Regina Calculation Engine
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Normal surfaces in 3-manifold triangulations. More...
Classes | |
struct | regina::NDiscSpec |
Specifies a single normal disc in a normal surface. More... | |
class | regina::NDiscSetTet |
Represents a set of normal discs inside a single tetrahedron. More... | |
class | regina::NDiscSetTetData< T > |
Stores data of type T for every normal disc inside a single tetrahedron. More... | |
class | regina::NDiscSetSurface |
Represents the set of all normal discs forming a normal surface. More... | |
class | regina::NDiscSetSurfaceData< T > |
Stores data of type T for every normal disc within a particular normal surface. More... | |
class | regina::NDiscSpecIterator |
An iterator used for running through all normal discs in a normal surface. More... | |
struct | regina::NDiscType |
Identifies a single normal or almost normal disc type within a triangulation. More... | |
class | regina::Triangulation< dim > |
A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets. More... | |
class | regina::Face< dim, subdim > |
Represents a subdim-face in the skeleton of a dim-dimensional triangulation. More... | |
struct | regina::NormalInfo< coordType > |
A template that stores information about a particular normal coordinate system. More... | |
class | regina::NNormalSurfaceVector |
Stores the vector of a single normal surface in a 3-manifold. More... | |
class | regina::NNormalSurface |
Represents a single normal surface in a 3-manifold. More... | |
class | regina::NNormalSurfaceList |
A packet representing a collection of normal surfaces in a 3-manifold. More... | |
struct | regina::NPrismSpec |
Specifies a single triangular prism in a tetrahedron. More... | |
class | regina::NPrismSetSurface |
Represents the set of prisms defined by slicing along all the quads in a particular normal surface. More... | |
class | regina::NNormalSurfaceVectorANStandard |
An almost normal surface vector using standard triangle-quad-oct coordinates. More... | |
class | regina::NNormalSurfaceVectorMirrored |
A normal surface vector that is mirrored in another coordinate system to avoid frequent lengthy calculations. More... | |
class | regina::NNormalSurfaceVectorOriented |
A normal surface vector using transversely oriented standard (triangle-quad) coordinates. More... | |
class | regina::NNormalSurfaceVectorOrientedQuad |
A normal surface vector using transversely oriented quadrilateral coordinates. More... | |
class | regina::NNormalSurfaceVectorQuad |
A normal surface vector using quad coordinates. More... | |
class | regina::NNormalSurfaceVectorQuadOct |
An almost normal surface vector using quad-oct coordinates. More... | |
class | regina::NNormalSurfaceVectorStandard |
A normal surface vector using standard triangle-quad coordinates. More... | |
struct | regina::SurfaceFilterInfo< filterType > |
A template that stores information about a particular type of normal surface filter. More... | |
class | regina::NSurfaceFilter |
A packet that accepts or rejects normal surfaces. More... | |
class | regina::NSurfaceSubset |
Represents a subset of a normal surface list. More... | |
class | regina::NXMLFilterReader |
An XML element reader that reads the specific details of a normal surface filter. More... | |
class | regina::NXMLFilterPacketReader |
An XML packet reader that reads a single surface filter. More... | |
class | regina::NXMLNormalSurfaceReader |
An XML element reader that reads a single normal surface. More... | |
class | regina::NXMLNormalSurfaceListReader |
An XML packet reader that reads a single normal surface list. More... | |
class | regina::NSurfaceFilterCombination |
A normal surface filter that simply combines other filters. More... | |
class | regina::NSurfaceFilterProperties |
A normal surface filter that filters by basic properties of the normal surface. More... | |
Macros | |
#define | REGINA_NORMAL_SURFACE_FLAVOUR(class_, id) |
Defines various constants, types and virtual functions for a subclass of NNormalSurfaceVector. More... | |
#define | REGINA_SURFACE_FILTER(class_, id) |
