Regina Calculation Engine
Public Member Functions | Static Public Member Functions | List of all members
regina::NNormalSurfaceVectorOrientedQuad Class Reference

A normal surface vector using transversely oriented quadrilateral coordinates. More...

#include <surfaces/nsorientedquad.h>

Inheritance diagram for regina::NNormalSurfaceVectorOrientedQuad:
regina::NNormalSurfaceVectorMirrored regina::NNormalSurfaceVector regina::NRay regina::NVector< NLargeInteger >

Public Member Functions

 NNormalSurfaceVectorOrientedQuad (unsigned length)
 Creates a new vector all of whose entries are initialised to zero. More...
 
 NNormalSurfaceVectorOrientedQuad (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector. More...
 
virtual NNormalSurfaceVectormakeMirror (NTriangulation *triang) const
 Creates a new mirror vector corresponding to this vector. More...
 
virtual bool allowsAlmostNormal () const
 Determines if the specific underlying coordinate system allows for almost normal surfaces, that is, allows for octagonal discs. More...
 
virtual bool allowsSpun () const
 Determines if the specific underlying coordinate system allows for spun-normal surfaces; that is, surfaces with infinitely many triangles. More...
 
virtual bool allowsOriented () const
 Determines if the specific underlying coordinate system allows for transversely oriented normal surfaces. More...
 
virtual const NVertexisVertexLink (NTriangulation *triang) const
 Determines if a rational multiple of the normal surface represented is the link of a single vertex. More...
 
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. More...
 
virtual NLargeInteger getOrientedQuadCoord (unsigned long tetIndex, int quadType, NTriangulation *triang, bool orientation) const
 Returns the number of oriented quadrilateral discs of the given type in this normal surface. More...
 
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. More...
 
virtual NNormalSurfaceVectorclone () const
 Creates a newly allocated clone of this vector. More...
 
- Public Member Functions inherited from regina::NNormalSurfaceVectorMirrored
 NNormalSurfaceVectorMirrored (unsigned length)
 Creates a new vector all of whose entries are initialised to zero. More...
 
 NNormalSurfaceVectorMirrored (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector. More...
 
 NNormalSurfaceVectorMirrored (const NNormalSurfaceVectorMirrored &cloneMe)
 Creates a new vector that is a clone of the given vector. More...
 
virtual ~NNormalSurfaceVectorMirrored ()
 Destroys this vector and its mirror if appropriate. More...
 
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. More...
 
virtual NLargeInteger getOrientedTriangleCoord (unsigned long tetIndex, int vertex, NTriangulation *triang, bool orientation) const
 Returns the number of oriented triangular discs of the given type in this normal surface. More...
 
virtual NLargeInteger getEdgeWeight (unsigned long edgeIndex, NTriangulation *triang) const
 Returns the number of times this normal surface crosses the given edge. More...
 
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. More...
 
- Public Member Functions inherited from regina::NNormalSurfaceVector
 NNormalSurfaceVector (unsigned length)
 Creates a new vector all of whose entries are initialised to zero. More...
 
 NNormalSurfaceVector (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector. More...
 
virtual ~NNormalSurfaceVector ()
 A virtual destructor. More...
 
virtual bool hasMultipleOctDiscs (NTriangulation *triang) const
 Determines if this normal surface has more than one octagonal disc. More...
 
virtual bool isCompact (NTriangulation *triang) const
 Determines if the normal surface represented is compact (has finitely many discs). More...
 
virtual bool isVertexLinking (NTriangulation *triang) const
 Determines if the normal surface represented is vertex linking. More...
 
virtual std::pair< const NEdge
*, const NEdge * > 
isThinEdgeLink (NTriangulation *triang) const
 Determines if a rational multiple of the normal surface represented is the thin link of a single edge. More...
 
virtual bool isSplitting (NTriangulation *triang) const
 Determines if the normal surface represented is a splitting surface in the given triangulation. More...
 
virtual NLargeInteger isCentral (NTriangulation *triang) const
 Determines if the normal surface represented is a central surface in the given triangulation. More...
 
- Public Member Functions inherited from regina::NRay
 NRay (unsigned length)
 Creates a new ray all of whose coordinates are initialised to zero. More...
 
 NRay (const NVector< NLargeInteger > &cloneMe)
 Creates a new ray that is a clone of the given ray. More...
 
void scaleDown ()
 Scales this vector down by the greatest common divisor of all its elements. More...
 
void negate ()
 
- Public Member Functions inherited from regina::NVector< NLargeInteger >
 NVector (unsigned newVectorSize)
 Creates a new vector. More...
 
 NVector (unsigned newVectorSize, const NLargeInteger &initValue)
 Creates a new vector and initialises every element to the given value. More...
 
 NVector (const NVector< NLargeInteger > &cloneMe)
 Creates a new vector that is a clone of the given vector. More...
 
 ~NVector ()
 Destroys this vector. More...
 
unsigned size () const
 Returns the number of elements in the vector. More...
 
const NLargeIntegeroperator[] (unsigned index) const
 Returns the element at the given index in the vector. More...
 
void setElement (unsigned index, const NLargeInteger &value)
 Sets the element at the given index in the vector to the given value. More...
 
bool operator== (const NVector< NLargeInteger > &compare) const
 Determines if this vector is equal to the given vector. More...
 
NVector< NLargeInteger > & operator= (const NVector< NLargeInteger > &cloneMe)
 Sets this vector equal to the given vector. More...
 
void operator+= (const NVector< NLargeInteger > &other)
 Adds the given vector to this vector. More...
 
void operator-= (const NVector< NLargeInteger > &other)
 Subtracts the given vector from this vector. More...
 
void operator*= (const NLargeInteger &factor)
 Multiplies this vector by the given scalar. More...
 
