regina::NVertex Class Reference
[Triangulations]

Represents a vertex in the skeleton of a triangulation. More...

#include <nvertex.h>

Inheritance diagram for regina::NVertex:

regina::ShareableObject regina::NMarkedElement regina::boost::noncopyable

List of all members.

Public Member Functions

 NVertex (NComponent *myComponent)
 Creates a new vertex and specifies it as belonging to the given triangulation component.
virtual ~NVertex ()
 Default destructor.
const std::vector
< NVertexEmbedding > & 
getEmbeddings () const
 Returns the list of descriptors of how this vertex forms a part of various tetrahedra in the triangulation.
unsigned long getNumberOfEmbeddings () const
 Returns the number of descriptors in the list returned by getEmbeddings().
const NVertexEmbeddinggetEmbedding (unsigned long index) const
 Returns the requested descriptor from the list returned by getEmbeddings().
NComponentgetComponent () const
 Returns the component of the triangulation to which this vertex belongs.
NBoundaryComponentgetBoundaryComponent () const
 Returns the boundary component of the triangulation to which this vertex belongs.
unsigned long getDegree () const
 Returns the degree of this vertex.
int getLink () const
 Returns a description of the link of the vertex.
bool isLinkClosed () const
 Determines if the link of this vertex is closed.
bool isIdeal () const
 Determines if this vertex is an ideal vertex.
bool isBoundary () const
 Determines if this vertex lies on the boundary of the triangulation.
bool isStandard () const
 Determines if this vertex is standard.
bool isLinkOrientable () const
 Determines if the vertex link is orientable.
long getLinkEulerCharacteristic () const
 Returns the Euler characteristic of the vertex link.
void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream.

Static Public Attributes

static const int SPHERE
 Specifies a vertex link that is a sphere.
static const int DISC
 Specifies a vertex link that is a disc.
static const int TORUS
 Specifies a vertex link that is a torus.
static const int KLEIN_BOTTLE
 Specifies a vertex link that is a Klein bottle.
static const int NON_STANDARD_CUSP
 Specifies a vertex link that is closed and is not a sphere, torus or Klein bottle.
static const int NON_STANDARD_BDRY
 Specifies a vertex link that has boundary and is not a disc.

Friends

class NTriangulation
 Allow access to private members.


Detailed Description

Represents a vertex in the skeleton of a triangulation.

Vertices are highly temporary; once a triangulation changes, all its vertex objects will be deleted and new ones will be created.

Test:
Tested in the test suite, though not exhaustively.

Constructor & Destructor Documentation

regina::NVertex::NVertex ( NComponent myComponent  )  [inline]

Creates a new vertex and specifies it as belonging to the given triangulation component.

Python:
Not present.
Parameters:
myComponent the triangulation component to which this vertex belongs.

regina::NVertex::~NVertex (  )  [inline, virtual]

Default destructor.


Member Function Documentation

const std::vector< NVertexEmbedding > & regina::NVertex::getEmbeddings (  )  const [inline]

Returns the list of descriptors of how this vertex forms a part of various tetrahedra in the triangulation.

Note that if this vertex represents multiple vertices of a particular tetrahedron, there will be multiple embedding descriptors in the list regarding that tetrahedron.

Python:
This routine returns a python list.
Returns:
the list of embedding descriptors.
See also:
NVertexEmbedding

unsigned long regina::NVertex::getNumberOfEmbeddings (  )  const [inline]

Returns the number of descriptors in the list returned by getEmbeddings().

Note that this is identical to getDegree().

Returns:
the number of embedding descriptors.

const NVertexEmbedding & regina::NVertex::getEmbedding ( unsigned long  index  )  const [inline]

Returns the requested descriptor from the list returned by getEmbeddings().

Parameters:
index the index of the requested descriptor. This should be between 0 and getNumberOfEmbeddings()-1 inclusive.
Returns:
the requested embedding descriptor.

NComponent * regina::NVertex::getComponent (  )  const [inline]

Returns the component of the triangulation to which this vertex belongs.

Returns:
the component containing this vertex.

NBoundaryComponent * regina::NVertex::getBoundaryComponent (  )  const [inline]

Returns the boundary component of the triangulation to which this vertex belongs.

See the note in the NBoundaryComponent overview regarding what happens if the vertex link is a multiply punctured surface. Note that this makes the vertex non-standard and the triangulation invalid.

An ideal vertex will have its own individual boundary component to which it belongs.

Returns:
the boundary component containing this vertex, or 0 if this vertex is not on the boundary of the triangulation as determined by isBoundary().

unsigned long regina::NVertex::getDegree (  )  const [inline]

Returns the degree of this vertex.

Note that this is identical to getNumberOfEmbeddings().

Returns:
the degree of this vertex.

int regina::NVertex::getLink (  )  const [inline]

Returns a description of the link of the vertex.

Returns:
one of the predefined link constants in NVertex.

bool regina::NVertex::isLinkClosed (  )  const [inline]

Determines if the link of this vertex is closed.

Returns:
true if and only if the link of this vertex is closed.

bool regina::NVertex::isIdeal (  )  const [inline]

Determines if this vertex is an ideal vertex.

This requires the vertex link to be closed and not a 2-sphere.

Returns:
true if and only if this is an ideal vertex.

bool regina::NVertex::isBoundary (  )  const [inline]

Determines if this vertex lies on the boundary of the triangulation.

Ideal vertices are included as being on the boundary. In fact, the only vertices not considered as on the boundary are those whose links are spheres.

Returns:
true if and only if this vertex lies on the boundary.
See also:
isIdeal()

bool regina::NVertex::isStandard (  )  const [inline]

Determines if this vertex is standard.

This requires the vertex link to be a sphere, disc, torus or Klein bottle.

Returns:
true if and only if this vertex is standard.

bool regina::NVertex::isLinkOrientable (  )  const [inline]

Determines if the vertex link is orientable.

Returns:
true if and only if the vertex link is orientable.

long regina::NVertex::getLinkEulerCharacteristic (  )  const [inline]

Returns the Euler characteristic of the vertex link.

Returns:
the Euler characteristic of the vertex link.

void regina::NVertex::writeTextShort ( std::ostream &  out  )  const [virtual]

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

The output should fit on a single line and no newline should be written.

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

Implements regina::ShareableObject.


Friends And Related Function Documentation

friend class NTriangulation [friend]

Allow access to private members.


Member Data Documentation

const int regina::NVertex::SPHERE [static]

Specifies a vertex link that is a sphere.

const int regina::NVertex::DISC [static]

Specifies a vertex link that is a disc.

const int regina::NVertex::TORUS [static]

Specifies a vertex link that is a torus.

const int regina::NVertex::KLEIN_BOTTLE [static]

Specifies a vertex link that is a Klein bottle.

Specifies a vertex link that is closed and is not a sphere, torus or Klein bottle.

Specifies a vertex link that has boundary and is not a disc.


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

Copyright © 1999-2008, 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).