Regina Calculation Engine
Public Member Functions | Friends | List of all members
regina::Dim4BoundaryComponent Class Reference

Represents a component of the boundary of a 4-manifold triangulation. More...

#include <dim4/dim4boundarycomponent.h>

Inheritance diagram for regina::Dim4BoundaryComponent:
regina::Output< Dim4BoundaryComponent > regina::alias::FaceOfTriangulation< Dim4BoundaryComponent, 4 > regina::NMarkedElement

Public Member Functions

 ~Dim4BoundaryComponent ()
 Default destructor. More...
 
REGINA_INLINE_REQUIRED size_t index () const
 Returns the index of this boundary component in the underlying triangulation. More...
 
template<int subdim>
size_t countFaces () const
 Returns the number of subdim-faces in this boundary component. More...
 
template<int subdim>
Face< 4, subdim > * face (size_t index) const
 Returns the requested subdim-face in this boundary component. More...
 
Dim4Componentcomponent () const
 Returns the component of the triangulation to which this boundary component belongs. More...
 
REGINA_DEPRECATED Dim4ComponentgetComponent () const
 Deprecated routine that returns the component of the triangulation to which this boundary component belongs. More...
 
const NTriangulationbuild () const
 Returns the full 3-manifold triangulation of this boundary component. More...
 
bool isIdeal () const
 Determines if this boundary component is ideal. More...
 
bool isInvalidVertex () const
 Determines if this boundary component consists of a single invalid vertex and nothing else. More...
 
void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object to the given output stream. More...
 
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...
 
REGINA_DEPRECATED std::string toString () const
 A deprecated alias for str(). More...
 
REGINA_DEPRECATED std::string toStringLong () const
 A deprecated alias for detail(). More...
 
size_t markedIndex () const
 Returns the index at which this object is stored in an NMarkedVector. More...
 

Friends

class Triangulation< 4 >
 Allow access to private members. More...
 

Detailed Description

Represents a component of the boundary of a 4-manifold triangulation.

Note that an ideal vertex constitutes a boundary component of its own - it consists of one vertex, no edges, no triangles, and no tetrahedra. Likewise, an invalid vertex is placed in its own boundary component if it does not already belong to some larger boundary component (for instance, if its link is an ideal 3-manifold triangulation). See Dim4Vertex::isBoundary() for details.

We can encounter some interesting cases with invalid triangulations. Consider some vertex in a 4-manifold triangulation. If the link of this vertex is itself a 3-manifold with more than one boundary component (which makes the vertex invalid), then different parts of the 4-manifold boundary are effectively "pinched" together. If this happens, the different parts of the boundary that are pinched might or might not be listed as part of the same boundary component; if not then the offending vertex will be included in all of these boundary components. Nevertheless, only one of these can be considered the "official" boundary component of the vertex as returned by Dim4Vertex::boundaryComponent(). This is all a bit of a mess (and even more so when you consider that the same thing can happen with invalid edges), but then again the entire 4-manifold triangulation is invalid and so you almost certainly have bigger problems to deal with.

Boundary components are highly temporary; once a triangulation changes, all its boundary component objects will be deleted and new ones will be created.

Constructor & Destructor Documentation

§ ~Dim4BoundaryComponent()

regina::Dim4BoundaryComponent::~Dim4BoundaryComponent ( )

Default destructor.

Member Function Documentation

§ build()

const NTriangulation * regina::Dim4BoundaryComponent::build ( ) const
inline

Returns the full 3-manifold triangulation of this boundary component.

Note that this triangulation is read-only (though of course you can clone it and then operate upon the clone).

If this boundary component contains one or more tetrahedra (i.e., it is a regular boundary built from pentachoron facets), then the triangulation of this boundary component is as follows. Let i lie between 0 and countTetrahedra()-1 inclusive. Then tetrahedron i of the boundary 3-manifold triangulation is a copy of tetrahedron tetrahedron(i) of this 4-manifold boundary component, and its vertices 0,1,2,3 are numbered in the same way. To relate tetrahedron vertex numbers to pentachoron vertex numbers, see Dim4Pentachoron::tetrahedronMapping().

If this boundary component consists only of a single vertex (which happens with ideal vertices and also some invalid vertices), then this routine returns the triangulation of the corresponding vertex link. See Dim4Vertex::link() for details.

This routine is fast (it uses a pre-computed triangulation). Moreover, it is guaranteed that the full skeleton of this 3-manifold triangulation will have been generated already.

Returns
the triangulation of this boundary component.

