Regina Calculation Engine
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A component of the boundary of a 3-manifold triangulation. More...
#include <triangulation/dim3.h>
Public Member Functions | |
long | eulerChar () const |
Returns the Euler characteristic of this boundary component. More... | |
size_t | index () const |
Returns the index of this boundary component in the underlying triangulation. More... | |
bool | isOrientable () const |
Determines if this boundary component is orientable. 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... | |
const Triangulation< dim-1 > * | build () const |
Returns the full (dim-1)-dimensional triangulation 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... | |
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... | |
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... | |
size_t | countFaces () const |
Returns the number of subdim-faces in this boundary component. More... | |
const std::vector< Face< dim, dim-1 > *> & | facets () const |
Returns all (dim-1)-faces in this boundary component. More... | |
const std::vector< Face< dim, subdim > *> & | faces () const |
Returns all subdim-faces in this boundary component. More... | |
Face< dim, dim-1 > * | facet (size_t index) const |
Returns the requested (dim-1)-face in this boundary component. More... | |
Face< dim, subdim > * | face (size_t index) const |
Returns the requested subdim-face in this boundary component. 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... | |
size_t | markedIndex () const |
Returns the index at which this object is stored in an MarkedVector. More... | |
Static Public Attributes | |
static constexpr bool | canBuild |
A compile-time constant indicating whether this boundary component class supports triangulating boundary components. More... | |
static constexpr bool | allowVertex |
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 | allFaces |
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 Member Functions | |
const Triangulation< dim-1 > * | buildVertexLink () const |
Triangulates the vertex link for an ideal or invalid vertex boundary component. More... | |
void | push_back (Face< dim, subdim > *face) |
Pushes the given face onto the end of the list of subdim-faces of this boundary component. More... | |
void | reorderAndRelabelFaces (Triangulation< dim-1 > *tri) const |
Reorders all lower-dimensional faces of the given triangulation so that they appear in the same order as the corresponding faces of this boundary component, and relabels these faces so that their vertices are numbered in a corresponding way. More... | |
void | reorderAndRelabelFaces (Triangulation< tridim > *tri, const std::vector< Face< dim, tridim > * > &tridimFaces) const |
Reorders and relabels all faces of all dimensions 0,...,subdim of the given triangulation, so that for each k, the k-faces of the given triangulation appear in the same order as the corresponding k-faces in this suite, and have their vertices numbered in a corresponding way. More... | |
Protected Attributes | |
bool | orientable_ |
Is this boundary component orientable? More... | |
Triangulation< dim-1 > * | boundary_ |
A full triangulation of the boundary component. More... | |
std::vector< Face< dim, subdim > * > | faces_ |
The list of faces. More... | |
Friends | |
class | Triangulation< 3 > |
class | detail::TriangulationBase< 3 > |
A component of the boundary of a 3-manifold triangulation.
This is a specialisation of the generic BoundaryComponent class template; see the BoundaryComponent documentation for an overview of how this class works.
This 3-dimensional specialisation contains some extra functionality. In particular, it allows you to query the Euler characteristic and orientability of a boundary component, without the heavyweight process of triangulating the boundary component first.
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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:
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>().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.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::link() 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.
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inlineprotectedinherited |
Triangulates the vertex link for an ideal or invalid vertex boundary component.
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inlineinherited |
Returns the connected component of the triangulation to which this boundary component belongs.
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inlineinherited |
Returns the number of subdim-faces in this boundary component.
This routine is only available where dim is one of Regina's standard dimensions.
countFaces(subdim)
; that is, the template parameter subdim becomes the first argument of the function.subdim | the dimension of the faces to query. This must be between 0 and dim-1 inclusive. |
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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.
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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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inline |
Returns the Euler characteristic of this boundary component.
If this boundary component is ideal, the Euler characteristic of the link of the corresponding ideal vertex is returned.
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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().
This routine is only available where dim is one of Regina's standard dimensions.
face(subdim, index)
; that is, the template parameter subdim becomes the first argument of the function.subdim | the dimension of the face to query. This must be between 0 and dim-1 inclusive. |
index | the index of the desired face, ranging from 0 to countFaces<subdim>()-1 inclusive. |
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inlineinherited |
Returns all subdim-faces in this boundary component.
