Regina Calculation Engine

Represents a tetrahedron in a triangulation. More...
#include <triangulation/ntetrahedron.h>
Public Member Functions  
NTetrahedron ()  
Creates a new tetrahedron with empty description and no faces joined to anything. More...  
NTetrahedron (const std::string &desc)  
Creates a new tetrahedron with the given description and no faces joined to anything. More...  
virtual  ~NTetrahedron () 
Destroys this tetrahedron. More...  
const std::string &  getDescription () const 
Returns the text description associated with this tetrahedron. More...  
void  setDescription (const std::string &desc) 
Sets the text description associated with this tetrahedron. More...  
unsigned long  index () const 
Returns the index of this tetrahedron in the underlying triangulation. More...  
NTetrahedron *  adjacentTetrahedron (int face) const 
Returns the adjacent tetrahedron glued to the given face of this tetrahedron, or 0 if the given face is on the triangulation boundary. More...  
NTetrahedron *  adjacentSimplex (int face) const 
A dimensionagnostic alias for adjacentTetrahedron(). More...  
NTetrahedron *  getAdjacentTetrahedron (int face) const 
Deprecated in favour of adjacentTetrahedron(). More...  
NPerm4  adjacentGluing (int face) const 
Returns a permutation describing the correspondence between vertices of this tetrahedron and vertices of the adjacent tetrahedron glued to the given face of this tetrahedron. More...  
NPerm4  getAdjacentTetrahedronGluing (int face) const 
Deprecated in favour of adjacentGluing(). More...  
int  adjacentFace (int face) const 
Examines the tetrahedron glued to the given face of this tetrahedron, and returns the corresponding face of that tetrahedron. More...  
int  adjacentFacet (int facet) const 
A dimensionagnostic alias for adjacentFace(). More...  
int  getAdjacentFace (int face) const 
Deprecated in favour of adjacentFace(). More...  
bool  hasBoundary () const 
Determines if this tetrahedron has any faces that are boundary triangles. More...  
void  joinTo (int myFace, NTetrahedron *you, NPerm4 gluing) 
Joins the given face of this tetrahedron to another tetrahedron. More...  
NTetrahedron *  unjoin (int myFace) 
Unglues the given face of this tetrahedron from whatever is joined to it. More...  
void  isolate () 
Undoes any face gluings involving this tetrahedron. More...  
NTriangulation *  getTriangulation () const 
Returns the triangulation to which this tetrahedron belongs. More...  
NComponent *  getComponent () const 
Returns the triangulation component to which this tetrahedron belongs. More...  
NVertex *  getVertex (int vertex) const 
Returns the vertex in the triangulation skeleton corresponding to the given vertex of this tetrahedron. More...  
NEdge *  getEdge (int edge) const 
Returns the edge in the triangulation skeleton corresponding to the given edge of this tetrahedron. More...  
NTriangle *  getTriangle (int face) const 
Returns the triangle in the triangulation skeleton corresponding to the given face of this tetrahedron. More...  
NTriangle *  getFace (int face) const 
A deprecated alias for getTriangle(). More...  
NPerm4  getVertexMapping (int vertex) const 
Returns a permutation that maps 0 to the given vertex of this tetrahedron, and that maps (1,2,3) to the three remaining vertices in the following "orientationpreserving" fashion. More...  
NPerm4  getEdgeMapping (int edge) const 
Examines the given edge of this tetrahedron, and returns a permutation that maps the "canonical" vertices (0,1) of the corresponding edge of the triangulation to the matching vertices of this tetrahedron. More...  
NPerm4  getTriangleMapping (int face) const 
Examines the given face of this tetrahedron, and returns a mapping from the "canonical" vertices of the corresponding triangle of the triangulation to the matching vertices of this tetrahedron. More...  
NPerm4  getFaceMapping (int face) const 
A deprecated alias for getTriangleMapping(). More...  
int  orientation () const 
Returns the orientation of this tetrahedron in the triangulation. More...  
void  writeTextShort (std::ostream &out) const 
Writes this object in short text format to the given output stream. More...  
void  writeTextLong (std::ostream &out) const 
Writes this object in long text format to the given output stream. More...  
long  markedIndex () const 
Returns the index at which this object is stored in an NMarkedVector. More...  
Input and Output  
std::string  str () const 
Returns the output from writeTextShort() as a string. More...  
std::string  toString () const 
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...  
std::string  detail () const 
Returns the output from writeTextLong() as a string. More...  
std::string  toStringLong () const 
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...  
Friends  
class  NTriangulation 
Allow access to private members. More...  
Represents a tetrahedron in a triangulation.
With each tetrahedron is stored various pieces of information regarding the overall skeletal structure and component structure of the triangulation. This skeletal information will be allocated, calculated and deallocated by the NTriangulation object containing the corresponding tetrahedra.
The management of tetrahedra has changed significantly as of Regina 4.90:
These changes are designed to ensure that triangulations and tetrahedra are always in a consistent state, and to make it more difficult for users to inadvertently crash the program.
regina::NTetrahedron::NTetrahedron  (  ) 
Creates a new tetrahedron with empty description and no faces joined to anything.
The new tetrahedron will not belong to any triangulation.
regina::NTetrahedron::NTetrahedron  (  const std::string &  desc  ) 
Creates a new tetrahedron with the given description and no faces joined to anything.
The new tetrahedron will not belong to any triangulation.
desc  the description to give the new tetrahedron. 

