regina::NNormalSurfaceVector Class Reference
[Normal Surfaces]

Stores the vector of a single normal surface in a 3-manifold. More...

#include <nnormalsurface.h>

Inheritance diagram for regina::NNormalSurfaceVector:

regina::NRay regina::NVectorDense< T > regina::NVector< T > regina::NNormalSurfaceVectorANStandard regina::NNormalSurfaceVectorMirrored regina::NNormalSurfaceVectorStandard regina::NNormalSurfaceVectorQuad List of all members.

Public Member Functions

 NNormalSurfaceVector (unsigned length)
 Creates a new vector all of whose entries are initialised to zero.
 NNormalSurfaceVector (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector.
virtual bool allowsAlmostNormal () const=0
 Determines if the specific underlying coordinate system allows for almost normal surfaces, that is, allows for octahedral discs.
virtual bool hasMultipleOctDiscs (NTriangulation *triang) const
 Determines if this normal surface has more than one octahedral disc.
virtual bool isCompact (NTriangulation *triang) const
 Determines if the normal surface represented is compact (has finitely many discs).
virtual bool isVertexLinking (NTriangulation *triang) const
 Determines if the normal surface represented is vertex linking.
virtual const NVertexisVertexLink (NTriangulation *triang) const
 Determines if a rational multiple of the normal surface represented is the link of a single vertex.
virtual std::pair< const NEdge *,
const NEdge * > 
isThinEdgeLink (NTriangulation *triang) const
 Determines if a rational multiple of the normal surface represented is the link of a single thin edge.
virtual bool isSplitting (NTriangulation *triang) const
 Determines if the normal surface represented is a splitting surface in the given triangulation.
virtual NLargeInteger isCentral (NTriangulation *triang) const
 Determines if the normal surface represented is a central surface in the given triangulation.
virtual NLargeInteger getTriangleCoord (unsigned long tetIndex, int vertex, NTriangulation *triang) const=0
 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=0
 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 =0
 Returns the number of octahedral discs of the given type in this normal surface.
virtual NLargeInteger getEdgeWeight (unsigned long edgeIndex, NTriangulation *triang) const=0
 Returns the number of times this normal surface crosses the given edge.
virtual NLargeInteger getFaceArcs (unsigned long faceIndex, int faceVertex, NTriangulation *triang) const=0
 Returns the number of arcs in which this normal surface intersects the given face in the given direction.

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

Stores the vector of a single normal surface in a 3-manifold.

The different subclasses of NNormalSurfaceVector use different underlying coordinate systems for the normal solution space. However, the various coordinate retrieval routines will return values that are independent of the underlying coordinate system. Thus the coordinates of the normal surface in any coordinate system can be determined without knowledge of the specific underlying coordinate system being used.

Note that if a mirrored vector class is being used (see NNormalSurfaceVectorMirrored), the vector may not change once the first coordinate lookup routine (such as getTriangleCoord() and the like) has been called. See NNormalSurfaceVectorMirrored for further explanation.

Note that non-compact surfaces (surfaces with infinitely many discs, such as spun normal surfaces) are allowed; in these cases, the corresponding coordinate lookup routines should return NLargeInteger::infinity where appropriate.

All subclasses of NNormalSurfaceVector must have the property that multiplying a normal surface by k corresponds to multiplying the underlying vector by k for any non-negative integer k.

When deriving classes from NNormalSurfaceVector:

Test:
Tested in the test suite, though not exhaustively.
Todo:
Feature: Implement quad-oct space.
Todo:
Optimise (long-term): Investigate using sparse vectors for storage.
Python:
Not present.


Constructor & Destructor Documentation

regina::NNormalSurfaceVector::NNormalSurfaceVector ( 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::NNormalSurfaceVector::NNormalSurfaceVector ( 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::NNormalSurfaceVector::allowsAlmostNormal (  )  const [pure virtual]

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

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

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

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.

virtual bool regina::NNormalSurfaceVector::hasMultipleOctDiscs ( NTriangulation triang  )  const [virtual]

Determines if this normal surface has more than one octahedral disc.

It may be assumed that at most one octahedral type exists in this surface. This routine will return true if an octahedral type does exist and its coordinate is greater than one.

The default implementation for this routine simply calculates all the octahedral coordinates and returns as soon as a positive or negative result can be established. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

If a subclass does not allow for almost normal surfaces, this routine will never be called and thus does not need to be overwritten.

Precondition:
At most one octahedral type exists in this surface.

