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

#include <surfaces/nsorientedquad.h>

Inheritance diagram for regina::NNormalSurfaceVectorOrientedQuad:

Public Member Functions
	NNormalSurfaceVectorOrientedQuad (size_t 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 NNormalSurfaceVector *	makeMirror (NTriangulation *triang) const
	Creates a new mirror vector corresponding to this vector. More...

virtual const NVertex *	isVertexLink (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...

Public Member Functions inherited from regina::NNormalSurfaceVectorMirrored
	NNormalSurfaceVectorMirrored (size_t 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	getTriangleArcs (unsigned long triIndex, int triVertex, NTriangulation *triang) const
	Returns the number of arcs in which this normal surface intersects the given triangle in the given direction. More...

Public Member Functions inherited from regina::NNormalSurfaceVector
	NNormalSurfaceVector (size_t 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 NNormalSurfaceVector *	clone () const =0
	Creates a newly allocated clone of this vector. More...

virtual bool	allowsAlmostNormal () const =0
	Determines if the specific underlying coordinate system allows for almost normal surfaces, that is, allows for octagonal discs. More...

virtual bool	allowsSpun () const =0
	Determines if the specific underlying coordinate system allows for spun-normal surfaces; that is, surfaces with infinitely many triangles. More...

virtual bool	allowsOriented () const =0
	Determines if the specific underlying coordinate system allows for transversely oriented normal surfaces. 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...

NLargeInteger	getFaceArcs (unsigned long triIndex, int triVertex, NTriangulation *triang) const
	A deprecated alias for getTriangleArcs(). More...

Public Member Functions inherited from regina::NRay
	NRay (size_t 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 ()
	Negates every element of this vector. More...

Public Member Functions inherited from regina::NVector< NLargeInteger >
	NVector (size_t newVectorSize)
	Creates a new vector. More...

	NVector (size_t 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...

size_t	size () const
	Returns the number of elements in the vector. More...

const NLargeInteger &	operator[] (size_t index) const
	Returns the element at the given index in the vector. More...

void	setElement (size_t 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 NNormalSurfaceVector *	makeZeroVector (const NTriangulation *triangulation)

static NMatrixInt *	makeMatchingEquations (NTriangulation *triangulation)

static NEnumConstraintList *	makeEmbeddedConstraints (NTriangulation *triangulation)

Static Public Member Functions inherited from regina::NNormalSurfaceVector
static NNormalSurfaceVector *	makeZeroVector (const NTriangulation *triangulation)
	Returns a new normal surface vector of the appropriate length for the given triangulation and for the coordinate system corresponding to this subclass of NNormalSurfaceVector. More...

static NMatrixInt *	makeMatchingEquations (NTriangulation *triangulation)
	Creates a new set of normal surface matching equations for the given triangulation using the coordinate system corresponding to this particular subclass of NNormalSurfaceVector. More...

static NEnumConstraintList *	makeEmbeddedConstraints (NTriangulation *triangulation)
	Creates a new set of validity constraints representing the condition that normal surfaces be embedded. More...

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 >
NLargeInteger *	elements
	The internal array containing all vector elements. More...

NLargeInteger *	end
	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 ( size_t 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::NNormalSurfaceVectorOrientedQuad::NNormalSurfaceVectorOrientedQuad ( 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

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

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.

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

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.
orientation	the 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

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.

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

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 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

triang the 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:

surfaces/nsorientedquad.h

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation