#include <ntriangulation.h>
Public Types | |
typedef std::vector < NTetrahedron * > ::const_iterator | TetrahedronIterator |
Used to iterate through tetrahedra. | |
typedef std::vector< NFace * > ::const_iterator | FaceIterator |
Used to iterate through faces. | |
typedef std::vector< NEdge * > ::const_iterator | EdgeIterator |
Used to iterate through edges. | |
typedef std::vector< NVertex * > ::const_iterator | VertexIterator |
Used to iterate through vertices. | |
typedef std::vector < NComponent * > ::const_iterator | ComponentIterator |
Used to iterate through components. | |
typedef std::vector < NBoundaryComponent * > ::const_iterator | BoundaryComponentIterator |
Used to iterate through boundary components. | |
typedef std::map< std::pair < unsigned long, unsigned long > , double > | TuraevViroSet |
A map from (r, whichRoot) pairs to Turaev-Viro invariants. | |
Public Member Functions | |
Constructors and Destructors | |
NTriangulation () | |
Default constructor. | |
NTriangulation (const NTriangulation &cloneMe) | |
Copy constructor. | |
virtual | ~NTriangulation () |
Destroys this triangulation. | |
Packet Administration | |
(end: Constructors and Destructors) | |
virtual int | getPacketType () const |
Returns the integer ID representing this type of packet. | |
virtual std::string | getPacketTypeName () const |
Returns an English name for this type of packet. | |
virtual void | writePacket (NFile &out) const |
Writes the packet details to the given old-style binary file. | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. | |
virtual bool | dependsOnParent () const |
Determines if this packet depends upon its parent. | |
virtual void | readIndividualProperty (NFile &infile, unsigned propType) |
Reads an individual property from an old-style binary file. | |
Tetrahedra | |
(end: Packet Administration) | |
unsigned long | getNumberOfTetrahedra () const |
Returns the number of tetrahedra in the triangulation. | |
const std::vector < NTetrahedron * > & | getTetrahedra () const |
Returns all tetrahedra in the triangulation. | |
NTetrahedron * | getTetrahedron (unsigned long index) |
Returns the tetrahedron with the given index number in the triangulation. | |
const NTetrahedron * | getTetrahedron (unsigned long index) const |
Returns the tetrahedron with the given index number in the triangulation. | |
long | tetrahedronIndex (const NTetrahedron *tet) const |
Returns the index of the given tetrahedron in the triangulation. | |
long | getTetrahedronIndex (const NTetrahedron *tet) const |
Returns the index of the given tetrahedron in the triangulation. | |
void | addTetrahedron (NTetrahedron *tet) |
Inserts the given tetrahedron into the triangulation. | |
NTetrahedron * | removeTetrahedron (NTetrahedron *tet) |
Removes the given tetrahedron from the triangulation. | |
NTetrahedron * | removeTetrahedronAt (unsigned long index) |
Removes the tetrahedron with the given index number from the triangulation. | |
void | removeAllTetrahedra () |
Removes all tetrahedra from the triangulation. | |
void | gluingsHaveChanged () |
This must be called whenever the gluings of tetrahedra are changed! Clears appropriate properties and performs other necessary tasks. | |
Skeletal Queries | |
(end: Tetrahedra) | |
unsigned long | getNumberOfBoundaryComponents () const |
Returns the number of boundary components in this triangulation. | |
unsigned long | getNumberOfComponents () const |
Returns the number of components in this triangulation. | |
unsigned long | getNumberOfVertices () const |
Returns the number of vertices in this triangulation. | |
unsigned long | getNumberOfEdges () const |
Returns the number of edges in this triangulation. | |
unsigned long | getNumberOfFaces () const |
Returns the number of faces in this triangulation. | |
const std::vector< NComponent * > & | getComponents () const |
Returns all components of this triangulation. | |
const std::vector < NBoundaryComponent * > & | getBoundaryComponents () const |
Returns all boundary components of this triangulation. | |
const std::vector< NVertex * > & | getVertices () const |
Returns all vertices of this triangulation. | |
const std::vector< NEdge * > & | getEdges () const |
Returns all edges of this triangulation. | |
const std::vector< NFace * > & | getFaces () const |
Returns all faces of this triangulation. | |
NComponent * | getComponent (unsigned long index) const |
Returns the requested triangulation component. | |
NBoundaryComponent * | getBoundaryComponent (unsigned long index) const |
Returns the requested triangulation boundary component. | |
NVertex * | getVertex (unsigned long index) const |
Returns the requested triangulation vertex. | |
NEdge * | getEdge (unsigned long index) const |
Returns the requested triangulation edge. | |
NFace * | getFace (unsigned long index) const |
Returns the requested triangulation face. | |
long | componentIndex (const NComponent *component) const |
Returns the index of the given component in the triangulation. | |
long | getComponentIndex (const NComponent *component) const |
Returns the index of the given component in the triangulation. | |
long | boundaryComponentIndex (const NBoundaryComponent *bc) const |
Returns the index of the given boundary component in the triangulation. | |
long | getBoundaryComponentIndex (const NBoundaryComponent *bc) const |
Returns the index of the given boundary component in the triangulation. | |
long | vertexIndex (const NVertex *vertex) const |
Returns the index of the given vertex in the triangulation. | |
long | getVertexIndex (const NVertex *vertex) const |
Returns the index of the given vertex in the triangulation. | |
long | edgeIndex (const NEdge *edge) const |
Returns the index of the given edge in the triangulation. | |
long | getEdgeIndex (const NEdge *edge) const |
Returns the index of the given edge in the triangulation. | |
long | faceIndex (const NFace *face) const |
Returns the index of the given face in the triangulation. | |
long | getFaceIndex (const NFace *face) const |
Returns the index of the given face in the triangulation. | |
bool | hasTwoSphereBoundaryComponents () const |
Determines if this triangulation contains any two-sphere boundary components. | |
bool | hasNegativeIdealBoundaryComponents () const |
Determines if this triangulation contains any ideal boundary components with negative Euler characteristic. | |
Isomorphism Testing | |
(end: Skeletal Queries) | |
std::auto_ptr< NIsomorphism > | isIsomorphicTo (const NTriangulation &other) const |
Determines if this triangulation is combinatorially isomorphic to the given triangulation. | |
std::auto_ptr< NIsomorphism > | isContainedIn (const NTriangulation &other) const |
Determines if an isomorphic copy of this triangulation is contained within the given triangulation, possibly as a subcomplex of some larger component (or components). | |
unsigned long | findAllSubcomplexesIn (const NTriangulation &other, std::list< NIsomorphism * > &results) const |
Finds all ways in which an isomorphic copy of this triangulation is contained within the given triangulation, possibly as a subcomplex of some larger component (or components). | |
Basic Properties | |
(end: Isomorphism Testing) | |
long | getEulerCharTri () const |
Returns the Euler characteristic of this triangulation. | |
long | getEulerCharManifold () const |
Returns the Euler characteristic of the corresponding compact 3-manifold. | |
long | getEulerCharacteristic () const |
A deprecated alias for getEulerCharTri(). | |
bool | isValid () const |
Determines if this triangulation is valid. | |
bool | isIdeal () const |
Determines if this triangulation is ideal. | |
bool | isStandard () const |
Determines if this triangulation is standard. | |
bool | hasBoundaryFaces () const |
Determines if this triangulation has any boundary faces. | |
bool | isClosed () const |
Determines if this triangulation is closed. | |
bool | isOrientable () const |
Determines if this triangulation is orientable. | |
bool | isConnected () const |
Determines if this triangulation is connected. | |
Algebraic Properties | |
(end: Basic Properties) | |
const NGroupPresentation & | getFundamentalGroup () const |
Returns the fundamental group of this triangulation. | |
void | simplifiedFundamentalGroup (NGroupPresentation *newGroup) |
Notifies the triangulation that you have simplified the presentation of its fundamental group. | |
const NAbelianGroup & | getHomologyH1 () const |
Returns the first homology group for this triangulation. | |
const NAbelianGroup & | getHomologyH1Rel () const |
Returns the relative first homology group with respect to the boundary for this triangulation. | |
const NAbelianGroup & | getHomologyH1Bdry () const |
Returns the first homology group of the boundary for this triangulation. | |
const NAbelianGroup & | getHomologyH2 () const |
Returns the second homology group for this triangulation. | |
unsigned long | getHomologyH2Z2 () const |
Returns the second homology group with coefficients in Z_2 for this triangulation. | |
double | turaevViro (unsigned long r, unsigned long whichRoot) const |
Computes the Turaev-Viro state sum invariant of this 3-manifold based upon the given initial data. | |
const TuraevViroSet & | allCalculatedTuraevViro () const |
Returns the set of all Turaev-Viro state sum invariants that have already been calculated for this 3-manifold. | |
Normal Surface Properties | |
(end: Algebraic Properties) | |
bool | isZeroEfficient () |
Determines if this triangulation is 0-efficient. | |
bool | knowsZeroEfficient () const |
Is it already known whether or not this triangulation is 0-efficient? See isZeroEfficient() for further details. | |
bool | hasSplittingSurface () |
Determines whether this triangulation has a normal splitting surface. | |
bool | knowsSplittingSurface () const |
Is it already known whether or not this triangulation has a splitting surface? See hasSplittingSurface() for further details. | |
Skeletal Transformations | |
(end: Normal Surface Properties) | |