This normal surface vector is using a flavour of coordinate system that allows for almost normal surfaces.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
true if and only if there is an octahedral type present and its coordinate is greater than one.

virtual bool regina::NNormalSurfaceVector::isCompact ( NTriangulation triang  )  const [virtual]

Determines if the normal surface represented is compact (has finitely many discs).

The default implementation for this routine simply runs through every disc type until a disc type with infinite disc count is found or all disc types have been examined. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
true if and only if the normal surface represented is compact.

virtual bool regina::NNormalSurfaceVector::isVertexLinking ( NTriangulation triang  )  const [virtual]

Determines if the normal surface represented is vertex linking.

A vertex linking surface contains only triangles.

The default implementation for this routine simply runs through every non-triangular disc type ensuring that each has no corresponding discs. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
true if and only if the normal surface represented is vertex linking.

virtual const NVertex* regina::NNormalSurfaceVector::isVertexLink ( NTriangulation triang  )  const [virtual]

Determines if a rational multiple of the normal surface represented is the link of a single vertex.

The default implementation for this routine involves counting the number of discs of every type. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
the vertex linked by this surface, or 0 if this surface is not the link of a single vertex.

Reimplemented in regina::NNormalSurfaceVectorQuad.

virtual std::pair<const NEdge*, const NEdge*> regina::NNormalSurfaceVector::isThinEdgeLink ( NTriangulation triang  )  const [virtual]

Determines if a rational multiple of the normal surface represented is the link of a single thin edge.

If there are two different thin edges e1 and e2 for which the surface could be expressed as either the link of e1 or the link of e2, the pair (e1,e2) will be returned. If the surface is the link of only one thin edge e, the pair (e,0) will be returned. If the surface is not the link of any thin edges, the pair (0,0) will be returned.

The default implementation for this routine involves counting the number of discs of every type. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
a pair containing the thin edge(s) linked by this surface, as described above.

virtual bool regina::NNormalSurfaceVector::isSplitting ( NTriangulation triang  )  const [virtual]

Determines if the normal surface represented is a splitting surface in the given triangulation.

A splitting surface is a compact surface containing precisely one quad per tetrahedron and no other normal (or almost normal) discs.

The default implementation for this routine simply runs through and checks the count for each disc type. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
true if and only if the normal surface represented is a splitting surface.

virtual NLargeInteger regina::NNormalSurfaceVector::isCentral ( NTriangulation triang  )  const [virtual]

Determines if the normal surface represented is a central surface in the given triangulation.

A central surface is a compact surface containing at most one normal or almost normal disc per tetrahedron. If the surface is central, the number of tetrahedra it meets (i.e., the number of discs in the surface) will be returned.

The default implementation for this routine simply runs through and checks the count for each disc type. Subclasses of NNormalSurfaceVector should override this if they can provide a faster implementation.

Parameters:
triang the triangulation in which this normal surface lives.
Returns:
the number of tetrahedra that the surface meets if it is a central surface, or 0 if it is not a central surface.

virtual NLargeInteger regina::NNormalSurfaceVector::getTriangleCoord ( unsigned long  tetIndex,
int  vertex,
NTriangulation triang 
) const [pure 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.

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.

virtual NLargeInteger regina::NNormalSurfaceVector::getQuadCoord ( unsigned long  tetIndex,
int  quadType,
NTriangulation triang 
) const [pure 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.

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.

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

Returns the number of octahedral 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 octahedrons reside; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
octType the number of the vertex splitting that this octahedron type represents; this should be between 0 and 2 inclusive.
triang the triangulation in which this normal surface lives.
Returns:
the number of octahedral discs of the given type.

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.

virtual NLargeInteger regina::NNormalSurfaceVector::getEdgeWeight ( unsigned long  edgeIndex,
NTriangulation triang 
) const [pure 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.

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.

virtual NLargeInteger regina::NNormalSurfaceVector::getFaceArcs ( unsigned long  faceIndex,
int  faceVertex,
NTriangulation triang 
) const [pure 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.

Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.

template<class RayOutputIterator, class FaceOutputIterator>
static void regina::NNormalSurfaceVector::createNonNegativeCone ( NTriangulation triangulation,
RayOutputIterator  rays,
FaceOutputIterator  faces 
) [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 in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.

static NMatrixInt* regina::NNormalSurfaceVector::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 in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.

static NCompConstraintSet* regina::NNormalSurfaceVector::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 in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.


The documentation for this class was generated from the following file:
Copyright © 1999-2006, 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).