Regina Calculation Engine
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regina::NNormalSurfaceList Class Reference

A packet representing a collection of normal surfaces in a 3-manifold. More...

#include <surfaces/nnormalsurfacelist.h>

Inheritance diagram for regina::NNormalSurfaceList:
regina::NPacket regina::ShareableObject regina::boost::noncopyable

Classes

struct  SurfaceInserter
 An output iterator used to insert surfaces into an NNormalSurfaceList. More...
 
class  VectorIterator
 A bidirectional iterator that runs through the raw vectors for surfaces in this list. More...
 

Public Member Functions

virtual ~NNormalSurfaceList ()
 Destroys this list and all the surfaces within. More...
 
NormalCoords getFlavour () const
 Deprecated routine to return the coordinate system being used by the surfaces stored in this set. More...
 
NormalCoords flavour () const
 Deprecated routine to return the coordinate system being used by the surfaces stored in this set. More...
 
NormalCoords coords () const
 Returns the coordinate system being used by the surfaces stored in this set. More...
 
NormalList which () const
 Returns details of which normal surfaces this list represents within the underlying triangulation. More...
 
NormalAlg algorithm () const
 Returns details of the algorithm that was used to enumerate this list. More...
 
bool allowsAlmostNormal () const
 Determines if the coordinate system being used allows for almost normal surfaces, that is, allows for octagonal discs. More...
 
bool allowsSpun () const
 Determines if the coordinate system being used allows for spun normal surfaces. More...
 
bool allowsOriented () const
 Determines if the coordinate system being used allows for transversely oriented normal surfaces. More...
 
bool isEmbeddedOnly () const
 Returns whether this list was constructed to contain only properly embedded surfaces. More...
 
NTriangulationgetTriangulation () const
 Returns the triangulation in which these normal surfaces live. More...
 
unsigned long getNumberOfSurfaces () const
 Returns the number of surfaces stored in this set. More...
 
const NNormalSurfacegetSurface (unsigned long index) const
 Returns the surface at the requested index in this set. More...
 
void writeAllSurfaces (std::ostream &out) const
 Writes the number of surfaces in this set followed by the details of each surface to the given output stream. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
virtual bool dependsOnParent () const
 Determines if this packet depends upon its parent. More...
 
NNormalSurfaceListquadToStandard () const
 Converts the set of all embedded vertex normal surfaces in quadrilateral space to the set of all embedded vertex normal surfaces in standard (tri-quad) space. More...
 
NNormalSurfaceListquadOctToStandardAN () const
 Converts the set of all embedded vertex almost normal surfaces in quadrilateral-octagon space to the set of all embedded vertex almost normal surfaces in the standard tri-quad-oct space. More...
 
NNormalSurfaceListstandardToQuad () const
 Converts the set of all embedded vertex normal surfaces in standard (tri-quad) space to the set of all embedded vertex normal surfaces in quadrilateral space. More...
 
NNormalSurfaceListstandardANToQuadOct () const
 Converts the set of all embedded vertex almost normal surfaces in standard tri-quad-oct space to the set of all embedded vertex almost normal surfaces in the smaller quadrilateral-octagon space. More...
 
NNormalSurfaceListfilterForLocallyCompatiblePairs () const
 Creates a new list filled with the surfaces from this list that have at least one locally compatible partner. More...
 
NNormalSurfaceListfilterForDisjointPairs () const
 Creates a new list filled with the surfaces from this list that have at least one disjoint partner. More...
 
NNormalSurfaceListfilterForPotentiallyIncompressible () const
 Creates a new list filled with only the surfaces from this list that "might" represent two-sided incompressible surfaces. More...
 
NMatrixIntrecreateMatchingEquations () const
 Returns a newly created matrix containing the matching equations that were used to create this normal surface list. More...
 
VectorIterator beginVectors () const
 An iterator that gives access to the raw vectors for surfaces in this list, pointing to the beginning of this surface list. More...
 
VectorIterator endVectors () const
 An iterator that gives access to the raw vectors for surfaces in this list, pointing past the end of this surface list. More...
 
- Public Member Functions inherited from regina::NPacket
 NPacket (NPacket *parent=0)
 Constructor that inserts the new packet into the overall tree structure. More...
 
virtual ~NPacket ()
 Destructor that also orphans this packet and destroys all of its descendants. More...
 
virtual PacketType getPacketType () const =0
 Returns the unique integer ID representing this type of packet. More...
 
virtual std::string getPacketTypeName () const =0
 Returns an English name for this type of packet. More...
 
const std::string & getPacketLabel () const
 Returns the label associated with this individual packet. More...
 
std::string getHumanLabel () const
 Returns the label associated with this individual packet, adjusted if necessary for human-readable output. More...
 
void setPacketLabel (const std::string &newLabel)
 Sets the label associated with this individual packet. More...
 
std::string getFullName () const
 Returns a descriptive text string for the packet. More...
 
std::string makeUniqueLabel (const std::string &base) const
 Returns a new label that cannot be found anywhere in the entire tree structure. More...
 
bool makeUniqueLabels (NPacket *reference)
 Ensures that all packet labels in both this and the given packet tree combined are distinct. More...
 