void | maximalForestInBoundary (stdhash::hash_set< NEdge *, HashPointer > &edgeSet, stdhash::hash_set< NVertex *, HashPointer > &vertexSet) const |
Produces a maximal forest in the 1-skeleton of the triangulation boundary. | |
void | maximalForestInSkeleton (stdhash::hash_set< NEdge *, HashPointer > &edgeSet, bool canJoinBoundaries=true) const |
Produces a maximal forest in the triangulation's 1-skeleton. | |
void | maximalForestInDualSkeleton (stdhash::hash_set< NFace *, HashPointer > &faceSet) const |
Produces a maximal forest in the triangulation's dual 1-skeleton. | |
bool | intelligentSimplify () |
Attempts to simplify the triangulation as intelligently as possible without further input. | |
bool | simplifyToLocalMinimum (bool perform=true) |
Uses all known simplification moves to reduce the triangulation monotonically to some local minimum number of tetrahedra. | |
bool | threeTwoMove (NEdge *e, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 3-2 move about the given edge. | |
bool | twoThreeMove (NFace *f, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 2-3 move about the given face. | |
bool | fourFourMove (NEdge *e, int newAxis, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 4-4 move about the given edge. | |
bool | twoZeroMove (NEdge *e, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 2-0 move about the given edge of degree 2. | |
bool | twoZeroMove (NVertex *v, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 2-0 move about the given vertex of degree 2. | |
bool | twoOneMove (NEdge *e, int edgeEnd, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a 2-1 move about the given edge. | |
bool | openBook (NFace *f, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a book opening move about the given face. | |
bool | closeBook (NEdge *e, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a book closing move about the given boundary edge. | |
bool | shellBoundary (NTetrahedron *t, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a boundary shelling move on the given tetrahedron. | |
bool | collapseEdge (NEdge *e, bool check=true, bool perform=true) |
Checks the eligibility of and/or performs a collapse of an edge in such a way that the topology of the manifold does not change and the number of vertices of the triangulation decreases by one. | |
void | reorderTetrahedraBFS (bool reverse=false) |
Reorders the tetrahedra of this triangulation using a breadth-first search, so that small-numbered tetrahedra are adjacent to other small-numbered tetrahedra. | |
Decompositions | |
(end: Skeletal Transformations) | |
unsigned long | splitIntoComponents (NPacket *componentParent=0, bool setLabels=true) |
Splits a disconnected triangulation into many smaller triangulations, one for each component. | |
unsigned long | connectedSumDecomposition (NPacket *primeParent=0, bool setLabels=true) |
Splits this triangulation into its connected sum decomposition. | |
bool | isThreeSphere () const |
Determines whether this is a triangulation of a 3-sphere. | |
bool | knowsThreeSphere () const |
Is it already known (or trivial to determine) whether or not this is a triangulation of a 3-sphere? See isThreeSphere() for further details. | |
bool | isBall () const |
Determines whether this is a triangulation of a 3-dimensional ball. | |
bool | knowsBall () const |
Is it already known (or trivial to determine) whether or not this is a triangulation of a 3-dimensional ball? See isBall() for further details. | |
NPacket * | makeZeroEfficient () |
Converts this into a 0-efficient triangulation of the same underlying 3-manifold. | |
Subdivisions, Extensions and Covers | |
(end: Decompositions) | |
void | makeDoubleCover () |
Converts this triangulation into its double cover. | |
bool | idealToFinite (bool forceDivision=false) |
Converts an ideal triangulation into a finite triangulation. | |
bool | finiteToIdeal () |
Converts each real boundary component into a cusp (i.e., an ideal vertex). | |
void | barycentricSubdivision () |
Does a barycentric subdivision of the triangulation. | |
Building Triangulations | |
(end: Subdivisions and Covers) | |
NTetrahedron * | layerOn (NEdge *edge) |
Performs a layering upon the given boundary edge of the triangulation. | |
NTetrahedron * | insertLayeredSolidTorus (unsigned long cuts0, unsigned long cuts1) |
Inserts a new layered solid torus into the triangulation. | |
void | insertLayeredLensSpace (unsigned long p, unsigned long q) |
Inserts a new layered lens space L(p,q) into the triangulation. | |
void | insertLayeredLoop (unsigned long length, bool twisted) |
Inserts a layered loop of the given length into this triangulation. | |
void | insertAugTriSolidTorus (long a1, long b1, long a2, long b2, long a3, long b3) |
Inserts an augmented triangular solid torus with the given parameters into this triangulation. | |
void | insertSFSOverSphere (long a1=1, long b1=0, long a2=1, long b2=0, long a3=1, long b3=0) |
Inserts an orientable Seifert fibred space with at most three exceptional fibres over the 2-sphere into this triangulation. | |
void | insertTriangulation (const NTriangulation &source) |
Inserts a copy of the given triangulation into this triangulation. | |
bool | insertRehydration (const std::string &dehydration) |
Inserts the rehydration of the given string into this triangulation. | |
std::string | dehydrate () const |
Dehydrates this triangulation into an alphabetical string. | |
void | insertConstruction (unsigned long nTetrahedra, const int adjacencies[][4], const int gluings[][4][4]) |
Inserts into this triangulation a set of tetrahedra and their gluings as described by the given integer arrays. | |
std::string | dumpConstruction () const |
Returns C++ code that can be used with insertConstruction() to reconstruct this triangulation. | |
Static Public Member Functions | |
static NTriangulation * | enterTextTriangulation (std::istream &in, std::ostream &out) |
(end: Building Triangulations) | |
static NXMLPacketReader * | getXMLReader (NPacket *parent) |
(end: File I/O) | |
static NTriangulation * | readPacket (NFile &in, NPacket *parent) |
Reads a single packet from the specified file and returns a newly created object containing that information. | |
Static Public Attributes | |
static const int | packetType |
Contains the integer ID for this packet. | |
Protected Member Functions | |
virtual NPacket * | internalClonePacket (NPacket *parent) const |
Makes a newly allocated copy of this packet. | |
virtual void | writeXMLPacketData (std::ostream &out) const |
Writes a chunk of XML containing the data for this packet only. | |
void | cloneFrom (const NTriangulation &from) |
Turns this triangulation into a clone of the given triangulation. | |
Friends | |
class | regina::NXMLTriangulationReader |
When the triangulation is deleted, the corresponding tetrahedra, the cellular structure and all other properties will be deallocated.
Faces, edges, vertices and components are always temporary; whenever a change occurs with the triangulation, these will be deleted and a new skeletal structure will be calculated. The same is true of various other triangulation properties.
Whenever the gluings of tetrahedra have been altered, the routine responsible for changing the gluings must call NTriangulation::gluingsHaveChanged() to ensure that relevant properties will be recalculated when necessary. It is not necessary to call this function when adding or removing tetrahedra.
Feature (long-term): Am I obviously a handlebody? (Simplify and see if there is nothing left). Am I obviously not a handlebody? (Compare homology with boundary homology).
Feature (long-term): Is the triangulation Haken?
Feature (long-term): What is the Heegaard genus?
Feature (long-term): Have a subcomplex as a child packet of a triangulation. Include routines to crush a subcomplex or to expand a subcomplex to a normal surface.
Feature (long-term): Implement writeTextLong() for skeletal objects.
typedef std::vector<NBoundaryComponent*>::const_iterator regina::NTriangulation::BoundaryComponentIterator |
Used to iterate through boundary components.
typedef std::vector<NComponent*>::const_iterator regina::NTriangulation::ComponentIterator |
Used to iterate through components.
typedef std::vector<NEdge*>::const_iterator regina::NTriangulation::EdgeIterator |
Used to iterate through edges.
typedef std::vector<NFace*>::const_iterator regina::NTriangulation::FaceIterator |
Used to iterate through faces.
typedef std::vector<NTetrahedron*>::const_iterator regina::NTriangulation::TetrahedronIterator |
Used to iterate through tetrahedra.
typedef std::map<std::pair<unsigned long, unsigned long>, double> regina::NTriangulation::TuraevViroSet |
A map from (r, whichRoot) pairs to Turaev-Viro invariants.
typedef std::vector<NVertex*>::const_iterator regina::NTriangulation::VertexIterator |
Used to iterate through vertices.
regina::NTriangulation::NTriangulation | ( | ) | [inline] |
Default constructor.
Creates an empty triangulation.
regina::NTriangulation::NTriangulation | ( | const NTriangulation & | cloneMe | ) | [inline] |
Copy constructor.
Creates a new triangulation identical to the given triangulation. The packet tree structure and packet label are not copied.
cloneMe | the triangulation to clone. |
regina::NTriangulation::~NTriangulation | ( | ) | [inline, virtual] |
Destroys this triangulation.
The constituent tetrahedra, the cellular structure and all other properties will also be deallocated.
void regina::NTriangulation::addTetrahedron | ( | NTetrahedron * | tet | ) | [inline] |
Inserts the given tetrahedron into the triangulation.
No face gluings anywhere will be examined or altered.
The new tetrahedron will be assigned a higher index in the triangulation than all tetrahedra already present.
There is no need to call gluingsHaveChanged() after calling this function.
tet | the tetrahedron to insert. |
const NTriangulation::TuraevViroSet & regina::NTriangulation::allCalculatedTuraevViro | ( | ) | const [inline] |
Returns the set of all Turaev-Viro state sum invariants that have already been calculated for this 3-manifold.
