regina::NNormalSurfaceVectorANStandard Class Reference
[Normal Surfaces]

An almost normal surface vector using standard triangle-quad-oct coordinates. More...

#include <nsanstandard.h>

Inheritance diagram for regina::NNormalSurfaceVectorANStandard:

regina::NNormalSurfaceVector regina::NRay regina::NVectorDense< T > regina::NVector< T >

List of all members.

Public Member Functions

 NNormalSurfaceVectorANStandard (unsigned length)
 Creates a new vector all of whose entries are initialised to zero.
 NNormalSurfaceVectorANStandard (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector.
virtual bool allowsAlmostNormal () const
 Determines if the specific underlying coordinate system allows for almost normal surfaces, that is, allows for octagonal discs.
virtual NLargeInteger getTriangleCoord (unsigned long tetIndex, int vertex, NTriangulation *triang) const
 Returns the number of triangular discs of the given type in this normal surface.
virtual NLargeInteger getQuadCoord (unsigned long tetIndex, int quadType, NTriangulation *triang) const
 Returns the number of quadrilateral discs of the given type in this normal surface.
virtual NLargeInteger getOctCoord (unsigned long tetIndex, int octType, NTriangulation *triang) const
 Returns the number of octagonal discs of the given type in this normal surface.
virtual NLargeInteger getEdgeWeight (unsigned long edgeIndex, NTriangulation *triang) const
 Returns the number of times this normal surface crosses the given edge.
virtual NLargeInteger getFaceArcs (unsigned long faceIndex, int faceVertex, NTriangulation *triang) const
 Returns the number of arcs in which this normal surface intersects the given face in the given direction.
virtual NVector< NLargeInteger > * clone () const
 Makes a newly allocated clone of this vector.

Static Public Member Functions

template<class RayOutputIterator, class FaceOutputIterator>
static void createNonNegativeCone (NTriangulation *triangulation, RayOutputIterator rays, FaceOutputIterator faces)
 Writes to the given output iterators newly allocated rays and faces representing the cone obtained by setting all coordinates non-negative in the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.
static NMatrixIntmakeMatchingEquations (NTriangulation *triangulation)
 Creates a new set of normal surface matching equations for the given triangulation using the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.
static NCompConstraintSetmakeEmbeddedConstraints (NTriangulation *triangulation)
 Creates a new set of compatibility constraints representing the condition that normal surfaces be embedded.


Detailed Description

An almost normal surface vector using standard triangle-quad-oct coordinates.

If there are t tetrahedra in the underlying triangulation, there must be precisely 10t coordinates. The first ten coordinates will be for the first tetrahedron, the next ten for the second tetrahedron and so on. For each tetrahedron, the first four represent the number of triangular discs about vertex 0, 1, 2 and 3, the next three represent the number of quadrilateral discs of type 0, 1 and 2 (see NNormalSurface::getQuadCoord()) and the final three represent the number of octagonal discs of type 0, 1 and 2 (see NNormalSurface::getOctCoord()).

Python:
Not present.

Constructor & Destructor Documentation

regina::NNormalSurfaceVectorANStandard::NNormalSurfaceVectorANStandard ( unsigned  length  )  [inline]

Creates a new vector all of whose entries are initialised to zero.

Parameters:
length the number of elements in the new vector.

regina::NNormalSurfaceVectorANStandard::NNormalSurfaceVectorANStandard ( const NVector< NLargeInteger > &  cloneMe  )  [inline]

Creates a new vector that is a clone of the given vector.

Parameters:
cloneMe the vector to clone.


Member Function Documentation

virtual bool regina::NNormalSurfaceVectorANStandard::allowsAlmostNormal (  )  const [virtual]

Determines if the specific underlying coordinate system allows for almost normal surfaces, that is, allows for octagonal discs.

Note that this has nothing to do with whether or not this specific surface contains octagonal discs.

Returns:
true if and only if almost normal surfaces are allowed.

Implements regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorANStandard::getTriangleCoord ( unsigned long  tetIndex,
int  vertex,
NTriangulation triang 
) const [inline, virtual]

Returns the number of triangular discs of the given type in this normal surface.

See NNormalSurface::getTriangleCoord() for further details.

Parameters:
tetIndex the index in the triangulation of the tetrahedron in which the requested triangles reside; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
vertex the vertex of the given tetrahedron around which the requested triangles lie; this should be between 0 and 3 inclusive.
triang the triangulation in which this normal surface lives.
Returns:
the number of triangular discs of the given type.

Implements regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorANStandard::getQuadCoord ( unsigned long  tetIndex,
int  quadType,
NTriangulation triang 
) const [inline, virtual]

Returns the number of quadrilateral discs of the given type in this normal surface.

