Regina Calculation Engine
Public Member Functions | Static Public Member Functions | Static Public Attributes | List of all members
regina::NPlugTriSolidTorus Class Reference

Represents a plugged triangular solid torus component of a triangulation. More...

#include <subcomplex/nplugtrisolidtorus.h>

Inheritance diagram for regina::NPlugTriSolidTorus:
regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

Public Member Functions

virtual ~NPlugTriSolidTorus ()
 Destroys this plugged solid torus; note that the corresponding triangular solid torus and layered chains will also be destroyed. More...
 
NPlugTriSolidTorusclone () const
 Returns a newly created clone of this structure. More...
 
const NTriSolidTorusgetCore () const
 Returns the triangular solid torus at the core of this triangulation. More...
 
const NLayeredChaingetChain (int annulus) const
 Returns the layered chain attached to the requested annulus on the boundary of the core triangular solid torus. More...
 
int getChainType (int annulus) const
 Returns the way in which a layered chain is attached to the requested annulus on the boundary of the core triangular solid torus. More...
 
int getEquatorType () const
 Returns which types of edges form the equator of the plug. More...
 
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition 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 NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. 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 NPlugTriSolidTorusisPlugTriSolidTorus (NComponent *comp)
 Determines if the given triangulation component is a plugged triangular solid torus. More...
 
static NStandardTriangulationisStandardTriangulation (NComponent *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static NStandardTriangulationisStandardTriangulation (NTriangulation *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...
 

Static Public Attributes

static const int CHAIN_NONE
 Indicates an annulus on the triangular solid torus boundary with no attached layered chain. More...
 
static const int CHAIN_MAJOR
 Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the major edge of the annulus. More...
 
static const int CHAIN_MINOR
 Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the minor edge of the annulus. More...
 
static const int EQUATOR_MAJOR
 Indicates that, if no layered chains were present, the equator of the plug would consist of major edges of the core triangular solid torus. More...
 
static const int EQUATOR_MINOR
 Indicates that, if no layered chains were present, the equator of the plug would consist of minor edges of the core triangular solid torus. More...
 

Detailed Description

Represents a plugged 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 class NTriSolidTorus). Observe that the three axis edges divide the boundary into three annuli.

To each of these annuli a layered chain may be optionally attached. If present, the chain should be attached so its hinge edges are identified with the axis edges of the corresonding annulus and its bottom tetrahedron is layered over either the major edge or minor edge of the corresponding annulus. The top two triangular faces of the layered chain should remain free.

Thus we now have three annuli on the boundary, each represented as a square two of whose (opposite) edges are axis edges of the original triangular solid torus (and possibly also hinge edges of a layered chain).

Create a plug by gluing two tetrahedra together along a single triangle. The six edges that do not run along this common triangle split the plug boundary into three squares. These three squares must be glued to the three boundary annuli previously described. Each axis edge meets two of the annuli; the two corresponding edges of the plug must be non-adjacent (have no common vertex) on the plug. In this way each of the six edges of the plug not running along its interior triangle corresponds to precisely one of the two instances of precisely one of the three axis edges.

If the axis edges are directed so that they all point the same way around the triangular solid torus, these axis edges when drawn on the plug must all point from one common tip of the plug to the other (where the tips of the plug are the vertices not meeting the interior triangle). The gluings must also be made so that the resulting triangulation component is orientable.

Of the optional NStandardTriangulation routines, getManifold() is implemented for most plugged triangular solid tori and getHomologyH1() is not implemented at all.

Constructor & Destructor Documentation

virtual regina::NPlugTriSolidTorus::~NPlugTriSolidTorus ( )
virtual

Destroys this plugged solid torus; note that the corresponding triangular solid torus and layered chains will also be destroyed.

Member Function Documentation

NPlugTriSolidTorus* regina::NPlugTriSolidTorus::clone ( ) const

Returns a newly created clone of this structure.

Returns
a newly created clone.
std::string regina::ShareableObject::detail ( ) const
inherited

Returns the output from writeTextLong() as a string.

Returns
a long text representation of this object.
const NLayeredChain * regina::NPlugTriSolidTorus::getChain ( int  annulus) const
inline

Returns the layered chain attached to the requested annulus on the boundary of the core triangular solid torus.

If there is no attached layered chain, null will be returned.

Note that the core triangular solid torus will be attached to the bottom (as opposed to the top) of the layered chain.

