Regina Calculation Engine
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Represents a saturated block in a Seifert fibred space. More...
#include <subcomplex/nsatblock.h>
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 | |
NSatBlock (const NSatBlock &cloneMe) | |
Creates a new clone of the given block. More... | |
~NSatBlock () | |
Destroys all internal arrays. More... | |
virtual NSatBlock * | clone () const =0 |
Returns a newly created clone of this saturated block structure. More... | |
unsigned | nAnnuli () const |
Returns the number of annuli on the boundary of this saturated block. More... | |
const NSatAnnulus & | annulus (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... | |
NSatBlock * | adjacentBlock (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 | adjustSFS (NSFSpace &sfs, bool reflect) const =0 |
Adjusts the given Seifert fibred space to insert the contents of this saturated 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... | |
virtual void | writeAbbr (std::ostream &out, bool tex=false) const =0 |
Writes an abbreviated name or symbol for this block to the given output stream. More... | |
bool | operator< (const NSatBlock &compare) const |
Implements a consistent ordering of saturated blocks. More... | |
Input and Output | |
virtual void | writeTextShort (std::ostream &out) const =0 |
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... | |
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 NSatBlock * | isBlock (const NSatAnnulus &annulus, TetList &avoidTets) |
Determines whether the given annulus is in fact a boundary annulus for a recognised type of saturated block. More... | |
Protected Member Functions | |
NSatBlock (unsigned nAnnuli, bool twistedBoundary=false) | |
Constructor for a block with the given number of annuli on the boundary. 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... | |
NSatAnnulus * | annulus_ |
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... | |
Represents a saturated block in a Seifert fibred space.
A saturated block is a connected set of tetrahedra built from a subset of fibres (no fibres may enter or exit the boundary of the block). In addition, the boundary of this block must be a ring of saturated annuli, as described by the NSatAnnulus class. Aside from this ring of saturated annuli, there may be no other boundary triangles within the block.
The boundary annuli are numbered consecutively as illustrated below, where the markings 0 and 1 within the triangles represent the first and second triangle of each annulus (see the NSatAnnulus class notes for details). Note that the following diagram is viewed from inside the block.
-+---+---+---+---+---+---+- |0 /|0 /|0 /|0 /|0 /|0 /| ... | / | / | / | / | / | / | ... |/ 1|/ 1|/ 1|/ 1|/ 1|/ 1| -+---+---+---+---+---+---+- Annulus # ... n-2 n-1 0 1 2 3 ...
The ring of boundary annuli may optionally be twisted, so that together the annuli form a long Mobius band. In this case, for the purposes of labelling and marking annuli, the twist occurs between annuli n-1 and 0. Be careful when dealing with blocks with twisted boundaries, since with twists it is possible to identify an edge with itself in reverse (thus producing something that is not a 3-manifold triangulation).
Each saturated block corresponds to a piece of the base orbifold of the larger Seifert fibred space. For the purpose of connecting the base orbifold together, we assume that the boundary of this particular piece runs horizontally in the diagram above (specifically following the horizontal edges of the boundary annuli, as described in the NSatAnnulus class notes). Insisting on such a boundary may lead to (1,k) twists within the block; these are accounted for by the virtual adjustSFS() routine.
Saturated blocks are generally joined to one another (or themselves) along their boundary annuli. For this purpose, each saturated block contains a list of which annulus of this block is adjacent to which annulus of which other block. Adjacencies may be reflected, meaning that the adjacent annulus has its fibres reversed (i.e., the adjacent annulus has undergone an up-to-down reflection); they may also be backwards, meaning that the first triangle of one annulus is joined to the second triangle of the other (and vice versa).
typedef std::set<NTetrahedron*> regina::NSatBlock::TetList |
The data structure used to store a list of tetrahedra that should not be examined by isBlock().
regina::NSatBlock::NSatBlock | ( | const NSatBlock & | cloneMe | ) |
Creates a new clone of the given block.
Note that the new adjBlock_ array will contain pointers to the same adjacent blocks as the original. That is, adjacent blocks will not be cloned also; instead pointers to adjacent blocks will simply be copied across.
cloneMe | the saturated block to clone. |
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inline |
Destroys all internal arrays.
