A component of the boundary of a dim-manifold triangulation. More...

#include <triangulation/generic.h>

Inheritance diagram for regina::BoundaryComponent< dim >:

Public Member Functions
size_t	index () const
	Returns the index of this boundary component in the underlying triangulation. More...

size_t	size () const
	Returns the number of (dim-1)-faces in this boundary component. More...

size_t	countRidges () const
	Returns the number of (dim-2)-faces in this boundary component. More...

template<int subdim>
size_t	countFaces () const
	Returns the number of subdim-faces in this boundary component. More...

size_t	countVertices () const
	A dimension-specific alias for countFaces<0>(). More...

size_t	countEdges () const
	A dimension-specific alias for countFaces<1>(). More...

size_t	countTriangles () const
	A dimension-specific alias for countFaces<2>(). More...

size_t	countTetrahedra () const
	A dimension-specific alias for countFaces<3>(). More...

size_t	countPentachora () const
	A dimension-specific alias for countFaces<4>(). More...

auto	facets () const
	Returns an object that allows iteration through and random access to all (dim-1)-faces in this boundary component. More...

template<int subdim>
auto	faces () const
	Returns an object that allows iteration through and random access to all subdim-faces in this boundary component. More...

auto	vertices () const
	A dimension-specific alias for faces<0>(). More...

auto	edges () const
	A dimension-specific alias for faces<1>(). More...

auto	triangles () const
	A dimension-specific alias for faces<2>(). More...

auto	tetrahedra () const
	A dimension-specific alias for faces<3>(). More...

auto	pentachora () const
	A dimension-specific alias for faces<4>(). More...

Face< dim, dim-1 > *	facet (size_t index) const
	Returns the requested (dim-1)-face in this boundary component. More...

template<int subdim>
Face< dim, subdim > *	face (size_t index) const
	Returns the requested subdim-face in this boundary component. More...

Face< dim, 0 > *	vertex (size_t index) const
	A dimension-specific alias for face<0>(). More...

Face< dim, 1 > *	edge (size_t index) const
	A dimension-specific alias for face<1>(). More...

Face< dim, 2 > *	triangle (size_t index) const
	A dimension-specific alias for face<2>(). More...

Face< dim, 3 > *	tetrahedron (size_t index) const
	A dimension-specific alias for face<3>(). More...

Face< dim, 4 > *	pentachoron (size_t index) const
	A dimension-specific alias for face<4>(). More...

Triangulation< dim > &	triangulation () const
	Returns the triangulation to which this boundary component belongs. More...

Component< dim > *	component () const
	Returns the connected component of the triangulation to which this boundary component belongs. More...

bool	isOrientable () const
	Determines if this boundary component is orientable. More...

long	eulerChar () const
	Returns the Euler characteristic of this boundary component. More...

bool	isReal () const
	Determines if this boundary component is real. 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...

const Triangulation< dim-1 > &	build () const
	Returns the full (dim-1)-dimensional triangulation of this boundary component. 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
	A default implementation for detailed output. 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...

size_t	markedIndex () const
	Returns the index at which this object is stored in an MarkedVector. More...

Static Public Attributes
static constexpr int	dimension = dim
	A compile-time constant that gives the dimension of the triangulation that contains this boundary component. More...

static constexpr bool	allowVertex = standardDim(dim) && (dim > 2)
	A compile-time constant indicating whether ideal and/or invalid vertex boundary components are both possible and recognised by this boundary component class. More...

static constexpr bool	canBuild = (dim > 2)
	A compile-time constant indicating whether this boundary component class supports triangulating boundary components. More...

static constexpr bool	allFaces = standardDim(dim)
	A compile-time constant indicating whether this boundary component class stores all lower-dimensional faces (`true`), or only faces of dimension dim-1 (`false`). More...

Protected Attributes
bool	orientable_
	Is this boundary component orientable? More...

EnableIf< canBuild, Triangulation< dim-1 > *, nullptr >	boundary_
	A full triangulation of the boundary component. More...

Friends
class	Triangulation< dim >

class	detail::TriangulationBase< dim >

Detailed Description

template<int dim>
class regina::BoundaryComponent< dim >

A component of the boundary of a dim-manifold triangulation.