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 > & getTags () const
 Returns the set of all tags associated with this packet. More...
 
bool listen (NPacketListener *listener)
 Registers the given packet listener to listen for events on this packet. More...
 
bool isListening (NPacketListener *listener)
 Determines whether the given packet listener is currently listening for events on this packet. More...
 
bool unlisten (NPacketListener *listener)
 Unregisters the given packet listener so that it no longer listens for events on this packet. More...
 
NPacketgetTreeParent () const
 Determines the parent packet in the tree structure. More...
 
NPacketgetFirstTreeChild () const
 Determines the first child of this packet in the tree structure. More...
 
NPacketgetLastTreeChild () const
 Determines the last child of this packet in the tree structure. More...
 
NPacketgetNextTreeSibling () const
 Determines the next sibling of this packet in the tree structure. More...
 
NPacketgetPrevTreeSibling () const
 Determines the previous sibling of this packet in the tree structure. More...
 
NPacketgetTreeMatriarch () const
 Determines the matriarch (the root) of the tree to which this packet belongs. More...
 
unsigned levelsDownTo (const NPacket *descendant) const
 Counts the number of levels between this packet and its given descendant in the tree structure. More...
 
unsigned levelsUpTo (const NPacket *ancestor) const
 Counts the number of levels between this packet and its given ancestor in the tree structure. More...
 
bool isGrandparentOf (const NPacket *descendant) const
 Determines if this packet is equal to or an ancestor of the given packet in the tree structure. More...
 
unsigned long getNumberOfChildren () const
 Returns the number of immediate children of this packet. More...
 
unsigned long getNumberOfDescendants () const
 Returns the total number of descendants of this packet. More...
 
unsigned long getTotalTreeSize () const
 Determines the total number of packets in the tree or subtree for which this packet is matriarch. More...
 
void insertChildFirst (NPacket *child)
 Inserts the given packet as the first child of this packet. More...
 
void insertChildLast (NPacket *child)
 Inserts the given packet as the last child of this packet. More...
 
void insertChildAfter (NPacket *newChild, NPacket *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 (NPacket *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 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...
 
NPacketnextTreePacket ()
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
const NPacketnextTreePacket () const
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
NPacketfirstTreePacket (const std::string &type)
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
const NPacketfirstTreePacket (const std::string &type) const
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
NPacketnextTreePacket (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 NPacketnextTreePacket (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...
 
NPacketfindPacketLabel (const std::string &label)
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
const NPacketfindPacketLabel (const std::string &label) const
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
bool isPacketEditable () const
 Determines whether this packet can be altered without invalidating or otherwise upsetting any of its immediate children. More...
 
NPacketclone (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...
 
void writeXMLFile (std::ostream &out) const
 Writes a complete XML file containing the subtree with this packet as matriarch. More...
 
std::string internalID () const
 Returns a unique string ID that identifies this packet. More...
 
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing. More...
 
virtual ~ShareableObject ()
 Default destructor that does nothing. More...
 
std::string str () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toString () const
 A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...
 
std::string detail () const
 Returns the output from writeTextLong() as a string. More...
 
std::string toStringLong () const
 A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...
 

Static Public Member Functions

static NNormalSurfaceListenumerate (NTriangulation *owner, NormalCoords coords, NormalList which=NS_LIST_DEFAULT, NormalAlg algHints=NS_ALG_DEFAULT, NProgressTracker *tracker=0)
 A unified routine for enumerating various classes of normal surfaces within a given triangulation. More...
 
static NNormalSurfaceListenumerate (NTriangulation *owner, NormalCoords coords, bool embeddedOnly, NProgressTracker *tracker=0)
 Deprecated method for enumerating all vertex normal surfaces using the given coordinate system. More...
 
static NNormalSurfaceListenumerateStandardDirect (NTriangulation *owner)
 Deprecated method that uses a slow-but-direct procedure to enumerate all embedded vertex normal surfaces in standard coordinates, without using the faster procedure that works via quadrilateral coordinates. More...
 
static NNormalSurfaceListenumerateStandardANDirect (NTriangulation *owner)
 Deprecated method that uses a slow-but-direct procedure to enumerate all embedded vertex almost normal surfaces in standard almost normal coordinates, without using the faster procedure that works via quadrilateral-octagon coordinates. More...
 
static NNormalSurfaceListenumerateFundPrimal (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true, NNormalSurfaceList *vtxSurfaces=0, NProgressTracker *tracker=0)
 Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the primal Hilbert basis algorithm. More...
 
static NNormalSurfaceListenumerateFundDual (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true, NProgressTracker *tracker=0)
 Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the dual Hilbert basis algorithm. More...
 
static NNormalSurfaceListenumerateFundFullCone (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true)
 Deprecated method that uses an extremely slow procedure to enumerate all embedded fundamental surfaces in the given triangulation, by running Normaliz over the full (and typically very large) solution cone, and only enforcing embedded constraints (such as the quadrilateral constraints) afterwards. More...
 
static NNormalSurfaceListenumerateFundCD (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true)
 Deprecated method that uses an extremely slow modified Contejean-Devie procedure to enumerate all embedded fundamental surfaces in the given triangulation. More...
 
static NXMLPacketReadergetXMLReader (NPacket *parent, NXMLTreeResolver &resolver)
 
- Static Public Member Functions inherited from regina::NPacket
static NXMLPacketReadergetXMLReader (NPacket *parent, NXMLTreeResolver &resolver)
 Returns a newly created XML element reader that will read the contents of a single XML packet element. More...
 

