Regina Calculation Engine
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regina::NCompactSearcher Class Reference

A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3-manifold triangulations are required. More...

#include <census/ngluingpermsearcher.h>

Inheritance diagram for regina::NCompactSearcher:
regina::NGluingPermSearcher regina::NGluingPerms regina::NGenericGluingPerms< 3 > regina::NClosedPrimeMinSearcher

Classes

struct  TetEdgeState
 A structure used to track equivalence classes of tetrahedron edges as the gluing permutation set is constructed. More...
 
struct  TetVertexState
 A structure used to track equivalence classes of tetrahedron vertices as the gluing permutation set is constructed. More...
 

Public Member Functions

 NCompactSearcher (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, int whichPurge, UseGluingPerms use, void *useArgs=0)
 Creates a new search manager for use when only compact 3-manifold triangulations are required. More...
 
 NCompactSearcher (std::istream &in, UseGluingPerms use, void *useArgs=0)
 Initialises a new search manager based on data read from the given input stream. More...
 
virtual ~NCompactSearcher ()
 Destroys this search manager and all supporting data structures. More...
 
virtual void dumpData (std::ostream &out) const
 Dumps all internal data in a plain text format to the given output stream. More...
 
virtual void runSearch (long maxDepth=-1)
 Generates all possible gluing permutation sets that satisfy the current search criteria. More...
 
- Public Member Functions inherited from regina::NGluingPermSearcher
 NGluingPermSearcher (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, bool finiteOnly, int whichPurge, UseGluingPerms use, void *useArgs=0)
 Initialises a new search for gluing permutation sets. More...
 
 NGluingPermSearcher (std::istream &in, UseGluingPerms use, void *useArgs=0)
 Initialises a new search manager based on data read from the given input stream. More...
 
virtual ~NGluingPermSearcher ()
 Destroys this search manager and all supporting data structures. More...
 
bool completePermSet () const
 Determines whether this search manager holds a complete gluing permutation set or just a partially completed search state. More...
 
void dumpTaggedData (std::ostream &out) const
 Dumps all internal data in a plain text format, along with a marker to signify which precise class the data belongs to. More...
 
- Public Member Functions inherited from regina::NGluingPerms
 NGluingPerms (const NGluingPerms &cloneMe)
 Creates a new set of gluing permutations that is a clone of the given permutation set. More...
 
 NGluingPerms (std::istream &in)
 Reads a new set of gluing permutations from the given input stream. More...
 
unsigned getNumberOfTetrahedra () const
 Returns the total number of tetrahedra under consideration. More...
 
const NFacePairinggetFacePairing () const
 Returns the specific pairing of tetrahedron faces that this set of gluing permutations complements. More...
 
- Public Member Functions inherited from regina::NGenericGluingPerms< 3 >
 NGenericGluingPerms (const NGenericGluingPerms< dim > &cloneMe)
 Creates a new set of gluing permutations that is a clone of the given permutation set. More...
 
 NGenericGluingPerms (std::istream &in)
 Reads a new set of gluing permutations from the given input stream. More...
 
virtual ~NGenericGluingPerms ()
 Deallocates any memory used by this structure. More...
 
bool inputError () const
 Was an error found during construction from an input stream? More...
 
unsigned size () const
 Returns the total number of simplices under consideration. More...
 
const FacetPairing * getFacetPairing () const
 Returns the specific pairing of simplex facets that this set of gluing permutations complements. More...
 
Perm gluingPerm (const NFacetSpec< dim > &source) const
 Returns the gluing permutation associated with the given simplex facet. More...
 
Perm gluingPerm (unsigned simp, unsigned facet) const
 Returns the gluing permutation associated with the given simplex facet. More...
 
Triangulation * triangulate () const
 Returns a newly created triangulation as modelled by this set of gluing permutations and the associated simplex facet pairing. More...
 

Static Public Attributes

static const char dataTag_
 A character used to identify this class when reading and writing tagged data in text format. More...
 
- Static Public Attributes inherited from regina::NGluingPermSearcher
static const char dataTag_
 A character used to identify this class when reading and writing tagged data in text format. More...
 

