Regina Calculation Engine
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Provides core functionality for constructing example dim-dimensional triangulations. More...
#include <triangulation/detail/example.h>
Public Member Functions | |
ExampleBase ()=delete | |
Closed Triangulations. More... | |
Static Public Member Functions | |
static Triangulation< dim > * | sphere () |
Returns a two-simplex triangulation of the dim-sphere. 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... | |
static Triangulation< dim > * | doubleCone (const Triangulation< dim-1 > &base) |
Returns a double cone over the given (dim-1)-dimensional triangulation. More... | |
static Triangulation< dim > * | singleCone (const Triangulation< dim-1 > &base) |
Returns a single cone over the given (dim-1)-dimensional triangulation. More... | |
Provides core functionality for constructing example dim-dimensional triangulations.
These example triangulations are made available through the class Example<dim>, which uses this as a base class. End users should not need to refer to ExampleBase directly.
See the Example class notes for further information.
dim | the dimension of the example triangulations to construct. This must be between 2 and 15 inclusive. |
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staticinherited |
Returns a double cone over the given (dim-1)-dimensional triangulation.
If the given triangulation represents the manifold M
, then this returns an ideal triangulation of the product M x I
(with two ideal boundary components). A copy of the original triangulation base can be found at the centre of this construction, formed from the dim-simplices that sit between the two ideal vertices.
Note that, as a special case, if M
is either a sphere or a ball, then this routine returns a (dim)-sphere or a (dim)-ball (since "ideal spheres" and "ideal balls" just become regular internal and boundary vertices respectively).
This construction is essentially the suspension of the triangulation base. We do not call it this however, since from a topological point of view, to form the ideal triangulation of M x I
we "remove" the vertices at the apex of each cone.
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staticinherited |
Returns a single cone over the given (dim-1)-dimensional triangulation.
If the given triangulation represents the manifold M
, then this returns a triangulation of the product M x I
that has one real boundary component and one ideal boundary component. The triangulation of the real boundary component will be identical to the original (dim-1)-dimensional triangulation base.