Represents a spiralled solid torus in a triangulation. More...

#include <subcomplex/spiralsolidtorus.h>

Inheritance diagram for regina::SpiralSolidTorus:

Public Member Functions
	SpiralSolidTorus (const SpiralSolidTorus &src)
	Creates a new copy of the given structure. More...

	SpiralSolidTorus (SpiralSolidTorus &&src) noexcept
	Moves the contents of the given structure into this new structure. More...

	~SpiralSolidTorus () override
	Destroys this structure. More...

SpiralSolidTorus &	operator= (const SpiralSolidTorus &src)
	Sets this to be a copy of the given structure. More...

SpiralSolidTorus &	operator= (SpiralSolidTorus &&src) noexcept
	Moves the contents of the given structure into this structure. More...

void	swap (SpiralSolidTorus &other) noexcept
	Swaps the contents of this and the given structure. More...

size_t	size () const
	Returns the number of tetrahedra in this spiralled solid torus. More...

Tetrahedron< 3 > *	tetrahedron (size_t index) const
	Returns the requested tetrahedron in this spiralled solid torus. More...

Perm< 4 >	vertexRoles (size_t index) const
	Returns a permutation represeting the role that each vertex of the requested tetrahedron plays in the solid torus. More...

bool	operator== (const SpiralSolidTorus &other) const
	Determines whether this and the given structure represent the same type of spiralled solid torus. More...

bool	operator!= (const SpiralSolidTorus &other) const
	Determines whether this and the given structure represent different types of spiralled solid torus. More...

void	reverse ()
	Reverses this spiralled solid torus. More...

void	cycle (size_t k)
	Cycles this spiralled solid torus by the given number of tetrahedra. More...

bool	makeCanonical ()
	Converts this spiralled solid torus into its canonical representation. More...

bool	isCanonical () const
	Determines whether this spiralled solid torus is in canonical form. More...

std::unique_ptr< Manifold >	manifold () const override
	Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...

AbelianGroup	homology () const override
	Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...

std::ostream &	writeName (std::ostream &out) const override
	Writes the name of this triangulation as a human-readable string to the given output stream. More...

std::ostream &	writeTeXName (std::ostream &out) const override
	Writes the name of this triangulation in TeX format to the given output stream. More...

void	writeTextShort (std::ostream &out) const override
	Writes a short text representation of this object to the given output stream. More...

std::string	name () const
	Returns the name of this specific triangulation as a human-readable string. More...

std::string	texName () const
	Returns the name of this specific triangulation in TeX format. 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 std::unique_ptr< SpiralSolidTorus >	recognise (Tetrahedron< 3 > *tet, Perm< 4 > useVertexRoles)
	Determines if the given tetrahedron forms part of a spiralled solid torus with its vertices playing the given roles in the solid torus. More...

static std::unique_ptr< StandardTriangulation >	recognise (Component< 3 > *component)
	Determines whether the given component represents one of the standard triangulations understood by Regina. More...

static std::unique_ptr< StandardTriangulation >	recognise (const Triangulation< 3 > &tri)
	Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...

Detailed Description

Represents a spiralled solid torus in a triangulation.

A spiralled solid torus is created by placing tetrahedra one upon another in a spiralling fashion to form a giant loop.

For each tetrahedron, label the vertices A, B, C and D. Draw the tetrahedron so that the vertices form an upward spiral in the order A-B-C-D, with D directly above A. Face BCD is on the top, face ABC is on the bottom and faces ABD and ACD are both vertical.

When joining two tetrahedra, face BCD of the lower tetrahedron will be joined to face ABC of the upper tetrahedron. In this way the tetrahedra are placed one upon another to form a giant loop (which is closed up by placing the bottommost tetrahedron above the topmost tetrahedron in a similar fashion), forming a solid torus overall.

In each tetrahedron, directed edges AB, BC and CD are major edges, directed edges AC and BD are minor edges and directed edge AD is an axis edge.

