Regina Calculation Engine
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Represents a plugged triangular solid torus component of a triangulation. More...
#include <subcomplex/nplugtrisolidtorus.h>
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... | |
NPlugTriSolidTorus * | clone () const |
Returns a newly created clone of this structure. More... | |
const NTriSolidTorus & | getCore () const |
Returns the triangular solid torus at the core of this triangulation. More... | |
const NLayeredChain * | getChain (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... | |
NManifold * | getManifold () 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 NAbelianGroup * | getHomologyH1 () 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 NPlugTriSolidTorus * | isPlugTriSolidTorus (NComponent *comp) |
Determines if the given triangulation component is a plugged triangular solid torus. 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... | |
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... | |
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.
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virtual |
Destroys this plugged solid torus; note that the corresponding triangular solid torus and layered chains will also be destroyed.
NPlugTriSolidTorus* regina::NPlugTriSolidTorus::clone | ( | ) | const |
Returns a newly created clone of this structure.
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inherited |
Returns the output from writeTextLong() as a string.
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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.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. |
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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.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. |
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inline |
Returns the triangular solid torus at the core of this triangulation.
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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.
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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.
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.
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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.
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inherited |
Returns the name of this specific triangulation as a human-readable string.
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inherited |
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
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static |
Determines if the given triangulation component is a plugged triangular solid torus.
comp | the triangulation component to examine. |
null
if the given component is not a plugged triangular solid torus.
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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. |
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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. |
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inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
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inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
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inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
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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.
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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.
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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.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.
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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.
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static |
Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the major edge of the annulus.
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static |
Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the minor edge of the annulus.
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static |
Indicates an annulus on the triangular solid torus boundary with no attached layered chain.
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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.
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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.