Regina recognises three types of boundary components:

A real boundary component is formed from unglued facets of top-dimensional simplices of the triangulation. For example, a real boundary component of a 3-manifold triangulation is formed from boundary triangles in the 2-skeleton.
An ideal boundary component consists of a single ideal vertex; that is, a vertex whose link is a closed (dim-1)-manifold but not a sphere. This is only possible for dimensions dim ≥ 3.
An invalid vertex boundary component consists of a single invalid invalid vertex that does not belong to a real boundary component. This means the vertex link must be an ideal (dim-1)-manifold, or an invalid (dim-1)-manifold with no real boundary. Invalid vertex boundary components are only possible for dimensions dim ≥ 4.

Ideal and invalid vertex boundary components are only recognised when dim is one of Regina's standard dimensions. This is because, in higher dimensions, the relevant conditions rely on undecidable problems.

Regina stores different skeletal information for different types of boundary components:

For real boundary components in standard dimensions, Regina stores all boundary faces of all dimensions 0,1,...,dim-1.
For real boundary components in higher (non-standard) dimensions, Regina only stores the boundary (dim-1)-faces (i.e., the unglued facets of top-dimensional simplices that make up the boundary component). This is simply to avoid excessive memory usage.
For ideal and invalid vertex boundary components, Regina stores the relevant vertex. Such boundary components do not contain any faces of any dimension greater than zero.

We can encounter some interesting cases with invalid triangulations. Consider some face whose link has more than one boundary component (which makes the face invalid). This means that different parts of the (dim)-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 face will be included in all of these boundary components. Nevertheless, only one of these can be considered the "official" boundary component of the face as returned by Face::boundaryComponent(). This is all a bit of a mess, but then again the entire triangulation is invalid and so you almost certainly have bigger problems to deal with.

Boundary components are highly temporary: whenever a triangulation changes, all of its boundary component objects will be deleted and new ones will be created in their place.

Boundary components do not support value semantics: they cannot be copied, swapped, or manually constructed. Their location in memory defines them, and they are often passed and compared by pointer. End users are never responsible for their memory management; this is all taken care of by the Triangulation to which they belong.

Python: Python does not support templates. Instead this class can be used by appending the dimension as a suffix (e.g., BoundaryComponent2 and BoundaryComponent3 for dimensions 2 and 3).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

Member Function Documentation

◆ build()

template<int dim>

const Triangulation< dim-1 > & regina::detail::BoundaryComponentBase< dim >::build ( ) const

inlineinherited

Returns the full (dim-1)-dimensional 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 is a real boundary component (i.e., it is built from one or more (dim-1)-faces), then the triangulation of this boundary component is as follows:

Let i lie between 0 and size()-1 inclusive. Then simplex i of the returned (dim-1)-dimensional triangulation is a copy of facet(i) of this boundary component, and its vertices 0,...,dim-1 are numbered in the same way. To relate these (dim-1)-face vertex numbers to the vertex numbers of top-dimensional simplices in the overall dim-dimensional triangulation, see Simplex<dim>::faceMapping<dim-1>().
If this boundary component stores lower-dimensional faces (i.e., if the class constant allFaces is true), then a similar correspondence holds for these lower-dimensional faces also: for each i, k-face i of the returned triangulation is a copy of face<k>(i) of this boundary component, and its vertices are numbered in the same way. As an exception, this correspondence will not hold for dimensions k where there exist pinched k-faces on the boundary (i.e., faces where different sections of the boundary are pinched together, meaning that these faces must be duplicated when the boundary is triangulated).

If this boundary component consists only of a single vertex (i.e., this is an ideal or invalid vertex boundary component), then this routine returns the triangulation of the corresponding vertex link. See Vertex::buildLink() for details.

This routine is fast, since it caches the boundary triangulation. Moreover, it is guaranteed that the full skeleton of this (dim-1)-dimensional triangulation will have been generated already.

Precondition: The dimension dim is greater than 2.

Returns: the triangulation of this boundary component.

