#include <nlayeredsolidtorus.h>
Inheritance diagram for regina::NLayeredSolidTorus:
Public Member Functions | |
NLayeredSolidTorus * | clone () const |
Returns a newly created clone of this structure. | |
unsigned long | getNumberOfTetrahedra () const |
Returns the number of tetrahedra in this layered solid torus. | |
NTetrahedron * | getBase () const |
Returns the tetrahedron that is glued to itself at the base of this layered solid torus. | |
int | getBaseEdge (int group, int index) const |
Returns the requested edge of the base tetrahedron belonging to the given group. | |
int | getBaseEdgeGroup (int edge) const |
Returns the group that the given edge of the base tetrahedron belongs to. | |
int | getBaseFace (int index) const |
Returns one of the two faces of the base tetrahedron that are glued to each other. | |
NTetrahedron * | getTopLevel () const |
Returns the top level tetrahedron in this layered solid torus. | |
unsigned long | getMeridinalCuts (int group) const |
Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group. | |
int | getTopEdge (int group, int index) const |
Returns the requested edge of the top level tetrahedron belonging to the given group. | |
int | getTopEdgeGroup (int edge) const |
Returns the group that the given edge of the top level tetrahedron belongs to. | |
int | getTopFace (int index) const |
Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus. | |
NTriangulation * | flatten (const NTriangulation *original, int mobiusBandBdry) const |
Flattens this layered solid torus to a Mobius band. | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. | |
NAbelianGroup * | getHomologyH1 () const |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. | |
std::ostream & | writeName (std::ostream &out) const |
Writes the name of this triangulation as a human-readable string to the given output stream. | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the name of this triangulation in TeX format to the given output stream. | |
void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. | |
Static Public Member Functions | |
NLayeredSolidTorus * | formsLayeredSolidTorusBase (NTetrahedron *tet) |
Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation. |
A layered solid torus must contain at least one tetrahedron.
Note that this class only represents layered solid tori with a (3,2,1) at their base. Thus triangulations that begin with a degenerate (2,1,1) mobius strip and layer over the mobius strip boundary (including the minimal (1,1,0) triangulation) are not described by this class.
All optional NStandardTriangulation routines are implemented for this class.
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Returns a newly created clone of this structure.
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Flattens this layered solid torus to a Mobius band. A newly created modified triangulation is returned; the original triangulation is unchanged. Note that there are three different ways in which this layered solid torus can be flattened, corresponding to the three different edges of the boundary torus that could become the boundary edge of the new Mobius band.
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Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation. The torus need not be the entire triangulation; the top level tetrahedron of the torus may be glued to something else (or to itself). Note that the base tetrahedron of a layered solid torus is the tetrahedron furthest from the boundary of the torus, i.e. the tetrahedron glued to itself with a twist.
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Returns the tetrahedron that is glued to itself at the base of this layered solid torus.
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Returns the requested edge of the base tetrahedron belonging to the given group. The layering identifies the six edges of the base tetrahedron into a group of three, a group of two and a single unidentified edge; these are referred to as groups 3, 2 and 1 respectively.
Note that
Edges
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Returns the group that the given edge of the base tetrahedron belongs to. See getBaseEdge() for further details about groups.
Note that
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Returns one of the two faces of the base tetrahedron that are glued to each other.
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Returns the expected first homology group of this triangulation, if such a routine has been implemented. If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0. This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation. The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0. The homology group will be newly allocated and must be destroyed by the caller of this routine. If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.
Reimplemented from regina::NStandardTriangulation. |
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Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. If the 3-manifold cannot be recognised then this routine will return 0. The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0. It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases. The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.
Reimplemented from regina::NStandardTriangulation. |
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Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group. See getTopEdge() for further details about groups.
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Returns the number of tetrahedra in this layered solid torus.
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Returns the requested edge of the top level tetrahedron belonging to the given group. The layering reduces five of the top level tetrahedron edges to three boundary edges of the solid torus; this divides the five initial edges into groups of size two, two and one. Group 0 represents the boundary edge that the meridinal disc cuts fewest times. Group 2 represents the boundary edge that the meridinal disc cuts most times. Group 1 is in the middle.
Note that
Edges
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Returns the group that the given edge of the top level tetrahedron belongs to. See getTopEdge() for further details about groups.
Note that
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Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus.
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Returns the top level tetrahedron in this layered solid torus. This is the tetrahedron that would be on the boundary of the torus if the torus were the entire manifold.
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Writes the name of this triangulation as a human-readable string to the given output stream.
Implements regina::NStandardTriangulation. |
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Writes the name of this triangulation in TeX format to the given output stream. Leading and trailing dollar signs will be included.
Implements regina::NStandardTriangulation. |
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Writes this object in long text format to the given output stream. The output should provided the user with all the information they could want. The output should end with a newline. The default implementation of this routine merely calls writeTextShort() and adds a newline.
Reimplemented from regina::ShareableObject. |