Turaev-Viro invariants are described by an (r, whichRoot) pair as described in the turaevViro() notes. The set returned by this routine maps (r, whichRoot) pairs to the corresponding invariant values.
Each time turaevViro() is called, the result will be stored in this set (as well as being returned to the user). This set will be emptied whenever the triangulation is modified.
void regina::NTriangulation::barycentricSubdivision | ( | ) |
Does a barycentric subdivision of the triangulation.
Each tetrahedron is divided into 24 tetrahedra by placing an extra vertex at the centroid of each tetrahedron, the centroid of each face and the midpoint of each edge.
long regina::NTriangulation::boundaryComponentIndex | ( | const NBoundaryComponent * | bc | ) | const [inline] |
Returns the index of the given boundary component in the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getBoundaryComponentIndex(). The name has been changed because, unlike the old routine, it requires that the given boundary component belongs to the triangulation (a consequence of some significant memory optimisations).
bc | specifies which boundary component to find in the triangulation. |
void regina::NTriangulation::cloneFrom | ( | const NTriangulation & | from | ) | [protected] |
Turns this triangulation into a clone of the given triangulation.
The tree structure and label of this triangulation are not touched.
from | the triangulation from which this triangulation will be cloned. |
bool regina::NTriangulation::closeBook | ( | NEdge * | e, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a book closing move about the given boundary edge.
This involves taking a boundary edge of the triangulation and folding together the two boundary faces on either side. This move is the inverse of the openBook() move, and is used to simplify the boundary of the triangulation. This move can be done only if:
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument f) can no longer be used.
The given edge is an edge of this triangulation.
e | the edge about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. bool regina::NTriangulation::collapseEdge | ( | NEdge * | e, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a collapse of an edge in such a way that the topology of the manifold does not change and the number of vertices of the triangulation decreases by one.
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument e) can no longer be used.
The eligibility requirements for this move are somewhat involved, and are discussed in detail in the collapseEdge() source code for those who are interested.
The given edge is an edge of this triangulation.
e | the edge to collapse. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the given edge may be collapsed without changing the topology of the manifold. If check is false
, the function simply returns true
. long regina::NTriangulation::componentIndex | ( | const NComponent * | component | ) | const [inline] |
Returns the index of the given component in the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getComponentIndex(). The name has been changed because, unlike the old routine, it requires that the given component belongs to the triangulation (a consequence of some significant memory optimisations).
component | specifies which component to find in the triangulation. |
unsigned long regina::NTriangulation::connectedSumDecomposition | ( | NPacket * | primeParent = 0 , |
|
bool | setLabels = true | |||
) |
Splits this triangulation into its connected sum decomposition.
The individual prime 3-manifold triangulations that make up this decomposition will be inserted as children of the given parent packet. The original triangulation will be left unchanged.
Note that this routine is currently only available for closed orientable triangulations; see the list of preconditions for full details. The 0-efficiency prime decomposition algorithm of Jaco and Rubinstein is used.
If the given parent packet is 0, the new prime summand triangulations will be inserted as children of this triangulation.
This routine can optionally assign unique (and sensible) packet labels to each of the new prime summand triangulations. Note however that uniqueness testing may be slow, so this assignment of labels should be disabled if the summand triangulations are only temporary objects used as part of a larger routine.
If this is a triangulation of a 3-sphere, no prime summand triangulations will be created at all.
primeParent | the packet beneath which the new prime summand triangulations will be inserted, or 0 if they should be inserted directly beneath this triangulation. | |
setLabels | true if the new prime summand triangulations should be assigned unique packet labels, or false if they should be left without labels at all. |
std::string regina::NTriangulation::dehydrate | ( | ) | const |
Dehydrates this triangulation into an alphabetical string.
A dehydration string is a compact text representation of a triangulation, introduced by Callahan, Hildebrand and Weeks for their cusped hyperbolic census (see below). The dehydration string of an n-tetrahedron triangulation consists of approximately (but not precisely) 5n/2 lower-case letters.
Dehydration strings come with some restrictions:
The routine insertRehydration() can be used to recover a triangulation from a dehydration string. Note that the triangulation recovered might not be identical to the original, but it is guaranteed to be an isomorphic copy.
For a full description of the dehydrated triangulation format, see A Census of Cusped Hyperbolic 3-Manifolds, Callahan, Hildebrand and Weeks, Mathematics of Computation 68/225, 1999.
bool regina::NTriangulation::dependsOnParent | ( | ) | const [inline, virtual] |
Determines if this packet depends upon its parent.
This is true if the parent cannot be altered without invalidating or otherwise upsetting this packet.
true
if and only if this packet depends on its parent. Implements regina::NPacket.
std::string regina::NTriangulation::dumpConstruction | ( | ) | const |
Returns C++ code that can be used with insertConstruction() to reconstruct this triangulation.
The code produced will consist of the following:
The main purpose of this routine is to generate the two integer arrays, which can be tedious and error-prone to code up by hand.
Note that the number of lines of code produced grows linearly with the number of tetrahedra. If this triangulation is very large, the returned string will be very large as well.
long regina::NTriangulation::edgeIndex | ( | const NEdge * | edge | ) | const [inline] |
Returns the index of the given edge in the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getEdgeIndex(). The name has been changed because, unlike the old routine, it requires that the given edge belongs to the triangulation (a consequence of some significant memory optimisations).
edge | specifies which edge to find in the triangulation. |
static NTriangulation* regina::NTriangulation::enterTextTriangulation | ( | std::istream & | in, | |
std::ostream & | out | |||
) | [static] |
(end: Building Triangulations)
Allows the user to interactively enter a triangulation in plain text. Prompts will be sent to the given output stream and information will be read from the given input stream.
in | the input stream from which text will be read. | |
out | the output stream to which prompts will be written. |
long regina::NTriangulation::faceIndex | ( | const NFace * | face | ) | const [inline] |
Returns the index of the given face in the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getFaceIndex(). The name has been changed because, unlike the old routine, it requires that the given face belongs to the triangulation (a consequence of some significant memory optimisations).
face | specifies which face to find in the triangulation. |
unsigned long regina::NTriangulation::findAllSubcomplexesIn | ( | const NTriangulation & | other, | |
std::list< NIsomorphism * > & | results | |||
) | const |
Finds all ways in which an isomorphic copy of this triangulation is contained within the given triangulation, possibly as a subcomplex of some larger component (or components).
This routine behaves identically to isContainedIn(), except that instead of returning just one isomorphism (which may be boundary incomplete and need not be onto), all such isomorphisms are returned.
See the isContainedIn() notes for additional information.
The isomorphisms that are found will be inserted into the given list. These isomorphisms will be newly created, and the caller of this routine is responsible for destroying them. The given list will not be emptied before the new isomorphisms are inserted.
other | the triangulation in which to search for isomorphic copies of this triangulation. | |
results | the list in which any isomorphisms found will be stored. |
bool regina::NTriangulation::finiteToIdeal | ( | ) |
Converts each real boundary component into a cusp (i.e., an ideal vertex).
Only boundary components formed from real tetrahedron faces will be affected; ideal boundary components are already cusps and so will not be changed.
One side-effect of this operation is that all spherical boundary components will be filled in with balls.
This operation is performed by attaching a new tetrahedron to each boundary face and then gluing these new tetrahedra together in a way that mirrors the adjacencies of the underlying boundary faces. Each boundary component will thereby be pushed up through the new tetrahedra and converted into a cusp formed using vertices of these new tetrahedra.
Note that this operation is a loose converse of idealToFinite().
true
if changes were made, or false
if the original triangulation contained no real boundary components. bool regina::NTriangulation::fourFourMove | ( | NEdge * | e, | |
int | newAxis, | |||
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 4-4 move about the given edge.
This involves replacing the four tetrahedra joined at that edge with four tetrahedra joined along a different edge. Consider the octahedron made up of the four original tetrahedra; this has three internal axes. The initial four tetrahedra meet along the given edge which forms one of these axes; the new tetrahedra will meet along a different axis. This move can be done iff (i) the edge is valid and non-boundary, and (ii) the four tetrahedra are distinct.
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument e) can no longer be used.
The given edge is an edge of this triangulation.
e | the edge about which to perform the move. | |
newAxis | Specifies which axis of the octahedron the new tetrahedra should meet along; this should be 0 or 1. Consider the four original tetrahedra in the order described by NEdge::getEmbeddings(); call these tetrahedra 0, 1, 2 and 3. If newAxis is 0, the new axis will separate tetrahedra 0 and 1 from 2 and 3. If newAxis is 1, the new axis will separate tetrahedra 1 and 2 from 3 and 0. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. NBoundaryComponent * regina::NTriangulation::getBoundaryComponent | ( | unsigned long | index | ) | const [inline] |
Returns the requested triangulation boundary component.
Bear in mind that each time the triangulation changes, the boundary components will be deleted and replaced with new ones. Thus this object should be considered temporary only.
index | the index of the desired boundary component, ranging from 0 to getNumberOfBoundaryComponents()-1 inclusive. |
long regina::NTriangulation::getBoundaryComponentIndex | ( | const NBoundaryComponent * | bc | ) | const [inline] |
Returns the index of the given boundary component in the triangulation.
bc | specifies which boundary component to find in the triangulation. |
const std::vector< NBoundaryComponent * > & regina::NTriangulation::getBoundaryComponents | ( | ) | const [inline] |
Returns all boundary components of this triangulation.
