Regina Calculation Engine
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Represents an angle structure on a triangulation. More...
#include <angle/nanglestructure.h>
Public Member Functions | |
NAngleStructure (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... | |
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... | |
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... | |
void | writeToFile (NFile &out) const |
Writes this angle structure and all of its properties to the given old-style binary file. More... | |
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ShareableObject () | |
Default constructor that does nothing. More... | |
virtual | ~ShareableObject () |
Default destructor that does nothing. More... | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
std::string | toString () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toStringLong () const |
Returns the output from writeTextLong() as a string. More... | |
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virtual | ~NFilePropertyReader () |
Default destructor that does nothing. More... | |
Static Public Member Functions | |
static NAngleStructure * | readFromFile (NFile &in, NTriangulation *triangulation) |
Reads an angle structure and all its properties from the given old-style binary file. More... | |
Protected Member Functions | |
virtual void | readIndividualProperty (NFile &infile, unsigned propType) |
Reads an individual property from an old-style binary file. More... | |
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.
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 vertexSplit and 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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static |
Reads an angle structure and all its properties from the given old-style binary file.
This routine reads precisely what writeToFile() writes.
in | the file from which to read. |
triangulation | the triangulation on which this angle structure will lie. |
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protectedvirtual |
Reads an individual property from an old-style binary file.
The property type and bookmarking details should not read; merely the contents of the property that are written to file between NFile::writePropertyHeader() and NFile::writePropertyFooter(). See the NFile::writePropertyHeader() notes for details.
The property type of the property to be read will be passed in propType. If the property type is unrecognised, this routine should simply do nothing and return. If the property type is recognised, this routine should read the property and process it accordingly (e.g., store it in whatever data object is currently being read).
infile | the file from which to read the property. This should be open for reading and at the position immediately after writePropertyHeader() would have been called during the corresponding write operation. |
propType | the property type of the property about to be read. |
Implements regina::NFilePropertyReader.
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virtual |
Writes this object in short text format to the given output stream.
The output should fit on a single line and no newline should be written.
out | the output stream to which to write. |
Implements regina::ShareableObject.
void regina::NAngleStructure::writeToFile | ( | NFile & | out) | const |
Writes this angle structure and all of its properties to the given old-style binary file.
This routine writes precisely what readFromFile() reads.
out | the file to which to write. |
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. |