Regina Calculation Engine
|
Represents a layered solid torus in a triangulation. More...
#include <subcomplex/nlayeredsolidtorus.h>
Public Member Functions | |
NLayeredSolidTorus * | clone () const |
Returns a newly created clone of this structure. More... | |
unsigned long | getNumberOfTetrahedra () const |
Returns the number of tetrahedra in this layered solid torus. More... | |
NTetrahedron * | getBase () const |
Returns the tetrahedron that is glued to itself at the base of this layered solid torus. More... | |
int | getBaseEdge (int group, int index) const |
Returns the requested edge of the base tetrahedron belonging to the given group. More... | |
int | getBaseEdgeGroup (int edge) const |
Returns the group that the given edge of the base tetrahedron belongs to. More... | |
int | getBaseFace (int index) const |
Returns one of the two faces of the base tetrahedron that are glued to each other. More... | |
NTetrahedron * | getTopLevel () const |
Returns the top level tetrahedron in this layered solid torus. More... | |
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. More... | |
int | getTopEdge (int group, int index) const |
Returns the requested edge of the top level tetrahedron belonging to the given group. More... | |
int | getTopEdgeGroup (int edge) const |
Returns the group that the given edge of the top level tetrahedron belongs to. More... | |
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. More... | |
NTriangulation * | flatten (const NTriangulation *original, int mobiusBandBdry) const |
Flattens this layered solid torus to a Mobius band. More... | |
void | transform (const NTriangulation *originalTri, const NIsomorphism *iso, NTriangulation *newTri) |
Adjusts the details of this layered solid torus according to the given isomorphism between triangulations. More... | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More... | |
NAbelianGroup * | getHomologyH1 () const |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
std::ostream & | writeName (std::ostream &out) const |
Writes the name of this triangulation as a human-readable string to the given output stream. More... | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the name of this triangulation in TeX format to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
std::string | getName () const |
Returns the name of this specific triangulation as a human-readable string. More... | |
std::string | getTeXName () const |
Returns the name of this specific triangulation in TeX format. More... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
Input and Output | |
std::string | str () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toString () const |
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More... | |
std::string | detail () const |
Returns the output from writeTextLong() as a string. More... | |
std::string | toStringLong () const |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More... | |
Static Public Member Functions | |
static NLayeredSolidTorus * | formsLayeredSolidTorusBase (NTetrahedron *tet) |
Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation. More... | |
static NLayeredSolidTorus * | formsLayeredSolidTorusTop (NTetrahedron *tet, unsigned topFace1, unsigned topFace2) |
Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus. More... | |
static NLayeredSolidTorus * | isLayeredSolidTorus (NComponent *comp) |
Determines if the given triangulation component forms a layered solid torus in its entirity. More... | |
static NStandardTriangulation * | isStandardTriangulation (NComponent *component) |
Determines whether the given component represents one of the standard triangulations understood by Regina. More... | |
static NStandardTriangulation * | isStandardTriangulation (NTriangulation *tri) |
Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More... | |
Represents a layered solid torus in 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.
NLayeredSolidTorus* regina::NLayeredSolidTorus::clone | ( | ) | const |
Returns a newly created clone of this structure.
|
inherited |
Returns the output from writeTextLong() as a string.
NTriangulation* regina::NLayeredSolidTorus::flatten | ( | const NTriangulation * | original, |
int | mobiusBandBdry | ||
) | const |
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.
original | the triangulation containing this layered solid torus; this triangulation will not be changed. |
mobiusBandBdry | the edge group on the boundary of this layered solid torus that will become the boundary of the new Mobius band (the remaining edge groups will become internal edges of the new Mobius band). This must be 0, 1 or 2. See getTopEdge() for further details about edge groups. |
|
static |
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.
tet | the tetrahedron to examine as a potential base. |
null
if the given tetrahedron is not the base of a layered solid torus.
|
static |
Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus.
Note that the two given faces need not be boundary triangles in the overall triangulation. That is, the layered solid torus may be a subcomplex of some larger triangulation. For example, the two given faces may be joined to some other tetrahedra outside the layered solid torus or they may be joined to each other. In fact, they may even extend this smaller layered solid torus to a larger layered solid torus.
tet | the tetrahedron to examine as a potential top level of a layered solid torus. |
topFace1 | the face number of the given tetrahedron that should represent the first boundary triangle of the layered solid torus. This should be between 0 and 3 inclusive. |
topFace2 | the face number of the given tetrahedron that should represent the second boundary triangle of the layered solid torus. This should be between 0 and 3 inclusive, and should not be equal to topFace1. |
null
if the given tetrahedron with its two faces do not form the top level of a layered solid torus.
|
inline |
Returns the tetrahedron that is glued to itself at the base of this layered solid torus.
|
inline |
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 getBaseEdgeGroup(getBaseEdge(group, index)) == group
for all values of group
and index
.