NLargeInteger operator* (const NVector< NLargeInteger > &other) const
 Calculates the dot product of this vector and the given vector. More...
 
void negate ()
 Negates every element of this vector. More...
 
NLargeInteger norm () const
 Returns the norm of this vector. More...
 
NLargeInteger elementSum () const
 Returns the sum of all elements of this vector. More...
 
void addCopies (const NVector< NLargeInteger > &other, const NLargeInteger &multiple)
 Adds the given multiple of the given vector to this vector. More...
 
void subtractCopies (const NVector< NLargeInteger > &other, const NLargeInteger &multiple)
 Subtracts the given multiple of the given vector to this vector. More...
 

Static Public Member Functions

static NNormalSurfaceVectormakeZeroVector (const NTriangulation *triangulation)
 
static NMatrixIntmakeMatchingEquations (NTriangulation *triangulation)
 
static NEnumConstraintListmakeEmbeddedConstraints (NTriangulation *triangulation)
 

Additional Inherited Members

- Static Public Attributes inherited from regina::NVector< NLargeInteger >
static NLargeInteger zero
 Zero in the underlying number system. More...
 
static NLargeInteger one
 One in the underlying number system. More...
 
static NLargeInteger minusOne
 Negative one in the underlying number system. More...
 
- Protected Attributes inherited from regina::NVector< NLargeInteger >
NLargeIntegerelements
 The internal array containing all vector elements. More...
 
NLargeIntegerend
 A pointer just beyond the end of the internal array. More...
 

Detailed Description

A normal surface vector using transversely oriented quadrilateral coordinates.

If there are t tetrahedra in the underlying triangulation, there must be precisely 6t coordinates. For each i, coordinates 2i and 2i+1 represent the true and false orientations for coordinate i in the 3t-dimensional quadrilateral coordinate system. See NNormalSurfaceVectorQuad for further details.

Warning
Support for transversely oriented normal surfaces is still experimental, and some features will break (e.g., testing connectedness, disjointness or embeddedness).
Python:
Not present.

Constructor & Destructor Documentation

regina::NNormalSurfaceVectorOrientedQuad::NNormalSurfaceVectorOrientedQuad ( unsigned  length)
inline

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

Parameters
lengththe number of elements in the new vector.
regina::NNormalSurfaceVectorOrientedQuad::NNormalSurfaceVectorOrientedQuad ( const NVector< NLargeInteger > &  cloneMe)
inline

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

Parameters
cloneMethe vector to clone.

Member Function Documentation

virtual bool regina::NNormalSurfaceVectorOrientedQuad::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.

virtual bool regina::NNormalSurfaceVectorOrientedQuad::allowsOriented ( ) const
virtual

Determines if the specific underlying coordinate system allows for transversely oriented normal surfaces.

Returns
true if and only if transverse orientations are supported.

Implements regina::NNormalSurfaceVector.

virtual bool regina::NNormalSurfaceVectorOrientedQuad::allowsSpun ( ) const
virtual

Determines if the specific underlying coordinate system allows for spun-normal surfaces; that is, surfaces with infinitely many triangles.

Note that this has nothing to do with whether or not this specific surface contains infinitely many triangles.

Returns
true if and only if spun-normal surfaces are allowed.

Implements regina::NNormalSurfaceVector.

virtual NNormalSurfaceVector* regina::NNormalSurfaceVectorOrientedQuad::clone ( ) const
virtual

Creates a newly allocated clone of this vector.

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

Implements regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorOrientedQuad::getOctCoord ( unsigned long  tetIndex,
int  octType,
NTriangulation triang 
) const
inlinevirtual

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

See NNormalSurface::getOctCoord() for further details.

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

Reimplemented from regina::NNormalSurfaceVectorMirrored.

NLargeInteger regina::NNormalSurfaceVectorOrientedQuad::getOrientedQuadCoord ( unsigned long  tetIndex,
int  quadType,
NTriangulation triang,
bool  orientation 
) const
inlinevirtual

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

See NNormalSurface::getOrientedQuadCoord() for further details.

The default implementation of this routine returns zero, which is suitable for coordinate systems that do not support transverse orientation.

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

Reimplemented from regina::NNormalSurfaceVectorMirrored.

NLargeInteger regina::NNormalSurfaceVectorOrientedQuad::getQuadCoord ( unsigned long  tetIndex,
int  quadType,
NTriangulation triang 
) const
inlinevirtual

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

See NNormalSurface::getQuadCoord() for further details.

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

Reimplemented from regina::NNormalSurfaceVectorMirrored.

const NVertex * regina::NNormalSurfaceVectorOrientedQuad::isVertexLink ( NTriangulation triang) const
inlinevirtual

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
triangthe 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 from regina::NNormalSurfaceVector.

virtual NNormalSurfaceVector* regina::NNormalSurfaceVectorOrientedQuad::makeMirror ( NTriangulation triang) const
virtual

Creates a new mirror vector corresponding to this vector.

The mirror vector should represent the same normal surface as this vector, and should have fast coordinate lookup routines (getTriangleCoord(), getQuadCord() and so on). It is recommended that the mirror vector be an NNormalSurfaceVectorStandard or an NNormalSurfaceVectorANStandard.

Parameters
triangthe triangulation in which this normal surface lives.
Returns
a newly created mirror vector.

Implements regina::NNormalSurfaceVectorMirrored.


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

Copyright © 1999-2012, The Regina development team
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).