Regina Calculation Engine
Public Types | Public Member Functions | Static Public Member Functions | Static Protected Member Functions | Protected Attributes | List of all members
regina::NSatMobius Class Reference

A degenerate zero-tetrahedron saturated block that corresponds to attaching a Mobius band to a single annulus boundary. More...

#include <subcomplex/nsatblocktypes.h>

Inheritance diagram for regina::NSatMobius:
regina::NSatBlock regina::ShareableObject regina::boost::noncopyable

Public Types

typedef std::set< NTetrahedron * > TetList
 The data structure used to store a list of tetrahedra that should not be examined by isBlock(). More...
 

Public Member Functions

 NSatMobius (const NSatMobius &cloneMe)
 Constructs a clone of the given block structure. More...
 
int position () const
 Describes how the Mobius band is attached to the boundary annulus. More...
 
virtual NSatBlockclone () const
 Returns a newly created clone of this saturated block structure. More...
 
virtual void adjustSFS (NSFSpace &sfs, bool reflect) const
 Adjusts the given Seifert fibred space to insert the contents of this saturated block. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
virtual void writeAbbr (std::ostream &out, bool tex=false) const
 Writes an abbreviated name or symbol for this block to the given output stream. More...
 
unsigned nAnnuli () const
 Returns the number of annuli on the boundary of this saturated block. More...
 
const NSatAnnulusannulus (unsigned which) const
 Returns details of the requested annulus on the boundary of this saturated block. More...
 
bool twistedBoundary () const
 Is the ring of boundary annuli twisted to form a long Mobius strip? More...
 
bool hasAdjacentBlock (unsigned whichAnnulus) const
 Returns whether there is another saturated block listed as being adjacent to the given boundary annulus of this block. More...
 
NSatBlockadjacentBlock (unsigned whichAnnulus) const
 Returns the saturated block listed as being adjacent to the given boundary annulus of this block. More...
 
unsigned adjacentAnnulus (unsigned whichAnnulus) const
 Returns which specific annulus of the adjacent block is listed as being adjacent to the given boundary annulus of this block. More...
 
bool adjacentReflected (unsigned whichAnnulus) const
 Returns whether the adjacency along the given boundary annulus of this block is reflected. More...
 
bool adjacentBackwards (unsigned whichAnnulus) const
 Returns whether the adjacency along the given boundary annulus of this block is backwards. More...
 
void setAdjacent (unsigned whichAnnulus, NSatBlock *adjBlock, unsigned adjAnnulus, bool adjReflected, bool adjBackwards)
 Lists the given saturated block as being adjacent to the given boundary annulus of this block. More...
 
virtual void transform (const NTriangulation *originalTri, const NIsomorphism *iso, NTriangulation *newTri)
 Adjusts the structure of this block according to the given isomorphism between triangulations. More...
 
void nextBoundaryAnnulus (unsigned thisAnnulus, NSatBlock *&nextBlock, unsigned &nextAnnulus, bool &refVert, bool &refHoriz, bool followPrev)
 Finds the next (or previous) boundary annulus around from this, treating all adjacent blocks as part of a single large saturated region. More...
 
std::string getAbbr (bool tex=false) const
 Returns an abbreviated name or symbol for this block. More...
 
bool operator< (const NSatBlock &compare) const
 Implements a consistent ordering of saturated blocks. More...
 
Input and Output
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. 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 NSatMobiusisBlockMobius (const NSatAnnulus &annulus, TetList &avoidTets)
 Determines whether the given annulus is a boundary annulus for a block of this type (Mobius band). More...
 
static NSatBlockisBlock (const NSatAnnulus &annulus, TetList &avoidTets)
 Determines whether the given annulus is in fact a boundary annulus for a recognised type of saturated block. More...
 