Defines various constants, types and virtual functions for a descendant class of NSurfaceFilter. More... | |
Typedefs | |
typedef Face< 3, 0 > | regina::NVertex |
A convenience typedef for Face<3, 0>. More... | |
typedef Face< 3, 1 > | regina::NEdge |
A convenience typedef for Face<3, 1>. More... | |
typedef regina::Flags< NormalListFlags > | regina::NormalList |
A combination of flags for types of normal surface lists. More... | |
typedef regina::Flags< NormalAlgFlags > | regina::NormalAlg |
A combination of flags for types of normal surface lists. More... | |
Functions | |
template<typename FunctionObject , typename... Args> | |
ReturnsTraits< FunctionObject >::ReturnType | regina::forCoords (NormalCoords coords, FunctionObject &&func, typename ReturnsTraits< FunctionObject >::ReturnType defaultReturn, Args &&... args) |
Allows the user to call a template function whose template parameter matches a given value of NormalCoords, which is not known until runtime. More... | |
template<typename FunctionObject , typename... Args> | |
ReturnsTraits< FunctionObject >::Void | regina::forCoords (NormalCoords coords, FunctionObject &&func, Args &&... args) |
Allows the user to call a template function whose template parameter matches a given value of NormalCoords, which is not known until runtime. More... | |
template<typename FunctionObject > | |
REGINA_DEPRECATED FunctionObject::ReturnType | regina::forFlavour (NormalCoords coords, FunctionObject func, typename FunctionObject::ReturnType defaultReturn) |
A deprecated alias for the registry-based template function forCoords(). More... | |
template<typename VoidFunctionObject > | |
REGINA_DEPRECATED void | regina::forFlavour (NormalCoords coords, VoidFunctionObject func) |
A deprecated alias for the registry-based template function forCoords(). More... | |
template<typename FunctionObject , typename... Args> | |
ReturnsTraits< FunctionObject >::ReturnType | regina::forFilter (SurfaceFilterType filter, FunctionObject &&func, typename ReturnsTraits< FunctionObject >::ReturnType defaultReturn, Args &&... args) |
Allows the user to call a template function whose template parameter matches a given value of SurfaceFilterType, which is not known until runtime. More... | |
template<typename FunctionObject , typename... Args> | |
ReturnsTraits< FunctionObject >::Void | regina::forFilter (SurfaceFilterType filter, FunctionObject &&func, Args &&... args) |
Allows the user to call a template function whose template parameter matches a given value of SurfaceFilterType, which is not known until runtime. More... | |
REGINA_API std::ostream & | regina::operator<< (std::ostream &out, const NDiscSpec &spec) |
Writes the given disc specifier to the given output stream. More... | |
REGINA_API bool | regina::numberDiscsAwayFromVertex (int discType, int vertex) |
Determines whether or not normal discs of the given type are numbered away from the given vertex. More... | |
REGINA_API bool | regina::discOrientationFollowsEdge (int discType, int vertex, int edgeStart, int edgeEnd) |
Determines whether or not the natural boundary orientation of a normal disc of the given type follows the given directed normal arc. More... | |
REGINA_API std::ostream & | regina::operator<< (std::ostream &out, const NDiscType &type) |
Writes the given disc type to the given output stream. More... | |
REGINA_API NNormalSurfaceVector * | regina::makeZeroVector (const NTriangulation *triangulation, NormalCoords coords) |
Returns a new normal surface vector of the appropriate length for the given triangulation and the given coordinate system. More... | |
REGINA_API NMatrixInt * | regina::makeMatchingEquations (const NTriangulation *triangulation, NormalCoords coords) |
Creates a new set of normal surface matching equations for the given triangulation using the given coordinate system. More... | |
REGINA_API NEnumConstraintList * | regina::makeEmbeddedConstraints (const NTriangulation *triangulation, NormalCoords coords) |
Creates a new set of validity constraints representing the condition that normal surfaces be embedded. More... | |
NormalList | regina::operator| (NormalListFlags lhs, NormalListFlags rhs) |