Static Public Attributes

static const NormalCoords STANDARD
 Represents standard triangle-quadrilateral coordinates for normal surfaces. More...
 
static const NormalCoords AN_STANDARD
 Represents standard triangle-quadrilateral-octagon coordinates for octagonal almost normal surfaces. More...
 
static const NormalCoords QUAD
 Represents quadrilateral coordinates for normal surfaces. More...
 
static const NormalCoords AN_QUAD_OCT
 Represents quadrilateral-octagon coordinates for octagonal almost normal surfaces. More...
 
static const NormalCoords EDGE_WEIGHT
 Represents edge weight coordinates for normal surfaces. More...
 
static const NormalCoords FACE_ARCS
 Represents triangle arc coordinates for normal surfaces. More...
 
static const NormalCoords AN_LEGACY
 Indicates that a list of almost normal surfaces was created using Regina 4.5.1 or earlier, where surfaces with more than one octagon of the same type were stripped out of the final solution set. More...
 
static const NormalCoords ORIENTED
 Represents standard triangle-quadrilateral coordinates for transversely oriented normal surfaces. More...
 
static const NormalCoords ORIENTED_QUAD
 Represents quadrilateral coordinates for transversely oriented normal surfaces. More...
 

Protected Member Functions

 NNormalSurfaceList (NormalCoords coords, NormalList which, NormalAlg algorithm)
 Creates an empty list of normal surfaces with the given parameters. More...
 
virtual NPacketinternalClonePacket (NPacket *parent) const
 Makes a newly allocated copy of this packet. More...
 
virtual void writeXMLPacketData (std::ostream &out) const
 Writes a chunk of XML containing the data for this packet only. More...
 
- Protected Member Functions inherited from regina::NPacket
void writeXMLPacketTree (std::ostream &out) const
 Writes a chunk of XML containing the subtree with this packet as matriarch. More...
 

Protected Attributes

std::vector< NNormalSurface * > surfaces
 Contains the normal surfaces stored in this packet. More...
 
NormalCoords coords_
 Stores which coordinate system is being used by the normal surfaces in this packet. More...
 
NormalList which_
 Indicates which normal surfaces these represent within the underlying triangulation. More...
 
NormalAlg algorithm_
 Stores the details of the enumeration algorithm that was used to generate this list. More...
 

Friends

class regina::NXMLNormalSurfaceListReader
 

Additional Inherited Members

- Public Types inherited from regina::NPacket
typedef ChangeEventSpan ChangeEventBlock
 A deprecated typedef for ChangeEventSpan. More...
 

Detailed Description

A packet representing a collection of normal surfaces in a 3-manifold.

Such a packet must always be a child packet of the triangulation from which the surfaces were obtained. If this triangulation changes, the information contained in this packet will become invalid.

See the NNormalSurfaceVector class notes for details of what to do when introducing a new coordinate system.

Normal surface lists should be created using the routine enumerate(), which is new as of Regina 3.95.

Test:
Included in the test suite.
Todo:

Feature: Allow custom matching equations.

Feature: Allow enumeration with some coordinates explicitly set to zero.

Feature: Allow generating only closed surfaces.

Feature: Generate facets of the solution space representing embedded surfaces.

Constructor & Destructor Documentation

regina::NNormalSurfaceList::~NNormalSurfaceList ( )
inlinevirtual

Destroys this list and all the surfaces within.

regina::NNormalSurfaceList::NNormalSurfaceList ( NormalCoords  coords,
NormalList  which,
NormalAlg  algorithm 
)
inlineprotected

Creates an empty list of normal surfaces with the given parameters.

Parameters
coordsthe coordinate system to be used for filling this list.
whichindicates which normal surfaces these will represent within the underlying triangulation.
algorithmdetails of the enumeration algorithm that will be used to fill this list.

Member Function Documentation

NormalAlg regina::NNormalSurfaceList::algorithm ( ) const
inline

Returns details of the algorithm that was used to enumerate this list.

These may not be the same NormalAlg flags that were passed to enumerate(). In particular, default values will have be explicitly filled in, invalid and/or redundant values will have been removed, and unavailable and/or unsupported combinations of algorithm flags will be replaced with whatever algorithm was actually used.

Returns
details of the algorithm used to enumerate this list.
bool regina::NNormalSurfaceList::allowsAlmostNormal ( ) const

Determines if the coordinate system being used allows for almost normal surfaces, that is, allows for octagonal discs.

Returns
true if and only if almost normal surfaces are allowed.
bool regina::NNormalSurfaceList::allowsOriented ( ) const

Determines if the coordinate system being used allows for transversely oriented normal surfaces.

Returns
true if and only if transverse orientations are supported.
bool regina::NNormalSurfaceList::allowsSpun ( ) const

Determines if the coordinate system being used allows for spun normal surfaces.

Returns
true if and only if spun normal surface are supported.
NNormalSurfaceList::VectorIterator regina::NNormalSurfaceList::beginVectors ( ) const
inline

An iterator that gives access to the raw vectors for surfaces in this list, pointing to the beginning of this surface list.

Python:
Not present.
Returns
an iterator at the beginning of this surface list.
NormalCoords regina::NNormalSurfaceList::coords ( ) const
inline

Returns the coordinate system being used by the surfaces stored in this set.

Returns
the coordinate system used.
bool regina::NNormalSurfaceList::dependsOnParent ( ) const
inlinevirtual

Determines if this packet depends upon its parent.