Static Protected Member Functions

static bool isBad (NTetrahedron *t, const TetList &list)
 Determines whether the given tetrahedron is contained within the given list. More...
 
template<class List >
static bool isBad (NTetrahedron *t, const List &list)
 Determines whether the given tetrahedron is contained within the given list. More...
 
static bool notUnique (NTetrahedron *test)
 Determines whether the given tetrahedron pointer is null. More...
 
static bool notUnique (NTetrahedron *test, NTetrahedron *other1)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (NTetrahedron *test, NTetrahedron *other1, NTetrahedron *other2)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (NTetrahedron *test, NTetrahedron *other1, NTetrahedron *other2, NTetrahedron *other3)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (NTetrahedron *test, NTetrahedron *other1, NTetrahedron *other2, NTetrahedron *other3, NTetrahedron *other4)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 

Protected Attributes

unsigned nAnnuli_
 The number of boundary annuli. More...
 
NSatAnnulusannulus_
 Details of each boundary annulus, as seen from the inside of this saturated block. More...
 
bool twistedBoundary_
 Is the ring of boundary annuli twisted to form a Mobius band? More...
 
NSatBlock ** adjBlock_
 The saturated block joined to each boundary annulus; this may be null if there is no adjacency or if this information is not known. More...
 
unsigned * adjAnnulus_
 Describes which specific annulus of the adjacent saturated block is joined to each boundary annulus of this block. More...
 
bool * adjReflected_
 Describes whether the adjacency for each boundary annulus is reflected (see the class notes above). More...
 
bool * adjBackwards_
 Describes whether the adjacency for each boundary annulus is backwards (see the class notes above). More...
 

Detailed Description

A degenerate zero-tetrahedron saturated block that corresponds to attaching a Mobius band to a single annulus boundary.

This is a degenerate case of the layered solid torus (see the class NSatLST), where instead of joining a solid torus to an annulus boundary we join a Mobius band. The Mobius band can be thought of as a zero-tetrahedron solid torus with two boundary triangles, which in fact are opposite sides of the same triangle. By attaching a zero-tetrahedron Mobius band to an annulus boundary, we are effectively joining the two triangles of the annulus together.

The meridinal disc of this zero-tetrahedron solid torus meets the three edges of the annulus in 1, 1 and 2 places, so it is in fact a degenerate (1,1,2) layered solid torus. Note that the weight 2 edge is the boundary edge of the Mobius strip.

Member Typedef Documentation

typedef std::set<NTetrahedron*> regina::NSatBlock::TetList
inherited

The data structure used to store a list of tetrahedra that should not be examined by isBlock().

Constructor & Destructor Documentation

regina::NSatMobius::NSatMobius ( const NSatMobius cloneMe)
inline

Constructs a clone of the given block structure.

Parameters
cloneMethe block structure to clone.

Member Function Documentation

unsigned regina::NSatBlock::adjacentAnnulus ( unsigned  whichAnnulus) const
inlineinherited

Returns which specific annulus of the adjacent block is listed as being adjacent to the given boundary annulus of this block.

Precondition
The given annulus of this block actually has an adjacent block listed.
Parameters
whichAnnulusindicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive.
Returns
the corresponding annulus number on the other block that is adjacent along this annulus.
bool regina::NSatBlock::adjacentBackwards ( unsigned  whichAnnulus) const
inlineinherited

Returns whether the adjacency along the given boundary annulus of this block is backwards.

See the class notes for a discussion of backwards adjacencies.

Precondition
The given annulus of this block actually has an adjacent block listed.
Parameters
whichAnnulusindicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive.
Returns
true if the corresponding adjacency is backwards, or false if it is not.
NSatBlock * regina::NSatBlock::adjacentBlock ( unsigned  whichAnnulus) const
inlineinherited

Returns the saturated block listed as being adjacent to the given boundary annulus of this block.

Parameters
whichAnnulusindicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive.
Returns
the other block adjacent along this annulus, or 0 if there is no adjacent block listed.
bool regina::NSatBlock::adjacentReflected ( unsigned  whichAnnulus) const
inlineinherited

Returns whether the adjacency along the given boundary annulus of this block is reflected.

See the class notes for a discussion of reflected adjacencies.