The major edges all combined form a single longitude of the solid torus. Using this directed longitude, using the directed meridinal curve ACBA and assuming the spiralled solid torus contains n tetrahedra, the minor edges all combined form a (2, n) curve and the axis edges all combined form a (3, n) curve on the torus boundary.

Note that all tetrahedra in the spiralled solid torus must be distinct and there must be at least one tetrahedron.

Note also that class TriSolidTorus represents a spiralled solid torus with precisely three tetrahedra. A spiralled solid torus with only one tetrahedron is in fact a (1,2,3) layered solid torus.

All optional StandardTriangulation routines are implemented for this class.

This class implements C++ move semantics and adheres to the C++ Swappable requirement. It is designed to avoid deep copies wherever possible, even when passing or returning objects by value. Note, however, that the only way to create objects of this class (aside from copying or moving) is via the static member function recognise().

Constructor & Destructor Documentation

◆ SpiralSolidTorus() [1/2]

regina::SpiralSolidTorus::SpiralSolidTorus ( const SpiralSolidTorus & src )

inline

Creates a new copy of the given structure.

This will induce a deep copy of src.

Parameters

src	the structure to copy.

◆ SpiralSolidTorus() [2/2]

regina::SpiralSolidTorus::SpiralSolidTorus ( SpiralSolidTorus && src )

inlinenoexcept

Moves the contents of the given structure into this new structure.

This is a fast (constant time) operation.

The structure that was passed (src) will no longer be usable.

Parameters

src	the structure to move from.

◆ ~SpiralSolidTorus()

regina::SpiralSolidTorus::~SpiralSolidTorus ( )

inlineoverride

Destroys this structure.

Member Function Documentation

◆ cycle()

void regina::SpiralSolidTorus::cycle ( size_t k )

Cycles this spiralled solid torus by the given number of tetrahedra.

Tetrahedra k, k+1, k+2 and so on will become tetrahedra 0, 1, 2 and so on respectively. Note that this operation will not change the vertex roles.

The underlying triangulation is not changed; all that changes is how this spiralled solid torus is represented.

Parameters

k	the number of tetrahedra through which we should cycle.

◆ detail()

std::string regina::Output< StandardTriangulation , 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.

◆ homology()

AbelianGroup regina::SpiralSolidTorus::homology ( ) const

overridevirtual

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

This routine does not work by calling Triangulation<3>::homology() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

This means that homology() needs to be implemented separately for each class of standard triangulation. See the class notes for each subclass of StandardTriangulation for details on whether homology has been implemented for that particular subclass. The default implementation of this routine just throws a NotImplemented exception.

Most users will not need this routine, since presumably you already have an explicit Triangulation<3> available and so you can just call Triangulation<3>::homology() instead (which, unlike this routine, is always implemented). This StandardTriangulation::homology() routine should be seen as more of a verification/validation tool for the Regina developers.

If this StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::homology() upon the associated real triangulation.

Exceptions

NotImplemented	Homology calculation has not yet been implemented for this particular type of standard triangulation.
FileError	The homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusTri, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this triangulation, if this functionality has been implemented.

Reimplemented from regina::StandardTriangulation.

◆ isCanonical()

bool regina::SpiralSolidTorus::isCanonical ( ) const

Determines whether this spiralled solid torus is in canonical form.

Canonical form is described in detail in the description for makeCanonical().

Returns: true if and only if this spiralled solid torus is in canonical form.

◆ makeCanonical()

bool regina::SpiralSolidTorus::makeCanonical ( )

Converts this spiralled solid torus into its canonical representation.

The canonical representation of a spiralled solid torus is unique in a given triangulation.

Tetrahedron 0 in the spiralled solid torus will be the tetrahedron with the lowest index in the triangulation, and under permutation vertexRoles(0) the image of 0 will be less than the image of 3.

Returns: true if and only if the representation of this spiralled solid torus was actually changed.

◆ manifold()

std::unique_ptr< Manifold > regina::SpiralSolidTorus::manifold ( ) const

overridevirtual

Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.

If the 3-manifold cannot be recognised then this routine will return null.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of StandardTriangulation. The default implementation of this routine returns null.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

Returns: the underlying 3-manifold.

