Regina Calculation Engine
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regina::NNormalSurfaceVectorMirrored Class Referenceabstract

A normal surface vector that is mirrored in another coordinate system to avoid frequent lengthy calculations. More...

#include <surfaces/nsmirrored.h>

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

Public Member Functions

 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 NNormalSurfaceVectormakeMirror (NTriangulation *triang) const =0
 Creates a new mirror vector corresponding to this vector. 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 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 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 NNormalSurfaceVectorclone () 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 const NVertexisVertexLink (NTriangulation *triang) const
 Determines if a rational multiple of the normal surface represented is the link of a single vertex. 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...
 

Additional Inherited Members

- Static Public Member Functions inherited from regina::NNormalSurfaceVector
static NNormalSurfaceVectormakeZeroVector (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. More...
 
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. More...
 
static NEnumConstraintListmakeEmbeddedConstraints (NTriangulation *triangulation)
 Creates a new set of validity constraints representing the condition that normal surfaces be embedded. More...
 
- 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 that is mirrored in another coordinate system to avoid frequent lengthy calculations.

When it is difficult to convert from the native coordinate system to standard tri-quad-oct coordinates, use this as a base class. The conversion of the entire vector will be done once only, and future coordinate lookups will be performed through the pre-converted mirror vector.

Once the first coordinate lookup has taken place (via getTriangleCoord() or the like), this vector may not change! The mirror will be created at this point and will not change, so if the native coordinates change further then any requests passed to the mirror will return incorrect results.

Subclasses need not implement any of the coordinate lookup routines. The default implementation will be to pass the lookup to the mirror. If any particular lookup can be done more efficiently in the native coordinate system, the corresponding routine should be overridden.

Subclasses must however implement the routine makeMirror() which creates the alternate mirror vector from this vector.

Note that cloning a vector of this class will not clone the mirror. Thus a clone may be safely modified before its first coordinate lookup routine is called.

Todo:
Bug: Allow modification of the vector by overwriting setValue(); this will require documentation changes in both this class and in NNormalSurfaceVector.
Python:
Not present.

Constructor & Destructor Documentation

regina::NNormalSurfaceVectorMirrored::NNormalSurfaceVectorMirrored ( 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::NNormalSurfaceVectorMirrored::NNormalSurfaceVectorMirrored ( const NVector< NLargeInteger > &  cloneMe)
inline

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

Parameters
cloneMethe vector to clone.
regina::NNormalSurfaceVectorMirrored::NNormalSurfaceVectorMirrored ( const NNormalSurfaceVectorMirrored cloneMe)
inline

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

Parameters
cloneMethe vector to clone.
regina::NNormalSurfaceVectorMirrored::~NNormalSurfaceVectorMirrored ( )
inlinevirtual

Destroys this vector and its mirror if appropriate.

Member Function Documentation

NLargeInteger regina::NNormalSurfaceVectorMirrored::getEdgeWeight ( unsigned long  edgeIndex,
NTriangulation triang 
) const
inlinevirtual

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

See NNormalSurface::getEdgeWeight() for further details.

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

Implements regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorMirrored::getFaceArcs ( unsigned long  faceIndex,
int  faceVertex,
NTriangulation triang 
) const
inlinevirtual

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
faceIndexthe index in the triangulation of the face in which we are interested; this should be between 0 and NTriangulation::getNumberOfFaces()-1 inclusive.
faceVertexthe 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.
triangthe 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.

NLargeInteger regina::NNormalSurfaceVectorMirrored::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.

Implements regina::NNormalSurfaceVector.

Reimplemented in regina::NNormalSurfaceVectorOrientedQuad, and regina::NNormalSurfaceVectorQuad.

NLargeInteger regina::NNormalSurfaceVectorMirrored::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::NNormalSurfaceVector.

Reimplemented in regina::NNormalSurfaceVectorOrientedQuad.

NLargeInteger regina::NNormalSurfaceVectorMirrored::getOrientedTriangleCoord ( unsigned long  tetIndex,
int  vertex,
NTriangulation triang,
bool  orientation 
) const
inlinevirtual

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

See NNormalSurface::getOrientedTriangleCoord() 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 triangles reside; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
vertexthe vertex of the given tetrahedron around which the requested triangles lie; this should be between 0 and 3 inclusive.
triangthe triangulation in which this normal surface lives.
orientationthe orientation of the normal discs.
Returns
the number of triangular discs of the given type.

Reimplemented from regina::NNormalSurfaceVector.

NLargeInteger regina::NNormalSurfaceVectorMirrored::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.

Implements regina::NNormalSurfaceVector.

Reimplemented in regina::NNormalSurfaceVectorOrientedQuad.

NLargeInteger regina::NNormalSurfaceVectorMirrored::getTriangleCoord ( unsigned long  tetIndex,
int  vertex,
NTriangulation triang 
) const
inlinevirtual

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

See NNormalSurface::getTriangleCoord() for further details.

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

Implements regina::NNormalSurfaceVector.

virtual NNormalSurfaceVector* regina::NNormalSurfaceVectorMirrored::makeMirror ( NTriangulation triang) const
pure 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.

Implemented in regina::NNormalSurfaceVectorOrientedQuad, regina::NNormalSurfaceVectorQuadOct, and regina::NNormalSurfaceVectorQuad.


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).