◆ component()

template<int dim>

Component< dim > * regina::detail::BoundaryComponentBase< dim >::component ( ) const

inlineinherited

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

Returns: the component containing this boundary component.

◆ countEdges()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countEdges ( ) const

inlineinherited

A dimension-specific alias for countFaces<1>().

This alias is available only when dim is one of Regina's standard dimensions.

See countFaces() for further information.

◆ countFaces()

template<int dim>

template<int subdim>

size_t regina::detail::BoundaryComponentBase< dim >::countFaces ( ) const

inlineinherited

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

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.

Template Parameters

subdim the dimension of the faces to query. If dim is one of Regina's standard dimensions, then subdim must be between 0 and dim-1 inclusive. Otherwise, the only allowable values of subdim are the facet dimension (dim-1) and the ridge dimension (dim-2).

Returns: the number of subdim-faces.

◆ countPentachora()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countPentachora ( ) const

inlineinherited

A dimension-specific alias for countFaces<4>().

This alias is only available for dimensions dim = 5 and 6.

See countFaces() for further information.

◆ countRidges()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countRidges ( ) const

inlineinherited

Returns the number of (dim-2)-faces in this boundary component.

If this is an ideal or invalid vertex boundary component, then this routine will return 0.

Returns: the number of (dim-2)-faces in this boundary component.

◆ countTetrahedra()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countTetrahedra ( ) const

inlineinherited

A dimension-specific alias for countFaces<3>().

This alias is only available for dimensions dim = 4 and 5.

See countFaces() for further information.

◆ countTriangles()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countTriangles ( ) const

inlineinherited

A dimension-specific alias for countFaces<2>().

This alias is available only when dim is one of Regina's standard dimensions and dim ≥ 3.

See countFaces() for further information.

◆ countVertices()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::countVertices ( ) const

inlineinherited

A dimension-specific alias for countFaces<0>().

This alias is available only when dim is one of Regina's standard dimensions.

See countFaces() for further information.

◆ detail()

std::string regina::Output< BoundaryComponentBase< dim > , supportsUtf8 >::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.

◆ edge()

template<int dim>

Face< dim, 1 > * regina::detail::BoundaryComponentBase< dim >::edge ( size_t index ) const

inlineinherited

A dimension-specific alias for face<1>().

This alias is available only when dim is one of Regina's standard dimensions.

See face() for further information.

◆ edges()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::edges ( ) const

inlineinherited

A dimension-specific alias for faces<1>().

This alias is available only when dim is one of Regina's standard dimensions.

See faces() for further information.

◆ eulerChar()

template<int dim>

long regina::detail::BoundaryComponentBase< dim >::eulerChar ( ) const

inlineinherited

Returns the Euler characteristic of this boundary component.

If the boundary component consists of a single vertex and nothing else (e.g., it is an ideal vertex), then the Euler characteristic of the vertex link will be returned.

This function is, in all "normal" cases, equivalent to triangulating the boundary component via build() and then calling Triangulation<dim-1>::eulerCharTri() on the result.

The exception comes from triangulations with "pinched" faces whose links have multiple boundary components (e.g., a vertex whose link is a multiply-punctured sphere, marking a point where different parts of the boundary are "pinched together"). If there are such faces, then this routine will return a well-defined but topologically meaningless result. Essentially, this routine only counts such faces once, even though they "should" be counted multiple times on the boundary since they can be "seen" from distinct sections of the (dim-1)-dimensional boundary. Of course such a triangulation cannot represent a dim-manifold anyway, and so if you do have pinched faces then you almost certainly have bigger problems to deal with.

Precondition: dim is one of Regina's standard dimensions.

Warning: If this boundary component itself forms an ideal (dim-1)-dimensional triangulation, then again this result is well-defined but topologically meaningless (since it is equivalent to calling eulerCharTri() and not eulerCharManifold() on the triangulated boundary). However, again such boundary components cannot appear in a dim-manifold, and so if you have such boundary components then you almost certainly have bigger problems than this.

Returns: the Euler characteristic of this boundary component.

