Regina Calculation Engine
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Represents an angle structure on a triangulation. More...
#include <angle/nanglestructure.h>
Public Member Functions | |
NAngleStructure (const NTriangulation *triang, NAngleStructureVector *newVector) | |
Creates a new angle structure on the given triangulation with the given coordinate vector. More... | |
virtual | ~NAngleStructure () |
Destroys this angle structure. More... | |
NAngleStructure * | clone () const |
Creates a newly allocated clone of this angle structure. More... | |
NRational | getAngle (unsigned long tetIndex, int edgePair) const |
Returns the requested angle in this angle structure. More... | |
const NTriangulation * | getTriangulation () const |
Returns the triangulation on which this angle structure lies. More... | |
bool | isStrict () const |
Determines whether this is a strict angle structure. More... | |
bool | isTaut () const |
Determines whether this is a taut angle structure. More... | |
bool | isVeering () const |
Determines whether this is a veering structure. More... | |
const NAngleStructureVector * | rawVector () const |
Gives read-only access to the raw vector that sits beneath this angle structure. More... | |
void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
void | writeXMLData (std::ostream &out) const |
Writes a chunk of XML containing this angle structure and all of its properties. More... | |
Input and Output | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
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... | |
Protected Member Functions | |
void | calculateType () const |
Calculates the structure type (strict or taut) and stores it as a property. More... | |
Friends | |
class | regina::NXMLAngleStructureReader |
Represents an angle structure on a triangulation.
Once the underlying triangulation changes, this angle structure is no longer valid.
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inline |
Creates a new angle structure on the given triangulation with the given coordinate vector.
triang | the triangulation on which this angle structure lies. |
newVector | a vector containing the individual angles in the angle structure. |
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inlinevirtual |
Destroys this angle structure.
The underlying vector of angles will also be deallocated.
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protected |
Calculates the structure type (strict or taut) and stores it as a property.
NAngleStructure* regina::NAngleStructure::clone | ( | ) | const |
Creates a newly allocated clone of this angle structure.
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inherited |
Returns the output from writeTextLong() as a string.
NRational regina::NAngleStructure::getAngle | ( | unsigned long | tetIndex, |
int | edgePair | ||
) | const |
Returns the requested angle in this angle structure.
The angle returned will be scaled down; the actual angle is the returned value multiplied by pi.
tetIndex | the index in the triangulation of the tetrahedron in which the requested angle lives; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive. |
edgePair | the number of the vertex splitting representing the pair of edges holding the requested angle; this should be between 0 and 2 inclusive. See regina::vertexSplit and regina::vertexSplitDefn for details regarding vertex splittings. |
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inline |
Returns the triangulation on which this angle structure lies.
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inline |
Determines whether this is a strict angle structure.
A strict angle structure has all angles strictly between (not including) 0 and pi.
true
if and only if this is a strict angle structure.
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inline |
Determines whether this is a taut angle structure.
A taut angle structure contains only angles 0 and pi.
Here we use the Kang-Rubinstein definition of a taut angle structure [1], which is based on the angles alone. In his original paper [2], Lackenby has an extra condition whereby 2-faces of the triangulation must have consistent coorientations, which we do not enforce here.
[1] E. Kang and J. H. Rubinstein, "Ideal triangulations of 3-manifolds II; Taut and angle structures", Algebr. Geom. Topol. 5 (2005), pp. 1505-1533.
[2] M. Lackenby, "Taut ideal triangulations of 3-manifolds", Geom. Topol. 4 (2000), pp. 369-395.
true
if and only if this is a taut structure.
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inline |
Determines whether this is a veering structure.
A veering structure is taut angle structure with additional strong combinatorial constraints, which we do not outline here. For a definition, see C. D. Hodgson, J. H. Rubinstein, H. Segerman, and S. Tillmann, "Veering triangulations admit strict angle structures", Geom. Topol., 15 (2011), pp. 2073-2089.
Note that the Hodgson et al. definition is slightly more general than Agol's veering taut triangulations from his original paper: I. Agol, " Ideal triangulations of pseudo-Anosov mapping tori", in "Topology and Geometry in Dimension Three", volume 560 of Contemp. Math., pp. 1-17, Amer. Math. Soc., 2011. This mirrors the way in which the Kang-Rubinstein definition of taut angle structure is slightly more general than Lackenby's. See the Hodgson et al. paper for full details and comparisons between the two settings.
If this angle structure is not taut, or if the underlying triangulation is non-orientable, then this routine will return false
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true
if and only if this is a veering structure.
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inline |
Gives read-only access to the raw vector that sits beneath this angle structure.
Generally users should not need this function. However, it is provided here in case the need should arise (e.g., for reasons of efficiency).
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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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inlinevirtualinherited |
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 in regina::NSnapPeaTriangulation, regina::NGroupPresentation, regina::NHomMarkedAbelianGroup, regina::NNormalSurfaceList, regina::NTetrahedron, regina::NSatRegion, regina::NVertex, regina::NEdge, regina::Dim2Triangle, regina::NTriangle, regina::NLayeredSolidTorus, regina::NHomGroupPresentation, regina::NGenericIsomorphism< dim >, regina::NGenericIsomorphism< 2 >, regina::NGenericIsomorphism< 3 >, regina::NTriangulation, regina::NComponent, regina::NTxICore, regina::NTriSolidTorus, regina::NAngleStructureList, regina::Dim2Edge, regina::NBoundaryComponent, regina::NLayeredChain, regina::Dim2Vertex, regina::Dim2Component, regina::NScript, regina::NAugTriSolidTorus, regina::NSpiralSolidTorus, regina::NSurfaceFilterProperties, regina::NLayeredTorusBundle, regina::NManifold, regina::NPlugTriSolidTorus, regina::NMatrixInt, regina::NBlockedSFSTriple, regina::NPluggedTorusBundle, regina::Dim2Triangulation, regina::NSurfaceSubset, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NFileInfo, regina::NBlockedSFSLoop, regina::NSnappedBall, regina::NBlockedSFSPair, regina::Dim2BoundaryComponent, regina::NTrivialTri, regina::NL31Pillow, regina::NLayeredChainPair, regina::NText, regina::NSurfaceFilterCombination, and regina::NBlockedSFS.
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virtual |
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.
void regina::NAngleStructure::writeXMLData | ( | std::ostream & | out | ) | const |
Writes a chunk of XML containing this angle structure and all of its properties.
This routine will be called from within NAngleStructureList::writeXMLPacketData().
out | the output stream to which the XML should be written. |