Precondition
The given annulus of this block actually has an adjacent block listed.
Parameters
whichAnnulusindicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive.
Returns
true if the corresponding adjacency is reflected, or false if it is not.
virtual void regina::NSatMobius::adjustSFS ( NSFSpace sfs,
bool  reflect 
) const
virtual

Adjusts the given Seifert fibred space to insert the contents of this saturated block.

In particular, the space should be adjusted as though an ordinary solid torus (base orbifold a disc, no twists or exceptional fibres) had been replaced by this block. This description does not make sense for blocks with twisted boundary; the twisted case is discussed below.

If the argument reflect is true, it should be assumed that this saturated block is being reflected before being inserted into the larger Seifert fibred space. That is, any twists or exceptional fibres should be negated before being added.

Regarding the signs of exceptional fibres: Consider a saturated block containing a solid torus whose meridinal curve runs p times horizontally around the boundary in order through annuli 0,1,... and follows the fibres q times from bottom to top (as depicted in the diagram in the NSatBlock class notes). Then this saturated block adds a positive (p, q) fibre to the underlying Seifert fibred space.

If the ring of saturated annuli bounding this block is twisted then the situation becomes more complex. It can be proven that such a block must contain a twisted reflector boundary in the base orbifold (use Z_2 homology with fibre-reversing paths to show that the base orbifold must contain another twisted boundary component, and then recall that real boundaries are not allowed inside blocks).

In this twisted boundary case, it should be assumed that the twisted reflector boundary is already stored in the given Seifert fibred space. This routine should make any further changes that are required (there may well be none). That is, the space should be adjusted as though a trivial Seifert fibred space over the annulus with one twisted reflector boundary (and one twisted puncture corresponding to the block boundary) had been replaced by this block. In particular, this routine should not add the reflector boundary itself.

Parameters
sfsthe Seifert fibred space to adjust.
reflecttrue if this block is to be reflected, or false if it should be inserted directly.

Implements regina::NSatBlock.

const NSatAnnulus & regina::NSatBlock::annulus ( unsigned  which) const
inlineinherited

Returns details of the requested annulus on the boundary of this saturated block.

Annuli are numbered from 0 to nAnnuli()-1 as described in the class notes.

Parameters
whichindicates which boundary annulus is requested; this must be between 0 and nAnnuli()-1 inclusive.
Returns
a reference to the requested boundary annulus.
NSatBlock * regina::NSatMobius::clone ( ) const
inlinevirtual

Returns a newly created clone of this saturated block structure.

A clone of the correct subclass of NSatBlock will be returned. For this reason, each subclass of NSatBlock must implement this routine.

Returns
a new clone of this block.

Implements regina::NSatBlock.

std::string regina::ShareableObject::detail ( ) const
inherited

Returns the output from writeTextLong() as a string.

Returns
a long text representation of this object.
std::string regina::NSatBlock::getAbbr ( bool  tex = false) const
inherited

Returns an abbreviated name or symbol for this block.

This name will reflect the particular block type, but may not provide thorough details.

The name will be no more than a handful of characters long, and will not include a newline (or surrounding dollar signs in TeX mode).

Parameters
textrue if the name should be formatted for TeX, or false if it should be in plain text format.
Returns
an abbreviated name for this block.
bool regina::NSatBlock::hasAdjacentBlock ( unsigned  whichAnnulus) const
inlineinherited

Returns whether there is another saturated block listed as being adjacent to the given boundary annulus of this block.

Parameters
whichAnnulusindicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive.
Returns
true if the given boundary annulus has an adjacent block listed, or false otherwise.
static bool regina::NSatBlock::isBad ( NTetrahedron t,
const TetList list 
)
staticprotectedinherited

Determines whether the given tetrahedron is contained within the given list.

This is intended as a helper routine for isBlock() and related routines.

Parameters
tthe tetrahedron to search for.
listthe list in which to search.
Returns
true if and only if the given tetrahedron was found.
template<class List >
static bool regina::NSatBlock::isBad ( NTetrahedron t,
const List &  list 
)
inlinestaticprotectedinherited

Determines whether the given tetrahedron is contained within the given list.

