Regina Calculation Engine
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regina::Triangulation< dim > Class Template Referenceabstract

A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets. More...

#include <triangulation/generic.h>

Inheritance diagram for regina::Triangulation< dim >:
regina::Packet regina::detail::TriangulationBase< dim > regina::Output< Packet > regina::SafePointeeBase< Packet > regina::detail::FaceListSuite< dim, dim - 1 > regina::alias::Simplices< TriangulationBase< dim >, dim > regina::alias::SimplexAt< TriangulationBase< dim >, dim, true > regina::alias::FaceOfTriangulation< TriangulationBase< dim >, dim > regina::alias::FacesOfTriangulation< TriangulationBase< dim >, dim > regina::FaceList< dim, subdim >

Public Types

typedef Packet SafePointeeType
 The type of object being pointed to. More...
 
typedef std::vector< Simplex< dim > * >::const_iterator SimplexIterator
 Used to iterate through top-dimensional simplices. More...
 
typedef std::vector< Component< dim > * >::const_iterator ComponentIterator
 Used to iterate through connected components. More...
 
typedef std::vector< BoundaryComponent< dim > * >::const_iterator BoundaryComponentIterator
 Used to iterate through boundary components. More...
 

Public Member Functions

std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 
bool hasSafePtr () const
 Is there one or more SafePtr currently pointing to this object? More...
 
Iterator begin () const
 Returns an iterator pointing to the first subdim-face. More...
 
Iterator end () const
 Returns an iterator pointing beyond the last subdim-face. More...
 
Constructors and Destructors
 Triangulation ()
 Default constructor. More...
 
 Triangulation (const Triangulation &copy)
 Creates a new copy of the given triangulation. More...
 
 Triangulation (const Triangulation &copy, bool cloneProps)
 Creates a new copy of the given triangulation, with the option of whether or not to clone its computed properties also. More...
 
virtual ~Triangulation ()
 Destroys this triangulation. More...
 
Packet Identification
virtual PacketType type () const =0
 Returns the unique integer ID representing this type of packet. More...
 
virtual std::string typeName () const =0
 Returns an English name for this type of packet. More...
 
const std::string & label () const
 Returns the label associated with this individual packet. More...
 
std::string humanLabel () const
 Returns the label associated with this individual packet, adjusted if necessary for human-readable output. More...
 
std::string adornedLabel (const std::string &adornment) const
 Returns the label of this packet adorned with the given string. More...
 
void setLabel (const std::string &label)
 Sets the label associated with this individual packet. More...
 
std::string fullName () const
 Returns a descriptive text string for the packet. More...
 
Tags
bool hasTag (const std::string &tag) const
 Determines whether this packet has the given associated tag. More...
 
bool hasTags () const
 Determines whether this packet has any associated tags at all. More...
 
bool addTag (const std::string &tag)
 Associates the given tag with this packet. More...
 
bool removeTag (const std::string &tag)
 Removes the association of the given tag with this packet. More...
 
void removeAllTags ()
 Removes all associated tags from this packet. More...
 
const std::set< std::string > & tags () const
 Returns the set of all tags associated with this packet. More...
 
Event Handling
bool listen (PacketListener *listener)
 Registers the given packet listener to listen for events on this packet. More...
 
bool isListening (PacketListener *listener)
 Determines whether the given packet listener is currently listening for events on this packet. More...
 
bool unlisten (PacketListener *listener)
 Unregisters the given packet listener so that it no longer listens for events on this packet. More...
 
Tree Queries
Packetparent () const
 Determines the parent packet in the tree structure. More...
 
PacketfirstChild () const
 Determines the first child of this packet in the tree structure. More...
 
PacketlastChild () const
 Determines the last child of this packet in the tree structure. More...
 
PacketnextSibling () const
 Determines the next sibling of this packet in the tree structure. More...
 
PacketprevSibling () const
 Determines the previous sibling of this packet in the tree structure. More...
 
Packetroot () const
 Determines the root of the tree to which this packet belongs. More...
 
unsigned levelsDownTo (const Packet *descendant) const
 Counts the number of levels between this packet and its given descendant in the tree structure. More...
 
unsigned levelsUpTo (const Packet *ancestor) const
 Counts the number of levels between this packet and its given ancestor in the tree structure. More...
 
bool isGrandparentOf (const Packet *descendant) const
 Determines if this packet is equal to or an ancestor of the given packet in the tree structure. More...
 
size_t countChildren () const
 Returns the number of immediate children of this packet. More...
 
size_t countDescendants () const
 Returns the total number of strict descendants of this packet. More...
 
size_t totalTreeSize () const
 Determines the total number of packets in the tree or subtree for which this packet is matriarch. More...
 