This is true if the parent cannot be altered without invalidating or otherwise upsetting this packet.

Returns
true if and only if this packet depends on its parent.

Implements regina::NPacket.

NNormalSurfaceList::VectorIterator regina::NNormalSurfaceList::endVectors ( ) const
inline

An iterator that gives access to the raw vectors for surfaces in this list, pointing past the end of this surface list.

This iterator is not dereferenceable.

Python:
Not present.
Returns
an iterator past the end of this surface list.
static NNormalSurfaceList* regina::NNormalSurfaceList::enumerate ( NTriangulation owner,
NormalCoords  coords,
NormalList  which = NS_LIST_DEFAULT,
NormalAlg  algHints = NS_ALG_DEFAULT,
NProgressTracker tracker = 0 
)
static

A unified routine for enumerating various classes of normal surfaces within a given triangulation.

The NormalCoords argument allows you to specify an underlying coordinate system (e.g., standard coordinates, quadrilateral coordinates or almost normal coordinates).

The NormalList argument is a combination of flags that allows you to specify exactly which normal surfaces you require. This includes (i) whether you want all vertex surfaces or all fundamental surfaces, which defaults to NS_VERTEX if you specify neither or both; and (ii) whether you want only properly embedded surfaces or you also wish to include immersed and/or singular surfaces, which defaults to NS_EMBEDDED_ONLY if you specify neither or both.

The NormalAlg argument is a combination of flags that allows you to control the underlying enumeration algorithm. These flags are treated as hints only: if your selection of algorithm is invalid, unavailable or unsupported then Regina will choose something more appropriate. Unless you have some specialised need, the default NS_ALG_DEFAULT (which makes no hints at all) will allow Regina to choose what it thinks will be the most efficient method.

The enumerated surfaces will be stored in a new normal surface list, and their representations will be scaled down to use the smallest possible integer coordinates. This normal surface list will be inserted into the packet tree as the last child of the given triangulation. This triangulation must remain the parent of this normal surface list, and must not change while this normal surface list remains in existence.

If a progress tracker is passed, the normal surface enumeration will take place in a new thread and this routine will return immediately. If the user cancels the operation from another thread, then the normal surface list will not be inserted into the packet tree (but the caller of this routine will still need to delete it). Regarding progress tracking, this routine will declare and work through a series of stages whose combined weights sum to 1; typically this means that the given tracker must not have been used before.

If no progress tracker is passed, the enumeration will run in the current thread and this routine will return only when the enumeration is complete. Note that this enumeration can be extremely slow for larger triangulations.

Parameters
ownerthe triangulation upon which this list of normal surfaces will be based.
coordsthe coordinate system to be used.
whichindicates which normal surfaces should be enumerated.
algHintspasses requests to Regina for which specific enumeration algorithm should be used.
trackera progress tracker through which progress will be reported, or 0 if no progress reporting is required.
Returns
the newly created normal surface list. Note that if a progress tracker is passed then this list may not be completely filled when this routine returns. If a progress tracker is passed and a new thread could not be started, this routine returns 0 (and no normal surface list is created).
NNormalSurfaceList * regina::NNormalSurfaceList::enumerate ( NTriangulation owner,
NormalCoords  coords,
bool  embeddedOnly,
NProgressTracker tracker = 0 
)
inlinestatic

Deprecated method for enumerating all vertex normal surfaces using the given coordinate system.

Users should now call enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details, including all arguments, returns values, preconditions and postconditions.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, coords, NS_EMBEDDED_ONLY, NS_ALG_DEFAULT, tracker) if embeddedOnly is true, or enumerate(owner, coords, NS_IMMERSED_SINGULAR, NS_ALG_DEFAULT, tracker) if embeddedOnly is false.
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateFundCD ( NTriangulation owner,
NormalCoords  coords,
bool  embeddedOnly = true 
)
inlinestatic

Deprecated method that uses an extremely slow modified Contejean-Devie procedure to enumerate all embedded fundamental surfaces in the given triangulation.

For details of the algorithm, see B. A. Burton, "Fundamental normal surfaces and the enumeration of Hilbert bases", arXiv:1111.7055v1, Nov 2011.

Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, coords, NS_FUNDAMENTAL | NS_EMBEDDED_ONLY, NS_HILBERT_CD) if embeddedOnly is true, or enumerate(owner, coords, NS_FUNDAMENTAL | NS_IMMERSED_SINGULAR, NS_HILBERT_CD) if embeddedOnly is false.
Warning
This routine is extremely slow, and users will not want to call it unless they have some specialised need.
Parameters
ownerthe triangulation upon which this list of normal surfaces will be based.
coordsthe coordinate system to be used.
embeddedOnlytrue if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true.
Returns
the newly created normal surface list.
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateFundDual ( NTriangulation owner,
NormalCoords  coords,
bool  embeddedOnly = true,
NProgressTracker tracker = 0 
)
inlinestatic

Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the dual Hilbert basis algorithm.

For details of the algorithm, see B. A. Burton, "Enumerating fundamental normal surfaces: Algorithms, experiments and invariants", to appear in ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments, arXiv:1111.7055.