Protected Member Functions

virtual char dataTag () const
 Returns the character used to identify this class when storing tagged data in text format. More...
 
int findEdgeClass (int edgeID) const
 Returns the representative of the equivalence class containing the given tetrahedron edge. More...
 
int findEdgeClass (int edgeID, char &twisted) const
 Returns the representative of the equivalence class containing the given tetrahedron edge. More...
 
int mergeVertexClasses ()
 Merge the classes of tetrahedron vertices as required by the new gluing made at stage orderElt of the search. More...
 
bool mergeEdgeClasses ()
 Merge the classes of tetrahedron edges as required by the new gluing made at stage orderElt of the search. More...
 
void splitVertexClasses ()
 Split the classes of tetrahedron vertices to mirror the undoing of the gluing at stage orderElt of the search. More...
 
void splitEdgeClasses ()
 Split the classes of tetrahedron edges to mirror the undoing of the gluing at stage orderElt of the search. More...
 
void vtxBdryJoin (int vertexID, char end, int adjVertexID, char twist)
 Signifies that the boundary edges supplied by the vertex linking triangles for the two given tetrahedron vertices should be marked as adjacent. More...
 
void vtxBdryFixAdj (int vertexID)
 Adjusts the bdryNext and bdryTwist arrays for nearby tetrahedron vertices, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given vertex. More...
 
void vtxBdryBackup (int vertexID)
 Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given tetrahedron vertex. More...
 
void vtxBdryRestore (int vertexID)
 Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given tetrahedron vertex. More...
 
void vtxBdryNext (int vertexID, int tet, int vertex, int bdryFace, int next[2], char twist[2])
 Assuming the given edge of the vertex linking triangle for the given tetrahedron vertex lies on the boundary of the vertex link, this routine identifies the adjacent boundary edges of the vertex link in each direction. More...
 
bool vtxBdryLength1 (int vertexID)
 Determines whether one of the edges of the vertex linking triangle for the given tetrahedron vertex in fact forms an entire one-edge boundary component of the overall vertex link. More...
 
bool vtxBdryLength2 (int vertexID1, int vertexID2)
 Determines whether edges of the vertex linking triangles for each of the given tetrahedron vertices combine to form an entire two-edge boundary component of the overall vertex link, with one edge from each triangle. More...
 
void vtxBdryConsistencyCheck ()
 Runs a number of tests on all tetrahedron vertices to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the TetVertexState class. More...
 
void vtxBdryDump (std::ostream &out)
 Dumps a summary of bdryNext, bdryTwist and bdryEdges for every vertex of every tetrahedron to the given output stream. More...
 
- Protected Member Functions inherited from regina::NGluingPermSearcher
bool isCanonical () const
 Compares the current set of gluing permutations with its preimage under each automorphism of the underlying face pairing, in order to see whether the current set is in canonical form (i.e., is lexicographically smallest). More...
 
bool badEdgeLink (const NTetFace &face) const
 Determines whether the permutations already constructed model a triangulation with an edge identified with itself in reverse. More...
 
bool lowDegreeEdge (const NTetFace &face, bool testDegree12, bool testDegree3) const
 Determines whether the permutations already constructed model a triangulation with a low degree edge. More...
 
bool mayPurge (const NTetFace &face) const
 Determines whether the permutations under construction are doomed to model a triangulation that can be purged from the census. More...
 
- Protected Member Functions inherited from regina::NGluingPerms
 NGluingPerms (const NFacePairing *pairing)
 Creates a new permutation set. More...
 
- Protected Member Functions inherited from regina::NGenericGluingPerms< 3 >
 NGenericGluingPerms (const FacetPairing *pairing)
 Creates a new permutation set. More...
 
int & permIndex (const NFacetSpec< dim > &source)
 Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...
 
int & permIndex (unsigned simp, unsigned facet)
 Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...
 
const int & permIndex (const NFacetSpec< dim > &source) const
 Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...
 
const int & permIndex (unsigned simp, unsigned facet) const
 Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...
 
int gluingToIndex (const NFacetSpec< dim > &source, const Perm &gluing) const
 Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
 
int gluingToIndex (unsigned simp, unsigned facet, const Perm &gluing) const
 Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
 
Perm indexToGluing (const NFacetSpec< dim > &source, int index) const
 Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1. More...
 
Perm indexToGluing (unsigned simp, unsigned facet, int index) const
 Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1. More...
 

