Regina Calculation Engine
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A normal surface vector using transversely oriented standard (triangle-quad) coordinates.
More...
#include <surfaces/nsvectororiented.h>
Public Member Functions | |
NSVectorOriented (size_t length) | |
Creates a new vector all of whose entries are initialised to zero. More... | |
NSVectorOriented (const Vector< LargeInteger > &cloneMe) | |
Creates a new vector that is a clone of the given vector. More... | |
virtual LargeInteger | triangles (size_t tetIndex, int vertex, const Triangulation< 3 > *triang) const override |
Returns the number of triangular discs of the given type in this normal surface. More... | |
virtual LargeInteger | quads (size_t tetIndex, int quadType, const Triangulation< 3 > *triang) const override |
Returns the number of quadrilateral discs of the given type in this normal surface. More... | |
virtual LargeInteger | orientedTriangles (size_t tetIndex, int vertex, const Triangulation< 3 > *triang, bool orientation) const override |
Returns the number of oriented triangular discs of the given type in this normal surface. More... | |
virtual LargeInteger | orientedQuads (size_t tetIndex, int quadType, const Triangulation< 3 > *triang, bool orientation) const override |
Returns the number of oriented quadrilateral discs of the given type in this normal surface. More... | |
virtual LargeInteger | octs (size_t tetIndex, int octType, const Triangulation< 3 > *triang) const override |
Returns the number of octagonal discs of the given type in this normal surface. More... | |
virtual LargeInteger | edgeWeight (size_t edgeIndex, const Triangulation< 3 > *triang) const override |
Returns the number of times this normal surface crosses the given edge. More... | |
virtual LargeInteger | arcs (size_t triIndex, int triVertex, const Triangulation< 3 > *triang) const override |
Returns the number of arcs in which this normal surface intersects the given triangle in the given direction. More... | |
const Ray & | coords () const |
Gives read-only access to the underlying vector of coordinates. More... | |
virtual NormalSurfaceVector * | clone () const =0 |
Creates a newly allocated clone of this vector. More... | |
size_t | size () const |
Returns the number of coordinates in the underlying vector. More... | |
const LargeInteger & | operator[] (size_t index) const |
Returns the given coordinate from the underlying vector. More... | |
virtual void | setElement (size_t index, const LargeInteger &value) |
Sets the given normal coordinate to the given value. More... | |
virtual void | operator+= (const NormalSurfaceVector &other) |
Adds the given vector to this vector. More... | |
virtual void | scaleDown () |
Scales this vector down by the greatest common divisor of all its elements. 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 (const Triangulation< 3 > *triang) const |
Determines if this normal surface has more than one octagonal disc. More... | |
virtual bool | isCompact (const Triangulation< 3 > *triang) const |
Determines if the normal surface represented is compact (has finitely many discs). More... | |
virtual bool | isVertexLinking (const Triangulation< 3 > *triang) const |
Determines if the normal surface represented is vertex linking. More... | |
virtual const Vertex< 3 > * | isVertexLink (const Triangulation< 3 > *triang) const |
Determines if a rational multiple of the normal surface represented is the link of a single vertex. More... | |
virtual std::pair< const Edge< 3 > *, const Edge< 3 > * > | isThinEdgeLink (const Triangulation< 3 > *triang) const |
Determines if a rational multiple of the normal surface represented is the thin link of a single edge. More... | |
virtual bool | isSplitting (const Triangulation< 3 > *triang) const |
Determines if the normal surface represented is a splitting surface in the given triangulation. More... | |
virtual LargeInteger | isCentral (const Triangulation< 3 > *triang) const |
Determines if the normal surface represented is a central surface in the given triangulation. More... | |
Static Public Member Functions | |
static NormalSurfaceVector * | makeZeroVector (const Triangulation< 3 > *triangulation) |
static MatrixInt * | makeMatchingEquations (const Triangulation< 3 > *triangulation) |
static EnumConstraints * | makeEmbeddedConstraints (const Triangulation< 3 > *triangulation) |
Protected Attributes | |
Ray | coords_ |
The raw vector of normal coordinates. More... | |
A normal surface vector using transversely oriented standard (triangle-quad) coordinates.
If there are t tetrahedra in the underlying triangulation, there must be precisely 14t coordinates. For each i, coordinates 2i and 2i+1 represent the true
and false
orientations for coordinate i in the 7t-dimensional standard coordinate system. See NSVectorStandard for further details.
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inline |
Creates a new vector all of whose entries are initialised to zero.
length | the number of elements in the new vector. |
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inline |
Creates a new vector that is a clone of the given vector.
cloneMe | the vector to clone. |
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pure virtualinherited |
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.
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pure virtualinherited |
Determines if the specific underlying coordinate system allows for transversely oriented normal surfaces.
true
if and only if transverse orientations are supported.
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pure virtualinherited |
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.
true
if and only if spun-normal surfaces are allowed.
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overridevirtual |
Returns the number of arcs in which this normal surface intersects the given triangle in the given direction.
See NormalSurface::arcs() for further details.
triIndex | the index in the triangulation of the triangle in which we are interested; this should be between 0 and Triangulation<3>::countTriangles()-1 inclusive. |
triVertex | the vertex of the triangle (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. |
Implements regina::NormalSurfaceVector.