Tree Manipulation
void insertChildFirst (Packet *child)
 Inserts the given packet as the first child of this packet. More...
 
void insertChildLast (Packet *child)
 Inserts the given packet as the last child of this packet. More...
 
void insertChildAfter (Packet *newChild, Packet *prevChild)
 Inserts the given packet as a child of this packet at the given location in this packet's child list. More...
 
void makeOrphan ()
 Cuts this packet away from its parent in the tree structure and instead makes it matriarch of its own tree. More...
 
void reparent (Packet *newParent, bool first=false)
 Cuts this packet away from its parent in the tree structure, and inserts it as a child of the given packet instead. More...
 
void transferChildren (Packet *newParent)
 Cuts all of this packet's children out of the packet tree, and reinserts them as children of the given packet instead. More...
 
void swapWithNextSibling ()
 Swaps this packet with its next sibling in the sequence of children beneath their common parent packet. More...
 
void moveUp (unsigned steps=1)
 Moves this packet the given number of steps towards the beginning of its sibling list. More...
 
void moveDown (unsigned steps=1)
 Moves this packet the given number of steps towards the end of its sibling list. More...
 
void moveToFirst ()
 Moves this packet to be the first in its sibling list. More...
 
void moveToLast ()
 Moves this packet to be the last in its sibling list. More...
 
void sortChildren ()
 Sorts the immediate children of this packet according to their packet labels. More...
 
Searching and Iterating
SubtreeIterator begin ()
 Returns an iterator at the beginning of the range of packets in the subtree rooted at this packet. More...
 
SubtreeIterator end ()
 Returns an iterator beyond the end of the range of packets in the subtree rooted at this packet. More...
 
PacketDescendants descendants () const
 Returns a lightweight object for iterating through all strict descendants of this packet in the packet tree. More...
 
PacketChildren children () const
 Returns a lightweight object for iterating through the immediate children of this packet. More...
 
PacketnextTreePacket ()
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
const PacketnextTreePacket () const
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
PacketnextTreePacket (const std::string &type)
 Finds the next packet after this of the requested type in a complete depth-first iteration of the entire tree structure. More...
 
const PacketnextTreePacket (const std::string &type) const
 Finds the next packet after this of the requested type in a complete depth-first iteration of the entire tree structure. More...
 
PacketfirstTreePacket (const std::string &type)
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
const PacketfirstTreePacket (const std::string &type) const
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
PacketfindPacketLabel (const std::string &label)
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
const PacketfindPacketLabel (const std::string &label) const
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
Packet Dependencies
bool isPacketEditable () const
 Determines whether this packet can be altered without invalidating or otherwise upsetting any of its immediate children. More...
 
Cloning
Packetclone (bool cloneDescendants=false, bool end=true) const
 Clones this packet (and possibly its descendants), assigns to it a suitable unused label and inserts the clone into the tree as a sibling of this packet. More...
 
Simplices
size_t size () const
 Returns the number of top-dimensional simplices in the triangulation. More...
 
const std::vector< Simplex< dim > * > & simplices () const
 Returns all top-dimensional simplices in the triangulation. More...
 
Simplex< dim > * simplex (size_t index)
 Returns the top-dimensional simplex at the given index in the triangulation. More...
 
const Simplex< dim > * simplex (size_t index) const
 Returns the top-dimensional simplex at the given index in the triangulation. More...
 
Simplex< dim > * newSimplex ()
 Creates a new top-dimensional simplex and adds it to this triangulation. More...
 
Simplex< dim > * newSimplex (const std::string &desc)
 Creates a new top-dimensional simplex with the given description and adds it to this triangulation. More...
 
void removeSimplex (Simplex< dim > *simplex)
 Removes the given top-dimensional simplex from this triangulation. More...
 
void removeSimplexAt (size_t index)
 Removes the top-dimensional simplex at the given index in this triangulation. More...
 
void removeAllSimplices ()
 Removes all simplices from the triangulation. More...
 
void swapContents (Triangulation< dim > &other)
 Swaps the contents of this and the given triangulation. More...
 
void moveContentsTo (Triangulation< dim > &dest)
 Moves the contents of this triangulation into the given destination triangulation, without destroying any pre-existing contents. More...
 