Reimplemented from regina::StandardTriangulation.

◆ name()

std::string regina::StandardTriangulation::name ( ) const

inherited

Returns the name of this specific triangulation as a human-readable string.

Returns: the name of this triangulation.

◆ operator!=()

bool regina::SpiralSolidTorus::operator!= ( const SpiralSolidTorus & other ) const

inline

Determines whether this and the given structure represent different types of spiralled solid torus.

Specifically, two spiralled solid tori will compare as equal if and only if they have the same size (i.e., the same number of tetrahedra).

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent different types of spiralled solid torus.

◆ operator=() [1/2]

SpiralSolidTorus & regina::SpiralSolidTorus::operator= ( const SpiralSolidTorus & src )

Sets this to be a copy of the given structure.

This will induce a deep copy of src.

Parameters

src	the structure to copy.

Returns: a reference to this structure.

◆ operator=() [2/2]

SpiralSolidTorus & regina::SpiralSolidTorus::operator= ( SpiralSolidTorus && src )

inlinenoexcept

Moves the contents of the given structure into this structure.

This is a fast (constant time) operation.

The structure that was passed (src) will no longer be usable.

Parameters

src	the structure to move from.

Returns: a reference to this structure.

◆ operator==()

bool regina::SpiralSolidTorus::operator== ( const SpiralSolidTorus & other ) const

inline

Determines whether this and the given structure represent the same type of spiralled solid torus.

Specifically, two spiralled solid tori will compare as equal if and only if they have the same size (i.e., the same number of tetrahedra).

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent the same type of spiralled solid torus.

◆ recognise() [1/3]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( Component< 3 > * component )

staticinherited

Determines whether the given component represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given component must have the same corresponding boundary triangles, i.e., the component cannot have any further identifications of these boundary triangles with each other.

Note that the triangulation-based routine recognise(const Triangulation<3>&) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters

component the triangulation component under examination.

Returns: the details of the standard triangulation if the given component is recognised, or null otherwise.

◆ recognise() [2/3]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( const Triangulation< 3 > & tri )

staticinherited

Determines whether the given triangulation represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given triangulation must have the same corresponding boundary triangles, i.e., the triangulation cannot have any further identifications of these boundary triangles with each other.

This routine may recognise more triangulations than the component-based recognise(Component<3>*), since passing an entire triangulation allows access to more information.

Parameters

tri	the triangulation under examination.

Returns: the details of the standard triangualation if the given triangulation is recognised, or null otherwise.

◆ recognise() [3/3]

static std::unique_ptr< SpiralSolidTorus > regina::SpiralSolidTorus::recognise	(	Tetrahedron< 3 > *	tet,
		Perm< 4 >	useVertexRoles
	)

static

Determines if the given tetrahedron forms part of a spiralled solid torus with its vertices playing the given roles in the solid torus.

Note that the boundary triangles of the spiralled solid torus need not be boundary triangles within the overall triangulation, i.e., they may be identified with each other or with triangles of other tetrahedra.

This function returns by (smart) pointer for consistency with StandardTriangulation::recognise(), which makes use of the polymorphic nature of the StandardTriangulation class hierarchy.

Parameters

tet	the tetrahedron to examine.
useVertexRoles	a permutation describing the role each tetrahedron vertex must play in the solid torus; this must be in the same format as the permutation returned by vertexRoles().

Returns: a structure containing details of the solid torus with the given tetrahedron as tetrahedron 0, or null if the given tetrahedron is not part of a spiralled solid torus with the given vertex roles.

◆ reverse()

void regina::SpiralSolidTorus::reverse ( )

Reverses this spiralled solid torus.

Tetrahedra 0, 1, 2, ..., size()-1 will become tetrahedra size()-1, ..., 2, 1, 0 respectively. Note that this operation will change the vertex roles as well.

The underlying triangulation is not changed; all that changes is how this spiralled solid torus is represented.

◆ size()

size_t regina::SpiralSolidTorus::size ( ) const

inline

Returns the number of tetrahedra in this spiralled solid torus.