Users can still access this procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, coords, NS_FUNDAMENTAL | NS_EMBEDDED_ONLY, NS_HILBERT_DUAL, tracker) if embeddedOnly is true, or enumerate(owner, coords, NS_FUNDAMENTAL | NS_IMMERSED_SINGULAR, NS_HILBERT_DUAL, tracker) if embeddedOnly is false.
Parameters
ownerthe triangulation upon which this list of normal surfaces will be based.
coordsthe coordinate system to be used.
embeddedOnlytrue if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true.
trackera progress tracker through which progress will be reported, or 0 if no progress reporting is required.
Returns
the newly created normal surface list. Note that if a progress tracker is passed then this list may not be completely filled when this routine returns. If a progress tracker is passed and a new thread could not be started, this routine returns 0 (and no normal surface list is created).
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateFundFullCone ( NTriangulation owner,
NormalCoords  coords,
bool  embeddedOnly = true 
)
inlinestatic

Deprecated method that uses an extremely slow procedure to enumerate all embedded fundamental surfaces in the given triangulation, by running Normaliz over the full (and typically very large) solution cone, and only enforcing embedded constraints (such as the quadrilateral constraints) afterwards.

Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, coords, NS_FUNDAMENTAL | NS_EMBEDDED_ONLY, NS_HILBERT_FULLCONE) if embeddedOnly is true, or enumerate(owner, coords, NS_FUNDAMENTAL | NS_IMMERSED_SINGULAR, NS_HILBERT_FULLCONE) if embeddedOnly is false.
Warning
This routine is extremely slow, and users will not want to call it unless they have some specialised need.
Parameters
ownerthe triangulation upon which this list of normal surfaces will be based.
coordsthe coordinate system to be used.
embeddedOnlytrue if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true.
Returns
the newly created normal surface list.
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateFundPrimal ( NTriangulation owner,
NormalCoords  coords,
bool  embeddedOnly = true,
NNormalSurfaceList vtxSurfaces = 0,
NProgressTracker tracker = 0 
)
inlinestatic

Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the primal Hilbert basis algorithm.

For details of the algorithm, see B. A. Burton, "Enumerating fundamental normal surfaces: Algorithms, experiments and invariants", to appear in ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments, arXiv:1111.7055.

Users can still access this procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Warning
As of Regina 4.94, the vtxSurfaces argument is ignored. Future versions of Regina will automatically search existing surface lists in the packet tree for a ready-made list of vertex normal surfaces that can be used.
Deprecated:
The correct way to access this procedure is to call enumerate(owner, coords, NS_FUNDAMENTAL | NS_EMBEDDED_ONLY, NS_HILBERT_PRIMAL, tracker) if embeddedOnly is true, or enumerate(owner, coords, NS_FUNDAMENTAL | NS_IMMERSED_SINGULAR, NS_HILBERT_PRIMAL, tracker) if embeddedOnly is false.
Parameters
ownerthe triangulation upon which this list of normal surfaces will be based.
coordsthe coordinate system to be used.
embeddedOnlytrue if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true.
vtxSurfacesthe set of all vertex normal surfaces as enumerated under the same coordinate system and constraints as given here; this may be 0 if unknown.
trackera progress tracker through which progress will be reported, or 0 if no progress reporting is required.
Returns
the newly created normal surface list. Note that if a progress tracker is passed then this list may not be completely filled when this routine returns. If a progress tracker is passed and a new thread could not be started, this routine returns 0 (and no normal surface list is created).
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateStandardANDirect ( NTriangulation owner)
inlinestatic

Deprecated method that uses a slow-but-direct procedure to enumerate all embedded vertex almost normal surfaces in standard almost normal coordinates, without using the faster procedure that works via quadrilateral-octagon coordinates.

Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, NS_AN_STANDARD, NS_LIST_DEFAULT, NS_VERTEX_STD_DIRECT).
Warning
This routine is slow, and users will not want to call it unless they have some specialised need.
Parameters
ownerthe triangulation upon which this list of surfaces will be based.
Returns
the newly created normal surface list.
NNormalSurfaceList * regina::NNormalSurfaceList::enumerateStandardDirect ( NTriangulation owner)
inlinestatic

Deprecated method that uses a slow-but-direct procedure to enumerate all embedded vertex normal surfaces in standard coordinates, without using the faster procedure that works via quadrilateral coordinates.

Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.

Deprecated:
The correct way to access this procedure is to call enumerate(owner, NS_STANDARD, NS_LIST_DEFAULT, NS_VERTEX_STD_DIRECT).
Warning
This routine is slow, and users will not want to call it unless they have some specialised need.
Parameters
ownerthe triangulation upon which this list of surfaces will be based.
Returns
the newly created normal surface list.
NNormalSurfaceList* regina::NNormalSurfaceList::filterForDisjointPairs ( ) const

Creates a new list filled with the surfaces from this list that have at least one disjoint partner.

In other words, a surface S from this list will be placed in the new list if and only if there is some other surface T in this list for which S and T can be made to intersect nowhere at all, without changing either normal isotopy class. See NNormalSurface::disjoint() for further details on disjointness testing.

This routine cannot deal with empty, disconnected or non-compact surfaces. Such surfaces will be silently ignored, and will not be used in any disjointness tests (in particular, they will never be considered as a "disjoint partner" for any other surface).

The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.

This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).

