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

A degenerate saturated block that is a single tetrahedron wrapped around so that two opposite edges touch. More...

#include <subcomplex/satblocktypes.h>

Inheritance diagram for regina::SatLayering:
regina::SatBlock regina::Output< SatBlock >

Public Types

typedef std::set< Tetrahedron< 3 > * > TetList
 The data structure used to store a list of tetrahedra that should not be examined by isBlock(). More...
 

Public Member Functions

 SatLayering (const SatLayering &cloneMe)=default
 Constructs a clone of the given block structure. More...
 
bool overHorizontal () const
 Does this describe a layering over the horizontal edge of the boundary annulus, or a layering over the diagonal edge? More...
 
virtual SatBlockclone () const override
 Returns a newly created clone of this saturated block structure. More...
 
virtual void adjustSFS (SFSpace &sfs, bool reflect) const override
 Adjusts the given Seifert fibred space to insert the contents of this saturated block. More...
 
virtual void writeTextShort (std::ostream &out) const override
 Writes a short text representation of this object to the given output stream. More...
 
virtual void writeAbbr (std::ostream &out, bool tex=false) const override
 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 SatAnnulusannulus (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...
 
SatBlockadjacentBlock (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, SatBlock *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 Triangulation< 3 > *originalTri, const Isomorphism< 3 > *iso, Triangulation< 3 > *newTri)
 Adjusts the structure of this block according to the given isomorphism between triangulations. More...
 
void nextBoundaryAnnulus (unsigned thisAnnulus, SatBlock *&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 abbr (bool tex=false) const
 Returns an abbreviated name or symbol for this block. More...
 
bool operator< (const SatBlock &compare) const
 Implements a consistent ordering of saturated blocks. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes a detailed text representation of this object to the given output stream. More...
 
std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 

Static Public Member Functions

static SatLayeringisBlockLayering (const SatAnnulus &annulus, TetList &avoidTets)
 Determines whether the given annulus is a boundary annulus for a block of this type (single layering). More...
 
static SatBlockisBlock (const SatAnnulus &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

 SatLayering (bool overHorizontal)
 Constructs a partially initialised block. More...
 

Static Protected Member Functions

static bool isBad (Tetrahedron< 3 > *t, const TetList &list)
 Determines whether the given tetrahedron is contained within the given list. More...
 
template<class List >
static bool isBad (Tetrahedron< 3 > *t, const List &list)
 Determines whether the given tetrahedron is contained within the given list. More...
 
static bool notUnique (Tetrahedron< 3 > *test)
 Determines whether the given tetrahedron pointer is null. More...
 
static bool notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2, Tetrahedron< 3 > *other3)
 Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
 
static bool notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2, Tetrahedron< 3 > *other3, Tetrahedron< 3 > *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...
 
SatAnnulusannulus_
 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...
 
SatBlock ** 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 saturated block that is a single tetrahedron wrapped around so that two opposite edges touch.

This forms a degenerate one-tetrahedron solid torus that is pinched along a single meridinal curve.

The four faces of this tetrahedron form two boundary annuli, and the tetrahedron is effectively layered onto each boundary annulus. See the Layering class notes for more discussion on layerings in general.

Although this block is degenerate (the fibres are all pinched together where the opposite edges of the tetrahedron meet), it can be used without problems as long as the entire Seifert fibred space is not formed from degenerate blocks. In other words, using such blocks is fine as long as they eventually meet a real (non-degenerate) block, which will give room for the fibres to separate so that they are no longer pinched together.

The SatAnnulus class notes describe horizontal and diagonal edges of a saturated annulus. This block may be one of two types, according to how the tetrahedron is layered onto the boundary annuli. Either the tetrahedron can be layered over the horizontal edge of each annulus (with the fibres pinched together between the two diagonal edges), or the tetrahedron can be layered over the diagonal edge of each annulus (with the fibres pinched together between the two horizontal edges).

Member Function Documentation

◆ detail()

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

Returns a detailed text representation of this object.

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

Returns
a detailed text representation of this object.

◆ str()

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

Returns a short text representation of this object.

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

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

◆ utf8()

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

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

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

Returns
a short text representation of this object.

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

Copyright © 1999-2020, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).