Protected Attributes

unsigned nVertexClasses
 The number of equivalence classes of identified tetrahedron vertices. More...
 
TetVertexStatevertexState
 Used for tracking equivalence classes of identified tetrahedron vertices. More...
 
int * vertexStateChanged
 Tracks the way in which the vertexState[] array has been updated over time. More...
 
unsigned nEdgeClasses
 The number of equivalence classes of identified tetrahedron edges. More...
 
TetEdgeStateedgeState
 Used for tracking equivalence classes of identified tetrahedron edges. More...
 
int * edgeStateChanged
 Tracks the way in which the edgeState[] array has been updated over time. More...
 
- Protected Attributes inherited from regina::NGluingPermSearcher
const NFacePairing::IsoListautos_
 The set of isomorphisms that define equivalence of gluing permutation sets. More...
 
bool autosNew
 Did we create the isomorphism list autos_ ourselves (in which case we must destroy it also)? More...
 
bool orientableOnly_
 Are we only searching for gluing permutations that correspond to orientable triangulations? More...
 
bool finiteOnly_
 Are we only searching for gluing permutations that correspond to finite triangulations? More...
 
int whichPurge_
 Are there any types of triangulation that we may optionally avoid constructing? See the constructor documentation for further details on this search parameter. More...
 
UseGluingPerms use_
 A routine to call each time a gluing permutation set is found during the search. More...
 
void * useArgs_
 Additional user-supplied data to be passed as the second argument to the use_ routine. More...
 
bool started
 Has the search started yet? This helps distinguish between a new search and the resumption of a partially completed search. More...
 
int * orientation
 Keeps track of the orientation of each tetrahedron in the underlying triangulation. More...
 
NTetFaceorder
 Describes the order in which gluing permutations are assigned to faces. More...
 
int orderSize
 The total number of edges in the face pairing graph, i.e., the number of elements of interest in the order[] array. More...
 
int orderElt
 Marks which element of order[] we are currently examining at this stage of the search. More...
 

Static Protected Attributes

static const char VLINK_CLOSED
 Signifies that a vertex link has been closed off (i.e., the link has no remaining boundary edges). More...
 
static const char VLINK_NON_SPHERE
 Signifies that a vertex link has been made into something other than a 2-sphere with zero or more punctures. More...
 
static const int vertexLinkNextFace [4][4]
 Maintains an ordering of the three tetrahedron faces surrounding a vertex in a tetrahedron. More...
 
static const int vertexLinkPrevFace [4][4]
 Provides backwards links for the ordering described by vertexLinkNextFace. More...
 

Additional Inherited Members

- Public Types inherited from regina::NGenericGluingPerms< 3 >
typedef DimTraits< dim >
::FacetPairing 
FacetPairing
 
typedef DimTraits< dim >::Perm Perm
 
typedef DimTraits< dim >::Simplex Simplex
 
typedef DimTraits< dim >
::Triangulation 
Triangulation
 
- Static Public Member Functions inherited from regina::NGluingPermSearcher
static void findAllPerms (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, bool finiteOnly, int whichPurge, UseGluingPerms use, void *useArgs=0)
 The main entry routine for running a search for all gluing permutation sets that complement a given face pairing. More...
 
static NGluingPermSearcherbestSearcher (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, bool finiteOnly, int whichPurge, UseGluingPerms use, void *useArgs=0)
 Constructs a search manager of the best possible class for the given search parameters. More...
 
static NGluingPermSearcherreadTaggedData (std::istream &in, UseGluingPerms use, void *useArgs=0)
 Creates a new search manager based on tagged data read from the given input stream. More...
 

Detailed Description

A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3-manifold triangulations are required.

The only constraints placed upon a triangulation are that every edge must be valid (i.e., not identified with itself in reverse), and that the link of every vertex must be a disk or a sphere.

The search algorithm uses modified union-find structures on both edge and vertex equivalence classes to prune searches that are guaranteed to lead to bad edge or vertex links. For details see "Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find", Benjamin A. Burton, Discrete Comput. Geom. 38 (2007), no. 3, 527–571; and "Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations", Benjamin A. Burton, in "ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation", ACM, 2011, pp. 59-66.