§ component()

Dim4Component * regina::Dim4BoundaryComponent::component ( ) const
inline

Returns the component of the triangulation to which this boundary component belongs.

Returns
the component containing this boundary component.

§ countFaces()

template<int subdim>
size_t regina::Dim4BoundaryComponent::countFaces ( ) const

Returns the number of subdim-faces in this boundary component.

Precondition
The template argument subdim is between 0 and 3 inclusive.
Python:
Python does not support templates. Instead, Python users should call this function in the form countFaces(subdim); that is, the template parameter subdim becomes the first argument of the function.
Returns
the number of subdim-faces.

§ detail()

std::string regina::Output< Dim4BoundaryComponent , 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.

§ face()

template<int subdim>
Face<4, subdim>* regina::Dim4BoundaryComponent::face ( size_t  index) const

Returns the requested subdim-face in this boundary component.

Note that the index of a face in the boundary component need not be the index of the same face in the overall triangulation. However, if this boundary component is built from one or more tetrahedra (i.e., it is not ideal), then the index of each subdim-face in this boundary component matches the index of the corresponding subdim-face in the 3-manifold triangulation returned by build().

Precondition
The template argument subdim is between 0 and 3 inclusive.
Python:
Python does not support templates. Instead, Python users should call this function in the form face(subdim, index); that is, the template parameter subdim becomes the first argument of the function.
Parameters
indexthe index of the desired face, ranging from 0 to countFaces<subdim>()-1 inclusive.
Returns
the requested face.

§ getComponent()

Dim4Component * regina::Dim4BoundaryComponent::getComponent ( ) const
inline

Deprecated routine that returns the component of the triangulation to which this boundary component belongs.

Deprecated:
This routine has been renamed to component(). See the component() documentation for further details.

§ index()

size_t regina::Dim4BoundaryComponent::index ( ) const
inline

Returns the index of this boundary component in the underlying triangulation.

This is identical to calling the deprecated function boundaryComponentIndex(this) on the underlying triangulation.

Returns
the index of this boundary component.

§ isIdeal()

bool regina::Dim4BoundaryComponent::isIdeal ( ) const

Determines if this boundary component is ideal.

This is the case if and only if it consists of a single ideal vertex and no tetrahedra.

Note that a boundary component formed from a single invalid vertex is not considered to be ideal. This means that, if a boundary component contains no tetrahedra at all, then one and only one of isIdeal() and isInvalidVertex() will return true.

Returns
true if and only if this boundary component is ideal.

§ isInvalidVertex()

bool regina::Dim4BoundaryComponent::isInvalidVertex ( ) const

Determines if this boundary component consists of a single invalid vertex and nothing else.

In particular, such a boundary component must contain no tetrahedra at all.

An invalid vertex is only placed in its own boundary component if it does not already belong to some larger boundary component (for instance, if its link is an ideal 3-manifold triangulation). This means that, for a boundary component consisting of one or more tetrahedra, this routine will return false even if the boundary tetrahedra include one or more invalid vertices.

Note that, if a boundary component contains no tetrahedra at all, then one and only one of isIdeal() and isInvalidVertex() will return true.

Returns
true if and only if this boundary component consists of a single invalid vertex and nothing else.

§ markedIndex()

size_t regina::NMarkedElement::markedIndex ( ) const
inlineinherited

Returns the index at which this object is stored in an NMarkedVector.

If this object does not belong to an NMarkedVector, the return value is undefined.

Returns
the index at which this object is stored.

§ str()

std::string regina::Output< Dim4BoundaryComponent , 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:
In addition to str(), this is also used as the Python "stringification" function __str__().
Returns
a short text representation of this object.

§ toString()

REGINA_DEPRECATED std::string regina::Output< Dim4BoundaryComponent , false >::toString ( ) const
inherited

A deprecated alias for str().

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

§ toStringLong()

REGINA_DEPRECATED std::string regina::Output< Dim4BoundaryComponent , false >::toStringLong ( ) const
inherited

A deprecated alias for detail().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.

§ utf8()

std::string regina::Output< Dim4BoundaryComponent , 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.

§ writeTextLong()

void regina::Dim4BoundaryComponent::writeTextLong ( std::ostream &  out) const

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

Python:
Not present.
Parameters
outthe output stream to which to write.

§ writeTextShort()

void regina::Dim4BoundaryComponent::writeTextShort ( std::ostream &  out) const
inline

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

Python:
Not present.
Parameters
outthe output stream to which to write.

Friends And Related Function Documentation

§ Triangulation< 4 >

friend class Triangulation< 4 >
friend

Allow access to private members.


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

Copyright © 1999-2016, 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).