Regina Calculation Engine
|
A utility class used to form a complete census of 3-manifold triangulations satisfying certain constraints. More...
#include <census/ncensus.h>
Public Types | |
typedef bool(* | AcceptTriangulation )(NTriangulation *, void *) |
A routine used to determine whether a particular triangulation should be included in a census. More... | |
Static Public Member Functions | |
static unsigned long | formCensus (NPacket *parent, unsigned nTetrahedra, NBoolSet finiteness, NBoolSet orientability, NBoolSet boundary, int nBdryFaces, int whichPurge, AcceptTriangulation sieve=0, void *sieveArgs=0, NProgressManager *manager=0) |
Fills the given packet with all triangulations in a census of 3-manifold triangulations satisfying the given constraints. More... | |
static unsigned long | formPartialCensus (const NFacePairing *pairing, NPacket *parent, NBoolSet finiteness, NBoolSet orientability, int whichPurge, AcceptTriangulation sieve=0, void *sieveArgs=0) |
Fills the given packet with all triangulations in a partial census of 3-manifold triangulations satisfying the given constraints. More... | |
static bool | mightBeMinimal (NTriangulation *tri, void *ignore=0) |
Determines whether the given triangulation even has a chance at being minimal. More... | |
Static Public Attributes | |
static const int | PURGE_NON_MINIMAL |
Indicates that non-minimal triangulations may be ignored. More... | |
static const int | PURGE_NON_PRIME |
Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum) and any bounded triangulation that is reducible over a disc may be ignored. More... | |
static const int | PURGE_NON_MINIMAL_PRIME |
Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum), any bounded triangulation that is reducible over a disc and any triangulation that is non-minimal may be ignored. More... | |
static const int | PURGE_P2_REDUCIBLE |
Indicates that any triangulation containing an embedded two-sided projective plane may be ignored. More... | |
A utility class used to form a complete census of 3-manifold triangulations satisfying certain constraints.
typedef bool(* regina::NCensus::AcceptTriangulation)(NTriangulation *, void *) |
A routine used to determine whether a particular triangulation should be included in a census.
Routines of this type are used by NCensus::formCensus().
The first parameter passed should be a triangulation currently under consideration. The second parameter may contain arbitrary data as passed to NCensus::formCensus().
The return value should be true
if the triangulation passed should be included in the census, or false
otherwise.
|
static |
Fills the given packet with all triangulations in a census of 3-manifold triangulations satisfying the given constraints.
Each triangulation in the census will appear as a child of the given packet.
This routine will conduct a census of all valid triangulations containing a given number of tetrahedra. All such triangulations are included in the census up to combinatorial isomorphism; given any isomorphism class, exactly one representative will appear in the census.
The census can be optionally restricted to only include triangulations satisfying further constraints (such as orientability and finiteness); see the individual parameter descriptions for further details. In particular, parameter sieve can be used to impose arbitrary restrictions that are not hard-coded into this class.
Note that if constraints may be imposed using the hard-coded parameters (such as orientability and finiteness), it is generally better to do this than to use the arbitrary constraint parameter sieve. Hard-coded parameters will be tested earlier, and some (such as orientability) can be incorporated directly into the census algorithm to give a vast performance increase.
Parameter whichPurge may be used to further avoid constructing triangulations satisfying particular constraints (such as non-minimality). This can significantly speed up the census. In this case however not all such triangulations will be avoided, but it is guaranteed that every triangulation that does not satisfy the constraints defined by whichPurge will be produced.
Only valid triangulations will be produced; see NTriangulation::isValid() for further details.
Note that this routine should only be used if the census contains a small enough total number of triangulations to avoid any memory disasters.
If a progress manager is passed, the calculation will run in a new thread and this routine will return immediately. Otherwise the calculation will run in the current thread and this routine will only return once the census is complete.
parent | the packet beneath which members of the census will be placed. |
nTetrahedra | the number of tetrahedra in each triangulation in the census. |
finiteness | determines whether to include finite and/or ideal triangulations. The set should contain true if finite (non-ideal) triangulations are to be included, and should contain false if ideal triangulations are to be included. |
orientability | determines whether to include orientable and/or non-orientable triangulations. The set should contain true if orientable triangulations are to be included, and should contain false if non-orientable triangulations are to be included. |
boundary | determines whether to include triangulations with and/or without boundary faces. The set should contain true if triangulations with boundary faces are to be included, and should contain false if triangulations with only internal faces are to be included. |
nBdryFaces | specifies the precise number of boundary faces that should be present in the triangulations produced. If this parameter is negative, it is ignored and no additional restriction is imposed. See the documentation for routine NFacePairing::findAllPairings() for details regarding this parameter and how it interacts with parameter boundary. |
whichPurge | specifies which triangulations we may further avoid constructing (see the function notes above for details). This should be a bitwise OR of purge constants defined in this class, or 0 if no additional pruning should take place. If a variety of purge constants are bitwise ORed together, a triangulation satisfying any of these constraints may be avoided. Note that not all such triangulations will be avoided, but enough are avoided that the performance increase is noticeable. |
sieve | an additional constraint function that may be used to exclude certain triangulations from the census. If this parameter is non-zero, each triangulation produced (after passing all other criteria) will be passed through this function. If this function returns true then the triangulation will be included in the census; otherwise it will not. When this function is called, the first (triangulation) argument will be a triangulation under consideration for inclusion in the census. The second argument will be parameter sieveArgs as passed to formCensus(). Parameter sieve may be passed as null (in which case no additional constraint function will be used). |
sieveArgs | the pointer to pass as the final parameter for the function sieve which will be called upon each triangulation found. If sieve is null then sieveArgs will be ignored. |
manager | a progress manager via which progess will be reported, or 0 if no progress reporting is required. If non-zero, manager must point to a progress manager for which NProgressManager::isStarted() is still false . |
|
static |
Fills the given packet with all triangulations in a partial census of 3-manifold triangulations satisfying the given constraints.
