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regina::NSnappedBall Class Reference
[Standard Triangulations and Subcomplexes]

Represents a snapped 3-ball in a triangulation. More...

#include <nsnappedball.h>

Inheritance diagram for regina::NSnappedBall:

regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable List of all members.

Public Member Functions

NSnappedBallclone () const
 Returns a newly created clone of this structure.
NTetrahedrongetTetrahedron () const
 Returns the tetrahedron that forms this snapped ball.
int getBoundaryFace (int index) const
 Returns one of the two faces that forms the boundary of this snapped ball.
int getInternalFace (int index) const
 Returns one of the two faces internal to this snapped ball.
int getEquatorEdge () const
 Returns the edge that forms the equator of the boundary sphere of this ball.
int getInternalEdge () const
 Returns the edge internal to this snapped ball.
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented.
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream.
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.

Static Public Member Functions

NSnappedBallformsSnappedBall (NTetrahedron *tet)
 Determines if the given tetrahedron forms a snapped 3-ball within a triangulation.

Detailed Description

Represents a snapped 3-ball in a triangulation.

A snapped 3-ball is a single tetrahedron with two faces glued to each other to form a 3-ball with a two triangle boundary.

All optional NStandardTriangulation routines are implemented for this class.


Member Function Documentation

NSnappedBall* regina::NSnappedBall::clone  )  const
 

Returns a newly created clone of this structure.

Returns:
a newly created clone.

NSnappedBall* regina::NSnappedBall::formsSnappedBall NTetrahedron tet  )  [static]
 

Determines if the given tetrahedron forms a snapped 3-ball within a triangulation.

The ball need not be the entire triangulation; the boundary faces may be glued to something else (or to each other).

Note that the two boundary faces of the snapped 3-ball need not be boundary faces within the overall triangulation, i.e., they may be identified with each other or with faces of other tetrahedra.

Parameters:
tet the tetrahedron to examine as a potential 3-ball.
Returns:
a newly created structure containing details of the snapped 3-ball, or null if the given tetrahedron is not a snapped 3-ball.

int regina::NSnappedBall::getBoundaryFace int  index  )  const [inline]
 

Returns one of the two faces that forms the boundary of this snapped ball.

You are guaranteed that index 0 will return a smaller face number than index 1.

Parameters:
index specifies which of the two boundary faces to return; this must be either 0 or 1.
Returns:
the corresponding face number in the tetrahedron.

int regina::NSnappedBall::getEquatorEdge  )  const [inline]
 

Returns the edge that forms the equator of the boundary sphere of this ball.

Returns:
the corresponding edge number in the tetrahedron.

NAbelianGroup* regina::NSnappedBall::getHomologyH1  )  const [virtual]
 

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0.

This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

The homology group will be newly allocated and must be destroyed by the caller of this routine.

If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.

Returns:
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NStandardTriangulation.

int regina::NSnappedBall::getInternalEdge  )  const [inline]
 

Returns the edge internal to this snapped ball.

Returns:
the corresponding edge number in the tetrahedron.

int regina::NSnappedBall::getInternalFace int  index  )  const [inline]
 

Returns one of the two faces internal to this snapped ball.

You are guaranteed that index 0 will return a smaller face number than index 1.

Parameters:
index specifies which of the two internal faces to return; this must be either 0 or 1.
Returns:
the corresponding face number in the tetrahedron.

NManifold* regina::NSnappedBall::getManifold  )  const [virtual]
 

Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.

If the 3-manifold cannot be recognised then this routine will return 0.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.

Returns:
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

NTetrahedron * regina::NSnappedBall::getTetrahedron  )  const [inline]
 

Returns the tetrahedron that forms this snapped ball.

Returns:
the tetrahedron.

std::ostream & regina::NSnappedBall::writeName std::ostream &  out  )  const [inline, virtual]
 

Writes the name of this triangulation as a human-readable string to the given output stream.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream & regina::NSnappedBall::writeTeXName std::ostream &  out  )  const [inline, virtual]
 

Writes the name of this triangulation in TeX format to the given output stream.

Leading and trailing dollar signs will be included.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NSnappedBall::writeTextLong std::ostream &  out  )  const [inline, virtual]
 

Writes this object in long text format to the given output stream.

The output should provided the user with all the information they could want. The output should end with a newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.

Reimplemented from regina::ShareableObject.


The documentation for this class was generated from the following file:
Copyright © 1999-2004, Ben Burton
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).