Regina Calculation Engine
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Stores the vector of a single normal surface in a 3-manifold. More...
#include <surfaces/normalsurface.h>
Public Member Functions | |
NormalSurfaceVector (size_t length) | |
Creates a new vector all of whose entries are initialised to zero. More... | |
NormalSurfaceVector (const Vector< LargeInteger > &cloneMe) | |
Creates a new vector that is a clone of the given vector. More... | |
virtual | ~NormalSurfaceVector () |
A virtual destructor. 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 NLargeInteger & | 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... | |
virtual LargeInteger | triangles (size_t tetIndex, int vertex, const Triangulation< 3 > *triang) const =0 |
Returns the number of triangular 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 |
Returns the number of oriented triangular discs of the given type in this normal surface. More... | |
virtual LargeInteger | quads (size_t tetIndex, int quadType, const Triangulation< 3 > *triang) const =0 |
Returns the number of quadrilateral 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 |
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 =0 |
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 =0 |
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 =0 |
Returns the number of arcs in which this normal surface intersects the given triangle in the given direction. More... | |
Static Public Member Functions | |
static NormalSurfaceVector * | makeZeroVector (const Triangulation< 3 > *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 NormalSurfaceVector. More... | |
static MatrixInt * | makeMatchingEquations (const Triangulation< 3 > *triangulation) |
Creates a new set of normal surface matching equations for the given triangulation using the coordinate system corresponding to this particular subclass of NormalSurfaceVector. More... | |
static EnumConstraints * | makeEmbeddedConstraints (const Triangulation< 3 > *triangulation) |
Creates a new set of validity constraints representing the condition that normal surfaces be embedded. More... | |
Protected Attributes | |
Ray | coords_ |
The raw vector of normal coordinates. More... | |
Stores the vector of a single normal surface in a 3-manifold.
The different subclasses of NormalSurfaceVector 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 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 LargeInteger::infinity where appropriate.
All subclasses of NormalSurfaceVector must have the following properties:
When deriving classes from NormalSurfaceVector:
class(size_t length)
and class(const Vector<LargeInteger>& cloneMe)
must be declared and implemented; these will usually just call the corresponding superclass constructors. void makeZeroVector(const Triangulation<3>*)
, MatrixInt* makeMatchingEquations(const Triangulation<3>*)
and makeEmbeddedConstraints(const Triangulation<3>*) must be declared and implemented.