Regina Calculation Engine
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Represents a component of the boundary of a 4-manifold triangulation. More...
#include <dim4/dim4boundarycomponent.h>
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... | |
Dim4Component * | component () const |
Returns the component of the triangulation to which this boundary component belongs. More... | |
REGINA_DEPRECATED Dim4Component * | getComponent () const |
Deprecated routine that returns the component of the triangulation to which this boundary component belongs. More... | |
const NTriangulation * | build () 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... | |
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.
regina::Dim4BoundaryComponent::~Dim4BoundaryComponent | ( | ) |
Default destructor.
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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.
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inline |
Returns the component of the triangulation to which this boundary component belongs.
size_t regina::Dim4BoundaryComponent::countFaces | ( | ) | const |
Returns the number of subdim-faces in this boundary component.
countFaces(subdim)
; that is, the template parameter subdim becomes the first argument of the function.
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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.
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().
face(subdim, index)
; that is, the template parameter subdim becomes the first argument of the function.index | the index of the desired face, ranging from 0 to countFaces<subdim>()-1 inclusive. |
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inline |
Deprecated routine that returns the component of the triangulation to which this boundary component belongs.
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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.
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
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true
if and only if this boundary component is ideal. 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
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true
if and only if this boundary component consists of a single invalid vertex and nothing else.
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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.
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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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inherited |
A deprecated alias for str().
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inherited |
A deprecated alias for detail().
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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.
void regina::Dim4BoundaryComponent::writeTextLong | ( | std::ostream & | out | ) | const |
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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inline |
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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friend |
Allow access to private members.