Parameters
annulusspecifies which annulus to examine; this must be 0, 1 or 2.
Returns
the corresponding layered chain.
int regina::NPlugTriSolidTorus::getChainType ( int  annulus) const
inline

Returns the way in which a layered chain is attached to the requested annulus on the boundary of the core triangular solid torus.

This will be one of the chain type constants defined in this class.

Parameters
annulusspecifies which annulus to examine; this must be 0, 1 or 2.
Returns
the type of layered chain, or CHAIN_NONE if there is no layered chain attached to the requested annulus.
const NTriSolidTorus & regina::NPlugTriSolidTorus::getCore ( ) const
inline

Returns the triangular solid torus at the core of this triangulation.

Returns
the core triangular solid torus.
int regina::NPlugTriSolidTorus::getEquatorType ( ) const
inline

Returns which types of edges form the equator of the plug.

In the absence of layered chains these will either all be major edges or all be minor edges.

Layered chains complicate matters, but the roles that the major and minor edges play on the boundary annuli of the triangular solid torus can be carried up to the annuli at the top of each layered chain; the edges filling the corresponding major or minor roles will then form the equator of the plug.

Returns
the types of edges that form the equator of the plug; this will be one of the equator type constants defined in this class.
NAbelianGroup * regina::NStandardTriangulation::getHomologyH1 ( ) const
inlinevirtualinherited

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.

Returns
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented in regina::NLayeredSolidTorus, regina::NTriSolidTorus, regina::NLayeredChain, regina::NSpiralSolidTorus, regina::NLayeredTorusBundle, regina::NSnapPeaCensusTri, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NSnappedBall, regina::NTrivialTri, regina::NL31Pillow, and regina::NLayeredChainPair.

NManifold* regina::NPlugTriSolidTorus::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.

Returns
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

std::string regina::NStandardTriangulation::getName ( ) const
inherited

Returns the name of this specific triangulation as a human-readable string.

Returns
the name of this triangulation.
std::string regina::NStandardTriangulation::getTeXName ( ) const
inherited

Returns the name of this specific triangulation in TeX format.

No leading or trailing dollar signs will be included.

Warning
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Returns
the name of this triangulation in TeX format.
static NPlugTriSolidTorus* regina::NPlugTriSolidTorus::isPlugTriSolidTorus ( NComponent comp)
static

Determines if the given triangulation component is a plugged triangular solid torus.

Parameters
compthe triangulation component to examine.
Returns
a newly created structure containing details of the plugged triangular solid torus, or null if the given component is not a plugged triangular solid torus.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NComponent component)
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.

Parameters
componentthe triangulation component under examination.
Returns
the details of the standard triangulation if the given component is recognised, or 0 otherwise.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NTriangulation tri)
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.

Parameters
trithe triangulation under examination.
Returns
the details of the standard triangualation if the given triangulation is recognised, or 0 otherwise.
std::string regina::ShareableObject::str ( ) const
inherited

Returns the output from writeTextShort() as a string.

Python:
This implements the __str__() function.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toString ( ) const
inlineinherited

A deprecated alias for str(), which returns the output from writeTextShort() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toStringLong ( ) const
inlineinherited

A deprecated alias for detail(), which returns the output from writeTextLong() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.
std::ostream& regina::NPlugTriSolidTorus::writeName ( std::ostream &  out) const
virtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream& regina::NPlugTriSolidTorus::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.

Warning
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NPlugTriSolidTorus::writeTextLong ( std::ostream &  out) const
virtual

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.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Reimplemented from regina::ShareableObject.

void regina::NStandardTriangulation::writeTextShort ( std::ostream &  out) const
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.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Implements regina::ShareableObject.

Member Data Documentation

const int regina::NPlugTriSolidTorus::CHAIN_MAJOR
static

Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the major edge of the annulus.

const int regina::NPlugTriSolidTorus::CHAIN_MINOR
static

Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the minor edge of the annulus.

const int regina::NPlugTriSolidTorus::CHAIN_NONE
static

Indicates an annulus on the triangular solid torus boundary with no attached layered chain.

const int regina::NPlugTriSolidTorus::EQUATOR_MAJOR
static

Indicates that, if no layered chains were present, the equator of the plug would consist of major edges of the core triangular solid torus.

const int regina::NPlugTriSolidTorus::EQUATOR_MINOR
static

Indicates that, if no layered chains were present, the equator of the plug would consist of minor edges of the core triangular solid torus.


The documentation for this class was generated from the following file:

Copyright © 1999-2014, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).