Precondition
This list contains only embedded normal surfaces. More precisely, isEmbeddedOnly() must return true.
All surfaces within this list are stored using the same coordinate system (i.e., the same subclass of NNormalSurfaceVector).
Warning
If this list contains a vertex link (plus at least one other surface), then the new list will be identical to the old (i.e., every surface will be copied across).
Todo:
Deal properly with surfaces that are too large to handle.
Returns
the new list, which will also have been inserted as a new child packet of the underlying triangulation.
NNormalSurfaceList* regina::NNormalSurfaceList::filterForLocallyCompatiblePairs ( ) const

Creates a new list filled with the surfaces from this list that have at least one locally compatible partner.

In other words, a surface S from this list will be placed in the new list if and only if there is some other surface T in this list for which S and T are locally compatible. See NNormalSurface::locallyCompatible() for further details on compatibility testing.

The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.

This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).

Precondition
This list contains only embedded normal surfaces. More precisely, isEmbeddedOnly() must return true.
Warning
If this list contains a vertex link (plus at least one other surface), then the new list will be identical to the old (i.e., every surface will be copied across).
Returns
the new list, which will also have been inserted as a new child packet of the underlying triangulation.
NNormalSurfaceList* regina::NNormalSurfaceList::filterForPotentiallyIncompressible ( ) const

Creates a new list filled with only the surfaces from this list that "might" represent two-sided incompressible surfaces.

More precisely, we consider all two-sided surfaces in this list, as well as the two-sided double covers of all one-sided surfaces in this list (see below for details on how one-sided surfaces are handled). Each of these surfaces is examined using relatively fast heuristic tests for incompressibility. Any surface that is definitely not incompressible is thrown away, and all other surfaces are placed in the new list.

Therefore, it is guaranteed that every incompressible surface from the old list will be placed in the new list. However, it is not known whether any given surface in the new list is indeed incompressible.

See NNormalSurface::isIncompressible() for the definition of incompressibility that is used here. Note in particular that spheres are never considered incompressible.

As indicated above, this filter works exclusively with two-sided surfaces. If a surface in this list is one-sided, the heuristic incompressibility tests will be run on its two-sided double cover. Nevertheless, if the tests pass, the original one-sided surface (not the double cover) will be added to the new list.

The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.

This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).

Currently the heuristic tests include (i) throwing away all vertex links and thin edge links, and then (ii) cutting along the remaining surfaces and running NTriangulation::hasSimpleCompressingDisc() on the resulting bounded triangulations. For more details on these tests see "The Weber-Seifert dodecahedral space is non-Haken", Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann, Trans. Amer. Math. Soc. 364:2 (2012), pp. 911-932.

Precondition
The underlying 3-manifold triangulation is valid and closed. In particular, it has no ideal vertices.
This list contains only embedded normal surfaces. More precisely, isEmbeddedOnly() must return true.
This list contains only compact, connected normal surfaces.
No surfaces in this list contain any octagonal discs.
Warning
The behaviour of this routine is subject to change in future versions of Regina, since additional tests may be added to improve the power of this filtering.
Todo:
Add progress tracking.
Returns
the new list, which will also have been inserted as a new child packet of the underlying triangulation.
NormalCoords regina::NNormalSurfaceList::flavour ( ) const
inline

Deprecated routine to return the coordinate system being used by the surfaces stored in this set.

Deprecated:
Users should switch to the identical routine coords() instead.
Returns
the coordinate system used.
NormalCoords regina::NNormalSurfaceList::getFlavour ( ) const
inline

Deprecated routine to return the coordinate system being used by the surfaces stored in this set.

Deprecated:
Users should switch to the identical routine coords() instead.
Returns
the coordinate system used.
unsigned long regina::NNormalSurfaceList::getNumberOfSurfaces ( ) const
inline

Returns the number of surfaces stored in this set.

Returns
the number of surfaces.
const NNormalSurface * regina::NNormalSurfaceList::getSurface ( unsigned long  index) const
inline

Returns the surface at the requested index in this set.

Parameters
indexthe index of the requested surface in this set; this must be between 0 and getNumberOfSurfaces()-1 inclusive.
Returns
the normal surface at the requested index in this set.
NTriangulation* regina::NNormalSurfaceList::getTriangulation ( ) const

Returns the triangulation in which these normal surfaces live.

Returns
the triangulation in which these surfaces live.
virtual NPacket* regina::NNormalSurfaceList::internalClonePacket ( NPacket parent) const
protectedvirtual

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.

Parameters
parentthe parent beneath which the new packet will eventually be inserted.
Returns
the newly allocated packet.

Implements regina::NPacket.

bool regina::NNormalSurfaceList::isEmbeddedOnly ( ) const
inline

Returns whether this list was constructed to contain only properly embedded surfaces.

If this returns false, it does not guarantee that immersed and/or singular surfaces are present; it merely indicates that they were not deliberately excluded (for instance, the quadrilateral constraints were not enforced).

Returns
true if this list was constructed to contain only properly embedded surfaces, or false otherwise.
NNormalSurfaceList* regina::NNormalSurfaceList::quadOctToStandardAN ( ) const

Converts the set of all embedded vertex almost normal surfaces in quadrilateral-octagon space to the set of all embedded vertex almost normal surfaces in the standard tri-quad-oct space.

This routine is the almost normal analogue to the quadToStandard() conversion routine; see the quadToStandard() documentation for further information.