Skeletal Queries
size_t countComponents () const
 Returns the number of connected components in this triangulation. More...
 
size_t countBoundaryComponents () const
 Returns the number of boundary components in this triangulation. More...
 
template<int subdim>
size_t countFaces () const
 Returns the number of subdim-faces in this triangulation. More...
 
std::vector< size_t > fVector () const
 Returns the f-vector of this triangulation, which counts the number of faces of all dimensions. More...
 
const std::vector< Component< dim > * > & components () const
 Returns all connected components of this triangulation. More...
 
const std::vector< BoundaryComponent< dim > * > & boundaryComponents () const
 Returns all boundary components of this triangulation. More...
 
template<int subdim>
const FaceList< dim, subdim > & faces () const
 Returns an object that allows iteration through and random access to all subdim-faces of this triangulation. More...
 
Component< dim > * component (size_t index) const
 Returns the requested connected component of this triangulation. More...
 
BoundaryComponent< dim > * boundaryComponent (size_t index) const
 Returns the requested boundary component of this triangulation. More...
 
template<int subdim>
Face< dim, subdim > * face (size_t index) const
 Returns the requested subdim-face of this triangulation. More...
 
Basic Properties
bool isEmpty () const
 Determines whether this triangulation is empty. More...
 
bool isValid () const
 Determines if this triangulation is valid. More...
 
bool hasBoundaryFacets () const
 Determines if this triangulation has any boundary facets. More...
 
size_t countBoundaryFacets () const
 Returns the total number of boundary facets in this triangulation. More...
 
bool isOrientable () const
 Determines if this triangulation is orientable. More...
 
bool isConnected () const
 Determines if this triangulation is connected. More...
 
bool isOriented () const
 Determines if this triangulation is oriented; that is, if the vertices of its top-dimensional simplices are labelled in a way that preserves orientation across adjacent facets. More...
 
long eulerCharTri () const
 Returns the Euler characteristic of this triangulation. More...
 
Algebraic Properties
const GroupPresentationfundamentalGroup () const
 Returns the fundamental group of this triangulation. More...
 
void simplifiedFundamentalGroup (GroupPresentation *newGroup)
 Notifies the triangulation that you have simplified the presentation of its fundamental group. More...
 
const AbelianGrouphomology () const
 Returns the first homology group for this triangulation. More...
 
const AbelianGrouphomologyH1 () const
 Returns the first homology group for this triangulation. More...
 
Skeletal Transformations
void orient ()
 Relabels the vertices of top-dimensional simplices in this triangulation so that all simplices are oriented consistently, if possible. More...
 
void reflect ()
 Relabels the vertices of top-dimensional simplices in this triangulation so that all simplices reflect their orientation. More...
 
template<int k>
bool pachner (Face< dim, k > *f, bool check=true, bool perform=true)
 Checks the eligibility of and/or performs a (dim + 1 - k)-(k + 1) Pachner move about the given k-face. More...
 
Subdivisions, Extensions and Covers
void makeDoubleCover ()
 Converts this triangulation into its double cover. More...
 
void barycentricSubdivision ()
 Does a barycentric subdivision of the triangulation. More...
 
bool finiteToIdeal ()
 Converts each real boundary component into a cusp (i.e., an ideal vertex). More...
 
Decompositions
size_t splitIntoComponents (Packet *componentParent=nullptr, bool setLabels=true)
 Splits a disconnected triangulation into many smaller triangulations, one for each component. More...
 
Isomorphism Testing
bool isIdenticalTo (const Triangulation< dim > &other) const
 Determines if this triangulation is combinatorially identical to the given triangulation. More...
 
std::unique_ptr< Isomorphism< dim > > isIsomorphicTo (const Triangulation< dim > &other) const
 Determines if this triangulation is combinatorially isomorphic to the given triangulation. More...
 
std::unique_ptr< Isomorphism< dim > > isContainedIn (const Triangulation< dim > &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). More...
 
template<typename OutputIterator >
size_t findAllIsomorphisms (const Triangulation< dim > &other, OutputIterator output) const
 Finds all ways in which this triangulation is combinatorially isomorphic to the given triangulation. More...
 
template<typename OutputIterator >
size_t findAllSubcomplexesIn (const Triangulation< dim > &other, OutputIterator output) 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). More...
 
bool makeCanonical ()
 Relabel the top-dimensional simplices and their vertices so that this triangulation is in canonical form. More...
 
Building Triangulations
void insertTriangulation (const Triangulation< dim > &source)
 Inserts a copy of the given triangulation into this triangulation. More...
 
void insertConstruction (size_t nSimplices, const int adjacencies[][dim+1], const int gluings[][dim+1][dim+1])
 Inserts a given triangulation into this triangulation, where the given triangulation is described by a pair of integer arrays. More...
 