Note that each ideal vertex forms its own boundary component.
Bear in mind that each time the triangulation changes, the boundary components will be deleted and replaced with new ones. Thus the objects contained in this list should be considered temporary only.
This reference to the list however will remain valid and up-to-date for as long as the triangulation exists.
NComponent * regina::NTriangulation::getComponent | ( | unsigned long | index | ) | const [inline] |
Returns the requested triangulation component.
Bear in mind that each time the triangulation changes, the components will be deleted and replaced with new ones. Thus this object should be considered temporary only.
index | the index of the desired component, ranging from 0 to getNumberOfComponents()-1 inclusive. |
long regina::NTriangulation::getComponentIndex | ( | const NComponent * | component | ) | const [inline] |
Returns the index of the given component in the triangulation.
component | specifies which component to find in the triangulation. |
const std::vector< NComponent * > & regina::NTriangulation::getComponents | ( | ) | const [inline] |
Returns all components of this triangulation.
Bear in mind that each time the triangulation changes, the components will be deleted and replaced with new ones. Thus the objects contained in this list should be considered temporary only.
This reference to the list however will remain valid and up-to-date for as long as the triangulation exists.
NEdge * regina::NTriangulation::getEdge | ( | unsigned long | index | ) | const [inline] |
Returns the requested triangulation edge.
Bear in mind that each time the triangulation changes, the edges will be deleted and replaced with new ones. Thus this object should be considered temporary only.
index | the index of the desired edge, ranging from 0 to getNumberOfEdges()-1 inclusive. |
long regina::NTriangulation::getEdgeIndex | ( | const NEdge * | edge | ) | const [inline] |
Returns the index of the given edge in the triangulation.
edge | specifies which edge to find in the triangulation. |
const std::vector< NEdge * > & regina::NTriangulation::getEdges | ( | ) | const [inline] |
Returns all edges of this triangulation.
Bear in mind that each time the triangulation changes, the edges will be deleted and replaced with new ones. Thus the objects contained in this list should be considered temporary only.
This reference to the list however will remain valid and up-to-date for as long as the triangulation exists.
long regina::NTriangulation::getEulerCharacteristic | ( | ) | const [inline] |
A deprecated alias for getEulerCharTri().
This routine calculates the Euler characteristic of this triangulation. Since it treats cusps in a non-standard way, it was renamed to getEulerCharTri() in Regina 4.4 to clarify that this might differ from the Euler characteristic of the corresponding compact manifold.
See getEulerCharTri() for further details.
long regina::NTriangulation::getEulerCharManifold | ( | ) | const |
Returns the Euler characteristic of the corresponding compact 3-manifold.
Instead of simply calculating V-E+F-T, this routine also:
For ideal triangulations, this routine therefore computes the proper Euler characteristic of the manifold (unlike getEulerCharTri(), which does not).
For triangulations whose vertex links are all spheres or discs, this routine and getEulerCharTri() give identical results.
long regina::NTriangulation::getEulerCharTri | ( | ) | const [inline] |
Returns the Euler characteristic of this triangulation.
This will be evaluated strictly as V-E+F-T.
Note that this routine handles cusps in a non-standard way. Since it computes the Euler characteristic of the triangulation (and not the underlying manifold), this routine will treat each cusp as a single vertex, and not as a surface boundary component.
For a routine that handles cusps properly (i.e., treats them as surface boundary components when computing the Euler characteristic), see getEulerCharManifold() instead.
This routine was previously called getEulerCharacteristic() in Regina 4.3.1 and earlier. It was renamed in Regina 4.4 to clarify the non-standard handling of cusps.
NFace * regina::NTriangulation::getFace | ( | unsigned long | index | ) | const [inline] |
Returns the requested triangulation face.
Bear in mind that each time the triangulation changes, the faces will be deleted and replaced with new ones. Thus this object should be considered temporary only.
index | the index of the desired face, ranging from 0 to getNumberOfFaces()-1 inclusive. |
long regina::NTriangulation::getFaceIndex | ( | const NFace * | face | ) | const [inline] |
Returns the index of the given face in the triangulation.
face | specifies which face to find in the triangulation. |
const std::vector< NFace * > & regina::NTriangulation::getFaces | ( | ) | const [inline] |
Returns all faces of this triangulation.
Bear in mind that each time the triangulation changes, the faces will be deleted and replaced with new ones. Thus the objects contained in this list should be considered temporary only.
This reference to the list however will remain valid and up-to-date for as long as the triangulation exists.
const NGroupPresentation& regina::NTriangulation::getFundamentalGroup | ( | ) | const |
Returns the fundamental group of this triangulation.
If this triangulation contains any ideal or non-standard vertices, the fundamental group will be calculated as if each such vertex had been truncated.
If this triangulation contains any invalid edges, the calculations will be performed without any truncation of the corresponding projective plane cusp. Thus if a barycentric subdivision is performed on the triangulation, the result of getFundamentalGroup() will change.
Bear in mind that each time the triangulation changes, the fundamental group will be deleted. Thus the reference that is returned from this routine should not be kept for later use. Instead, getFundamentalGroup() should be called again; this will be instantaneous if the group has already been calculated.
Note that this triangulation is not required to be valid (see isValid()).
const NAbelianGroup& regina::NTriangulation::getHomologyH1 | ( | ) | const |
Returns the first homology group for this triangulation.
If this triangulation contains any ideal or non-standard vertices, the homology group will be calculated as if each such vertex had been truncated.
If this triangulation contains any invalid edges, the calculations will be performed without any truncation of the corresponding projective plane cusp. Thus if a barycentric subdivision is performed on the triangulation, the result of getHomologyH1() will change.
Bear in mind that each time the triangulation changes, the homology groups will be deleted. Thus the reference that is returned from this routine should not be kept for later use. Instead, getHomologyH1() should be called again; this will be instantaneous if the group has already been calculated.
Note that this triangulation is not required to be valid (see isValid()).
const NAbelianGroup& regina::NTriangulation::getHomologyH1Bdry | ( | ) | const |
Returns the first homology group of the boundary for this triangulation.
Note that ideal vertices are considered part of the boundary.
Bear in mind that each time the triangulation changes, the homology groups will be deleted. Thus the reference that is returned from this routine should not be kept for later use. Instead, getHomologyH1Bdry() should be called again; this will be instantaneous if the group has already been calculated.
This routine is fairly fast, since it deduces the homology of each boundary component through knowing what kind of surface it is.
const NAbelianGroup& regina::NTriangulation::getHomologyH1Rel | ( | ) | const |
Returns the relative first homology group with respect to the boundary for this triangulation.
Note that ideal vertices are considered part of the boundary.
Bear in mind that each time the triangulation changes, the homology groups will be deleted. Thus the reference that is returned from this routine should not be kept for later use. Instead, getHomologyH1Rel() should be called again; this will be instantaneous if the group has already been calculated.
const NAbelianGroup& regina::NTriangulation::getHomologyH2 | ( | ) | const |
Returns the second homology group for this triangulation.
If this triangulation contains any ideal vertices, the homology group will be calculated as if each such vertex had been truncated. The algorithm used calculates various first homology groups and uses homology and cohomology theorems to deduce the second homology group.
Bear in mind that each time the triangulation changes, the homology groups will be deleted. Thus the reference that is returned from this routine should not be kept for later use. Instead, getHomologyH2() should be called again; this will be instantaneous if the group has already been calculated.
unsigned long regina::NTriangulation::getHomologyH2Z2 | ( | ) | const [inline] |
Returns the second homology group with coefficients in Z_2 for this triangulation.
If this triangulation contains any ideal vertices, the homology group will be calculated as if each such vertex had been truncated. The algorithm used calculates the relative first homology group with respect to the boundary and uses homology and cohomology theorems to deduce the second homology group.
This group will simply be the direct sum of several copies of Z_2, so the number of Z_2 terms is returned.
unsigned long regina::NTriangulation::getNumberOfBoundaryComponents | ( | ) | const [inline] |
Returns the number of boundary components in this triangulation.
Note that each ideal vertex forms its own boundary component.
unsigned long regina::NTriangulation::getNumberOfComponents | ( | ) | const [inline] |
Returns the number of components in this triangulation.
unsigned long regina::NTriangulation::getNumberOfEdges | ( | ) | const [inline] |
Returns the number of edges in this triangulation.
unsigned long regina::NTriangulation::getNumberOfFaces | ( | ) | const [inline] |
Returns the number of faces in this triangulation.
unsigned long regina::NTriangulation::getNumberOfTetrahedra | ( | ) | const [inline] |
Returns the number of tetrahedra in the triangulation.
unsigned long regina::NTriangulation::getNumberOfVertices | ( | ) | const [inline] |
Returns the number of vertices in this triangulation.
virtual int regina::NTriangulation::getPacketType | ( | ) | const [virtual] |
Returns the integer ID representing this type of packet.
This is the same for all packets of this class.
Implements regina::NPacket.
virtual std::string regina::NTriangulation::getPacketTypeName | ( | ) | const [virtual] |
Returns an English name for this type of packet.
An example is NTriangulation
. This is the same for all packets of this class.
Implements regina::NPacket.
const std::vector< NTetrahedron * > & regina::NTriangulation::getTetrahedra | ( | ) | const [inline] |
Returns all tetrahedra in the triangulation.