This is intended as a helper routine for isBlock() and related routines. It is a generic routine for working with arbitrary list types.

Precondition
Forward iterators of type List::const_iterator that span the given list can be obtained by calling list.begin() and list.end().
Parameters
tthe tetrahedron to search for.
listthe list in which to search.
Returns
true if and only if the given tetrahedron was found.
static NSatBlock* regina::NSatBlock::isBlock ( const NSatAnnulus annulus,
TetList avoidTets 
)
staticinherited

Determines whether the given annulus is in fact a boundary annulus for a recognised type of saturated block.

The annulus should be represented from the inside of the proposed saturated block.

Only certain types of saturated block are recognised by this routine. More exotic saturated blocks will not be identified, and this routine will return null in such cases.

The given list of tetrahedra will not be examined by this routine. That is, only saturated blocks that do not contain any of these tetrahedra will be considered. As a consequence, if the given annulus uses any of these tetrahedra then null will be returned.

If a block is found on the other hand, all of the tetrahedra within this block will be added to the given list.

In the event that a block is found, it is guaranteed that the given annulus will be listed as annulus number 0 in the block structure, without any horizontal or vertical reflection.

Python:
The second argument avoidTets is not present. An empty list will be passed instead.
Parameters
annulusthe proposed boundary annulus that should form part of the new saturated block.
avoidTetsthe list of tetrahedra that should not be considered, and to which any new tetrahedra will be added.
Returns
details of the saturated block if one was found, or null if none was found.
static NSatMobius* regina::NSatMobius::isBlockMobius ( const NSatAnnulus annulus,
TetList avoidTets 
)
static

Determines whether the given annulus is a boundary annulus for a block of this type (Mobius band).

This routine is a specific case of NSatBlock::isBlock(); see that routine for further details.

Parameters
annulusthe proposed boundary annulus that should form part of the new saturated block.
avoidTetsthe list of tetrahedra that should not be considered, and to which any new tetrahedra will be added.
Returns
details of the saturated block if one was found, or null if none was found.
unsigned regina::NSatBlock::nAnnuli ( ) const
inlineinherited

Returns the number of annuli on the boundary of this saturated block.

Returns
the number of boundary annuli.
void regina::NSatBlock::nextBoundaryAnnulus ( unsigned  thisAnnulus,
NSatBlock *&  nextBlock,
unsigned &  nextAnnulus,
bool &  refVert,
bool &  refHoriz,
bool  followPrev 
)
inherited

Finds the next (or previous) boundary annulus around from this, treating all adjacent blocks as part of a single large saturated region.

Suppose that all saturated blocks are merged together according to adjacent boundary annuli, forming larger saturated structures. The remaining annuli that do not have adjacent blocks will group together to form several large boundary rings. Note that each boundary ring might involve annuli from several different blocks, and might or might not have a twist (thus forming a large Klein bottle instead of a large torus).

This routine is used to trace around such a boundary ring. It is assumed that annulus thisAnnulus of this block forms part of a boundary ring (i.e., it has no adjacent block). This routine will then return the next/previous annulus around from this in the large boundary ring. Here "next" means in the direction following from the second triangle of this annulus, and "previous" means in the direction following from the first triangle; the boolean argument followPrev controls which we will be used. This next/previous annulus might belong to another block, or it might even be this original annulus again.

The next/previous annulus itself is not returned, but rather a reference as to how it appears within its enclosing saturated block. Specifically, a block and corresponding annulus number will be returned in the arguments nextBlock and nextAnnulus respectively.

It is possible that the next/previous annulus as it appears within the returned block is oriented differently from how it appears within this large boundary ring. For this reason, two booleans are returned also. The argument refVert will describe whether the annulus is reflected vertically as it appears within the large boundary ring (i.e., the first and second triangles remain the same but the fibre direction is reversed). Similarly, the argument refHoriz will describe whether the annulus is reflected horizontally as it appears within the large boundary ring (i.e., first and second triangles are switched but the fibre direction is unchanged).