Edges getBaseEdge(2,0)
and getBaseEdge(3,0)
will both belong to face getBaseFace(0)
. Edges getBaseEdge(2,1)
and getBaseEdge(3,2)
will both belong to face getBaseFace(1)
.
group | the group that the requested edge should belong to; this must be 1, 2 or 3. |
index | the index within the given group of the requested edge; this must be between 0 and group-1 inclusive. Note that in group 3 the edge at index 1 is adjacent to both the edges at indexes 0 and 2. |
|
inline |
Returns the group that the given edge of the base tetrahedron belongs to.
See getBaseEdge() for further details about groups.
Note that getBaseEdgeGroup(getBaseEdge(group, index)) == group
for all values of group
and index
.
edge | the edge number in the base tetrahedron of the given edge; this must be between 0 and 5 inclusive. |
|
inline |
Returns one of the two faces of the base tetrahedron that are glued to each other.
index | specifies which of the two faces to return; this must be 0 or 1. |
|
virtual |
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.
|
virtual |
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.
|
inline |
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.
group | the given edge group; this must be 0, 1 or 2. |
|
inherited |
Returns the name of this specific triangulation as a human-readable string.
|
inline |
Returns the number of tetrahedra in this layered solid torus.
|
inherited |
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
|
inline |
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 getTopEdgeGroup(getTopEdge(group, index)) == group
for all values of group
and index
that actually correspond to an edge.
Edges getTopEdge(group, 0)
will all belong to face getTopFace(0)
. Edges getTopEdge(group, 1)
(if they exist) will all belong to face getTopFace(1)
.
group | the group that the requested edge should belong to; this must be 0, 1 or 2. |
index | the index within the given group of the requested edge; this must be 0 or 1. Note that one of the groups only contains one tetrahedron edge, in which case this edge will be stored at index 0. |
|
inline |
Returns the group that the given edge of the top level tetrahedron belongs to.
See getTopEdge() for further details about groups.
Note that getTopEdgeGroup(getTopEdge(group, index)) == group
for all values of group
and index
that actually correspond to an edge.
edge | the edge number in the top level tetrahedron of the given edge; this must be between 0 and 5 inclusive. |
|
inline |
Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus.
index | specifies which of the two faces to return; this must be 0 or 1. |
|
inline |
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.
|
static |
Determines if the given triangulation component forms a layered solid torus in its entirity.
Note that, unlike formsLayeredSolidTorusBase(), this routine tests for a component that is a layered solid torus with no additional tetrahedra or gluings. That is, the two boundary triangles of the layered solid torus must in fact be boundary triangles of the component.
comp | the triangulation component to examine. |
null
if the given component is not a layered solid torus.
|
staticinherited |
Determines whether the given component represents one of the standard triangulations understood by Regina.
The list of recognised triangulations is expected to grow between releases.
If the standard triangulation returned has boundary triangles then the given component must have the same corresponding boundary triangles, i.e., the component cannot have any further identifications of these boundary triangles with each other.
Note that the triangulation-based routine isStandardTriangulation(NTriangulation*) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.
component | the triangulation component under examination. |
|
staticinherited |
Determines whether the given triangulation represents one of the standard triangulations understood by Regina.
The list of recognised triangulations is expected to grow between releases.
If the standard triangulation returned has boundary triangles then the given triangulation must have the same corresponding boundary triangles, i.e., the triangulation cannot have any further identifications of these boundary triangles with each other.
This routine may recognise more triangulations than the component-based isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.
tri | the triangulation under examination. |
|
inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
|
inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
|
inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
void regina::NLayeredSolidTorus::transform | ( | const NTriangulation * | originalTri, |
const NIsomorphism * | iso, | ||
NTriangulation * | newTri | ||
) |
Adjusts the details of this layered solid torus according to the given isomorphism between triangulations.
The given isomorphism must describe a mapping from originalTri to newTri, and this layered solid torus must currently refer to tetrahedra in originalTri. After this routine is called this structure will instead refer to the corresponding tetrahedra in newTri (with changes in vertex/face numbering also accounted for).
originalTri | the triangulation currently referenced by this layered solid torus. |
iso | the mapping from originalTri to newTri. |
newTri | the triangulation to be referenced by the updated layered solid torus. |
|
inlinevirtual |
Writes the name of this triangulation as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::NStandardTriangulation.
|
inlinevirtual |
Writes the name of this triangulation in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out | the output stream to which to write. |
Implements regina::NStandardTriangulation.
|
inlinevirtual |
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.
|
inlinevirtualinherited |
Writes this object in short text format to the given output stream.
The output should be human-readable, should fit on a single line, and should not end with a newline.
out | the output stream to which to write. |
Implements regina::ShareableObject.