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pure virtualinherited |
Creates a newly allocated clone of this vector.
The clone will be of the same subclass of NormalSurfaceVector as this vector.
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inlineinherited |
Gives read-only access to the underlying vector of coordinates.
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overridevirtual |
Returns the number of times this normal surface crosses the given edge.
See NormalSurface::edgeWeight() for further details.
edgeIndex | the index in the triangulation of the edge in which we are interested; this should be between 0 and Triangulation<3>::countEdges()-1 inclusive. |
triang | the triangulation in which this normal surface lives. |
Implements regina::NormalSurfaceVector.
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virtualinherited |
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 NormalSurfaceVector 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.
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.
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virtualinherited |
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 NormalSurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal surface lives. |
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virtualinherited |
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 NormalSurfaceVector 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.
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virtualinherited |
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 NormalSurfaceVector 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.
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virtualinherited |
Determines if a rational multiple of the normal surface represented is the thin link of a single edge.
If there are two different edges e1 and e2 for which the surface could be expressed as the thin link of either e1 or e2, the pair (e1,e2) will be returned. If the surface is the thin link of only one edge e, the pair (e,0) will be returned. If the surface is not the thin link of any 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 NormalSurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal surface lives. |
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virtualinherited |
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 NormalSurfaceVector should override this if they can provide a faster implementation.
triang | the triangulation in which this normal surface lives. |
Reimplemented in regina::NSVectorOrientedQuad, regina::NSVectorQuadOct, and regina::NSVectorQuad.
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virtualinherited |
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 NormalSurfaceVector 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.
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inlineoverridevirtual |
Returns the number of octagonal discs of the given type in this normal surface.
See NormalSurface::octs() for further details.
tetIndex | the index in the triangulation of the tetrahedron in which the requested octagons reside; this should be between 0 and Triangulation<3>::size()-1 inclusive. |
octType | the type of this octagon in the given tetrahedron; this should be 0, 1 or 2. |
triang | the triangulation in which this normal surface lives. |
Implements regina::NormalSurfaceVector.
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inlinevirtualinherited |
Adds the given vector to this vector.
This behaves correctly in the case where other is this.
The default implementation simply adds the coordinates of the underlying vectors. Subclasses should reimplement this if they carry any additional information that also needs adjusting.
other | the vector to add to this vector. |
Reimplemented in regina::NSVectorMirrored.
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inlineinherited |
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inlineoverridevirtual |
Returns the number of oriented quadrilateral discs of the given type in this normal surface.
See NormalSurface::orientedQuads() for further details.
The default implementation of this routine returns zero, which is suitable for coordinate systems that do not support transverse orientation.
tetIndex | the index in the triangulation of the tetrahedron in which the requested quadrilaterals reside; this should be between 0 and Triangulation<3>::size()-1 inclusive. |
quadType | the type of this quadrilateral in the given tetrahedron; this should be 0, 1 or 2. |
triang | the triangulation in which this normal surface lives. |
orientation | the orientation of the normal discs. |
Reimplemented from regina::NormalSurfaceVector.
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inlineoverridevirtual |
Returns the number of oriented triangular discs of the given type in this normal surface.
See NormalSurface::orientedTriangles() for further details.
The default implementation of this routine returns zero, which is suitable for coordinate systems that do not support transverse orientation.
tetIndex | the index in the triangulation of the tetrahedron in which the requested triangles reside; this should be between 0 and Triangulation<3>::size()-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. |
orientation | the orientation of the normal discs. |
Reimplemented from regina::NormalSurfaceVector.
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inlineoverridevirtual |
Returns the number of quadrilateral discs of the given type in this normal surface.
See NormalSurface::quads() for further details.
tetIndex | the index in the triangulation of the tetrahedron in which the requested quadrilaterals reside; this should be between 0 and Triangulation<3>::size()-1 inclusive. |
quadType | the type of this quadrilateral in the given tetrahedron; this should be 0, 1 or 2. |
triang | the triangulation in which this normal surface lives. |
Implements regina::NormalSurfaceVector.
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inlinevirtualinherited |
Scales this vector down by the greatest common divisor of all its elements.
The resulting vector will be the smallest multiple of the original that maintains integral entries, and these entries will have the same signs as the originals.
This routine poses no problem for vectors containing infinite elements; such elements are simply ignored and left at infinity.
The default implementation simply scales down the underlying vector. Subclasses should reimplement this if they carry any additional information that also needs adjusting.
Reimplemented in regina::NSVectorMirrored.
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inlinevirtualinherited |
Sets the given normal coordinate to the given value.
The default implementation simply sets the coordinate in the underlying vector. Subclasses should reimplement this if they carry any additional information that also need adjusting.
index | the index of the coordinate to set; this must be between 0 and size()-1 inclusive. |
value | the new value to assign to the given coordinate. |
Reimplemented in regina::NSVectorMirrored.
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inlineinherited |
Returns the number of coordinates in the underlying vector.
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inlineoverridevirtual |
Returns the number of triangular discs of the given type in this normal surface.
See NormalSurface::triangles() for further details.
tetIndex | the index in the triangulation of the tetrahedron in which the requested triangles reside; this should be between 0 and Triangulation<3>::size()-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. |
Implements regina::NormalSurfaceVector.
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protectedinherited |
The raw vector of normal coordinates.