Returns the bitwise OR of the two given flags. More... | |
NormalAlg | regina::operator| (NormalAlgFlags lhs, NormalAlgFlags rhs) |
Returns the bitwise OR of the two given flags. More... | |
REGINA_API std::ostream & | regina::operator<< (std::ostream &out, const NPrismSpec &spec) |
Writes the given prism specifier to the given output stream. More... | |
Variables | |
REGINA_DEPRECATED typedef NewFunction1< NNormalSurfaceVector, size_t > | regina::NewNormalSurfaceVector |
A legacy typedef provided for backward compatibility only. More... | |
REGINA_API const int | regina::quadSeparating [4][4] |
Lists which quadrilateral types separate which pairs of vertices in a tetrahedron. More... | |
REGINA_DEPRECATED REGINA_API const int(* | regina::vertexSplit )[4] |
Deprecated alias for regina::quadSeparating. More... | |
REGINA_API const int | regina::quadMeeting [4][4][2] |
Lists which quadrilateral types meet which edges in a tetrahedron. More... | |
REGINA_DEPRECATED REGINA_API const int(* | regina::vertexSplitMeeting )[4][2] |
Deprecated alias for regina::quadMeeting. More... | |
REGINA_DEPRECATED REGINA_API const int | regina::vertexSplitDefn [3][4] |
Deprecated array that lists the vertices which each quadrilateral type separates within a tetrahedron. More... | |
REGINA_API const int | regina::quadPartner [3][4] |
Lists the second vertex with which each vertex is paired under each quadrilateral type in a tetrahedron. More... | |
REGINA_DEPRECATED REGINA_API const int(* | regina::vertexSplitPartner )[4] |
Deprecated alias for regina::quadPartner. More... | |
REGINA_API const char | regina::quadString [3][6] |
Contains strings that can be used to represent each quadrilateral type in a tetrahedron. More... | |
REGINA_DEPRECATED REGINA_API const char(* | regina::vertexSplitString )[6] |
Deprecated alias for regina::quadString. More... | |
REGINA_API const NPerm4 | regina::triDiscArcs [4][3] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of triangular normal disc. More... | |
REGINA_API const NPerm4 | regina::quadDiscArcs [3][4] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of quadrilateral normal disc. More... | |
REGINA_API const NPerm4 | regina::octDiscArcs [3][8] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of octagonal normal disc. More... | |
Normal surfaces in 3-manifold triangulations.
#define REGINA_NORMAL_SURFACE_FLAVOUR | ( | class_, | |
id | |||
) |
Defines various constants, types and virtual functions for a subclass of NNormalSurfaceVector.
Every subclass of NNormalSurfaceVector must include REGINA_NORMAL_SURFACE_FLAVOUR at the beginning of the class definition.
This macro provides the class with:
class_ | the name of this subclass of NNormalSurfaceVector. |
id | the corresponding NNormalCoords constant. |
#define REGINA_SURFACE_FILTER | ( | class_, | |
id | |||
) |
Defines various constants, types and virtual functions for a descendant class of NSurfaceFilter.
Every descendant class of NSurfaceFilter must include REGINA_SURFACE_FILTER at the beginning of the class definition.
This macro provides the class with:
class_ | the name of this descendant class of NSurfaceFilter. |
id | the corresponding SurfaceFilterType constant. |
typedef Face< 3, 1 > regina::NEdge |
A convenience typedef for Face<3, 1>.
typedef regina::Flags<NormalAlgFlags> regina::NormalAlg |
A combination of flags for types of normal surface lists.
A combination of flags for types of normal surface lists.
typedef Face< 3, 0 > regina::NVertex |
A convenience typedef for Face<3, 0>.
Represents options and variants of algorithms for enumerating various types of normal surfaces in 3-manifold triangulations.
These options are typically combined in a bitwise fashion using the NormalAlg type, and then passed to enumeration routines such as NNormalSurfaceList::enumerate().
enum regina::NormalCoords |
Represents different coordinate systems that can be used for enumerating and displaying normal surfaces.
IDs 0-9999 are reserved for future use by Regina. If you are extending Regina to include your own coordinate system, you should choose an ID >= 10000.
