Regina 7.0 Calculation Engine
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Represents a spiralled solid torus in a triangulation. More...
#include <subcomplex/spiralsolidtorus.h>
Public Member Functions | |
SpiralSolidTorus (const SpiralSolidTorus &src) | |
Creates a new copy of this 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... | |
SpiralSolidTorus * | clone () const |
Deprecated routine that returns a new copy of this 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... | |
std::string | TeXName () const |
Deprecated routine that returns the name of this specific triangulation in TeX format. More... | |
AbelianGroup | homologyH1 () const |
A deprecated alias for homology(). 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< SpiralSolidTorus > | formsSpiralSolidTorus (Tetrahedron< 3 > *tet, Perm< 4 > useVertexRoles) |
A deprecated alias to recognise if a tetrahedron forms part of a spiral solid torus with its vertices playing given roles. 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... | |
static std::unique_ptr< StandardTriangulation > | isStandardTriangulation (Component< 3 > *component) |
A deprecated alias to determine whether a component represents one of the standard triangulations understood by Regina. More... | |
static std::unique_ptr< StandardTriangulation > | isStandardTriangulation (const Triangulation< 3 > &tri) |
A deprecated alias to determine whether a triangulation represents one of the standard triangulations understood by Regina. More... | |
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().
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inline |
Creates a new copy of this structure.
This will induce a deep copy of src.
src | the structure to copy. |
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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.
src | the structure to move from. |
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inlineoverride |
Destroys this structure.
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inline |
Deprecated routine that returns a new copy of this structure.
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.
k | the number of tetrahedra through which we should cycle. |
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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.
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inlinestatic |
A deprecated alias to recognise if a tetrahedron forms part of a spiral solid torus with its vertices playing given roles.
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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.
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. |
Reimplemented from regina::StandardTriangulation.
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inlineinherited |
A deprecated alias for homology().
NotImplemented | homology calculation has not yet been implemented for this particular type of standard triangulation. |
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().
true
if and only if this spiralled solid torus is in canonical form.
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inlinestaticinherited |
A deprecated alias to determine whether a component represents one of the standard triangulations understood by Regina.
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inlinestaticinherited |
A deprecated alias to determine whether a triangulation represents one of the standard triangulations understood by Regina.
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.
true
if and only if the representation of this spiralled solid torus was actually changed.
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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.
Reimplemented from regina::StandardTriangulation.
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inherited |
Returns the name of this specific triangulation as a human-readable string.
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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).
other | the structure with which this will be compared. |
true
if and only if this and the given structure represent different types of spiralled solid torus. 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.
src | the structure to copy. |
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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.
src | the structure to move from. |
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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).
other | the structure with which this will be compared. |
true
if and only if this and the given structure represent the same type of spiralled solid torus.
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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.
component | the triangulation component under examination. |
null
otherwise.
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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.
tri | the triangulation under examination. |
null
otherwise.
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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.
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(). |
null
if the given tetrahedron is not part of a spiralled solid torus with the given vertex roles. 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.
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inline |
Returns the number of tetrahedra in this spiralled solid torus.
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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.
str()
will use precisely this function, and for most classes the Python repr()
function will incorporate this into its output.
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inlinenoexcept |
Swaps the contents of this and the given structure.
other | the structure whose contents should be swapped with this. |
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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.
index | specifies which tetrahedron to return; this must be between 0 and size()-1 inclusive. |
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inherited |
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
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inlineinherited |
Deprecated routine that returns the name of this specific triangulation in TeX format.
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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.
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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.
index | specifies which tetrahedron in the solid torus to examine; this must be between 0 and size()-1 inclusive. |
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inlineoverridevirtual |
Writes the name of this triangulation as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::StandardTriangulation.
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inlineoverridevirtual |
Writes the name of this triangulation in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out | the output stream to which to write. |
Implements regina::StandardTriangulation.
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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().
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.
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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().
out | the output stream to which to write. |
Reimplemented from regina::StandardTriangulation.