Exporting Triangulations
std::string isoSig (Isomorphism< dim > **relabelling=0) const
 Constructs the isomorphism signature for this triangulation. More...
 
std::string dumpConstruction () const
 Returns C++ code that can be used with insertConstruction() to reconstruct this triangulation. More...
 

Static Public Member Functions

Constructors and Destructors
static void safeDelete (Packet *p)
 Either destroys or orphans the given packet, according to whether it has safe pointers that currently reference it. More...
 

Static Public Attributes

static constexpr int dimension = dim
 A compile-time constant that gives the dimension of the triangulation. More...
 

Protected Types

typedef std::vector< Face< dim, subdim > * >::const_iterator Iterator
 An iterator type for iterating through this list of faces. More...
 

Protected Member Functions

void deleteFaces ()
 Deletes all faces of dimension subdim and below. More...
 
void swapFaces (FaceListSuite< dim, subdim > &other)
 Swaps all faces of dimension subdim and below with those of the given triangulation. More...
 
void fillFVector (std::vector< size_t > &result) const
 Fills the given vector with the first (subdim + 1) elements of the f-vector. More...
 
bool sameFVector (const FaceListSuite< dim, subdim > &other) const
 Tests whether this and the given triangulation have the same number of k-faces, for each facial dimension ksubdim. More...
 
bool sameDegrees (const FaceListSuite< dim, subdim > &other) const
 Tests whether this and the given triangulation have the same k-face degree sequences, for each facial dimension ksubdim. More...
 
bool sameDegrees (const FaceList< dim, subdim > &other) const
 Tests whether this and the given triangulation have the same subdim-face degree sequences. More...
 
Face< dim, subdim > * operator[] (size_t index) const
 Returns the requested subdim-face. More...
 
void push_back (Face< dim, subdim > *face)
 Pushes the given face onto the end of this list. More...
 
void destroy ()
 Destroys all faces in this list, and clears the list itself. More...
 
void swap (FaceList< dim, subdim > &other)
 Swaps all faces in this list with those in the given list. More...
 

Protected Attributes

MarkedVector< Simplex< dim > > simplices_
 The top-dimensional simplices that form the triangulation. More...
 
MarkedVector< BoundaryComponent< dim > > boundaryComponents_
 The components that form the boundary of the triangulation. More...
 
bool valid_
 Is this triangulation valid? See isValid() for details on what this means. More...
 
int topologyLock_
 If non-zero, this will cause Triangulation<dim>::clearAllProperties() to preserve any computed properties that related to the manifold (as opposed to the specific triangulation). More...
 

Packet Administration

class detail::SimplexBase< dim >
 
class detail::TriangulationBase< dim >
 
virtual void writeTextShort (std::ostream &out) const override
 Writes a short text representation of this object to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const override
 Writes a detailed text representation of this object to the given output stream. More...
 
virtual bool dependsOnParent () const override
 Determines if this packet depends upon its parent. More...
 
static XMLPacketReaderxmlReader (Packet *parent, XMLTreeResolver &resolver)
 
virtual PacketinternalClonePacket (Packet *parent) const override
 Makes a newly allocated copy of this packet. More...
 
virtual void writeXMLPacketData (std::ostream &out) const override
 Writes a chunk of XML containing the data for this packet only. More...
 

File I/O

bool save (const char *filename, bool compressed=true) const
 Saves the subtree rooted at this packet to the given Regina data file, using Regina's native XML file format. More...
 
bool save (std::ostream &s, bool compressed=true) const
 Writes the subtree rooted at this packet to the given output stream, in the format of a Regina XML data file. More...
 
void writeXMLFile (std::ostream &out) const
 Writes the subtree rooted at this packet to the given output stream in Regina's native XML file format. More...
 
std::string internalID () const
 Returns a unique string ID that identifies this packet. More...
 
bool hasOwner () const
 Indicates whether some other object in the calculation engine is responsible for ultimately destroying this object. More...
 
void writeXMLPacketTree (std::ostream &out) const
 Writes a chunk of XML containing the subtree with this packet as matriarch. More...
 