Enumerator | |
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NS_STANDARD | Represents standard triangle-quadrilateral coordinates for normal surfaces. |
NS_QUAD | Represents quadrilateral coordinates for normal surfaces. For details, see "Normal surface Q-theory", Jeffrey L. Tollefson, Pacific J. Math. 183 (1998), no. 2, 359–374. |
NS_AN_LEGACY | Indicates that a list of almost normal surfaces was created using Regina 4.5.1 or earlier, where surfaces with more than one octagon of the same type were stripped out of the final solution set. As of Regina 4.6 such surfaces are now included in the solution set, since we need them if we wish to enumerate all almost normal surfaces (not just the vertex almost normal surfaces). This coordinate system is only used with legacy data files; new vectors and lists cannot be created in this coordinate system. The underlying coordinates are identical to those of NS_AN_STANDARD. |
NS_AN_QUAD_OCT | Represents quadrilateral-octagon coordinates for octagonal almost normal surfaces. For details, see "Quadrilateral-octagon coordinates for almost normal surfaces", Benjamin A. Burton, Experiment. Math. 19 (2010), 285-315. |
NS_AN_STANDARD | Represents standard triangle-quadrilateral-octagon coordinates for octagonal almost normal surfaces. |
NS_EDGE_WEIGHT | Represents edge weight coordinates for normal surfaces. This coordinate system is for display only; surface vectors and lists cannot be created in this coordinate system. |
NS_TRIANGLE_ARCS | Represents triangle arc coordinates for normal surfaces. This coordinate system is for display only; surface vectors and lists cannot be created in this coordinate system. |
REGINA_DEPRECATED_ENUM | A deprecated alias for NS_TRIANGLE_ARCS. This represents triangle arc coordinates for normal surfaces. See NS_TRIANGLE_ARCS for further details.
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NS_ORIENTED | Represents standard triangle-quadrilateral coordinates for transversely oriented normal surfaces. |
NS_ORIENTED_QUAD | Represents quadrilateral coordinates for transversely oriented normal surfaces. |
NS_ANGLE | Represents angle structure coordinates. This coordinate system is not for use with normal surfaces: it cannot be used either to display them or enumerate them. Instead it is for use with angle structures on triangulations. Because the combinatorics and linear algebra of angle strutures are tightly related to those of normal surfaces, we include NS_ANGLE here so that angle structure routines can make use of some of Regina's existing normal surface machinery. For a triangulation with n tetrahedra, this system has 3n+1 coordinates. The first 3n are analogous to quadrilateral coordinates (specifically, for each quadrilateral type Q, the corresponding angle structure coordinate represents the pair of angles in the same tetrahedron that Q does not meet). The final coordinate is a scaling coordinate, used to projectivise the angle structure polytope so that it becomes a polyhedral cone that is invariant under (positive) scaling. If the final scaling coordinate is s, then a rational value of x in any other coordinate position should be interpreted as the angle x.π/s.
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Represents different lists of normal surfaces that might be constructed for a given 3-manifold triangulation.
The NormalList enumeration refers to the contents of the list, whereas the NormalAlgFlags enumeration refers to the algorithm used to build it.
Used to describe a field, or a set of fields, that can be exported alongside a normal surface list.
This enumeration type is used with export routines such as NNormalSurfaceList::saveCSVStandard() or NNormalSurfaceList::saveCSVEdgeWeight().
This type describes fields in addition to normal coordinates, not the normal coordinates themselves (which are always exported). Each field describes some property of a single normal surface, and corresponds to a single column in a table of normal surfaces.
This type should be treated as a bitmask: you can describe a set of fields by combining the values for individual fields using bitwise or.
The list of available fields may grow with future releases of Regina.