The reference returned will remain valid for as long as the triangulation exists, always reflecting the tetrahedra currently in the triangulation.
const NTetrahedron * regina::NTriangulation::getTetrahedron | ( | unsigned long | index | ) | const [inline] |
Returns the tetrahedron with the given index number in the triangulation.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the triangulation.
index | specifies which tetrahedron to return; this value should be between 0 and getNumberOfTetrahedra()-1 inclusive. |
index
th tetrahedron in the triangulation. NTetrahedron * regina::NTriangulation::getTetrahedron | ( | unsigned long | index | ) | [inline] |
Returns the tetrahedron with the given index number in the triangulation.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the triangulation.
index | specifies which tetrahedron to return; this value should be between 0 and getNumberOfTetrahedra()-1 inclusive. |
index
th tetrahedron in the triangulation. long regina::NTriangulation::getTetrahedronIndex | ( | const NTetrahedron * | tet | ) | const [inline] |
Returns the index of the given tetrahedron in the triangulation.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the triangulation.
tet | specifies which tetrahedron to find in the triangulation. |
NVertex * regina::NTriangulation::getVertex | ( | unsigned long | index | ) | const [inline] |
Returns the requested triangulation vertex.
Bear in mind that each time the triangulation changes, the vertices will be deleted and replaced with new ones. Thus this object should be considered temporary only.
index | the index of the desired vertex, ranging from 0 to getNumberOfVertices()-1 inclusive. |
long regina::NTriangulation::getVertexIndex | ( | const NVertex * | vertex | ) | const [inline] |
Returns the index of the given vertex in the triangulation.
vertex | specifies which vertex to find in the triangulation. |
const std::vector< NVertex * > & regina::NTriangulation::getVertices | ( | ) | const [inline] |
Returns all vertices of this triangulation.
Bear in mind that each time the triangulation changes, the vertices will be deleted and replaced with new ones. Thus the objects contained in this list should be considered temporary only.
This reference to the list however will remain valid and up-to-date for as long as the triangulation exists.
static NXMLPacketReader* regina::NTriangulation::getXMLReader | ( | NPacket * | parent | ) | [static] |
(end: File I/O)
Returns a newly created XML element reader that will read the contents of a single XML packet element. You may assume that the packet to be read is of the same type as the class in which you are implementing this routine.
The XML element reader should read exactly what writeXMLPacketData() writes, and vice versa.
parent represents the packet which will become the new packet's parent in the tree structure, and may be assumed to have already been read from the file. This information is for reference only, and does not need to be used. The XML element reader can either insert or not insert the new packet beneath parent in the tree structure as it pleases. Note however that parent will be 0 if the new packet is to become a tree matriarch.
This routine is not actually provided for NPacket itself, but must be declared and implemented for every packet subclass that will be instantiated.
parent | the packet which will become the new packet's parent in the tree structure, or 0 if the new packet is to be tree matriarch. |
Reimplemented from regina::NPacket.
void regina::NTriangulation::gluingsHaveChanged | ( | ) | [inline] |
This must be called whenever the gluings of tetrahedra are changed! Clears appropriate properties and performs other necessary tasks.
The responsibility of calling gluingsHaveChanged() falls upon the routine that alters the gluings (such as a component of a triangulation editor, or so on).
bool regina::NTriangulation::hasBoundaryFaces | ( | ) | const [inline] |
Determines if this triangulation has any boundary faces.
true
if and only if there are boundary faces. bool regina::NTriangulation::hasNegativeIdealBoundaryComponents | ( | ) | const [inline] |
Determines if this triangulation contains any ideal boundary components with negative Euler characteristic.
true
if and only if there is at least one such boundary component. bool regina::NTriangulation::hasSplittingSurface | ( | ) |
Determines whether this triangulation has a normal splitting surface.
See NNormalSurface::isSplitting() for details regarding normal splitting surfaces.
true
if and only if this triangulation has a normal splitting surface. bool regina::NTriangulation::hasTwoSphereBoundaryComponents | ( | ) | const [inline] |
Determines if this triangulation contains any two-sphere boundary components.
true
if and only if there is at least one two-sphere boundary component. bool regina::NTriangulation::idealToFinite | ( | bool | forceDivision = false |
) |
Converts an ideal triangulation into a finite triangulation.
All ideal or non-standard vertices are truncated and thus converted into real boundary components made from unglued faces of tetrahedra.
Note that this operation is a loose converse of finiteToIdeal().
Currently, the presence of an invalid edge will force the triangulation to be subdivided regardless of the value of parameter forceDivision. The final triangulation will still have the projective plane cusp caused by the invalid edge.
forceDivision | specifies what to do if the triangulation has no ideal or non-standard vertices. If true , the triangulation will be subdivided anyway, as if all vertices were ideal. If false (the default), the triangulation will be left alone. |
true
if and only if the triangulation was changed. void regina::NTriangulation::insertAugTriSolidTorus | ( | long | a1, | |
long | b1, | |||
long | a2, | |||
long | b2, | |||
long | a3, | |||
long | b3 | |||
) |
Inserts an augmented triangular solid torus with the given parameters into this triangulation.
Almost all augmented triangular solid tori represent Seifert fibred spaces with three or fewer exceptional fibres. Augmented triangular solid tori are described in more detail in the NAugTriSolidTorus class notes.
The resulting Seifert fibred space will be SFS((a1,b1) (a2,b2) (a3,b3) (1,1)), where the parameters a1, ..., b3 are passed as arguments to this routine. The three layered solid tori that are attached to the central triangular solid torus will be LST(|a1|, |b1|, |-a1-b1|), ..., LST(|a3|, |b3|, |-a3-b3|).
The new tetrahedra will be inserted at the end of the list of tetrahedra in the triangulation.
gcd(a2, b2) = 1.
gcd(a3, b3) = 1.
a1 | a parameter describing the first layered solid torus in the augmented triangular solid torus; this may be either positive or negative. | |
b1 | a parameter describing the first layered solid torus in the augmented triangular solid torus; this may be either positive or negative. | |
a2 | a parameter describing the second layered solid torus in the augmented triangular solid torus; this may be either positive or negative. | |
b2 | a parameter describing the second layered solid torus in the augmented triangular solid torus; this may be either positive or negative. | |
a3 | a parameter describing the third layered solid torus in the augmented triangular solid torus; this may be either positive or negative. | |
b3 | a parameter describing the third layered solid torus in the augmented triangular solid torus; this may be either positive or negative. |
void regina::NTriangulation::insertConstruction | ( | unsigned long | nTetrahedra, | |
const int | adjacencies[][4], | |||
const int | gluings[][4][4] | |||
) |
Inserts into this triangulation a set of tetrahedra and their gluings as described by the given integer arrays.
This routine is provided to make it easy to hard-code a medium-sized triangulation in a C++ source file. All of the pertinent data can be hard-coded into a pair of integer arrays at the beginning of the source file, avoiding an otherwise tedious sequence of many joinTo() calls.
An additional nTetrahedra tetrahedra will be inserted into this triangulation. The relationships between these tetrahedra should be stored in the two arrays as follows. Note that the new tetrahedra are numbered from 0 to (nTetrahedra - 1), and individual tetrahedron faces are numbered from 0 to 3.
The adjacencies array describes which tetrahedron faces are joined to which others. Specifically, adjacencies[t][f]
should contain the number of the tetrahedron joined to face f of tetrahedron t. If this face is to be left as a boundary face, adjacencies[t][f]
should be -1.
The gluings array describes the particular gluing permutations used when joining these tetrahedron faces together. Specifically, gluings[t][f][0..3]
should describe the permutation used to join face f of tetrahedron t to its adjacent tetrahedron. These four integers should be 0, 1, 2 and 3 in some order, so that gluings[t][f][i]
contains the image of i under this permutation. If face f of tetrahedron t is to be left as a boundary face, gluings[t][f][0..3]
may contain anything (and will be duly ignored).
It is the responsibility of the caller of this routine to ensure that the given arrays are correct and consistent. No error checking will be performed by this routine.
Note that, for an existing triangulation, dumpConstruction() will output a pair of C++ arrays that can be copied into a source file and used to reconstruct the triangulation via this routine.
nTetrahedra | the number of additional tetrahedra to insert. | |
adjacencies | describes which of the new tetrahedron faces are to be identified. This array must have initial dimension at least nTetrahedra. | |
gluings | describes the specific gluing permutations by which these new tetrahedron faces should be identified. This array must also have initial dimension at least nTetrahedra. |
void regina::NTriangulation::insertLayeredLensSpace | ( | unsigned long | p, | |
unsigned long | q | |||
) |
Inserts a new layered lens space L(p,q) into the triangulation.
The lens space will be created by gluing together two layered solid tori in a way that uses the fewest possible tetrahedra.
The new tetrahedra will be inserted at the end of the list of tetrahedra in the triangulation.
gcd(p, q) = 1.
p | a parameter of the desired lens space. | |
q | a parameter of the desired lens space. |
void regina::NTriangulation::insertLayeredLoop | ( | unsigned long | length, | |
bool | twisted | |||
) |
Inserts a layered loop of the given length into this triangulation.
Layered loops are described in more detail in the NLayeredLoop class notes.
The new tetrahedra will be inserted at the end of the list of tetrahedra in the triangulation.
length | the length of the new layered loop; this must be strictly positive. | |
twisted | true if the new layered loop should be twisted, or false if it should be untwisted. |
NTetrahedron* regina::NTriangulation::insertLayeredSolidTorus | ( | unsigned long | cuts0, | |
unsigned long | cuts1 | |||
) |
Inserts a new layered solid torus into the triangulation.