Precondition
The underlying triangulation (the parent packet of this normal surface list) is valid, and the link of every vertex is either a sphere or a disc.
This surface list is precisely the set of all embedded vertex almost normal surfaces in quadrilateral-octagon space; no more, no less. Moreover, these vectors are stored using quadrilateral-octagon coordinates. Typically this means that it was obtained through enumerate(), with the coordinate system set to NS_AN_QUAD_OCT and with embeddedOnly set to true.
Returns
a full list of vertex almost normal surfaces in standard tri-quad-oct coordinates, or 0 if any of the basic sanity checks failed.
NNormalSurfaceList* regina::NNormalSurfaceList::quadToStandard ( ) const

Converts the set of all embedded vertex normal surfaces in quadrilateral space to the set of all embedded vertex normal surfaces in standard (tri-quad) space.

The initial list in quadrilateral space is taken to be this normal surface list; the final list in standard space will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the final list will also be returned from this routine.

This routine can only be used with normal surfaces, not almost normal surfaces. For almost normal surfaces, see the similar routine quadOctToStandardAN().

This procedure is available for any triangulation whose vertex links are all spheres and/or discs, and is much faster than enumerating surfaces directly in standard tri-quad coordinates. The underlying algorithm is described in detail in "Converting between quadrilateral and standard solution sets in normal surface theory", Benjamin A. Burton, Algebr. Geom. Topol. 9 (2009), 2121-2174.

Typically users do not need to call this routine directly, since the standard enumerate() routine will use it implicitly where possible. That is, when asked for standard vertex surfaces, enumerate() will first find all quadrilateral vertex surfaces and then use this procedure to convert them to standard vertex surfaces; this is generally orders of magnitude faster than enumerating surfaces directly in standard coordinates.

Nevertheless, this standalone routine is provided as a convenience for users who already have a set of quadrilateral vertex surfaces, and who simply wish to convert them to a set of standard vertex surfaces without the cost of implicitly enumerating the quadrilateral vertex surfaces again.

It should be noted that this routine does not simply convert vectors from one form to another; instead it converts a full solution set of vertex surfaces in quadrilateral coordinates to a full solution set of vertex surfaces in standard coordinates. Typically there are many more vertex surfaces in standard coordinates (all of which this routine will find).

This routine will run some very basic sanity checks before starting. Specifically, it will check the validity and vertex links of the underlying triangulation, and will verify that the coordinate system and embedded-only flag are set to NS_QUAD and true respectively. If any of these checks fails, this routine will do nothing and return 0.

Precondition
The underlying triangulation (the parent packet of this normal surface list) is valid, and the link of every vertex is either a sphere or a disc.
This normal surface list is precisely the set of all embedded vertex normal surfaces in quadrilateral space; no more, no less. Moreover, these vectors are stored using quadrilateral coordinates. Typically this means that it was obtained through enumerate(), with the coordinate system set to NS_QUAD and with embeddedOnly set to true.
Returns
a full list of vertex normal surfaces in standard (tri-quad) coordinates, or 0 if any of the basic sanity checks failed.
NMatrixInt * regina::NNormalSurfaceList::recreateMatchingEquations ( ) const
inline

Returns a newly created matrix containing the matching equations that were used to create this normal surface list.

The destruction of this matrix is the responsibility of the caller of this routine. Multiple calls to this routine will result in the construction of multiple matrices. This routine in fact merely calls makeMatchingEquations() with the appropriate parameters.

The format of the matrix is identical to that returned by makeMatchingEquations().

Returns
the matching equations used to create this normal surface list.
NNormalSurfaceList* regina::NNormalSurfaceList::standardANToQuadOct ( ) const

Converts the set of all embedded vertex almost normal surfaces in standard tri-quad-oct space to the set of all embedded vertex almost normal surfaces in the smaller quadrilateral-octagon space.

This routine is the almost normal analogue to the standardToQuad() conversion routine; see the standardToQuad() documentation for further information.

Precondition
The underlying triangulation (the parent packet of this normal surface list) is valid, and the link of every vertex is either a sphere or a disc.
This normal surface list is precisely the set of all embedded vertex almost normal surfaces in standard tri-quad-oct space; no more, no less. Typically this means that it was obtained through enumerate(), with the coordinate system set to NS_AN_STANDARD and with embeddedOnly set to true.
Returns
a full list of vertex almost normal surfaces in quadrilateral-octagon coordinates, or 0 if any of the basic sanity checks failed.
NNormalSurfaceList* regina::NNormalSurfaceList::standardToQuad ( ) const

Converts the set of all embedded vertex normal surfaces in standard (tri-quad) space to the set of all embedded vertex normal surfaces in quadrilateral space.

The initial list in standard space is taken to be this normal surface list; the final list in quadrilateral space will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the final list will also be returned from this routine.

This routine can only be used with normal surfaces, not almost normal surfaces. For almost normal surfaces, see the similar routine standardANToQuadOct().

This procedure is available for any triangulation whose vertex links are all spheres and/or discs. The underlying algorithm is described in detail in "Converting between quadrilateral and standard solution sets in normal surface theory", Benjamin A. Burton, Algebr. Geom. Topol. 9 (2009), 2121-2174.

It should be noted that this routine does not simply convert vectors from one form to another; instead it converts a full solution set of vertex surfaces in standard coordinates to a full solution set of vertex surfaces in quadrilateral coordinates. Typically there are far fewer vertex surfaces in quadrilateral coordinates (all of which this routine will find).

