Regina Calculation Engine
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Represents an augmented triangular solid torus component of a triangulation. More...
#include <naugtrisolidtorus.h>
Public Member Functions | |
virtual | ~NAugTriSolidTorus () |
Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed. | |
NAugTriSolidTorus * | clone () const |
Returns a newly created clone of this structure. | |
const NTriSolidTorus & | getCore () const |
Returns the triangular solid torus at the core of this triangulation. | |
const NLayeredSolidTorus * | getAugTorus (int annulus) const |
Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus. | |
NPerm | getEdgeGroupRoles (int annulus) const |
Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus. | |
unsigned long | getChainLength () const |
Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus. | |
int | getChainType () const |
Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus. | |
int | getTorusAnnulus () const |
Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached. | |
bool | hasLayeredChain () const |
Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes. | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition 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 | |
static NAugTriSolidTorus * | isAugTriSolidTorus (const NComponent *comp) |
Determines if the given triangulation component is an augmented triangular solid torus. | |
Static Public Attributes | |
static const int | CHAIN_NONE |
Indicates that this augmented triangular solid torus contains no layered chain. | |
static const int | CHAIN_MAJOR |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedMajor(). | |
static const int | CHAIN_AXIS |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedAxis(). |
Represents an augmented triangular solid torus component of a triangulation.
Such a component is obtained as follows. Begin with a three-tetrahedron triangular solid torus (as described by NTriSolidTorus). Observe that the three axis edges divide the boundary into three annuli. Then take one of the following actions.
It will be assumed that all layered solid tori other than the degenerate (2,1,1) will have (3,2,1) layered solid tori at their bases. That is, layered solid tori that begin with the degenerate (2,1,1) and layer over the boundary of the mobius strip are not considered in this class.
Note that (unless a (1,1,0) layered solid torus is used with the 0 edge glued to an axis edge) the resulting space will be a Seifert fibred space over the 2-sphere with at most three exceptional fibres.
Of the optional NStandardTriangulation routines, getManifold() is implemented for most augmented triangular solid tori and getHomologyH1() is not implemented at all.
virtual regina::NAugTriSolidTorus::~NAugTriSolidTorus | ( | ) | [virtual] |
Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed.
NAugTriSolidTorus* regina::NAugTriSolidTorus::clone | ( | ) | const |
Returns a newly created clone of this structure.
const NLayeredSolidTorus * regina::NAugTriSolidTorus::getAugTorus | ( | int | annulus | ) | const [inline] |
Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus.
If the layered solid torus is a degenerate (2,1,1) mobius band (i.e., the two faces of the corresponding annulus have simply been glued together), null
will be returned.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. |
unsigned long regina::NAugTriSolidTorus::getChainLength | ( | ) | const [inline] |
Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus.
Note that this count does not include any of the tetrahedra actually belonging to the triangular solid torus.
int regina::NAugTriSolidTorus::getChainType | ( | ) | const [inline] |
Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus.
This will be one of the chain type constants defined in this class.
const NTriSolidTorus & regina::NAugTriSolidTorus::getCore | ( | ) | const [inline] |
Returns the triangular solid torus at the core of this triangulation.
NPerm regina::NAugTriSolidTorus::getEdgeGroupRoles | ( | int | annulus | ) | const [inline] |
Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus.
See NLayeredSolidTorus::getTopEdge() for details regarding edge groups.
If the permutation returned is p
, edge group p[0]
will be glued to an axis edge, group p[1]
will be glued to a major edge and group p[2]
will be glued to a minor edge. p[3]
will always be 3.
Even if the corresponding layered solid torus is a degenerate (2,1,1) mobius band (i.e., getAugTorus() returns null
), the concept of edge groups is still meaningful and this routine will return correct results.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. It is the layered solid torus glued to this annulus whose edge groups will be described. |
NManifold* regina::NAugTriSolidTorus::getManifold | ( | ) | const [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.
int regina::NAugTriSolidTorus::getTorusAnnulus | ( | ) | const [inline] |
Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached.
This routine is only meaningful if the other two annuli are linked by a layered chain.
The integer returned will be 0, 1 or 2; see the NTriSolidTorus class notes for how the boundary annuli are numbered.
bool regina::NAugTriSolidTorus::hasLayeredChain | ( | ) | const [inline] |
Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes.
true
if and only if the layered chain described in the class notes is present. static NAugTriSolidTorus* regina::NAugTriSolidTorus::isAugTriSolidTorus | ( | const NComponent * | comp | ) | [static] |
Determines if the given triangulation component is an augmented triangular solid torus.
comp | the triangulation component to examine. |
null
if the given component is not an augmented triangular solid torus. std::ostream& regina::NAugTriSolidTorus::writeName | ( | std::ostream & | out | ) | const [virtual] |
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.
std::ostream& regina::NAugTriSolidTorus::writeTeXName | ( | std::ostream & | out | ) | const [virtual] |
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.
void regina::NAugTriSolidTorus::writeTextLong | ( | std::ostream & | out | ) | const [virtual] |
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.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.
const int regina::NAugTriSolidTorus::CHAIN_AXIS [static] |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedAxis().
const int regina::NAugTriSolidTorus::CHAIN_MAJOR [static] |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedMajor().
const int regina::NAugTriSolidTorus::CHAIN_NONE [static] |
Indicates that this augmented triangular solid torus contains no layered chain.