It is possible that both a horizontal and vertical reflection take place. Note that any kind of reflection will also affect the locations of the 0/1/2 markings as described in the NSatAnnulus class notes.

Finally, note that if the large boundary ring is twisted (i.e., it forms a Klein bottle), then following the entire boundary ring around using this routine will bring you back to the starting annulus but with the refVert flag set.

Precondition
Annulus thisAnnulus of this block has no block adjacent to it.
Warning
If you wish to trace around an entire boundary ring, you will need to adjust the argument followPrev according to whether or not the current annulus is reflected horizontally (since, under a horizontal reflection, "next" becomes "previous" and vice versa).
Python:
This routine only takes two arguments (thisAnnulus and followPrev). The return value is a tuple of four values: the block returned in nextBlock, the integer returned in nextAnnulus, the boolean returned in refVert, and the boolean returned in refHoriz.
Parameters
thisAnnulusdescribes which original boundary annulus of this block to examine; this must be between 0 and nAnnuli()-1 inclusive.
nextBlocka reference used to return the block containing the next boundary annulus around from thisAnnulus.
nextAnnulusa reference used to return the specific annulus number within nextBlock of the next annulus around; this will be between 0 and nextBlock->nAnnuli()-1 inclusive, and the corresponding annulus will have no block adjacent to it.
refVerta reference used to return true if the next annulus around is vertically reflected, or false if not; see above for details.
refHoriza reference used to return true if the next annulus around is horizontally reflected, or false if not; see above for details.
followPrevtrue if we should find the previous boundary annulus, or false if we should find the next boundary annulus.
bool regina::NSatBlock::notUnique ( NTetrahedron test)
inlinestaticprotectedinherited

Determines whether the given tetrahedron pointer is null.

This is intended as a helper routine for isBlock() and related routines. Despite its trivial implementation, it is provided to make long blocks of code easier to read and distinguish by functionality.

The name notUnique() may seem strang for what is essentially a nullity test; in fact this routine is offered as a degenerate case of other variants of notUnique() that take more tetrahedra as arguments.

Parameters
testthe tetrahedron pointer to test.
Returns
true if test is null, or false otherwise.
bool regina::NSatBlock::notUnique ( NTetrahedron test,
NTetrahedron other1 
)
inlinestaticprotectedinherited

Determines whether the given tetrahedron pointer is null or equal to another from the given list.

This is intended as a helper routine for isBlock() and related routines. Despite its trivial implementation, it is provided to make long blocks of code easier to read and distinguish by functionality.

Parameters
testthe tetrahedron pointer to test.
other1another tetrahedron that will be compared with test.
Returns
true if test is null or equal to other1, or false otherwise.
bool regina::NSatBlock::notUnique ( NTetrahedron test,
NTetrahedron other1,
NTetrahedron other2 
)
inlinestaticprotectedinherited

Determines whether the given tetrahedron pointer is null or equal to another from the given list.

This is intended as a helper routine for isBlock() and related routines. Despite its trivial implementation, it is provided to make long blocks of code easier to read and distinguish by functionality.

Parameters
testthe tetrahedron pointer to test.
other1another tetrahedron that will be compared with test.
other2another tetrahedron that will be compared with test.
Returns
true if test is null or equal to other1 or other2, or false otherwise.
bool regina::NSatBlock::notUnique ( NTetrahedron test,
NTetrahedron other1,
NTetrahedron other2,
NTetrahedron other3 
)
inlinestaticprotectedinherited

Determines whether the given tetrahedron pointer is null or equal to another from the given list.

This is intended as a helper routine for isBlock() and related routines. Despite its trivial implementation, it is provided to make long blocks of code easier to read and distinguish by functionality.

Parameters
testthe tetrahedron pointer to test.
other1another tetrahedron that will be compared with test.
other2another tetrahedron that will be compared with test.
other3another tetrahedron that will be compared with test.
Returns
true if test is null or equal to other1, other2 or other3, or false otherwise.
bool regina::NSatBlock::notUnique ( NTetrahedron test,
NTetrahedron other1,
NTetrahedron other2,
NTetrahedron other3,
NTetrahedron other4 
)
inlinestaticprotectedinherited

Determines whether the given tetrahedron pointer is null or equal to another from the given list.