This routine will run some very basic sanity checks before starting. Specifically, it will check the validity and vertex links of the underlying triangulation, and will verify that the coordinate system and embedded-only flag are set to NS_STANDARD and true respectively. If any of these checks fails, this routine will do nothing and return 0.

Precondition
The underlying triangulation (the parent packet of this normal surface list) is valid, and the link of every vertex is either a sphere or a disc.
This normal surface list is precisely the set of all embedded vertex normal surfaces in standard (tri-quad) space; no more, no less. Moreover, these vectors are stored using standard coordinates. Typically this means that this list was obtained through enumerate(), with the coordinate system set to NS_STANDARD and with embeddedOnly set to true.
Returns
a full list of vertex normal surfaces in quadrilateral coordinates, or 0 if any of the basic sanity checks failed.
NormalList regina::NNormalSurfaceList::which ( ) const
inline

Returns details of which normal surfaces this list represents within the underlying triangulation.

This may not be the same NormalList that was passed to enumerate(). In particular, default values will have be explicitly filled in (such as NS_VERTEX and/or NS_EMBEDDED_ONLY), and invalid and/or redundant values will have been removed.

Returns
details of what this list represents.
void regina::NNormalSurfaceList::writeAllSurfaces ( std::ostream &  out) const

Writes the number of surfaces in this set followed by the details of each surface to the given output stream.

Output will be over many lines.

Python:
Parameter out is not present and is assumed to be standard output.
Parameters
outthe output stream to which to write.
virtual void regina::NNormalSurfaceList::writeTextLong ( std::ostream &  out) const
virtual

Writes this object in long text format to the given output stream.

The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Reimplemented from regina::ShareableObject.

virtual void regina::NNormalSurfaceList::writeTextShort ( std::ostream &  out) const
virtual

Writes this object in short text format to the given output stream.

The output should be human-readable, should fit on a single line, and should not end with a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Implements regina::ShareableObject.

virtual void regina::NNormalSurfaceList::writeXMLPacketData ( std::ostream &  out) const
protectedvirtual

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.

Parameters
outthe output stream to which the XML should be written.

Implements regina::NPacket.

Member Data Documentation

NormalAlg regina::NNormalSurfaceList::algorithm_
protected

Stores the details of the enumeration algorithm that was used to generate this list.

This might not be the same as the algorithmHints flag passed to the corresponding enumeration routine (e.g., if invalid or inappropriate flags were passed).

const NormalCoords regina::NNormalSurfaceList::AN_LEGACY
static

Indicates that a list of almost normal surfaces was created using Regina 4.5.1 or earlier, where surfaces with more than one octagon of the same type were stripped out of the final solution set.

As of Regina 4.6 such surfaces are now included in the solution set, since we need them if we wish to enumerate all almost normal surfaces (not just the vertex almost normal surfaces).

This coordinate system is only used with legacy data files; new vectors and lists cannot be created in this coordinate system. The underlying coordinates are identical to those of AN_STANDARD.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_AN_LEGACY directly.
const NormalCoords regina::NNormalSurfaceList::AN_QUAD_OCT
static

Represents quadrilateral-octagon coordinates for octagonal almost normal surfaces.

For details, see "Quadrilateral-octagon coordinates for almost normal surfaces", Benjamin A. Burton, Experiment. Math. 19 (2010), 285-315.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_AN_QUAD_OCT directly.
const NormalCoords regina::NNormalSurfaceList::AN_STANDARD
static

Represents standard triangle-quadrilateral-octagon coordinates for octagonal almost normal surfaces.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_AN_STANDARD directly.
NormalCoords regina::NNormalSurfaceList::coords_
protected

Stores which coordinate system is being used by the normal surfaces in this packet.

const NormalCoords regina::NNormalSurfaceList::EDGE_WEIGHT
static

Represents edge weight coordinates for normal surfaces.

This coordinate system is for representation only; surface vectors and lists cannot be created in this coordinate system.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_EDGE_WEIGHT directly.
const NormalCoords regina::NNormalSurfaceList::FACE_ARCS
static

Represents triangle arc coordinates for normal surfaces.

This coordinate system is for representation only; surface vectors and lists cannot be created in this coordinate system.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_TRIANGLE_ARCS.
const NormalCoords regina::NNormalSurfaceList::ORIENTED
static

Represents standard triangle-quadrilateral coordinates for transversely oriented normal surfaces.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_ORIENTED directly.
const NormalCoords regina::NNormalSurfaceList::ORIENTED_QUAD
static

Represents quadrilateral coordinates for transversely oriented normal surfaces.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_ORIENTED_QUAD directly.
const NormalCoords regina::NNormalSurfaceList::QUAD
static

Represents quadrilateral coordinates for normal surfaces.

For details, see "Normal surface Q-theory", Jeffrey L. Tollefson, Pacific J. Math. 183 (1998), no. 2, 359–374.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_QUAD directly.
const NormalCoords regina::NNormalSurfaceList::STANDARD
static

Represents standard triangle-quadrilateral coordinates for normal surfaces.

Deprecated:
Instead of this class constant, you should use the NormalCoords enum value NS_STANDARD directly.
std::vector<NNormalSurface*> regina::NNormalSurfaceList::surfaces
protected

Contains the normal surfaces stored in this packet.

NormalList regina::NNormalSurfaceList::which_
protected

Indicates which normal surfaces these represent within the underlying triangulation.


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

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