Enumerator | |
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surfaceExportName | Represents the user-assigned surface name. |
surfaceExportEuler | Represents the calculated Euler characteristic of a surface. This will be an integer, and will be left empty if the Euler characteristic cannot be computed. |
surfaceExportOrient | Represents the calculated property of whether a surface is orientable. This will be the string |
surfaceExportSides | Represents the calculated property of whether a surface is one-sided or two-sided. This will be the integer 1 or 2, or will be left empty if the "sidedness" cannot be computed. |
surfaceExportBdry | Represents the calculated property of whether a surface is bounded. In most cases, this will be one of the strings "closed", "real bdry" or "infinite" (where "infinite" indicates a surface with infinitely many discs). For spun-normal surfaces in certain ideal triangulations, this string will be followed by the boundary slopes of the surface at the cusps: these written as a list of pairs (p, q), one for each cusp, indicating that the boundary curves of the surface run p times around the meridian and q times around the longitude. See NNormalSurface::boundaryIntersections() for further information on interpreting these values. |
surfaceExportLink | Represents whether a surface is a single vertex link or a thin edge link. See NNormalSurface::isVertexLink() and NNormalSurface::isThinEdgeLink() for details. This will be written as a human-readable string. |
surfaceExportType | Represents any additional high-level properties of a surface, such as whether it is a splitting surface or a central surface. This will be written as a human-readable string. This field is somewhat arbitrary, and the precise properties it describes are subject to change in future releases of Regina. |
surfaceExportNone | Indicates that no additional fields should be exported. |
surfaceExportAllButName | Indicates that all available fields should be exported, except for the user-assigned surface name. Since the list of available fields may grow with future releases, the numerical value of this constant may change as a result. |
surfaceExportAll | Indicates that all available fields should be exported, including the user-assigned surface name. Since the list of available fields may grow with future releases, the numerical value of this constant may change as a result. |
Represents different types of filter classes that can be used to filter lists of normal surfaces in 3-manifold triangulations.
IDs 0-9999 are reserved for future use by Regina. If you are extending Regina to include your own filter class, you should choose an ID >= 10000.
Enumerator | |
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NS_FILTER_DEFAULT | Represents the NSurfaceFilter class: a do-nothing filter that accepts any normal surface. |
NS_FILTER_PROPERTIES | Represents the NSurfaceFilterProperties subclass: a filter that examines simple properties of a normal surface. |
NS_FILTER_COMBINATION | Represents the NSurfaceFilterCombination subclass: a filter that combines other filters using boolean AND or OR. |
REGINA_API bool regina::discOrientationFollowsEdge | ( | int | discType, |
int | vertex, | ||
int | edgeStart, | ||
int | edgeEnd | ||
) |
Determines whether or not the natural boundary orientation of a normal disc of the given type follows the given directed normal arc.
Natural boundary orientation is defined by arrays regina::triDiscArcs, regina::quadDiscArcs and regina::octDiscArcs.
discType | the normal disc type under consideration; this should be between 0 and 9 inclusive, as described by the NDiscSpec class notes. |
vertex | the vertex about which the normal arc runs. |
edgeStart | the start vertex of the edge to which the normal arc is parallel. |
edgeEnd | the end vertex of the edge to which the normal arc is parallel. |
ReturnsTraits<FunctionObject>::ReturnType regina::forCoords | ( | NormalCoords | coords, |
FunctionObject && | func, | ||
typename ReturnsTraits< FunctionObject >::ReturnType | defaultReturn, | ||
Args &&... | args | ||
) |
Allows the user to call a template function whose template parameter matches a given value of NormalCoords, which is not known until runtime.
In essence, this routine contains a switch/case statement that runs through all possible coordinate sytems.
The advantages of this routine are that (i) the user does not need to repeatedly type such switch/case statements themselves; and (ii) if a new coordinate system is added then only a small amount of code needs to be extended to incorporate it.
This function can only work with coordinate systems in which you can create and store normal surfaces. All other coordinate systems are considered invalid for our purposes here.
In detail: the function object func must define a templated bracket operator, so that func.operator()<NormalInfo<c>>(...)
is defined for any valid NormalCoords enum value c. Then, when the user calls forCoords(coords, func, defaultReturn, ...)
, this routine will call func.operator()<NormalInfo<coords>>(...)
and pass back the corresponding return value. If coords does not denote a valid coordinate system as described above, then forCoords() will pass back defaultReturn instead.