Note that any adjacent blocks that are referenced by the adjBlock array will not be destroyed.
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inlineprotected |
Constructor for a block with the given number of annuli on the boundary.
All arrays will be constructed but their contents will remain uninitialised, with the exception that the adjBlock array will be filled with null pointers.
nAnnuli | the number of annuli on the boundary of this block; this must be strictly positive. |
twistedBoundary | true if the ring of boundary annuli is twisted to form a long Mobius band, or false (the default) if it is not. |
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inline |
Returns which specific annulus of the adjacent block is listed as being adjacent to the given boundary annulus of this block.
whichAnnulus | indicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive. |
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inline |
Returns whether the adjacency along the given boundary annulus of this block is backwards.
See the class notes for a discussion of backwards adjacencies.
whichAnnulus | indicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive. |
true
if the corresponding adjacency is backwards, or false
if it is not.
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inline |
Returns the saturated block listed as being adjacent to the given boundary annulus of this block.
whichAnnulus | indicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive. |
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inline |
Returns whether the adjacency along the given boundary annulus of this block is reflected.
See the class notes for a discussion of reflected adjacencies.
whichAnnulus | indicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive. |
true
if the corresponding adjacency is reflected, or false
if it is not.
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pure 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.
sfs | the Seifert fibred space to adjust. |
reflect | true if this block is to be reflected, or false if it should be inserted directly. |
Implemented in regina::NSatLayering, regina::NSatReflectorStrip, regina::NSatCube, regina::NSatTriPrism, regina::NSatLST, and regina::NSatMobius.
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inline |
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.
which | indicates which boundary annulus is requested; this must be between 0 and nAnnuli()-1 inclusive. |
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pure virtual |
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.
Implemented in regina::NSatLayering, regina::NSatReflectorStrip, regina::NSatCube, regina::NSatTriPrism, regina::NSatLST, and regina::NSatMobius.
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inherited |
Returns the output from writeTextLong() as a string.
std::string regina::NSatBlock::getAbbr | ( | bool | tex = false | ) | const |
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).
tex | true if the name should be formatted for TeX, or false if it should be in plain text format. |
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inline |
Returns whether there is another saturated block listed as being adjacent to the given boundary annulus of this block.
whichAnnulus | indicates which boundary annulus of this block should be examined; this must be between 0 and nAnnuli()-1 inclusive. |
true
if the given boundary annulus has an adjacent block listed, or false
otherwise.
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staticprotected |
Determines whether the given tetrahedron is contained within the given list.
This is intended as a helper routine for isBlock() and related routines.
t | the tetrahedron to search for. |
list | the list in which to search. |
true
if and only if the given tetrahedron was found.
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inlinestaticprotected |
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.
List::const_iterator
that span the given list can be obtained by calling list.begin()
and list.end()
.t | the tetrahedron to search for. |
list | the list in which to search. |
true
if and only if the given tetrahedron was found.
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static |
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.
annulus | the proposed boundary annulus that should form part of the new saturated block. |
avoidTets | the list of tetrahedra that should not be considered, and to which any new tetrahedra will be added. |
null
if none was found.
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inline |
Returns the number of annuli on the boundary of this saturated block.
void regina::NSatBlock::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.
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.
thisAnnulus | describes which original boundary annulus of this block to examine; this must be between 0 and nAnnuli()-1 inclusive. |
nextBlock | a reference used to return the block containing the next boundary annulus around from thisAnnulus. |
nextAnnulus | a 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. |
refVert | a reference used to return true if the next annulus around is vertically reflected, or false if not; see above for details. |
refHoriz | a reference used to return true if the next annulus around is horizontally reflected, or false if not; see above for details. |
followPrev | true if we should find the previous boundary annulus, or false if we should find the next boundary annulus. |
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inlinestaticprotected |
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.
test | the tetrahedron pointer to test. |
true
if test is null, or false
otherwise.
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inlinestaticprotected |
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.
test | the tetrahedron pointer to test. |
other1 | another tetrahedron that will be compared with test. |
true
if test is null or equal to other1, or false
otherwise.