No additional unwanted triangulations will be produced by this search (in contrast to other search classes, such as NClosedPrimeMinSearcher). That is, only compact 3-manifolds will be produced.

Python:
Not present.

Constructor & Destructor Documentation

regina::NCompactSearcher::NCompactSearcher ( const NFacePairing pairing,
const NFacePairing::IsoList autos,
bool  orientableOnly,
int  whichPurge,
UseGluingPerms  use,
void *  useArgs = 0 
)

Creates a new search manager for use when only compact 3-manifold triangulations are required.

For details on how a search manager is used, see the NGluingPermSearcher documentation. Note in particular that this class will be automatically used by NGluingPermSearcher::findAllPerms() if possible, so there is often no need for an end user to instantiate this class directly.

All constructor arguments are the same as for the NGluingPermSearcher constructor, though some arguments (such as finiteOnly) are not needed here since they are already implied by the specialised search context.

Precondition
The given face pairing is connected, i.e., it is possible to reach any tetrahedron from any other tetrahedron via a series of matched face pairs.
The given face pairing is in canonical form as described by NFacePairing::isCanonical(). Note that all face pairings constructed by NFacePairing::findAllPairings() are of this form.
regina::NCompactSearcher::NCompactSearcher ( std::istream &  in,
UseGluingPerms  use,
void *  useArgs = 0 
)

Initialises a new search manager based on data read from the given input stream.

This may be a new search or a partially completed search.

This routine reads data in the format written by dumpData(). If you wish to read data whose precise class is unknown, consider using dumpTaggedData() and readTaggedData() instead.

If the data found in the input stream is invalid or incorrectly formatted, the routine inputError() will return true but the contents of this object will be otherwise undefined.

The arguments use and useArgs are the same as for the NGluingPermSearcher constructor.

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
inthe input stream from which to read.
regina::NCompactSearcher::~NCompactSearcher ( )
inlinevirtual

Destroys this search manager and all supporting data structures.

Member Function Documentation

char regina::NCompactSearcher::dataTag ( ) const
inlineprotectedvirtual

Returns the character used to identify this class when storing tagged data in text format.

Returns
the class tag.

Reimplemented from regina::NGluingPermSearcher.

Reimplemented in regina::NClosedPrimeMinSearcher.

virtual void regina::NCompactSearcher::dumpData ( std::ostream &  out) const
virtual

Dumps all internal data in a plain text format to the given output stream.

This object can be recreated from this text data by calling the input stream constructor for this class.

This routine may be useful for transferring objects from one processor to another.

Note that subclass data is written after superclass data, so it is safe to dump data from a subclass and then recreate a new superclass object from that data (though subclass-specific information will of course be lost).

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
outthe output stream to which the data should be written.

Reimplemented from regina::NGluingPermSearcher.

Reimplemented in regina::NClosedPrimeMinSearcher.

int regina::NCompactSearcher::findEdgeClass ( int  edgeID) const
inlineprotected

Returns the representative of the equivalence class containing the given tetrahedron edge.

The class representative is defined to be the root of the corresponding union-find tree.

See the TetEdgeState class for further details. See also the other variant of findEdgeClass(), which is slightly slower but which also tracks edge orientation.

Parameters
edgeIDthe index of a single tetrahedron edge; this must be between 0 and 6t-1 inclusive, where t is the number of tetrahedra. See the TetEdgeState class notes for details on edge indexing.
Returns
the index of the tetrahedron edge at the root of the union-find tree, i.e., the representative of the equivalence class.
int regina::NCompactSearcher::findEdgeClass ( int  edgeID,
char &  twisted 
) const
inlineprotected

Returns the representative of the equivalence class containing the given tetrahedron edge.

The class representative is defined to be the root of the corresponding union-find tree.

The argument twisted is also modified to indicate whether or not the identification of the given edge with the class representative preserves orientation. Note that this arugment is not initialised. Instead, if the identification is orientation-preserving then twisted will be left unmodified, and if it is orientation-reversing then twisted will be changed from 0 to 1 or vice-versa.

See the TetEdgeState class for further details. See also the other variant of findEdgeClass(), which is slightly faster but which does not track edge orientation.