◆ face()

template<int dim>

template<int subdim>

Face< dim, subdim > * regina::detail::BoundaryComponentBase< dim >::face ( size_t index ) const

inlineinherited

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 is a real boundary component (i.e., it is built from one or more (dim-1)-faces), then the index of each subdim-face in this boundary component will match the index of the corresponding subdim-face in the (dim-1)-manifold triangulation returned by build().

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.

Template Parameters

subdim the dimension of the faces to query. If dim is one of Regina's standard dimensions, then subdim must be between 0 and dim-1 inclusive. Otherwise, the only allowable value of subdim is the facet dimension (dim-1).

Parameters

index the index of the desired face, ranging from 0 to countFaces<subdim>()-1 inclusive.

Returns: the requested face.

◆ faces()

template<int dim>

template<int subdim>

auto regina::detail::BoundaryComponentBase< dim >::faces ( ) const

inlineinherited

Returns an object that allows iteration through and random access to all subdim-faces in this boundary component.

The object that is returned is lightweight, and can be happily copied by value. The C++ type of the object is subject to change, so C++ users should use auto (just like this declaration does).

The returned object is guaranteed to be an instance of ListView, which means it offers basic container-like functions and supports range-based for loops. Note that the elements of the list will be pointers, so your code might look like:

for (Face<dim, subdim>* f : bc.faces<subdim>()) { ... }

The object that is returned will remain valid only for as long as this boundary component object exists. In particular, the object will become invalid any time that the triangulation changes (since all boundary component objects will be destroyed and others rebuilt in their place). Therefore it is best to treat this object as temporary only, and to call faces() again each time you need it.

Python: Python does not support templates. Instead, Python users should call this function in the form faces(subdim).

Template Parameters

subdim the dimension of the faces to query. If dim is one of Regina's standard dimensions, then subdim must be between 0 and dim-1 inclusive. Otherwise, the only allowable value of subdim is the facet dimension (dim-1).

Returns: access to the list of all subdim-faces.

◆ facet()

template<int dim>

Face< dim, dim-1 > * regina::detail::BoundaryComponentBase< dim >::facet ( size_t index ) const

inlineinherited

Returns the requested (dim-1)-face in this boundary component.

These are the top-dimensional faces for a real 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 is a real boundary component (i.e., it is built from one or more (dim-1)-faces), then the index of each (dim-1)-face in this boundary component will match the index of the corresponding top-dimensional simplex in the (dim-1)-manifold triangulation returned by build().

Parameters

index the index of the desired face, ranging from 0 to size()-1 inclusive.

Returns: the requested face.

◆ facets()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::facets ( ) const

inlineinherited

Returns an object that allows iteration through and random access to all (dim-1)-faces in this boundary component.

The object that is returned is lightweight, and can be happily copied by value. The C++ type of the object is subject to change, so C++ users should use auto (just like this declaration does).

The returned object is guaranteed to be an instance of ListView, which means it offers basic container-like functions and supports range-based for loops. Note that the elements of the list will be pointers, so your code might look like:

for (Face<dim, dim-1>* f : bc.facets()) { ... }

The object that is returned will remain valid only for as long as this boundary component object exists. In particular, the object will become invalid any time that the triangulation changes (since all boundary component objects will be destroyed and others rebuilt in their place). Therefore it is best to treat this object as temporary only, and to call facets() again each time you need it.

Returns: access to the list of all (dim-1)-faces.

◆ index()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::index ( ) const

inlineinherited

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

Returns: the index of this boundary component.

◆ isIdeal()

template<int dim>

bool regina::detail::BoundaryComponentBase< dim >::isIdeal ( ) const

inlineinherited

Determines if this boundary component is ideal.

This is the case if and only if it consists of a single ideal vertex and no faces of any other dimensions.

See the BoundaryComponent class notes for an overview of ideal boundary components, which can only occur in dimensions ≥ 3, and which are only recognised where dim is one of Regina's standard dimensions.

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 faces of positive dimension, then one and only one of isIdeal() and isInvalidVertex() will return true.

Note: If dim is not one of Regina's standard dimensions, then real boundary components are the only types of boundary component that Regina will recognise, which means that this routine will always return false.

