Regina Calculation Engine
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Represents an angle structure on a triangulation. More...
#include <angle/anglestructure.h>
Public Member Functions | |
AngleStructure (const Triangulation< 3 > *triang, AngleStructureVector *newVector) | |
Creates a new angle structure on the given triangulation with the given coordinate vector. More... | |
~AngleStructure () | |
Destroys this angle structure. More... | |
AngleStructure * | clone () const |
Creates a newly allocated clone of this angle structure. More... | |
Rational | angle (size_t tetIndex, int edgePair) const |
Returns the requested angle in this angle structure. More... | |
const Triangulation< 3 > * | triangulation () 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 AngleStructureVector * | rawVector () const |
Gives read-only access to the raw vector that sits beneath this angle structure. More... | |
void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object 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 | writeTextLong (std::ostream &out) const |
A default implementation for detailed output. More... | |
std::string | str () const |
Returns a short text representation of this object. More... | |
std::string | utf8 () const |
Returns a short text representation of this object using unicode characters. More... | |
std::string | detail () const |
Returns a detailed text representation of this object. More... | |
Protected Member Functions | |
void | calculateType () const |
Calculates the structure type (strict or taut) and stores it as a property. More... | |
Friends | |
class | regina::XMLAngleStructureReader |
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Once the underlying triangulation changes, this angle structure is no longer valid.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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inline |
Destroys this angle structure.
The underlying vector of angles will also be deallocated.
Rational regina::AngleStructure::angle | ( | size_t | 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.
Within a tetrahedron, the three angles are indexed 0, 1 and 2. Angle i appears on edge i of the tetrahedron as well as its opposite edge (5-i).
tetIndex | the index in the triangulation of the tetrahedron in which the requested angle lives; this should be between 0 and Triangulation<3>::size()-1 inclusive. |
edgePair | the number representing the pair of edges holding the requested angle, as described above; this should be 0, 1 or 2. |
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protected |
Calculates the structure type (strict or taut) and stores it as a property.
AngleStructure* regina::AngleStructure::clone | ( | ) | const |
Creates a newly allocated clone of this angle structure.
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inherited |
Returns a detailed text representation of this object.
This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.
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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 a short text representation of this object.
This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
__str__()
.
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inline |
Returns the triangulation on which this angle structure lies.
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inherited |
Returns a short text representation of this object using unicode characters.
Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.
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inlineinherited |
A default implementation for detailed output.
This routine simply calls T::writeTextShort() and appends a final newline.
out | the output stream to which to write. |
void regina::AngleStructure::writeTextShort | ( | std::ostream & | out | ) | const |
Writes a short text representation of this object to the given output stream.
out | the output stream to which to write. |
void regina::AngleStructure::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 AngleStructures::writeXMLPacketData().
out | the output stream to which the XML should be written. |