Angle Structures

Angle structures on triangulations. More...

Classes
class	regina::AngleStructure
	Represents an angle structure on a triangulation. More...
class	regina::AngleStructures
	A collection of angle structures on a 3-manifold triangulation. More...

Enumerations
enum class	regina::AngleAlg {   regina::AngleAlg::Default = 0x0000 , regina::AngleAlg::Tree = 0x0010 , regina::AngleAlg::DD = 0x0020 , regina::AngleAlg::Legacy = 0x4000 ,   regina::AngleAlg::Custom = 0x8000 }
	Represents options and variants of algorithms for enumerating various types of angle structures on 3-manifold triangulations. More...

Functions
Flags< AngleAlg >	regina::operator| (AngleAlg lhs, AngleAlg rhs)
	Returns the bitwise OR of the two given flags.
void	regina::swap (AngleStructure &a, AngleStructure &b) noexcept
	Swaps the contents of the given angle structures.
void	regina::swap (AngleStructures &lhs, AngleStructures &rhs)
	Swaps the contents of the two given lists.
MatrixInt	regina::makeAngleEquations (const Triangulation< 3 > &tri)
	Generates the set of angle structure equations for the given triangulation.

Detailed Description

Angle structures on triangulations.

Enumeration Type Documentation

AngleAlg

enum class regina::AngleAlg

strong

Represents options and variants of algorithms for enumerating various types of angle structures on 3-manifold triangulations.

This enumeration type is used with angle structure enumeration routines, such as the AngleStructures class constructor.

These values can be combined using the bitwise OR operator (resulting in an object of type Flags<AngleAlg>). In particular, if a hypersurface enumeration function takes an argument of type Flags<AngleAlg>, then you can pass a single AngleAlg constant, or a bitwise combination of such constants (flag1 | flag2), or empty braces {} to indicate no flags at all (which is equivalent to passing AngleAlg::Default).

Enumerator
Default	An empty flag, indicating to an enumeration routine that it should use its default behaviour. The numeric value of this flag is zero (i.e., it has no effect when combined with other flags using bitwise OR).
Tree	When enumerating taut angle structures, this flag indicates that the tree traversal algorithm should be used. This algorithm is based on linear and integer programming techniques, and has many desirable properties including a relatively low overhead. Enumeration algorithms will use it if possible unless a different method is explicitly requested. This is a variant of the tree traversal algorithm from B. A. Burton and M. Ozlen, "A tree traversal algorithm for decision problems in knot theory and 3-manifold topology", Algorithmica 65 (2013), pp. 772-801. This flag is incompatible with DD.
DD	When enumerating vertex or taut angle structures, this flag indicates that a modified double description method should be used. This is currently the only supported algorithm for enumerating all vertex angle structures (not just taut structures). This flag is incompatible with Tree.
Legacy	Indicates that an angle structure list was enumerated using an older version of Regina (6.0.1 or earlier). These older versions did not retain details of the algorithm used to build each list, and so in such cases no further algorithmic information is available. If this flag is passed to an enumeration algorithm, it will be ignored.
Custom	Indicates that an angle structure list was built using a customised algorithm. In such cases, no further details on the algorithm are available. If this flag is passed to an enumeration algorithm, it will be ignored.

Function Documentation

makeAngleEquations()

MatrixInt regina::makeAngleEquations

(

const Triangulation< 3 > &

tri

)

Generates the set of angle structure equations for the given triangulation.

These are the angle equations that will be used when enumerating angle structures on the given triangulation.

Each equation will be represented as a row of the resulting matrix, and each column will represent a coordinate in the underlying coordinate system (which is described in the notes for AngleStructure::vector()).

Parameters

tri	the triangulation upon which these angle structure equations will be based.

Returns

the resulting set of angle structure equations.

operator|()

Flags< AngleAlg > regina::operator| ( AngleAlg lhs, AngleAlg rhs )

inline

Returns the bitwise OR of the two given flags.

Parameters

lhs	the first flag to combine.
rhs	the second flag to combine.

Returns

the combination of both flags.

swap() [1/2]

void regina::swap ( AngleStructure & a, AngleStructure & b )

inlinenoexcept

Swaps the contents of the given angle structures.

This global routine simply calls AngleStructure::swap(); it is provided so that AngleStructure meets the C++ Swappable requirements.

Parameters

a	the first angle structure whose contents should be swapped.
b	the second angle structure whose contents should be swapped.

swap() [2/2]

void regina::swap ( AngleStructures & lhs, AngleStructures & rhs )

inline

Swaps the contents of the two given lists.

This global routine simply calls AngleStructures::swap(); it is provided so that AngleStructures meets the C++ Swappable requirements.

See AngleStructures::swap() for more details.

Note

This swap function is not marked noexcept, since it fires change events on both lists which may in turn call arbitrary code via any registered packet listeners.

Parameters

lhs	the list whose contents should be swapped with rhs.
rhs	the list whose contents should be swapped with lhs.