There is also a variant of forCoords() that works with void functions, and so does not take the extra defaultReturn argument.
coords | the given normal coordinate system. |
func | the function object whose bracket operator we will call with a NormalInfo<coords> object. |
defaultReturn | the value to return if the given coordinate system is invalid. |
args | any additional arguments to pass to the bracket operator for func. These will be copied/moved, so if you wish to pass references then you may need to wrap them in std::ref or std::cref. |
ReturnsTraits<FunctionObject>::Void regina::forCoords | ( | NormalCoords | coords, |
FunctionObject && | func, | ||
Args &&... | args | ||
) |
Allows the user to call a template function whose template parameter matches a given value of NormalCoords, which is not known until runtime.
In essence, this routine contains a switch/case statement that runs through all possible coordinate sytems.
The advantages of this routine are that (i) the user does not need to repeatedly type such switch/case statements themselves; and (ii) if a new coordinate system is added then only a small amount of code needs to be extended to incorporate it.
This function can only work with coordinate systems in which you can create and store normal surfaces. All other coordinate systems are considered invalid for our purposes here.
In detail: the function object func must define a templated bracket operator, so that func.operator()<NormalInfo<c>>(...)
is defined for any valid NormalCoords enum value c. Then, when the user calls forCoords(coords, func, ...)
, this routine will call func.operator()<NormalInfo<coords>>(...)
in turn. If coords does not denote a valid coordinate system as described above, then forCoords() will do nothing.
There is also a variant of forCoords() that works with functions with return values, and which takes an extra defaultReturn argument.
coords | the given normal coordinate system. |
func | the function object whose bracket operator we will call with a NormalInfo<coords> object. |
args | any additional arguments to pass to the bracket operator for func. These will be copied/moved, so if you wish to pass references then you may need to wrap them in std::ref or std::cref. |
ReturnsTraits<FunctionObject>::Void
simply evaluates to void
. ReturnsTraits<FunctionObject>::ReturnType regina::forFilter | ( | SurfaceFilterType | filter, |
FunctionObject && | func, | ||
typename ReturnsTraits< FunctionObject >::ReturnType | defaultReturn, | ||
Args &&... | args | ||
) |
Allows the user to call a template function whose template parameter matches a given value of SurfaceFilterType, which is not known until runtime.
In essence, this routine contains a switch/case statement that runs through all possible normal surface filter types.
The advantages of this routine are that (i) the user does not need to repeatedly type such switch/case statements themselves; and (ii) if a new filter type is added then only a small amount of code needs to be extended to incorporate it.
In detail: the function object func must define a templated bracket operator, so that func.operator()<SurfaceFilterInfo<t>>(...)
is defined for any valid SurfaceFilterType enum value t. Then, when the user calls forFilter(filter, func, defaultReturn, ...)
, this routine will call func.operator()<SurfaceFilterInfo<filter>>(...)
and pass back the corresponding return value. If filter does not denote a valid filter type, then forFilter() will pass back defaultReturn instead.
There is also a variant of forFilter() that works with void functions, and so does not take the extra defaultReturn argument.
filter | the given type of normal surface filter. |
func | the function object whose bracket operator we will call with a SurfaceFilterInfo<filter> object. |
defaultReturn | the value to return if the given filter type is not valid. |
args | any additional arguments to pass to the bracket operator for func. These will be copied/moved, so if you wish to pass references then you may need to wrap then in std::ref or std::cref. |
ReturnsTraits<FunctionObject>::Void regina::forFilter | ( | SurfaceFilterType | filter, |
FunctionObject && | func, | ||
Args &&... | args | ||
) |
Allows the user to call a template function whose template parameter matches a given value of SurfaceFilterType, which is not known until runtime.
In essence, this routine contains a switch/case statement that runs through all possible normal surface filter types.
The advantages of this routine are that (i) the user does not need to repeatedly type such switch/case statements themselves; and (ii) if a new filter type is added then only a small amount of code needs to be extended to incorporate it.