The meridinal disc of the layered solid torus will intersect the three edges of the boundary torus in cuts0, cuts1 and (cuts0 + cuts1) points respectively.
The boundary torus will always consist of faces 012 and 013 of the tetrahedron containing this boundary torus (this tetrahedron will be returned). In face 012, edges 12, 02 and 01 will meet the meridinal disc cuts0, cuts1 and (cuts0 + cuts1) times respectively. The only exceptions are if these three intersection numbers are (1,1,2) or (0,1,1), in which case edges 12, 02 and 01 will meet the meridinal disc (1, 2 and 1) or (1, 1 and 0) times respectively.
The new tetrahedra will be inserted at the end of the list of tetrahedra in the triangulation.
cuts1 is non-zero;
gcd(cuts0, cuts1) = 1.
cuts0 | the smallest of the three desired intersection numbers. | |
cuts1 | the second smallest of the three desired intersection numbers. |
bool regina::NTriangulation::insertRehydration | ( | const std::string & | dehydration | ) |
Inserts the rehydration of the given string into this triangulation.
The given string will be rehydrated into a proper triangulation. The new tetrahedra will be inserted into this triangulation in the order in which they appear in the rehydrated triangulation, and the numbering of their vertices (0-3) will not change.
The routine dehydrate() can be used to extract a dehydration string from an existing triangulation. Dehydration followed by rehydration might not produce a triangulation identical to the original, but it is guaranteed to produce an isomorphic copy. See dehydrate() for the reasons behind this.
For a full description of the dehydrated triangulation format, see A Census of Cusped Hyperbolic 3-Manifolds, Callahan, Hildebrand and Weeks, Mathematics of Computation 68/225, 1999.
dehydration | a dehydrated representation of the triangulation to insert. Case is irrelevant; all letters will be treated as if they were lower case. |
true
if the insertion was successful, or false
if the given string could not be rehydrated. void regina::NTriangulation::insertSFSOverSphere | ( | long | a1 = 1 , |
|
long | b1 = 0 , |
|||
long | a2 = 1 , |
|||
long | b2 = 0 , |
|||
long | a3 = 1 , |
|||
long | b3 = 0 | |||
) |
Inserts an orientable Seifert fibred space with at most three exceptional fibres over the 2-sphere into this triangulation.
The inserted Seifert fibred space will be SFS((a1,b1) (a2,b2) (a3,b3) (1,1)), where the parameters a1, ..., b3 are passed as arguments to this routine.
The three pairs of parameters (a,b) do not need to be normalised, i.e., the parameters can be positive or negative and b may lie outside the range [0..a). There is no separate twisting parameter; each additional twist can be incorporated into the existing parameters by replacing some pair (a,b) with the pair (a,a+b). For Seifert fibred spaces with less than three exceptional fibres, some or all of the parameter pairs may be (1,k) or even (1,0).
The new tetrahedra will be inserted at the end of the list of tetrahedra in the triangulation.
gcd(a1, b1) = 1.
gcd(a2, b2) = 1.
gcd(a3, b3) = 1.
a1 | a parameter describing the first exceptional fibre. | |
b1 | a parameter describing the first exceptional fibre. | |
a2 | a parameter describing the second exceptional fibre. | |
b2 | a parameter describing the second exceptional fibre. | |
a3 | a parameter describing the third exceptional fibre. | |
b3 | a parameter describing the third exceptional fibre. |
void regina::NTriangulation::insertTriangulation | ( | const NTriangulation & | source | ) |
Inserts a copy of the given triangulation into this triangulation.
The new tetrahedra will be inserted into this triangulation in the order in which they appear in the given triangulation, and the numbering of their vertices (0-3) will not change. They will be given the same descriptions as appear in the given triangulation.
source | the triangulation whose copy will be inserted. |
bool regina::NTriangulation::intelligentSimplify | ( | ) |
Attempts to simplify the triangulation as intelligently as possible without further input.
This routine will attempt to reduce both the number of tetrahedra and the number of boundary faces (with the number of tetrahedra as its priority).
Currently this routine uses simplifyToLocalMinimum() in combination with random 4-4 moves, book opening moves and book closing moves.
true
if and only if the triangulation was changed. NPacket * regina::NTriangulation::internalClonePacket | ( | NPacket * | parent | ) | const [inline, protected, virtual] |
Makes a newly allocated copy of this packet.
This routine should not insert the new packet into the tree structure, clone the packet's associated tags or give the packet a label. It should also not clone any descendants of this packet.
You may assume that the new packet will eventually be inserted into the tree beneath either the same parent as this packet or a clone of that parent.
parent | the parent beneath which the new packet will eventually be inserted. |
Implements regina::NPacket.
bool regina::NTriangulation::isBall | ( | ) | const |
Determines whether this is a triangulation of a 3-dimensional ball.
This routine is based on isThreeSphere(), which in turn combines Rubinstein's 3-sphere recognition algorithm with Jaco and Rubinstein's 0-efficiency prime decomposition algorithm.
true
if and only if this is a triangulation of a 3-dimensional ball. bool regina::NTriangulation::isClosed | ( | ) | const [inline] |
Determines if this triangulation is closed.
This is the case if and only if it has no boundary. Note that ideal triangulations are not closed.
true
if and only if this triangulation is closed. bool regina::NTriangulation::isConnected | ( | ) | const [inline] |
Determines if this triangulation is connected.
true
if and only if this triangulation is connected. std::auto_ptr<NIsomorphism> regina::NTriangulation::isContainedIn | ( | const NTriangulation & | other | ) | const |
Determines if an isomorphic copy of this triangulation is contained within the given triangulation, possibly as a subcomplex of some larger component (or components).
Specifically, this routine determines if there is a boundary incomplete combinatorial isomorphism from this triangulation to other. Boundary incomplete isomorphisms are described in detail in the NIsomorphism class notes.
In particular, note that boundary faces of this triangulation need not correspond to boundary faces of other, and that other can contain more tetrahedra than this triangulation.
If a boundary incomplete isomorphism is found, the details of this isomorphism are returned. The isomorphism is newly constructed, and so to assist with memory management is returned as a std::auto_ptr. Thus, to test whether an isomorphism exists without having to explicitly deal with the isomorphism itself, you can call if (isContainedIn(other).get())
and the newly created isomorphism (if it exists) will be automatically destroyed.
If more than one such isomorphism exists, only one will be returned. For a routine that returns all such isomorphisms, see findAllSubcomplexesIn().
other | the triangulation in which to search for an isomorphic copy of this triangulation. |
bool regina::NTriangulation::isIdeal | ( | ) | const [inline] |
Determines if this triangulation is ideal.
This is the case if and only if one of the vertex links is closed and not a 2-sphere. Note that the triangulation is not required to be valid.
true
if and only if this triangulation is ideal. std::auto_ptr<NIsomorphism> regina::NTriangulation::isIsomorphicTo | ( | const NTriangulation & | other | ) | const |
Determines if this triangulation is combinatorially isomorphic to the given triangulation.
Specifically, this routine determines if there is a one-to-one and onto boundary complete combinatorial isomorphism from this triangulation to other. Boundary complete isomorphisms are described in detail in the NIsomorphism class notes.
In particular, note that this triangulation and other must contain the same number of tetrahedra for such an isomorphism to exist.
if (isIsomorphicTo(other).get())
and the newly created isomorphism (if it exists) will be automatically destroyed.
other | the triangulation to compare with this one. |
bool regina::NTriangulation::isOrientable | ( | ) | const [inline] |
Determines if this triangulation is orientable.
true
if and only if this triangulation is orientable. bool regina::NTriangulation::isStandard | ( | ) | const [inline] |
Determines if this triangulation is standard.
This is the case if and only if every vertex is standard. See NVertex::isStandard() for further details.
true
if and only if this triangulation is standard. bool regina::NTriangulation::isThreeSphere | ( | ) | const |
Determines whether this is a triangulation of a 3-sphere.
This routine relies upon a combination of Rubinstein's 3-sphere recognition algorithm and Jaco and Rubinstein's 0-efficiency prime decomposition algorithm.
true
if and only if this is a 3-sphere triangulation. bool regina::NTriangulation::isValid | ( | ) | const [inline] |
Determines if this triangulation is valid.
A triangulation is valid unless there is some vertex whose link has boundary but is not a disc (i.e., a vertex for which NVertex::getLink() returns NVertex::NON_STANDARD_BDRY), or unless there is some edge glued to itself in reverse (i.e., an edge for which NEdge::isValid() returns false
).
true
if and only if this triangulation is valid. bool regina::NTriangulation::isZeroEfficient | ( | ) |
Determines if this triangulation is 0-efficient.
A triangulation is 0-efficient if its only normal spheres and discs are vertex linking, and if it has no 2-sphere boundary components.
true
if and only if this triangulation is 0-efficient. bool regina::NTriangulation::knowsBall | ( | ) | const |
Is it already known (or trivial to determine) whether or not this is a triangulation of a 3-dimensional ball? See isBall() for further details.
If this property is indeed already known, future calls to isBall() will be very fast (simply returning the precalculated value).
If this property is not already known, this routine will nevertheless run some very fast preliminary tests to see if the answer is obviously no. If so, it will store false
as the precalculated value for isBall() and this routine will return true
.