Parameters
edgeIDthe index of a single tetrahedron edge; this must be between 0 and 6t-1 inclusive, where t is the number of tetrahedra. See the TetEdgeState class notes for details on edge indexing.
twistedused to track edge orientation, as described above. This must be either 0 or 1 as it is passed into the function, and it will also be either 0 or 1 upon returning from the function.
Returns
the index of the tetrahedron edge at the root of the union-find tree, i.e., the representative of the equivalence class.
bool regina::NCompactSearcher::mergeEdgeClasses ( )
protected

Merge the classes of tetrahedron edges as required by the new gluing made at stage orderElt of the search.

See the TetEdgeState class for details.

This routine returns a boolean that indicates whether this merge creates an invalid edge (i.e., an edge identified with itself in reverse).

Returns
true if this merge creates an invalid edge, or false if not.
int regina::NCompactSearcher::mergeVertexClasses ( )
protected

Merge the classes of tetrahedron vertices as required by the new gluing made at stage orderElt of the search.

See the TetVertexState class for details.

This routine returns a bitwise (OR) combination of the VLINK_... flags defined earlier in this class. These flags describe what happened to the vertex links during this particular merge. In particular, they note when a vertex link is closed off, or is made into something other than a punctured 2-sphere.

Returns
a combination of VLINK_... flags describing how the vertex links were changed, or 0 if none of the changes described by these flags were observed.
virtual void regina::NCompactSearcher::runSearch ( long  maxDepth = -1)
virtual

Generates all possible gluing permutation sets that satisfy the current search criteria.

The search criteria are specified in the class constructor, or through the static method findAllPerms().

Each set of gluing permutations will be produced precisely once up to equivalence, where equivalence is defined by the given set of automorphisms of the given face pairing.

For each permutation set that is generated, routine use_ (as passed to the class constructor) will be called with that permutation set as an argument.

Once the generation of permutation sets has finished, routine use_ will be called once more, this time with null as its first (permutation set) argument.

Subclasses corresponding to more specialised search criteria should override this routine to use a better optimised algorithm where possible.

It is possible to run only a partial search, branching to a given depth but no further. In this case, rather than producing complete gluing permutation sets, the search will produce a series of partially-complete NGluingPermSearcher objects. These partial searches may then be restarted by calling runSearch() once more (usually after being frozen or passed on to a different processor). If necessary, the use_ routine may call completePermSet() to distinguish between a complete set of gluing permutations and a partial search state.

Note that a restarted search will never drop below its initial depth. That is, calling runSearch() with a fixed depth can be used to subdivide the overall search space into many branches, and then calling runSearch() on each resulting partial search will complete each of these branches without overlap.

Todo:
Feature: Allow cancellation of permutation set generation.
Parameters
maxDepththe depth of the partial search to run, or a negative number if a full search should be run (the default).

Reimplemented from regina::NGluingPermSearcher.

Reimplemented in regina::NClosedPrimeMinSearcher.

void regina::NCompactSearcher::splitEdgeClasses ( )
protected

Split the classes of tetrahedron edges to mirror the undoing of the gluing at stage orderElt of the search.

See the TetEdgeState class for details.

void regina::NCompactSearcher::splitVertexClasses ( )
protected

Split the classes of tetrahedron vertices to mirror the undoing of the gluing at stage orderElt of the search.

See the TetVertexState class for details.

void regina::NCompactSearcher::vtxBdryBackup ( int  vertexID)
inlineprotected

Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given tetrahedron vertex.

See the TetVertexState class for further information.

Parameters
vertexIDthe tetrahedron vertex on which to operate; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
void regina::NCompactSearcher::vtxBdryConsistencyCheck ( )
protected

Runs a number of tests on all tetrahedron vertices to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the TetVertexState class.

Any errors that are identified will be written to standard error. Note that some errors might be harmless (for instance, when a call to mergeVertexClasses() leaves processing incomplete because it has located a bad vertex link and expects the merge to be immediately undone).

void regina::NCompactSearcher::vtxBdryDump ( std::ostream &  out)
protected

Dumps a summary of bdryNext, bdryTwist and bdryEdges for every vertex of every tetrahedron to the given output stream.

The output format is relatively compact, and is subject to change in future versions of Regina. The output uses one line only, and a final newline is written.

See the TetVertexState class for further information.