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inlinestaticprotected |
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.
test | the tetrahedron pointer to test. |
other1 | another tetrahedron that will be compared with test. |
other2 | another tetrahedron that will be compared with test. |
true
if test is null or equal to other1 or other2, or false
otherwise.
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inlinestaticprotected |
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.
test | the tetrahedron pointer to test. |
other1 | another tetrahedron that will be compared with test. |
other2 | another tetrahedron that will be compared with test. |
other3 | another tetrahedron that will be compared with test. |
true
if test is null or equal to other1, other2 or other3, or false
otherwise.
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inlinestaticprotected |
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.
test | the tetrahedron pointer to test. |
other1 | another tetrahedron that will be compared with test. |
other2 | another tetrahedron that will be compared with test. |
other3 | another tetrahedron that will be compared with test. |
other4 | another tetrahedron that will be compared with test. |
true
if test is null or equal to other1, other2, other3 or other4, or false
otherwise. bool regina::NSatBlock::operator< | ( | const NSatBlock & | compare | ) | const |
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.
compare | the saturated block with which this will be compared. |
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.
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inline |
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.
whichAnnulus | indicates which boundary annulus of this block has the new adjacency; this must be between 0 and nAnnuli()-1 inclusive. |
adjBlock | the other saturated block that is adjacent to this. |
adjAnnulus | indicates 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. |
adjReflected | indicates whether the new adjacency is reflected (see the class notes for details). |
adjBackwards | indicates whether the new adjacency is backwards (see the class notes for details). |
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inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
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inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
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inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
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virtual |
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).
originalTri | the triangulation currently used by this saturated block. |
iso | the mapping from originalTri to newTri. |
newTri | the triangulation to be used by the updated block structure. |
Reimplemented in regina::NSatLST.
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inline |
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.
true
if the ring of boundary annuli is twisted, or false
if not.
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pure 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.
out | the output stream to which to write. |
tex | true if the output should be formatted for TeX, or false if it should be in plain text format. |
Implemented in regina::NSatLayering, regina::NSatReflectorStrip, regina::NSatCube, regina::NSatTriPrism, regina::NSatLST, and regina::NSatMobius.
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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.
out | the 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.
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pure virtualinherited |
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.
out | the output stream to which to write. |
Implemented in regina::NSnapPeaTriangulation, regina::NGroupPresentation, regina::NHomMarkedAbelianGroup, regina::NNormalSurface, regina::NNormalSurfaceList, regina::NTetrahedron, regina::NGroupExpression, regina::NSatRegion, regina::NSatLayering, regina::NHomologicalData, regina::NVertex, regina::NSatReflectorStrip, regina::NEdge, regina::Dim2Triangle, regina::NTriangle, regina::NSatCube, regina::NMarkedAbelianGroup, regina::NHomGroupPresentation, regina::NAbelianGroup, regina::NGenericIsomorphism< dim >, regina::NGenericIsomorphism< 2 >, regina::NGenericIsomorphism< 3 >, regina::NTriangulation, regina::NSatTriPrism, regina::NComponent, regina::NTxICore, regina::NProgress, regina::NAngleStructureList, regina::Dim2Edge, regina::NAngleStructure, regina::NSurfaceFilter, regina::NBoundaryComponent, regina::NPDF, regina::Dim2Vertex, regina::Dim2Component, regina::NScript, regina::NSignature, regina::NManifold, regina::NSatLST, regina::NMatrixInt, regina::NCusp, regina::Dim2Triangulation, regina::NSurfaceSubset, regina::NStandardTriangulation, regina::NProgressManager, regina::NPillowTwoSphere, regina::NFileInfo, regina::Dim2BoundaryComponent, regina::NSnappedTwoSphere, regina::NText, regina::NSatMobius, and regina::NContainer.
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protected |
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.
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protected |
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.
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protected |
The saturated block joined to each boundary annulus; this may be null if there is no adjacency or if this information is not known.
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protected |
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.
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protected |
Details of each boundary annulus, as seen from the inside of this saturated block.
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protected |
The number of boundary annuli.
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protected |
Is the ring of boundary annuli twisted to form a Mobius band?