See NNormalSurface::getQuadCoord() for further details.

Parameters:
tetIndex the index in the triangulation of the tetrahedron in which the requested quadrilaterals reside; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
quadType the number of the vertex splitting that this quad type represents; this should be between 0 and 2 inclusive.
triang the triangulation in which this normal surface lives.
Returns:
the number of quadrilateral discs of the given type.

Implements regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorANStandard::getOctCoord ( unsigned long  tetIndex,
int  octType,
NTriangulation triang 
) const [inline, virtual]

Returns the number of octagonal discs of the given type in this normal surface.

See NNormalSurface::getOctCoord() for further details.

Parameters:
tetIndex the index in the triangulation of the tetrahedron in which the requested octagons reside; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
octType the number of the vertex splitting that this octagon type represents; this should be between 0 and 2 inclusive.
triang the triangulation in which this normal surface lives.
Returns:
the number of octagonal discs of the given type.

Implements regina::NNormalSurfaceVector.

virtual NLargeInteger regina::NNormalSurfaceVectorANStandard::getEdgeWeight ( unsigned long  edgeIndex,
NTriangulation triang 
) const [virtual]

Returns the number of times this normal surface crosses the given edge.

See NNormalSurface::getEdgeWeight() for further details.

Parameters:
edgeIndex the index in the triangulation of the edge in which we are interested; this should be between 0 and NTriangulation::getNumberOfEdges()-1 inclusive.
triang the triangulation in which this normal surface lives.
Returns:
the number of times this normal surface crosses the given edge.

Implements regina::NNormalSurfaceVector.

virtual NLargeInteger regina::NNormalSurfaceVectorANStandard::getFaceArcs ( unsigned long  faceIndex,
int  faceVertex,
NTriangulation triang 
) const [virtual]

Returns the number of arcs in which this normal surface intersects the given face in the given direction.

See NNormalSurface::getFaceArcs() for further details.

Parameters:
faceIndex the index in the triangulation of the face in which we are interested; this should be between 0 and NTriangulation::getNumberOfFaces()-1 inclusive.
faceVertex the vertex of the face (0, 1 or 2) around which the arcs of intersection that we are interested in lie; only these arcs will be counted.
triang the triangulation in which this normal surface lives.
Returns:
the number of times this normal surface intersect the given face with the given arc type.

Implements regina::NNormalSurfaceVector.

virtual NVector<NLargeInteger>* regina::NNormalSurfaceVectorANStandard::clone (  )  const [virtual]

Makes a newly allocated clone of this vector.

The clone will be of the same subclass of NVector as this vector.

Returns:
a clone of this vector.

Reimplemented from regina::NRay.

template<class RayOutputIterator, class FaceOutputIterator>
static void regina::NNormalSurfaceVectorANStandard::createNonNegativeCone ( NTriangulation triangulation,
RayOutputIterator  rays,
FaceOutputIterator  faces 
) [inline, static]

Writes to the given output iterators newly allocated rays and faces representing the cone obtained by setting all coordinates non-negative in the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.

The elements written to rays must be of this particular subclass of NNormalSurfaceVector.

See createNonNegativeCone() for further details.

Parameters:
triangulation the triangulation upon which the underlying coordinate system is based.
rays the output iterator to which the newly allocated extremal rays will be written; these rays must all be of this particular subclass of NNormalSurfaceVector. This iterator must accept objects of type NRay*.
faces the output iterator to which the newly allocated face perpendiculars will be written; these vectors may be of any subclass of NVector<NLargeInteger>. This iterator must accept objects of type NVector<NLargeInteger>*.

Reimplemented from regina::NNormalSurfaceVector.

static NMatrixInt* regina::NNormalSurfaceVectorANStandard::makeMatchingEquations ( NTriangulation triangulation  )  [static]

Creates a new set of normal surface matching equations for the given triangulation using the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.

See makeMatchingEquations() for further details.

Parameters:
triangulation the triangulation upon which these matching equations will be based.
Returns:
a newly allocated set of matching equations.

Reimplemented from regina::NNormalSurfaceVector.

static NCompConstraintSet* regina::NNormalSurfaceVectorANStandard::makeEmbeddedConstraints ( NTriangulation triangulation  )  [static]

Creates a new set of compatibility constraints representing the condition that normal surfaces be embedded.

The compatibility constraints will be expressed relative to the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.

Parameters:
triangulation the triangulation upon which these compatibility constraints will be based.
Returns:
a newly allocated set of constraints.

Reimplemented from regina::NNormalSurfaceVector.


The documentation for this class was generated from the following file:
Copyright © 1999-2007, 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).