Parameters
outthe output stream to which to write.
void regina::NCompactSearcher::vtxBdryFixAdj ( int  vertexID)
inlineprotected

Adjusts the bdryNext and bdryTwist arrays for nearby tetrahedron vertices, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given vertex.

It is assumed that the vertex linking triangle for the given tetrahedron vertex contributes at least one boundary edge to the vertex link. Recall from the TetVertexState class notes that the bdryNext and bdryTwist arrays for the given vertex describe the boundary edges that follow on in either direction from the boundary edges supplied by this triangle.

This routine locates the tetrahedron vertices that provide the neighbouring boundary edges, and adjusts the bdryNext and bdryTwist arrays for these neighbouring vertices to point back to the given vertex.

This routine is intended to assist with backtracking. This routine is safe to use if the given tetrahedron vertex points to itself (i.e., it provides a complete boundary cycle of three edges in the vertex link).

See the TetVertexState class for further information.

Precondition
The vertex linking triangle for the given tetrahedron vertex contributes at least one boundary edge to the vertex link.
Parameters
vertexIDthe tetrahedron vertex to examine; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
void regina::NCompactSearcher::vtxBdryJoin ( int  vertexID,
char  end,
int  adjVertexID,
char  twist 
)
inlineprotected

Signifies that the boundary edges supplied by the vertex linking triangles for the two given tetrahedron vertices should be marked as adjacent.

The bdryNext and bdryTwist arrays for each vertex will be adjusted to point to the other.

See the TetVertexState class for details.

Parameters
vertexIDthe first tetrahedron vertex on which to operate; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
endspecifies in which direction the adjacent boundary edges lie. This must be either 0 or 1, and its value should correspond to the relevant index in the bdryNext and bdryTwist arrays for vertex vertexID.
adjVertexIDthe tetrahedron vertex whose boundary edges are adjacent to the boundary edges supplied by vertexID; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
twist0 if the orientations of the two boundary segments of vertex link are oriented in the same direction, or 1 if they are oriented in opposite directions; see the bdryTwist documentation for details.
bool regina::NCompactSearcher::vtxBdryLength1 ( int  vertexID)
inlineprotected

Determines whether one of the edges of the vertex linking triangle for the given tetrahedron vertex in fact forms an entire one-edge boundary component of the overall vertex link.

See the TetVertexState class for further information.

Parameters
vertexIDthe tetrahedron vertex to examine; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
Returns
true if a one-edge boundary component is formed as described above, or false otherwise.
bool regina::NCompactSearcher::vtxBdryLength2 ( int  vertexID1,
int  vertexID2 
)
inlineprotected

Determines whether edges of the vertex linking triangles for each of the given tetrahedron vertices combine to form an entire two-edge boundary component of the overall vertex link, with one edge from each triangle.

See the TetVertexState class for further information.

Parameters
vertexID1the first tetrahedron vertex to examine; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
vertexID2the second tetrahedron vertex to examine; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
Returns
true if a two-edge boundary component is formed as described above, or false otherwise.
void regina::NCompactSearcher::vtxBdryNext ( int  vertexID,
int  tet,
int  vertex,
int  bdryFace,
int  next[2],
char  twist[2] 
)
inlineprotected

Assuming the given edge of the vertex linking triangle for the given tetrahedron vertex lies on the boundary of the vertex link, this routine identifies the adjacent boundary edges of the vertex link in each direction.

The given edge of the vertex linking triangle must belong to one of the two tetrahedron faces currently being joined.

The tetrahedron vertex to examine is passed in vertexID, tet and vertex, and the particular edge of the vertex linking triangle to examine is specified by bdryFace. Details of the adjacent boundary edges are returned in the arrays next and twist.

Note that the values returned might or might not correspond to the bdryNext and bdryTwist arrays of the TetVertexState class, since the TetVertexState arrays skip over adjacent edges belonging to the same vertex linking triangle.

If the given edge of the vertex linking triangle is not a boundary edge of the vertex link, the behaviour of this routine is undefined.

See the TetVertexState class for further information.