In detail: the function object func must define a templated bracket operator, so that func.operator()<SurfaceFilterInfo<t>>(...)
is defined for any valid SurfaceFilterType enum value t. Then, when the user calls forFilter(filter, func, ...)
, this routine will call func.operator()<SurfaceFilterInfo<filter>>(...)
in turn. If filter does not denote a valid filter type, then forFilter() will do nothing.
There is also a variant of forFilter() that works with functions with return values, and which takes an extra defaultReturn argument.
filter | the given type of normal surface filter. |
func | the function object whose bracket operator we will call with a SurfaceFilterInfo<filter> object. |
args | any additional arguments to pass to the bracket operator for func. These will be copied/moved, so if you wish to pass references then you may need to wrap then in std::ref or std::cref. |
ReturnsTraits<FunctionObject>::Void
simply evaluates to void
.
|
inline |
A deprecated alias for the registry-based template function forCoords().
See forCoords() for further details.
|
inline |
A deprecated alias for the registry-based template function forCoords().
See forCoords() for further details.
REGINA_API NEnumConstraintList* regina::makeEmbeddedConstraints | ( | const NTriangulation * | triangulation, |
NormalCoords | coords | ||
) |
Creates a new set of validity constraints representing the condition that normal surfaces be embedded.
The validity constraints will be expressed relative to the given coordinate system.
triangulation | the triangulation upon which these validity constraints will be based. |
coords | the coordinate system to be used. |
REGINA_API NMatrixInt* regina::makeMatchingEquations | ( | const NTriangulation * | triangulation, |
NormalCoords | coords | ||
) |
Creates a new set of normal surface matching equations for the given triangulation using the given coordinate system.
The returned matrix will be newly allocated and its destruction will be the responsibility of the caller of this routine.
Each equation will be represented as a row of the matrix. Each column of the matrix represents a coordinate in the given coordinate system.
triangulation | the triangulation upon which these matching equations will be based. |
coords | the coordinate system to be used. |
REGINA_API NNormalSurfaceVector* regina::makeZeroVector | ( | const NTriangulation * | triangulation, |
NormalCoords | coords | ||
) |
Returns a new normal surface vector of the appropriate length for the given triangulation and the given coordinate system.
All elements of this vector will be initialised to zero.
The new vector will be of the subclass of NNormalSurfaceVector corresponding to the given coordinate system. The caller of this routine is responsible for destroying the new vector.
triangulation | the triangulation upon which the underlying coordinate system is based. |
coords | the coordinate system to be used. |
REGINA_API bool regina::numberDiscsAwayFromVertex | ( | int | discType, |
int | vertex | ||
) |
Determines whether or not normal discs of the given type are numbered away from the given vertex.
discType | the normal disc type under consideration; this should be between 0 and 9 inclusive, as described by the NDiscSpec class notes. |
vertex | the vertex under consideration; this should be between 0 and 3 inclusive. |
true
if normal discs of the given type are numbered away from the given vertex, or false
if they are numbered towards the given vertex. REGINA_API std::ostream& regina::operator<< | ( | std::ostream & | out, |
const NPrismSpec & | spec | ||
) |
Writes the given prism specifier to the given output stream.
The prism specifier will be written as a pair (tetIndex, edge)
.
out | the output stream to which to write. |
spec | the prism specifier to write. |
REGINA_API std::ostream& regina::operator<< | ( | std::ostream & | out, |
const NDiscSpec & | spec | ||
) |
Writes the given disc specifier to the given output stream.
The disc specifier will be written as a triple (tetIndex, type, number)
.
out | the output stream to which to write. |
spec | the disc specifier to write. |
|
inline |
Writes the given disc type to the given output stream.
The disc type will be written as a pair (tetIndex, type)
.
out | the output stream to which to write. |
type | the disc type to write. |
|
inline |
Returns the bitwise OR of the two given flags.
lhs | the first flag to combine. |
rhs | the second flag to combine. |
|
inline |
Returns the bitwise OR of the two given flags.
lhs | the first flag to combine. |
rhs | the second flag to combine. |
REGINA_DEPRECATED typedef NewFunction1<NNormalSurfaceVector, size_t> regina::NewNormalSurfaceVector |
A legacy typedef provided for backward compatibility only.