Importing Triangulations

static Triangulation< dim > * fromIsoSig (const std::string &sig)
 Recovers a full triangulation from an isomorphism signature. More...
 
static size_t isoSigComponentSize (const std::string &sig)
 Deduces the number of top-dimensional simplices in a connected triangulation from its isomorphism signature. More...
 
void ensureSkeleton () const
 Ensures that all "on demand" skeletal objects have been calculated. More...
 
bool calculatedSkeleton () const
 Determines whether the skeletal objects and properties of this triangulation have been calculated. More...
 
void calculateSkeleton ()
 Calculates all skeletal objects for this triangulation. More...
 
void clearBaseProperties ()
 Clears all properties that are managed by this base class. More...
 
void swapBaseProperties (TriangulationBase< dim > &other)
 Swaps all properties that are managed by this base class, including skeletal data, with the given triangulation. More...
 
void writeXMLBaseProperties (std::ostream &out) const
 Writes a chunk of XML containing properties of this triangulation. More...
 

Detailed Description

template<int dim>
class regina::Triangulation< dim >

A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets.

Typically (but not necessarily) such triangulations are used to represent dim-manifolds.

Such triangulations are not the same as pure simplicial complexes, for two reasons:

Amongst other things, this definition is general enough to capture any reasonable definition of a dim-manifold triangulation. However, there is no requirement that a triangulation must actually represent a manifold (and indeed, testing this condition is undecidable for sufficiently large dim).

You can construct a triangulation from scratch using routines such as newSimplex() and Simplex<dim>::join(). There are also routines for importing and exporting triangulations in bulk, such as isoSig() and fromIsoSig() (which uses isomorphism signatures), or insertConstruction() and dumpConstruction() (which exports C++ code).

In additional to top-dimensional simplices, this class also tracks:

Such objects are temporary: whenever the triangulation changes, they will be deleted and rebuilt, and any pointers to them will become invalid. Likewise, if the triangulation is deleted then all component objects will be deleted alongside it.

For Regina's standard dimensions, this template is specialised and offers much more functionality. In order to use these specialised classes, you will need to include the corresponding headers (e.g., triangulation/dim2.h for dim = 2, or triangulation/dim3.h for dim = 3).

Python
Python does not support templates. Instead this class can be used by appending the dimension as a suffix (e.g., Triangulation2 and Triangulation3 for dimensions 2 and 3).
Template Parameters
dimthe dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

Member Typedef Documentation

◆ SafePointeeType

The type of object being pointed to.

Member Function Documentation

◆ deleteFaces()

void regina::detail::FaceListSuite< dim >::deleteFaces
inlineprotectedinherited

Deletes all faces of dimension subdim and below.

This routine destroys the corresponding Face objects and clears the lists that contain them.

◆ detail()

std::string regina::Output< Packet , false >::detail ( ) const
inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns
a detailed text representation of this object.

◆ fillFVector()

void regina::detail::FaceListSuite< dim >::fillFVector ( std::vector< size_t > &  result) const
inlineprotectedinherited

Fills the given vector with the first (subdim + 1) elements of the f-vector.

Specifically, this routine pushes the values f[0], ..., f[subdim] onto the end of the given vector, where f[k] denotes the number of k-faces that this object stores.

Parameters
resultthe vector in which the results will be placed.

◆ hasSafePtr()

bool regina::SafePointeeBase< Packet >::hasSafePtr
inlineinherited

Is there one or more SafePtr currently pointing to this object?

◆ sameDegrees()

bool regina::detail::FaceListSuite< dim >::sameDegrees ( const FaceListSuite< dim, subdim > &  other) const
inlineprotectedinherited

Tests whether this and the given triangulation have the same k-face degree sequences, for each facial dimension ksubdim.

For the purposes of this routine, degree sequences are considered to be unordered.

Precondition
This and the given triangulation are known to have the same number of k-faces as each other, for each facial dimension ksubdim.
Parameters
otherthe triangulation to compare against this.
Returns
true if and only if all degree sequences considered are equal.

◆ sameFVector()

bool regina::detail::FaceListSuite< dim >::sameFVector ( const FaceListSuite< dim, subdim > &  other) const
inlineprotectedinherited

Tests whether this and the given triangulation have the same number of k-faces, for each facial dimension ksubdim.

Parameters
otherthe triangulation to compare against this.
Returns
true if and only if the face counts considered are identical for both triangluations.

◆ str()

std::string regina::Output< Packet , false >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python
In addition to str(), this is also used as the Python "stringification" function str().
Returns
a short text representation of this object.

◆ swapFaces()

void regina::detail::FaceListSuite< dim >::swapFaces ( FaceListSuite< dim, subdim > &  other)
inlineprotectedinherited

Swaps all faces of dimension subdim and below with those of the given triangulation.

Parameters
otherthe face storage for the triangulation whose faces are to be swapped with this.

◆ utf8()

std::string regina::Output< Packet , false >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

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

Copyright © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).