This is intended as a helper routine for isBlock() and related routines. Despite its trivial implementation, it is provided to make long blocks of code easier to read and distinguish by functionality.

Parameters
testthe tetrahedron pointer to test.
other1another tetrahedron that will be compared with test.
other2another tetrahedron that will be compared with test.
other3another tetrahedron that will be compared with test.
other4another tetrahedron that will be compared with test.
Returns
true if test is null or equal to other1, other2, other3 or other4, or false otherwise.
bool regina::NSatBlock::operator< ( const NSatBlock compare) const
inherited

Implements a consistent ordering of saturated blocks.

This ordering is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.

Parameters
comparethe saturated block with which this will be compared.
Returns
true if this block comes before the given block according to the ordering of saturated blocks, or false if either the blocks are identical or this block comes after the given block.
int regina::NSatMobius::position ( ) const
inline

Describes how the Mobius band is attached to the boundary annulus.

The class notes discuss the weight two edge of the Mobius band (or equivalently the boundary edge of the Mobius band). The return value of this routine indicates which edge of the boundary annulus this weight two edge is joined to.

In the NSatAnnulus class notes, the three edges of the annulus are denoted vertical, horizontal and boundary, and the vertices of each triangle are given markings 0, 1 and 2.

The return value of this routine takes the value 0, 1 or 2 as follows:

  • 0 means that the weight two edge is joined to the diagonal edge of the annulus (markings 1 and 2);
  • 1 means that the weight two edge is joined to the horizontal edge of the annulus (markings 0 and 2);
  • 2 means that the weight two edge is joined to the vertical edge of the annulus (markings 0 and 1).
Returns
the value 0, 1 or 2 as described above.
void regina::NSatBlock::setAdjacent ( unsigned  whichAnnulus,
NSatBlock adjBlock,
unsigned  adjAnnulus,
bool  adjReflected,
bool  adjBackwards 
)
inlineinherited

Lists the given saturated block as being adjacent to the given boundary annulus of this block.

Both block structures (this and the given block) will be updated.

Parameters
whichAnnulusindicates which boundary annulus of this block has the new adjacency; this must be between 0 and nAnnuli()-1 inclusive.
adjBlockthe other saturated block that is adjacent to this.
adjAnnulusindicates which boundary annulus of the adjacent block meets the given boundary annulus of this block; this must be between 0 and adjBlock->nAnnuli()-1 inclusive.
adjReflectedindicates whether the new adjacency is reflected (see the class notes for details).
adjBackwardsindicates whether the new adjacency is backwards (see the class notes for details).
std::string regina::ShareableObject::str ( ) const
inherited

Returns the output from writeTextShort() as a string.

Python:
This implements the __str__() function.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toString ( ) const
inlineinherited

A deprecated alias for str(), which returns the output from writeTextShort() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toStringLong ( ) const
inlineinherited

A deprecated alias for detail(), which returns the output from writeTextLong() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.
virtual void regina::NSatBlock::transform ( const NTriangulation originalTri,
const NIsomorphism iso,
NTriangulation newTri 
)
virtualinherited

Adjusts the structure of this block according to the given isomorphism between triangulations.

Any triangulation-specific information will be transformed accordingly (for instance, the routine NSatAnnulus::transform() will be called for each boundary annulus).

Information regarding adjacent blocks will not be changed. Only structural information for this particular block will be updated.

The given isomorphism must describe a mapping from originalTri to newTri, and this block must currently refer to tetrahedra in originalTri. After this routine is called the block will instead refer to the corresponding tetrahedra in newTri (with changes in vertex/face numbering also accounted for).