The reference that is returned will remain valid only for as long as this boundary component object exists. In particular, the reference will become invalid any time that the triangulation changes (since all boundary component objects will be destroyed and others rebuilt in their place).
faces(subdim)
. It will then return a Python list containing all the subdim-faces of the boundary component. Be warned that, unlike in C++, this Python list will be a snapshot of the faces when this function is called, and will not be kept up-to-date as the triangulation changes.subdim | the dimension of the faces to query. This must be between 0 and dim-1 inclusive. |
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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().
index | the index of the desired face, ranging from 0 to size()-1 inclusive. |
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inlineinherited |
Returns all (dim-1)-faces in this boundary component.
The reference that is returned will remain valid only for as long as this boundary component object exists. In particular, the reference will become invalid any time that the triangulation changes (since all boundary component objects will be destroyed and others rebuilt in their place).
@return the list of all (<i>dim</i>-1)-faces.
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inlineinherited |
Returns the index of this boundary component in the underlying triangulation.
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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
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This routine is only available where dim is at least 3 and is one of Regina's standard dimensions.
true
if and only if this boundary component is ideal.
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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
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This routine is only available where dim is at least 3 and is one of Regina's standard dimensions.
true
if and only if this boundary component consists of a single invalid vertex and nothing else.
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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.
true
if and only if this boundary component is orientable.
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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.
This routine is only available where dim is at least 3 and is one of Regina's standard dimensions. (In other dimensions, real boundary components are the only types of boundary component that Regina will recognise.)
true
if and only if this boundary component is real.
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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.
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inlineprotectedinherited |
Pushes the given face onto the end of the list of subdim-faces of this boundary component.
This class does not take ownership of the given face.
subdim | the dimension of the face to append. This must be between 0 and dim-1 inclusive. |
face | the face to append to the list. |
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inlineprotectedinherited |
Reorders and relabels all faces of all dimensions 0,...,subdim of the given triangulation, so that for each k, the k-faces of the given triangulation appear in the same order as the corresponding k-faces in this suite, and have their vertices numbered in a corresponding way.
tri->simplex(j)
to the ith k-face of tridimFaces[j]
.tridim | the dimension of the given triangulation. This must be strictly larger than subdim, but it need not be equal to dim. |
tri | a tridim-dimensional triangulation, as described above. |
tridimFaces | a list of tridim-faces that together contain all of the faces in this suite, and that are in an ordered one-to-one correspondence with the top-dimensional simplices of tri as described in the precondition above. |
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inlineprotectedinherited |
Reorders all lower-dimensional faces of the given triangulation so that they appear in the same order as the corresponding faces of this boundary component, and relabels these faces so that their vertices are numbered in a corresponding way.
This affects all faces of dimensions 0,...,(dim-2).
tri | a triangulation of this boundary component, as described above. |
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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.
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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.
__str__()
.
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inlineinherited |
Returns the triangulation to which this boundary component belongs.
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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 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.
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inlineinherited |
Writes a detailed text representation of this object to the given output stream.
out | the output stream to which to write. |
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inlineinherited |
Writes a short text representation of this object to the given output stream.
out | the output stream to which to write. |
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staticinherited |
A compile-time constant indicating whether this boundary component class stores all lower-dimensional faces (true
), or only faces of dimension dim-1 (false
).
This is a compile-time constant only, with no linkage - any attempt to create a reference or pointer to it will give a linker error.
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staticinherited |
A compile-time constant indicating whether ideal and/or invalid vertex boundary components are both possible and recognised by this boundary component class.
This is a compile-time constant only, with no linkage - any attempt to create a reference or pointer to it will give a linker error.
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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.
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staticinherited |
A compile-time constant indicating whether this boundary component class supports triangulating boundary components.
This is a compile-time constant only, with no linkage - any attempt to create a reference or pointer to it will give a linker error.
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protectedinherited |
The list of faces.
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protectedinherited |
Is this boundary component orientable?