Otherwise a call to isBall() may potentially require more significant work, and so this routine will return false
.
true
if and only if this property is already known or trivial to calculate. bool regina::NTriangulation::knowsSplittingSurface | ( | ) | const [inline] |
Is it already known whether or not this triangulation has a splitting surface? See hasSplittingSurface() for further details.
If this property is already known, future calls to hasSplittingSurface() will be very fast (simply returning the precalculated value).
true
if and only if this property is already known. bool regina::NTriangulation::knowsThreeSphere | ( | ) | const |
Is it already known (or trivial to determine) whether or not this is a triangulation of a 3-sphere? See isThreeSphere() for further details.
If this property is indeed already known, future calls to isThreeSphere() will be very fast (simply returning the precalculated value).
If this property is not already known, this routine will nevertheless run some very fast preliminary tests to see if the answer is obviously no. If so, it will store false
as the precalculated value for isThreeSphere() and this routine will return true
.
Otherwise a call to isThreeSphere() may potentially require more significant work, and so this routine will return false
.
true
if and only if this property is already known or trivial to calculate. bool regina::NTriangulation::knowsZeroEfficient | ( | ) | const [inline] |
Is it already known whether or not this triangulation is 0-efficient? See isZeroEfficient() for further details.
If this property is already known, future calls to isZeroEfficient() will be very fast (simply returning the precalculated value).
true
if and only if this property is already known. NTetrahedron* regina::NTriangulation::layerOn | ( | NEdge * | edge | ) |
Performs a layering upon the given boundary edge of the triangulation.
See the NLayering class notes for further details on what a layering entails.
edge | the boundary edge upon which to layer. |
void regina::NTriangulation::makeDoubleCover | ( | ) |
Converts this triangulation into its double cover.
Each orientable component will be duplicated, and each non-orientable component will be converted into its orientable double cover.
NPacket* regina::NTriangulation::makeZeroEfficient | ( | ) |
Converts this into a 0-efficient triangulation of the same underlying 3-manifold.
A triangulation is 0-efficient if its only normal spheres and discs are vertex linking, and if it has no 2-sphere boundary components.
Note that this routine is currently only available for closed orientable triangulations; see the list of preconditions for details. The 0-efficiency algorithm of Jaco and Rubinstein is used.
If the underlying 3-manifold is prime, it can always be made 0-efficient (with the exception of the special cases RP3 and S2xS1 as noted below). In this case the original triangulation will be modified directly and 0 will be returned.
If the underyling 3-manifold is RP3 or S2xS1, it cannot be made 0-efficient; in this case the original triangulation will be reduced to a two-tetrahedron minimal triangulation and 0 will again be returned.
If the underlying 3-manifold is not prime, it cannot be made 0-efficient. In this case the original triangulation will remain unchanged and a new connected sum decomposition will be returned. This will be presented as a newly allocated container packet with one child triangulation for each prime summand.
void regina::NTriangulation::maximalForestInBoundary | ( | stdhash::hash_set< NEdge *, HashPointer > & | edgeSet, | |
stdhash::hash_set< NVertex *, HashPointer > & | vertexSet | |||
) | const |
Produces a maximal forest in the 1-skeleton of the triangulation boundary.
Both given sets will be emptied and the edges and vertices of the maximal forest will be placed into them. A vertex that forms its own boundary component (such as an ideal vertex) will still be placed in vertexSet
.
Note that the edge and vertex pointers returned will become invalid once the triangulation has changed.
edgeSet | the set to be emptied and into which the edges of the maximal forest will be placed. | |
vertexSet | the set to be emptied and into which the vertices of the maximal forest will be placed. |
void regina::NTriangulation::maximalForestInDualSkeleton | ( | stdhash::hash_set< NFace *, HashPointer > & | faceSet | ) | const |
Produces a maximal forest in the triangulation's dual 1-skeleton.
The given set will be emptied and will have the faces corresponding to the edges of the maximal forest in the dual 1-skeleton placed into it.
Note that the face pointers returned will become invalid once the triangulation has changed.
faceSet | the set to be emptied and into which the faces representing the maximal forest will be placed. |
void regina::NTriangulation::maximalForestInSkeleton | ( | stdhash::hash_set< NEdge *, HashPointer > & | edgeSet, | |
bool | canJoinBoundaries = true | |||
) | const |
Produces a maximal forest in the triangulation's 1-skeleton.
The given set will be emptied and will have the edges of the maximal forest placed into it. It can be specified whether or not different boundary components may be joined by the maximal forest.
An edge leading to an ideal vertex is still a candidate for inclusion in the maximal forest. For the purposes of this algorithm, any ideal vertex will be treated as any other vertex (and will still be considered part of its own boundary component).
Note that the edge pointers returned will become invalid once the triangulation has changed.
edgeSet | the set to be emptied and into which the edges of the maximal forest will be placed. | |
canJoinBoundaries | true if and only if different boundary components are allowed to be joined by the maximal forest. |
bool regina::NTriangulation::openBook | ( | NFace * | f, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a book opening move about the given face.
This involves taking a face meeting the boundary along two edges and ungluing it to create two new boundary faces and thus expose the tetrahedra it initially joined. This move is the inverse of the closeBook() move, and is used to open the way for new shellBoundary() moves.
This move can be done only if:
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument f) can no longer be used.
The given face is a face of this triangulation.
f | the face about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. virtual void regina::NTriangulation::readIndividualProperty | ( | NFile & | infile, | |
unsigned | propType | |||
) | [virtual] |
Reads an individual property from an old-style binary file.
The property type and bookmarking details should not read; merely the contents of the property that are written to file between NFile::writePropertyHeader() and NFile::writePropertyFooter(). See the NFile::writePropertyHeader() notes for details.
The property type of the property to be read will be passed in propType. If the property type is unrecognised, this routine should simply do nothing and return. If the property type is recognised, this routine should read the property and process it accordingly (e.g., store it in whatever data object is currently being read).
infile | the file from which to read the property. This should be open for reading and at the position immediately after writePropertyHeader() would have been called during the corresponding write operation. | |
propType | the property type of the property about to be read. |
Implements regina::NFilePropertyReader.
static NTriangulation* regina::NTriangulation::readPacket | ( | NFile & | in, | |
NPacket * | parent | |||
) | [static] |
Reads a single packet from the specified file and returns a newly created object containing that information.
You may assume that the packet to be read is of the same type as the class in which you are implementing this routine. The newly created object must also be of this type.
For instance, NTriangulation::readPacket() may assume that the packet is of type NTriangulation, and must return a pointer to a newly created NTriangulation. Deallocation of the newly created packet is the responsibility of whoever calls this routine.
The packet type and label may be assumed to have already been read from the file, and should not be reread. The readPacket() routine should read exactly what writePacket() writes, and vice versa.
parent represents the packet which will become the new packet's parent in the tree structure, and may be assumed to have already been read from the file. This information is for reference only, and does not need to be used. This routine can either insert or not insert the new packet beneath parent in the tree structure as it pleases. Note however that parent will be 0 if the new packet is to become a tree matriarch.
This routine is not actually provided for NPacket itself, but must be declared and implemented for every packet subclass that will be instantiated. Within each such subclass the function must be declared to return a pointer to an object of that subclass. For instance, NTriangulation::readPacket() must be declared to return an NTriangulation*, not simply an NPacket*.
New packet types should make this routine simply return 0 since this file format is now obsolete, and older calculation engines will not understand newer packet types anyway.
in | the file from which to read the packet. | |
parent | the packet which will become the new packet's parent in the tree structure, or 0 if the new packet is to be tree matriarch. |
Reimplemented from regina::NPacket.
void regina::NTriangulation::removeAllTetrahedra | ( | ) | [inline] |
Removes all tetrahedra from the triangulation.
All tetrahedra will be deallocated.
There is no need to call gluingsHaveChanged() after calling this function.
NTetrahedron * regina::NTriangulation::removeTetrahedron | ( | NTetrahedron * | tet | ) | [inline] |
Removes the given tetrahedron from the triangulation.
All faces glued to this tetrahedron will be unglued. The tetrahedron will not be deallocated.
There is no need to call gluingsHaveChanged() after calling this function.
tet | the tetrahedron to remove. |
NTetrahedron * regina::NTriangulation::removeTetrahedronAt | ( | unsigned long | index | ) | [inline] |
Removes the tetrahedron with the given index number from the triangulation.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the triangulation.
All faces glued to this tetrahedron will be unglued. The tetrahedron will not be deallocated.
There is no need to call gluingsHaveChanged() after calling this function.
index | specifies which tetrahedron to remove; this should be between 0 and getNumberOfTetrahedra()-1 inclusive. |
void regina::NTriangulation::reorderTetrahedraBFS | ( | bool | reverse = false |
) |
Reorders the tetrahedra of this triangulation using a breadth-first search, so that small-numbered tetrahedra are adjacent to other small-numbered tetrahedra.
Specifically, the reordering will operate as follows. Tetrahedron 0 will remain tetrahedron 0. Its immediate neighbours will be numbered 1, 2, 3 and 4 (though if these neighbours are not distinct then of course fewer labels will be required). Their immediate neighbours will in turn be numbered 5, 6, and so on, ultimately following a breadth-first search throughout the entire triangulation.