Returns: the number of tetrahedra.

◆ str()

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

inherited

Returns a short text representation of this object.

This text should be human-readable, should use plain ASCII characters where possible, and should not contain any newlines.

Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python __str__() and __repr__() functions.

Python: The Python "stringification" function __str__() will use precisely this function, and for most classes the Python __repr__() function will incorporate this into its output.

Returns: a short text representation of this object.

◆ swap()

void regina::SpiralSolidTorus::swap ( SpiralSolidTorus & other )

inlinenoexcept

Swaps the contents of this and the given structure.

Parameters

other the structure whose contents should be swapped with this.

◆ tetrahedron()

Tetrahedron< 3 > * regina::SpiralSolidTorus::tetrahedron ( size_t index ) const

inline

Returns the requested tetrahedron in this spiralled solid torus.

Tetrahedra are numbered from 0 to size()-1 inclusive, with tetrahedron i+1 being placed above tetrahedron i.

Parameters

index specifies which tetrahedron to return; this must be between 0 and size()-1 inclusive.

Returns: the requested tetrahedron.

◆ texName()

std::string regina::StandardTriangulation::texName ( ) const

inherited

Returns the name of this specific triangulation in TeX format.

No leading or trailing dollar signs will be included.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Returns: the name of this triangulation in TeX format.

◆ utf8()

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

inherited

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

Like str(), this text should be human-readable, should not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.

Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.

Returns: a short text representation of this object.

◆ vertexRoles()

Perm< 4 > regina::SpiralSolidTorus::vertexRoles ( size_t index ) const

inline

Returns a permutation represeting the role that each vertex of the requested tetrahedron plays in the solid torus.

The permutation returned (call this p) maps 0, 1, 2 and 3 to the four vertices of tetrahedron index so that vertices p[0], p[1], p[2] and p[3] correspond to vertices A, B, C and D respectively as described in the general class notes.

In particular, the directed edge from vertex p[0] to p[3] is an axis edge, directed edges p[0] to p[2] and p[1] to p[3] are minor edges and the directed path from vertices p[0] to p[1] to p[2] to p[3] follows the three major edges.

See the general class notes for further details.

Parameters

index specifies which tetrahedron in the solid torus to examine; this must be between 0 and size()-1 inclusive.

Returns: a permutation representing the roles of the vertices of the requested tetrahedron.

◆ writeName()

std::ostream & regina::SpiralSolidTorus::writeName ( std::ostream & out ) const

inlineoverridevirtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python: Not present. Instead use the variant name() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::StandardTriangulation.

◆ writeTeXName()

std::ostream & regina::SpiralSolidTorus::writeTeXName ( std::ostream & out ) const

inlineoverridevirtual

Writes the name of this triangulation in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Python: Not present. Instead use the variant texName() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::StandardTriangulation.

◆ writeTextLong()

void regina::StandardTriangulation::writeTextLong ( std::ostream & out ) const

inlinevirtualinherited

Writes a detailed text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeTextShort().

Python: Not present. Use detail() instead.

Parameters

out	the output stream to which to write.

Reimplemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, and regina::TrivialTri.

◆ writeTextShort()

void regina::SpiralSolidTorus::writeTextShort ( std::ostream & out ) const

overridevirtual

Writes a short text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeName().

Python: Not present. Use str() instead.

Parameters

out	the output stream to which to write.

Reimplemented from regina::StandardTriangulation.

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

subcomplex/spiralsolidtorus.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ SpiralSolidTorus() [1/2]

◆ SpiralSolidTorus() [2/2]

◆ ~SpiralSolidTorus()

Member Function Documentation

◆ cycle()

◆ detail()

◆ homology()

◆ isCanonical()

◆ makeCanonical()

◆ manifold()

◆ name()

◆ operator!=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ recognise() [1/3]

◆ recognise() [2/3]

◆ recognise() [3/3]

◆ reverse()

◆ size()

◆ str()

◆ swap()

◆ tetrahedron()

◆ texName()

◆ utf8()

◆ vertexRoles()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()