2 > * sphereOctahedron ()
 Returns the eight-triangle 2-sphere formed from the boundary of an octahedron. More...
 
static Triangulation< 2 > * disc ()
 Returns a one-triangle disc. More...
 
static Triangulation< 2 > * annulus ()
 Returns a two-triangle annulus. More...
 
static Triangulation< 2 > * mobius ()
 Returns a one-triangle Mobius band. More...
 
static Triangulation< 2 > * torus ()
 Returns a two-triangle torus. More...
 
static Triangulation< 2 > * rp2 ()
 Returns a two-triangle projective plane. More...
 
static Triangulation< 2 > * kb ()
 Returns a two-triangle Klein bottle. More...
 
static Triangulation< dim > * sphere ()
 Closed Triangulations. More...
 
static Triangulation< dim > * simplicialSphere ()
 Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex. More...
 
static Triangulation< dim > * sphereBundle ()
 Returns a two-simplex triangulation of the product space S^(dim-1) x S^1. More...
 
static Triangulation< dim > * twistedSphereBundle ()
 Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1. More...
 
static Triangulation< dim > * ball ()
 Bounded Triangulations. More...
 
static Triangulation< dim > * ballBundle ()
 Returns a triangulation of the product space B^(dim-1) x S^1. More...
 
static Triangulation< dim > * twistedBallBundle ()
 Returns a triangulation of the twisted product space B^(dim-1) x~ S^1. More...
 

Detailed Description

Offers routines for constructing a variety of sample 2-dimensional triangulations.

This is a specialisation of the generic Example class template; see the Example template documentation for a general overview of how the example triangulation classes work.

This 2-dimensional specialisation offers significant extra functionality, by providing several more hard-coded constructions.

Member Function Documentation

◆ ball()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ball
staticinherited

Bounded Triangulations.

Returns a one-simplex triangulation of the dim-ball.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ ballBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ballBundle
staticinherited

Returns a triangulation of the product space B^(dim-1) x S^1.

This will use one simplex in odd dimensions, or two simplices in even dimensions.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ simplicialSphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::simplicialSphere
staticinherited

Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ sphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphere
staticinherited

Closed Triangulations.

Returns a two-simplex triangulation of the dim-sphere.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ sphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphereBundle
staticinherited

Returns a two-simplex triangulation of the product space S^(dim-1) x S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ twistedBallBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedBallBundle
staticinherited

Returns a triangulation of the twisted product space B^(dim-1) x~ S^1.

This will use one simplex in even dimensions, or two simplices in odd dimensions.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ twistedSphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedSphereBundle
staticinherited

Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

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

Copyright © 1999-2021, 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).