Each triangulation in the partial census will appear as a child of the given packet.
This routine will conduct a census of all valid triangulations that are modelled by the given tetrahedron face pairing. All such triangulations are included in the census up to combinatorial isomorphism; given any isomorphism class, exactly one representative will appear in the census.
The census can be optionally restricted to only include triangulations satisfying further constraints (such as orientability and finiteness); see the individual parameter descriptions for further details. In particular, parameter sieve can be used to impose arbitrary restrictions that are not hard-coded into this class.
Note that if constraints may be imposed using the hard-coded parameters (such as orientability and finiteness), it is generally better to do this than to use the arbitrary constraint parameter sieve. Hard-coded parameters will be tested earlier, and some (such as orientability) can be incorporated directly into the census algorithm to give a vast performance increase.
Parameter whichPurge may be used to further avoid constructing triangulations satisfying particular constraints (such as non-minimality). The use of this parameter, combined with parameters finiteness and orientability, can significantly speed up the census. For some combinations of these parameters entirely different algorithms are used.
Note however that not all triangulations described by parameter whichPurge will be avoided. It is guaranteed however that every triangulation that does not satisfy the constraints defined by whichPurge will be produced.
Only valid triangulations will be produced; see NTriangulation::isValid() for further details.
Note that this routine should only be used if the partial census contains a small enough total number of triangulations to avoid any memory disasters.
The partial census will run in the current thread. This routine will only return once the partial census is complete.
pairing | the tetrahedron face pairing that triangulations in this partial census must be modelled by. |
parent | the packet beneath which members of the partial census will be placed. |
finiteness | determines whether to include finite and/or ideal triangulations. The set should contain true if finite (non-ideal) triangulations are to be included, and should contain false if ideal triangulations are to be included. |
orientability | determines whether to include orientable and/or non-orientable triangulations. The set should contain true if orientable triangulations are to be included, and should contain false if non-orientable triangulations are to be included. |
whichPurge | specifies which triangulations we may further avoid constructing (see the function notes above for details). This should be a bitwise OR of purge constants defined in this class, or 0 if no additional pruning should take place. If a variety of purge constants are bitwise ORed together, a triangulation satisfying any of these constraints may be avoided. Note that not all such triangulations will be avoided, but enough are avoided that the performance increase is noticeable. |
sieve | an additional constraint function that may be used to exclude certain triangulations from the census. If this parameter is non-zero, each triangulation produced (after passing all other criteria) will be passed through this function. If this function returns true then the triangulation will be included in the census; otherwise it will not. When this function is called, the first (triangulation) argument will be a triangulation under consideration for inclusion in the census. The second argument will be parameter sieveArgs as passed to formPartialCensus(). Parameter sieve may be passed as null (in which case no additional constraint function will be used). |
sieveArgs | the pointer to pass as the final parameter for the function sieve which will be called upon each triangulation found. If sieve is null then sieveArgs will be ignored. |
|
static |
Determines whether the given triangulation even has a chance at being minimal.
This routine can be passed as parameter sieve to routine NCensus::formCensus() to exclude obviously non-minimal triangulations from a census.
A variety of tests will be performed; these tests are subject to change between Regina releases. Currently this routine counts vertices and also tries to simplify the triangulation using NTriangulation::simplifyToLocalMinimum().
Currently this routine is only useful for triangulations whose faces are all internal; if the given triangulation has boundary faces then this routine will simply return true
.
tri | the triangulation to examine. |
ignore | a parameter that is ignored. |
false
if the given triangulation is known to be non-minimal, or true
if minimality of the given triangulation has not been determined.
|
static |
Indicates that non-minimal triangulations may be ignored.
|
static |
Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum), any bounded triangulation that is reducible over a disc and any triangulation that is non-minimal may be ignored.
Note that this is simply a combination of the constants PURGE_NON_MINIMAL and PURGE_NON_PRIME.
|
static |
Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum) and any bounded triangulation that is reducible over a disc may be ignored.
|
static |
Indicates that any triangulation containing an embedded two-sided projective plane may be ignored.