Precondition
The tetrahedron face (tet, bdryFace) is one of the two faces that are currently being joined together. That is, this face is either order[orderElt] or its partner in the underlying face pairing.
Parameters
vertexIDthe tetrahedron vertex to examine; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.
tetthe tetrahedron described by vertexID; this must be (vertexID / 4). It is passed separately to avoid a slow division operation.
vertexthe tetrahedron vertex number described by vertexID; this must be (vertexID % 4). It is passed separately to avoid a slow modulus operation.
bdryFacethe face number of the given tetrahedron containing the edge of the vertex linking triangle that is under consideration. This must be between 0 and 3 inclusive, and it may not be equal to vertex.
nextreturns the tetrahedron vertex supplying each adjacent boundary edge; see the TetVertexState::bdryNext notes for details on which directions correspond to array indices 0 and 1.
twistreturns whether the orientations of the adjacent boundary edges are consistent with the orientation of this boundary edge; see the TetVertexState::bdryTwist notes for further information on orientations in the vertex link.
void regina::NCompactSearcher::vtxBdryRestore ( int  vertexID)
inlineprotected

Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given tetrahedron vertex.

See the TetVertexState class for further information.

Parameters
vertexIDthe tetrahedron vertex on which to operate; this must be between 0 and 4n-1 inclusive, where n is the number of tetrahedra.

Member Data Documentation

const char regina::NCompactSearcher::dataTag_
static

A character used to identify this class when reading and writing tagged data in text format.

TetEdgeState* regina::NCompactSearcher::edgeState
protected

Used for tracking equivalence classes of identified tetrahedron edges.

See the TetEdgeState description for details. This array has size 6n, where edge e of tetrahedron t has index 6t+e.

int* regina::NCompactSearcher::edgeStateChanged
protected

Tracks the way in which the edgeState[] array has been updated over time.

This array has size 8n. Suppose the gluing for order[i] affects face f of tetrahedron t. Then element 4i+v of this array describes how the gluing for order[i] affects the edge of tetrahedron t opposite vertices f and v (note that a quarter of this array will remain unused, since f and v are never equal).

If this identification of edges results in the tree with root edgeState[p] being grafted beneath the tree with root edgeState[q], this array will store the value p. Otherwise it will store the value -1.

unsigned regina::NCompactSearcher::nEdgeClasses
protected

The number of equivalence classes of identified tetrahedron edges.

unsigned regina::NCompactSearcher::nVertexClasses
protected

The number of equivalence classes of identified tetrahedron vertices.

const int regina::NCompactSearcher::vertexLinkNextFace[4][4]
staticprotected

Maintains an ordering of the three tetrahedron faces surrounding a vertex in a tetrahedron.

This ordering is consistent with the orientations of triangles in the vertex link used by TetVertexState::twistUp.

For vertex v (0..3), the tetrahedron face that follows f (0..3) in this ordering is vertexLinkNextFace[v][f]. The remaining array elements vertexLinkNextFace[v][v] are all -1.

const int regina::NCompactSearcher::vertexLinkPrevFace[4][4]
staticprotected

Provides backwards links for the ordering described by vertexLinkNextFace.

For vertex v (0..3), the tetrahedron face that precedes f (0..3) in this ordering is vertexLinkPrevFace[v][f]. The remaining array elements vertexLinkPrevFace[v][v] are all -1.

TetVertexState* regina::NCompactSearcher::vertexState
protected

Used for tracking equivalence classes of identified tetrahedron vertices.

See the TetVertexState description for details. This array has size 4n, where vertex v of tetrahedron t has index 4t+v.

int* regina::NCompactSearcher::vertexStateChanged
protected

Tracks the way in which the vertexState[] array has been updated over time.

This array has size 8n, where element 4i+v describes how the gluing for order[i] affects vertex v of the corresponding tetrahedron (thus a quarter of this array will remain unused, since only three vertices are affected for each gluing).

If this identification of vertices results in the tree with root vertexState[p] being grafted beneath the tree with root vertexState[q], this array will store the value p. Otherwise it will store the value -1.

const char regina::NCompactSearcher::VLINK_CLOSED
staticprotected

Signifies that a vertex link has been closed off (i.e., the link has no remaining boundary edges).

const char regina::NCompactSearcher::VLINK_NON_SPHERE
staticprotected

Signifies that a vertex link has been made into something other than a 2-sphere with zero or more punctures.


The documentation for this class was generated from the following file:

Copyright © 1999-2013, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).