If the optional argument reverse is true
, then tetrahedron numbers will be assigned in reverse order. That is, tetrahedron 0 will become tetrahedron n-1, its neighbours will become tetrahedra n-2 down to n-5, and so on.
reverse | true if the new tetrahedron numbers should be assigned in reverse order, as described above. |
bool regina::NTriangulation::shellBoundary | ( | NTetrahedron * | t, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a boundary shelling move on the given tetrahedron.
This involves simply popping off a tetrahedron that touches the boundary. This can be done only if:
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects can no longer be used.
The given tetrahedron is a tetrahedron of this triangulation.
t | the tetrahedron upon which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. void regina::NTriangulation::simplifiedFundamentalGroup | ( | NGroupPresentation * | newGroup | ) | [inline] |
Notifies the triangulation that you have simplified the presentation of its fundamental group.
The old group presentation will be destroyed, and this triangulation will take ownership of the new (hopefully simpler) group that is passed.
This routine is useful for situations in which some external body (such as GAP) has simplified the group presentation better than Regina can.
Regina does not verify that the new group presentation is equivalent to the old, since this is - well, hard.
If the fundamental group has not yet been calculated for this triangulation, this routine will nevertheless take ownership of the new group, under the assumption that you have worked out the group through some other clever means without ever having needed to call getFundamentalGroup() at all.
Note that this routine will not fire a packet change event.
newGroup | a new (and hopefully simpler) presentation of the fundamental group of this triangulation. |
bool regina::NTriangulation::simplifyToLocalMinimum | ( | bool | perform = true |
) |
Uses all known simplification moves to reduce the triangulation monotonically to some local minimum number of tetrahedra.
Note that this will probably not give a globally minimal triangulation; see intelligentSimplify() for further assistance in achieving this goal.
The moves used include 3-2, 2-0 (edge and vertex), 2-1 and boundary shelling moves.
Note that moves that do not reduce the number of tetrahedra (such as 4-4 moves or book opening moves) are not used in this routine. Such moves do however feature in intelligentSimplify().
perform | true if we are to perform the simplifications, or false if we are only to investigate whether simplifications are possible (defaults to true ). |
true
, this routine returns true
if and only if the triangulation was changed to reduce the number of tetrahedra; if perform is false
, this routine returns true
if and only if it determines that it is capable of performing such a change. unsigned long regina::NTriangulation::splitIntoComponents | ( | NPacket * | componentParent = 0 , |
|
bool | setLabels = true | |||
) |
Splits a disconnected triangulation into many smaller triangulations, one for each component.
The new component triangulations will be inserted as children of the given parent packet. The original triangulation will be left unchanged.
If the given parent packet is 0, the new component triangulations will be inserted as children of this triangulation.
This routine can optionally assign unique (and sensible) packet labels to each of the new component triangulations. Note however that uniqueness testing may be slow, so this assignment of labels should be disabled if the component triangulations are only temporary objects used as part of a larger routine.
componentParent | the packet beneath which the new component triangulations will be inserted, or 0 if they should be inserted directly beneath this triangulation. | |
setLabels | true if the new component triangulations should be assigned unique packet labels, or false if they should be left without labels at all. |
long regina::NTriangulation::tetrahedronIndex | ( | const NTetrahedron * | tet | ) | const [inline] |
Returns the index of the given tetrahedron in the triangulation.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getTetrahedronIndex(). The name has been changed because, unlike the old routine, it requires that the given tetrahedron belongs to the triangulation (a consequence of some significant memory optimisations).
tet | specifies which tetrahedron to find in the triangulation. |
bool regina::NTriangulation::threeTwoMove | ( | NEdge * | e, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 3-2 move about the given edge.
This involves replacing the three tetrahedra joined at that edge with two tetrahedra joined by a face. This can be done iff (i) the edge is valid and non-boundary, and (ii) the three tetrahedra are distinct.
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument e) can no longer be used.
The given edge is an edge of this triangulation.
e | the edge about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. double regina::NTriangulation::turaevViro | ( | unsigned long | r, | |
unsigned long | whichRoot | |||
) | const |
Computes the Turaev-Viro state sum invariant of this 3-manifold based upon the given initial data.
The initial data is as described in the paper of Turaev and Viro, "State sum invariants of 3-manifolds and quantum 6j-symbols", Topology, vol. 31, no. 4, 1992, pp 865-902.
In particular, Section 7 describes the initial data as determined by an integer r >=3 and a root of unity q0 of degree 2r for which q0^2 is a primitive root of unity of degree r.
These invariants, although computed in the complex field, should all be reals. Thus the return type is an ordinary double.
r | the integer r as described above; this must be at least 3. | |
whichRoot | determines q0 to be the root of unity e^(2i * Pi * whichRoot / 2r); this argument must be strictly between 0 and 2r and must have no common factors with r. |
bool regina::NTriangulation::twoOneMove | ( | NEdge * | e, | |
int | edgeEnd, | |||
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 2-1 move about the given edge.
This involves taking an edge meeting only one tetrahedron just once and merging that tetrahedron with one of the tetrahedra joining it.
This can be done assuming the following conditions:
e
to the vertex of the second tetrahedron not touching the original tetrahedron. These edges must be distinct and may not both be in the boundary.
e
that is common to both tetrahedra should be distinct.Phew. Code documentation could really do with diagrams!
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument e) can no longer be used.
The given edge is an edge of this triangulation.
e | the edge about which to perform the move. | |
edgeEnd | the end of the edge opposite that at which the second tetrahedron (to be merged) is joined. The end is 0 or 1, corresponding to the labelling (0,1) of the vertices of the edge as described in NEdgeEmbedding::getVertices(). | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. bool regina::NTriangulation::twoThreeMove | ( | NFace * | f, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 2-3 move about the given face.
This involves replacing the two tetrahedra joined at that face with three tetrahedra joined by an edge. This can be done iff the two tetrahedra are distinct.
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument f) can no longer be used.
The given face is a face of this triangulation.
f | the face about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. bool regina::NTriangulation::twoZeroMove | ( | NVertex * | v, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 2-0 move about the given vertex of degree 2.
This involves taking the two tetrahedra joined at that vertex and squashing them flat. This can be done only if:
v
in each tetrahedron are distinct and not both boundary;
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument v) can no longer be used.
The given vertex is a vertex of this triangulation.
v | the vertex about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. bool regina::NTriangulation::twoZeroMove | ( | NEdge * | e, | |
bool | check = true , |
|||
bool | perform = true | |||
) |
Checks the eligibility of and/or performs a 2-0 move about the given edge of degree 2.
This involves taking the two tetrahedra joined at that edge and squashing them flat. This can be done only if:
e
in each tetrahedron are distinct and not both boundary;
If the routine is asked to both check and perform, the move will only be performed if the check shows it is legal.
Note that after performing this move, all skeletal objects (faces, components, etc.) will be reconstructed, which means any pointers to old skeletal objects (such as the argument e) can no longer be used.
The given edge is an edge of this triangulation.
e | the edge about which to perform the move. | |
check | true if we are to check whether the move is allowed (defaults to true ). | |
perform | true if we are to perform the move (defaults to true ). |
true
, the function returns true
if and only if the requested move may be performed without changing the topology of the manifold. If check is false
, the function simply returns true
. long regina::NTriangulation::vertexIndex | ( | const NVertex * | vertex | ) | const [inline] |
Returns the index of the given vertex in the triangulation.
This routine was introduced in Regina 4.5, and replaces the old getVertexIndex(). The name has been changed because, unlike the old routine, it requires that the given vertex belongs to the triangulation (a consequence of some significant memory optimisations).
vertex | specifies which vertex to find in the triangulation. |
virtual void regina::NTriangulation::writePacket | ( | NFile & | out | ) | const [virtual] |
Writes the packet details to the given old-style binary file.
You may assume that the packet type and label have already been written. Only the actual data stored in the packet need be written.
The default implementation for this routine does nothing; new packet types should not implement this routine since this file format is now obsolete, and older calculation engines will simply skip unknown packet types when reading from binary files.
out | the file to be written to. |
Reimplemented from regina::NPacket.
virtual void regina::NTriangulation::writeTextLong | ( | std::ostream & | out | ) | const [virtual] |
Writes this object in long text format to the given output stream.
The output should provided the user with all the information they could want. The output should end with a newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.
void regina::NTriangulation::writeTextShort | ( | std::ostream & | out | ) | const [inline, virtual] |
Writes this object in short text format to the given output stream.
The output should fit on a single line and no newline should be written.
out | the output stream to which to write. |
Implements regina::ShareableObject.
virtual void regina::NTriangulation::writeXMLPacketData | ( | std::ostream & | out | ) | const [protected, virtual] |
Writes a chunk of XML containing the data for this packet only.
You may assume that the packet opening tag (including the packet type and label) has already been written, and that all child packets followed by the corresponding packet closing tag will be written immediately after this routine is called. This routine need only write the internal data stored in this specific packet.
out | the output stream to which the XML should be written. |
Implements regina::NPacket.
const int regina::NTriangulation::packetType [static] |
Contains the integer ID for this packet.
Each distinct packet type must have a unique ID, and this should be a positive integer. See packetregistry.h for further requirements regarding ID selection.
This member is not actually provided for NPacket itself, but must be declared for every packet subclass that will be instantiated. A value need not be assigned; packetregistry.h will take care of this task when you register the packet.
Reimplemented from regina::NPacket.