REGINA_API const NPerm4 regina::octDiscArcs[3][8] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of octagonal normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array octDiscArcs[i]
lists the boundary arcs of the octagonal disc of type i. See NNormalSurface::octs() for further details.
Note that permutation octDiscArcs[i][j]
will be even precisely when j
is 0, 1, 4 or 5.
octDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. REGINA_API const NPerm4 regina::quadDiscArcs[3][4] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of quadrilateral normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array quadDiscArcs[i]
lists the boundary arcs of the quadrilateral disc of type i. See NNormalSurface::quads() for further details.
Note that permutation quadDiscArcs[i][j]
will be even precisely when j
is even.
quadDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. REGINA_API const int regina::quadMeeting[4][4][2] |
Lists which quadrilateral types meet which edges in a tetrahedron.
See regina::quadSeparating and NNormalSurface::quads() for more information on quadrilateral types.
quadMeeting[i][j][0,1]
are the numbers of the two quadrilateral types that meet the edge joining tetrahedron vertices i
and j
.
REGINA_API const int regina::quadPartner[3][4] |
Lists the second vertex with which each vertex is paired under each quadrilateral type in a tetrahedron.
See regina::quadSeparating and NNormalSurface::quads() for more information on quadrilateral types.
Quadrilateral type i
pairs vertex v
with vertex quadPartner[i][v]
.
REGINA_API const int regina::quadSeparating[4][4] |
Lists which quadrilateral types separate which pairs of vertices in a tetrahedron.
As outlined in NNormalSurface::quads(), there are three quadrilateral types in a tetrahedron, numbered 0, 1 and 2. Each quadrilateral type separates the four tetrahedron vertices 0,1,2,3 into two pairs. quadSeparating[i][j]
is the number of the quadrilateral type that keeps vertices i
and j
together.
It is guaranteed that quadrilateral type i will keep the vertices of edge i together (and will therefore also keep the vertices of edge 5-i together).
REGINA_API const char regina::quadString[3][6] |
Contains strings that can be used to represent each quadrilateral type in a tetrahedron.
See regina::quadSeparating and NNormalSurface::quads() for more information on quadrilateral types.
The string describing quadrilateral type i
is quadString[i]
and is of the form 02/13
, which in this case is the quadrilateral type that splits vertices 0,2 from vertices 1,3.
REGINA_API const NPerm4 regina::triDiscArcs[4][3] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of triangular normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array triDiscArcs[i]
lists the boundary arcs of the triangular disc of type i. See NNormalSurface::triangles() for further details.
Note that every permutation in this array is even.
triDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. REGINA_DEPRECATED REGINA_API const int(* regina::vertexSplit)[4] |
Deprecated alias for regina::quadSeparating.
REGINA_DEPRECATED REGINA_API const int regina::vertexSplitDefn[3][4] |
Deprecated array that lists the vertices which each quadrilateral type separates within a tetrahedron.
See regina::quadSeparating and NNormalSurface::quads() for more information on quadrilateral types.
Quadrilateral type i
splits the vertex pairs vertexSplitDefn[i][0,1]
and vertexSplitDefn[i][2,3]
.
It is guaranteed that:
vertexSplitDefn[i][0] < vertexSplitDefn[i][1]
;vertexSplitDefn[i][2] < vertexSplitDefn[i][3]
;vertexSplitDefn[i][0] < vertexSplitDefn[i][2]
.REGINA_DEPRECATED REGINA_API const int(* regina::vertexSplitMeeting)[4][2] |
Deprecated alias for regina::quadMeeting.
REGINA_DEPRECATED REGINA_API const int(* regina::vertexSplitPartner)[4] |
Deprecated alias for regina::quadPartner.
REGINA_DEPRECATED REGINA_API const char(* regina::vertexSplitString)[6] |
Deprecated alias for regina::quadString.