#include <nnormalsurface.h>
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 octagonal discs. | |
virtual bool | hasMultipleOctDiscs (NTriangulation *triang) const |
Determines if this normal surface has more than one octagonal 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 NVertex * | isVertexLink (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 octagonal 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 | |
static NNormalSurfaceVector * | makeZeroVector (const NTriangulation *triangulation) |
Returns a new normal surface vector of the appropriate length for the given triangulation and for the flavour of coordinate system corresponding to this subclass of NNormalSurfaceVector. | |
static NMatrixInt * | makeMatchingEquations (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 NEnumConstraintList * | makeEmbeddedConstraints (NTriangulation *triangulation) |
Creates a new set of validity constraints representing the condition that normal surfaces be embedded. |
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 following properties:
When deriving classes from NNormalSurfaceVector:
class(unsigned length)
and class(const NVector<NLargeInteger>& cloneMe)
must be declared and implemented; these will usually just call the corresponding superclass constructors. NVector<NLargeInteger>* clone() const
and bool allowsAlmostNormal() const
must be declared but not implemented. The registry utilities will take care of their implementations. void makeZeroVector(const NTriangulation*)
, NMatrixInt* makeMatchingEquations(NTriangulation*)
and makeEmbeddedConstraints(NTriangulation*) must be declared and implemented.
Optimise (long-term): Investigate using sparse vectors for storage.
regina::NNormalSurfaceVector::NNormalSurfaceVector | ( | unsigned | length | ) | [inline] |
Creates a new vector all of whose entries are initialised to zero.
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.
cloneMe | the vector to clone. |
virtual bool regina::NNormalSurfaceVector::allowsAlmostNormal | ( | ) | const [pure 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.
true
if and only if almost normal surfaces are allowed. Implemented in regina::NNormalSurfaceVectorANStandard, 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.
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. |
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.
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. |
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 octagonal discs of the given type in this normal surface.
See NNormalSurface::getOctCoord() for further details.
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. |
Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, regina::NNormalSurfaceVectorQuad, 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.
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. |
Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.
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.
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. |
Implemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorMirrored, and regina::NNormalSurfaceVectorStandard.
virtual bool regina::NNormalSurfaceVector::hasMultipleOctDiscs | ( | NTriangulation * | triang | ) | const [virtual] |
Determines if this normal surface has more than one octagonal disc.
It may be assumed that at most one octagonal disc type exists in this surface. This routine will return true
if an octagonal type does exist and its coordinate is greater than one.
The default implementation for this routine simply calculates all the octagonal 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.
This normal surface vector is using a flavour of coordinate system that allows for almost normal surfaces.
triang | the triangulation in which this normal surface lives. |
true
if and only if there is an octagonal disc type present and its coordinate is greater than one. 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.
triang | the triangulation in which this normal surface lives. |
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.
triang | the triangulation in which this normal surface lives. |
true
if and only if the normal surface represented is compact. 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.
triang | the triangulation in which this normal surface lives. |
true
if and only if the normal surface represented is a splitting surface. 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.
triang | the triangulation in which this normal surface lives. |
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.
triang | the triangulation in which this normal surface lives. |
Reimplemented in regina::NNormalSurfaceVectorQuad.
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.
triang | the triangulation in which this normal surface lives. |
true
if and only if the normal surface represented is vertex linking. static NEnumConstraintList* regina::NNormalSurfaceVector::makeEmbeddedConstraints | ( | NTriangulation * | triangulation | ) | [static] |
Creates a new set of validity constraints representing the condition that normal surfaces be embedded.
The validity constraints will be expressed relative to the flavour of coordinate system corresponding to this particular subclass of NNormalSurfaceVector.
triangulation | the triangulation upon which these validity constraints will be based. |
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.
triangulation | the triangulation upon which these matching equations will be based. |
Reimplemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.
static NNormalSurfaceVector* regina::NNormalSurfaceVector::makeZeroVector | ( | const NTriangulation * | triangulation | ) | [static] |
Returns a new normal surface vector of the appropriate length for the given triangulation and for the flavour of coordinate system corresponding to this subclass of NNormalSurfaceVector.
All elements of the new vector will be initialised to zero.
See makeZeroVector() for further details.
triangulation | the triangulation upon which the underlying coordinate system is based. |
Reimplemented in regina::NNormalSurfaceVectorANStandard, regina::NNormalSurfaceVectorQuad, and regina::NNormalSurfaceVectorStandard.