Precondition
This block currently refers to tetrahedra in originalTri, and iso describes a mapping from originalTri to newTri.
Warning
Any subclasses of NSatBlock that store additional triangulation-specific information will need to override this routine. When doing so, be sure to call NSatBlock::transform() so that the generic changes defined here will still take place.
Parameters
originalTrithe triangulation currently used by this saturated block.
isothe mapping from originalTri to newTri.
newTrithe triangulation to be used by the updated block structure.

Reimplemented in regina::NSatLST.

bool regina::NSatBlock::twistedBoundary ( ) const
inlineinherited

Is the ring of boundary annuli twisted to form a long Mobius strip?

Recall from the class notes that the twist occurs between boundary annuli nAnnuli()-1 and 0.

Returns
true if the ring of boundary annuli is twisted, or false if not.
virtual void regina::NSatMobius::writeAbbr ( std::ostream &  out,
bool  tex = false 
) const
virtual

Writes an abbreviated name or symbol for this block to the given output stream.

This name should reflect the particular block type, but need not provide thorough details.

The output should be no more than a handful of characters long, and no newline should be written. In TeX mode, no leading or trailing dollar signs should be written.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
textrue if the output should be formatted for TeX, or false if it should be in plain text format.

Implements regina::NSatBlock.

void regina::ShareableObject::writeTextLong ( std::ostream &  out) const
inlinevirtualinherited

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 in regina::NSnapPeaTriangulation, regina::NGroupPresentation, regina::NHomMarkedAbelianGroup, regina::NNormalSurfaceList, regina::NTetrahedron, regina::NSatRegion, regina::NVertex, regina::NEdge, regina::Dim2Triangle, regina::NTriangle, regina::NLayeredSolidTorus, regina::NHomGroupPresentation, regina::NGenericIsomorphism< dim >, regina::NGenericIsomorphism< 2 >, regina::NGenericIsomorphism< 3 >, regina::NTriangulation, regina::NComponent, regina::NTxICore, regina::NTriSolidTorus, regina::NAngleStructureList, regina::Dim2Edge, regina::NBoundaryComponent, regina::NLayeredChain, regina::Dim2Vertex, regina::Dim2Component, regina::NScript, regina::NAugTriSolidTorus, regina::NSpiralSolidTorus, regina::NSurfaceFilterProperties, regina::NLayeredTorusBundle, regina::NManifold, regina::NPlugTriSolidTorus, regina::NMatrixInt, regina::NBlockedSFSTriple, regina::NPluggedTorusBundle, regina::Dim2Triangulation, regina::NSurfaceSubset, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NFileInfo, regina::NBlockedSFSLoop, regina::NSnappedBall, regina::NBlockedSFSPair, regina::Dim2BoundaryComponent, regina::NTrivialTri, regina::NL31Pillow, regina::NLayeredChainPair, regina::NText, regina::NSurfaceFilterCombination, and regina::NBlockedSFS.

virtual void regina::NSatMobius::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.

Member Data Documentation

unsigned* regina::NSatBlock::adjAnnulus_
protectedinherited

Describes which specific annulus of the adjacent saturated block is joined to each boundary annulus of this block.

Values may be undefined if the corresponding entries in the adjBlock array is null.

bool* regina::NSatBlock::adjBackwards_
protectedinherited

Describes whether the adjacency for each boundary annulus is backwards (see the class notes above).

Values may be undefined if the corresponding entries in the adjBlock array is null.

NSatBlock** regina::NSatBlock::adjBlock_
protectedinherited

The saturated block joined to each boundary annulus; this may be null if there is no adjacency or if this information is not known.

bool* regina::NSatBlock::adjReflected_
protectedinherited

Describes whether the adjacency for each boundary annulus is reflected (see the class notes above).

Values may be undefined if the corresponding entries in the adjBlock array is null.

NSatAnnulus* regina::NSatBlock::annulus_
protectedinherited

Details of each boundary annulus, as seen from the inside of this saturated block.

unsigned regina::NSatBlock::nAnnuli_
protectedinherited

The number of boundary annuli.

bool regina::NSatBlock::twistedBoundary_
protectedinherited

Is the ring of boundary annuli twisted to form a Mobius band?


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

Copyright © 1999-2014, 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).