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

◆ isInvalidVertex()

template<int dim>

bool regina::detail::BoundaryComponentBase< dim >::isInvalidVertex ( ) const

inlineinherited

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

In particular, such a boundary component must contain no faces of any positive dimension.

See the BoundaryComponent class notes for an overview of invalid vertex boundary components, which can only occur in dimensions ≥ 4, and which are only recognised where dim is one of Regina's standard dimensions.

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 (dim-1)-manifold triangulation). This means that, for a boundary component consisting of one or more (dim-1)-faces, this routine will return false even if the boundary component also includes one or more invalid vertices.

Note that, if a boundary component contains no faces of positive dimension, then one and only one of isIdeal() and isInvalidVertex() will return true.

Note: If dim is not one of Regina's standard dimensions, then real boundary components are the only types of boundary component that Regina will recognise, which means that this routine will always return false.

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

◆ isOrientable()

template<int dim>

bool regina::detail::BoundaryComponentBase< dim >::isOrientable ( ) const

inlineinherited

Determines if this boundary component is orientable.

If this is an ideal or invalid vertex boundary component, then the orientability of the corresponding vertex link is returned.

This routine is fast; in particular, it is pre-computed and does not build a full triangulation of the boundary component.

Returns: true if and only if this boundary component is orientable.

◆ isReal()

template<int dim>

bool regina::detail::BoundaryComponentBase< dim >::isReal ( ) const

inlineinherited

Determines if this boundary component is real.

This is the case if and only if it is formed from one or more (dim-1)-faces.

See the BoundaryComponent class notes for an overview of real, ideal, and invalid vertex boundary components.

Note: If dim is not one of Regina's standard dimensions, then real boundary components are the only types of boundary component that Regina will recognise, which means that this routine will always return true.

Returns: true if and only if this boundary component is real.

◆ markedIndex()

size_t regina::MarkedElement::markedIndex ( ) const

inlineinherited

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

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

Returns: the index at which this object is stored.

◆ pentachora()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::pentachora ( ) const

inlineinherited

A dimension-specific alias for faces<4>().

This alias is only available for dimension dim = 5.

See faces() for further information.

◆ pentachoron()

template<int dim>

Face< dim, 4 > * regina::detail::BoundaryComponentBase< dim >::pentachoron ( size_t index ) const

inlineinherited

A dimension-specific alias for face<4>().

This alias is only available for dimension dim = 5.

See face() for further information.

◆ size()

template<int dim>

size_t regina::detail::BoundaryComponentBase< dim >::size ( ) const

inlineinherited

Returns the number of (dim-1)-faces in this boundary component.

These are the top-dimensional faces for a real boundary component.

If this is an ideal or invalid vertex boundary component, then this routine will return 0.

Returns: the number of (dim-1)-faces in this boundary component.

◆ str()

std::string regina::Output< BoundaryComponentBase< dim > , supportsUtf8 >::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.

◆ tetrahedra()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::tetrahedra ( ) const

inlineinherited

A dimension-specific alias for faces<3>().

This alias is only available for dimension dim = 4.

See faces() for further information.

◆ tetrahedron()

template<int dim>

Face< dim, 3 > * regina::detail::BoundaryComponentBase< dim >::tetrahedron ( size_t index ) const

inlineinherited

A dimension-specific alias for face<3>().

This alias is only available for dimension dim = 4.

See face() for further information.

◆ triangle()

template<int dim>

Face< dim, 2 > * regina::detail::BoundaryComponentBase< dim >::triangle ( size_t index ) const

inlineinherited

A dimension-specific alias for face<2>().

This alias is available only when dim is one of Regina's standard dimensions and dim ≥ 3.

See face() for further information.

◆ triangles()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::triangles ( ) const

inlineinherited

A dimension-specific alias for faces<2>().

This alias is available only when dim is one of Regina's standard dimensions and dim ≥ 3.

See faces() for further information.

◆ triangulation()

template<int dim>

Triangulation< dim > & regina::detail::BoundaryComponentBase< dim >::triangulation ( ) const

inlineinherited

Returns the triangulation to which this boundary component belongs.

Returns: a reference to the triangulation containing this boundary component.

