A gluing permutation search class that offers a specialised search algorithm for when all vertex links must all have a given fixed Euler characteristic.
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| EulerSearcher (int useEuler, const FacetPairing< 3 > *pairing, const FacetPairing< 3 >::IsoList *autos, bool orientableOnly, int whichPurge, GluingPermSearcher< 3 >::Use use, void *useArgs=0) |
| Creates a new search manager that restricts Euler characteristic on the vertex links, as described in the class overview. More...
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| EulerSearcher (std::istream &in, GluingPermSearcher< 3 >::Use use, void *useArgs=0) |
| Initialises a new search manager based on data read from the given input stream. More...
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virtual | ~EulerSearcher () |
| Destroys this search manager and all supporting data structures. More...
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virtual void | dumpData (std::ostream &out) const |
| Dumps all internal data in a plain text format to the given output stream. More...
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virtual void | runSearch (long maxDepth=-1) |
| Generates all possible gluing permutation sets that satisfy the current search criteria. More...
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bool | completePermSet () const |
| Determines whether this search manager holds a complete gluing permutation set or just a partially completed search state. More...
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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...
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bool | inputError () const |
| Was an error found during construction from an input stream? More...
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unsigned | size () const |
| Returns the total number of simplices under consideration. More...
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const FacetPairing< dim > * | facetPairing () const |
| Returns the specific pairing of simplex facets that this set of gluing permutations complements. More...
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Perm< dim+1 > | gluingPerm (const FacetSpec< dim > &source) const |
| Returns the gluing permutation associated with the given simplex facet. More...
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Perm< dim+1 > | gluingPerm (unsigned simp, unsigned facet) const |
| Returns the gluing permutation associated with the given simplex facet. More...
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Triangulation< dim > * | triangulate () const |
| Returns a newly created triangulation as modelled by this set of gluing permutations and the associated simplex facet pairing. More...
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virtual char | dataTag () const |
| Returns the character used to identify this class when storing tagged data in text format. More...
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int | findEdgeClass (int edgeID) const |
| Returns the representative of the equivalence class containing the given tetrahedron edge. More...
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int | findEdgeClass (int edgeID, char &twisted) const |
| Returns the representative of the equivalence class containing the given tetrahedron edge. More...
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int | mergeVertexClasses () |
| Merge the classes of tetrahedron vertices as required by the new gluing made at stage orderElt of the search. More...
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bool | mergeEdgeClasses () |
| Merge the classes of tetrahedron edges as required by the new gluing made at stage orderElt of the search. More...
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void | splitVertexClasses () |
| Split the classes of tetrahedron vertices to mirror the undoing of the gluing at stage orderElt of the search. More...
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void | splitEdgeClasses () |
| Split the classes of tetrahedron edges to mirror the undoing of the gluing at stage orderElt of the search. More...
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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...
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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...
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void | vtxBdryBackup (int vertexID) |
| Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given tetrahedron vertex. More...
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void | vtxBdryRestore (int vertexID) |
| Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given tetrahedron vertex. More...
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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...
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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...
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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...
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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...
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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...
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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...
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bool | badEdgeLink (const FacetSpec< 3 > &face) const |
| Determines whether the permutations already constructed model a triangulation with an edge identified with itself in reverse. More...
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bool | lowDegreeEdge (const FacetSpec< 3 > &face, bool testDegree12, bool testDegree3) const |
| Determines whether the permutations already constructed model a triangulation with a low degree edge. More...
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int & | permIndex (const FacetSpec< dim > &source) |
| Returns the index into array Perm<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
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int & | permIndex (unsigned simp, unsigned facet) |
| Returns the index into array Perm<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
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const int & | permIndex (const FacetSpec< dim > &source) const |
| Returns the index into array Perm<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
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const int & | permIndex (unsigned simp, unsigned facet) const |
| Returns the index into array Perm<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
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int | gluingToIndex (const FacetSpec< dim > &source, const Perm< dim+1 > &gluing) const |
| Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
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int | gluingToIndex (unsigned simp, unsigned facet, const Perm< dim+1 > &gluing) const |
| Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
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Perm< dim+1 > | indexToGluing (const FacetSpec< 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<dim+1>::Sn_1. More...
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Perm< dim+1 > | 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<dim+1>::Sn_1. More...
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int | euler_ |
| The Euler characteristic that vertex links must have. More...
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unsigned | nVertexClasses |
| The number of equivalence classes of identified tetrahedron vertices. More...
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TetVertexState * | vertexState |
| Used for tracking equivalence classes of identified tetrahedron vertices. More...
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int * | vertexStateChanged |
| Tracks the way in which the vertexState[] array has been updated over time. More...
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unsigned | nEdgeClasses |
| The number of equivalence classes of identified tetrahedron edges. More...
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TetEdgeState * | edgeState |
| Used for tracking equivalence classes of identified tetrahedron edges. More...
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int * | edgeStateChanged |
| Tracks the way in which the edgeState[] array has been updated over time. More...
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const FacetPairing< 3 >::IsoList * | autos_ |
| The set of isomorphisms that define equivalence of gluing permutation sets. More...
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bool | autosNew |
| Did we create the isomorphism list autos_ ourselves (in which case we must destroy it also)? More...
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bool | orientableOnly_ |
| Are we only searching for gluing permutations that correspond to orientable triangulations? More...
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bool | finiteOnly_ |
| Are we only searching for gluing permutations that correspond to finite triangulations? More...
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int | whichPurge_ |
| Are there any types of triangulation that we may optionally avoid constructing? This should be a bitwise OR of constants from the PurgeFlags enumeration. More...
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GluingPermSearcher< 3 >::Use | use_ |
| A routine to call each time a gluing permutation set is found during the search. More...
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void * | useArgs_ |
| Additional user-supplied data to be passed as the second argument to the use_ routine. More...
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bool | started |
| Has the search started yet? This helps distinguish between a new search and the resumption of a partially completed search. More...
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int * | orientation |
| Keeps track of the orientation of each tetrahedron in the underlying triangulation. More...
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FacetSpec< 3 > * | order |
| Describes the order in which gluing permutations are assigned to faces. More...
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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...
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int | orderElt |
| Marks which element of order[] we are currently examining at this stage of the search. More...
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const FacetPairing< dim > * | pairing_ |
| The facet pairing that this permutation set complements. More...
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int * | permIndices_ |
| The index into array Perm<dim+1>::Sn_1 describing how each simplex facet is glued to its partner. More...
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bool | inputError_ |
| Has an error occurred during construction from an input stream? More...
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A gluing permutation search class that offers a specialised search algorithm for when all vertex links must all have a given fixed Euler characteristic.
Examples might be Euler characteristic 2 (for closed manifolds), or Euler characteristic 0 (for manifolds with torus and/or Klein bottle cusps). In addition, we require that every edge must be valid (i.e., not identified with itself in reverse).
Vertices on boundary triangles are treated a little differently. If the underlying face pairing includes boundary triangles and the given Euler characteristic is E, then boundary vertex links must have Euler characteristic E-1, and must have exactly one puncture. For instance, if E is 2 and the face pairing includes boundary faces, then all vertex links must be either spheres (for internal vertices) or discs (for boundary vertices).
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 ClosedPrimeMinSearcher). That is, only 3-manifolds with the required vertex links will be produced.
- Python:\n Not present.