◆ utf8()

std::string regina::Output< BoundaryComponentBase< dim > , supportsUtf8 >::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.

◆ vertex()

template<int dim>

Face< dim, 0 > * regina::detail::BoundaryComponentBase< dim >::vertex ( size_t index ) const

inlineinherited

A dimension-specific alias for face<0>().

This alias is available only when dim is one of Regina's standard dimensions.

See face() for further information.

◆ vertices()

template<int dim>

auto regina::detail::BoundaryComponentBase< dim >::vertices ( ) const

inlineinherited

A dimension-specific alias for faces<0>().

This alias is available only when dim is one of Regina's standard dimensions.

See faces() for further information.

◆ writeTextLong()

void regina::ShortOutput< BoundaryComponentBase< dim > , false >::writeTextLong ( std::ostream & out ) const

inlineinherited

A default implementation for detailed output.

This routine simply calls T::writeTextShort() and appends a final newline.

Python: Not present. Instead you can call detail() from the subclass T, which returns this output as a string.

Parameters

out	the output stream to which to write.

◆ writeTextShort()

template<int dim>

void regina::detail::BoundaryComponentBase< dim >::writeTextShort ( std::ostream & out ) const

inlineinherited

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

Python: Not present. Use str() instead.

Parameters

out	the output stream to which to write.

Member Data Documentation

◆ allFaces

template<int dim>

constexpr bool regina::detail::BoundaryComponentBase< dim >::allFaces = standardDim(dim)

staticconstexprinherited

A compile-time constant indicating whether this boundary component class stores all lower-dimensional faces (true), or only faces of dimension dim-1 (false).

◆ allowVertex

template<int dim>

constexpr bool regina::detail::BoundaryComponentBase< dim >::allowVertex = standardDim(dim) && (dim > 2)

staticconstexprinherited

A compile-time constant indicating whether ideal and/or invalid vertex boundary components are both possible and recognised by this boundary component class.

◆ boundary_

template<int dim>

EnableIf<canBuild, Triangulation<dim-1>*, nullptr> regina::detail::BoundaryComponentBase< dim >::boundary_

protectedinherited

A full triangulation of the boundary component.

This may be pre-computed when the triangulation skeleton is constructed, or it may be null in which case it will be built on demand. For ideal or invalid vertices, this is always null since the triangulation is cached by the vertex class instead. We keep this as pointer to avoid issues with cascading template instantiations (this allows us to work with forward declarations of lower-dimensional types instead).

◆ canBuild

template<int dim>

constexpr bool regina::detail::BoundaryComponentBase< dim >::canBuild = (dim > 2)

staticconstexprinherited

A compile-time constant indicating whether this boundary component class supports triangulating boundary components.

◆ dimension

template<int dim>

constexpr int regina::detail::BoundaryComponentBase< dim >::dimension = dim

staticconstexprinherited

A compile-time constant that gives the dimension of the triangulation that contains this boundary component.

◆ orientable_

template<int dim>

bool regina::detail::BoundaryComponentBase< dim >::orientable_

protectedinherited

Is this boundary component orientable?

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

triangulation/forward.h
triangulation/generic/boundarycomponent.h

Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Member Function Documentation

◆ build()

◆ component()

◆ countEdges()

◆ countFaces()

◆ countPentachora()

◆ countRidges()

◆ countTetrahedra()

◆ countTriangles()

◆ countVertices()

◆ detail()

◆ edge()

◆ edges()

◆ eulerChar()

◆ face()

◆ faces()

◆ facet()

◆ facets()

◆ index()

◆ isIdeal()

◆ isInvalidVertex()

◆ isOrientable()

◆ isReal()

◆ markedIndex()

◆ pentachora()

◆ pentachoron()

◆ size()

◆ str()

◆ tetrahedra()

◆ tetrahedron()

◆ triangle()

◆ triangles()

◆ triangulation()

◆ utf8()

◆ vertex()

◆ vertices()

◆ writeTextLong()

◆ writeTextShort()

Member Data Documentation

◆ allFaces

◆ allowVertex

◆ boundary_

◆ canBuild

◆ dimension

◆ orientable_