inlinevirtual 
Destroys this tetrahedron.

inline 
Examines the tetrahedron glued to the given face of this tetrahedron, and returns the corresponding face of that tetrahedron.
That is, the returned face of the adjacent tetrahedron is glued to the given face of this tetrahedron.
face  the face of this tetrahedron whose gluing we will examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inline 
A dimensionagnostic alias for adjacentFace().
This is to assist with writing dimensionagnostic code that can be reused to work in different dimensions.
Here "facet" refers to a facet of a topdimensional simplex (which for 3manifold triangulations means a face of a tetrahedron).
See adjacentFace() for further information.

inline 
Returns a permutation describing the correspondence between vertices of this tetrahedron and vertices of the adjacent tetrahedron glued to the given face of this tetrahedron.
If we call this permutation p
, then for each vertex v
of this tetrahedron, p[v]
will be the vertex of the adjacent tetrahedron that is identified with v
according to the gluing along the given face of this tetrahedron.
face  the face of this tetrahedron whose gluing we will examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inline 
A dimensionagnostic alias for adjacentTetrahedron().
This is to assist with writing dimensionagnostic code that can be reused to work in different dimensions.
Here "simplex" refers to a topdimensional simplex (which for 3manifold triangulations means a tetrahedron).
See adjacentTetrahedron() for further information.

inline 
Returns the adjacent tetrahedron glued to the given face of this tetrahedron, or 0 if the given face is on the triangulation boundary.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inherited 
Returns the output from writeTextLong() as a string.

inline 
Deprecated in favour of adjacentFace().
The old routine getAdjacentFace() has been renamed to adjacentFace() as part of an effort to make programming and scripting with Regina a little less work on the fingers.
face  the face of this tetrahedron whose gluing we will examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inline 
Deprecated in favour of adjacentTetrahedron().
The old routine getAdjacentTetrahedron() has been renamed to adjacentTetrahedron() as part of an effort to make programming and scripting with Regina a little less work on the fingers.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inline 
Deprecated in favour of adjacentGluing().
The old routine getAdjacentTetrahedronGluing() has been renamed to adjacentGluing() as part of an effort to make programming and scripting with Regina a little less work on the fingers.
face  the face of this tetrahedron whose gluing we will examine. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

inline 
Returns the triangulation component to which this tetrahedron belongs.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.

inline 
Returns the text description associated with this tetrahedron.

inline 
Returns the edge in the triangulation skeleton corresponding to the given edge of this tetrahedron.
See NEdge::edgeNumber and NEdge::edgeVertex for the conventions of how edges are numbered within a tetrahedron.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
edge  the edge of this tetrahedron to examine. This should be between 0 and 5 inclusive. 

inline 
Examines the given edge of this tetrahedron, and returns a permutation that maps the "canonical" vertices (0,1) of the corresponding edge of the triangulation to the matching vertices of this tetrahedron.
This permutation also maps (2,3) to the remaining tetrahedron vertices in an "orientationpreserving" way, as described below.
In detail: Suppose several edges of several tetrahedra are identified within the overall triangulation. We call this a single "edge of the triangulation", and arbitrarily label its vertices (0,1). This routine then maps the vertices (0,1) of this edge of the triangulation to the individual vertices of this tetrahedron that make up the given edge.
Because we are passing the argument edge, we already know which vertices of this tetrahedron are involved. What this routine tells us is the order in which they appear to form the overall edge of the triangulation.
As a consequence: Consider some collection of tetrahedron edges that are identified together as a single edge of the triangulation, and choose some i from the set {0,1}. Then the vertices getEdgeMapping(...)[i]
of the individual tetrahedra are all identified together, since they all become the same vertex of the same edge of the triangulation (assuming of course that we pass the correct edge number in each case to getEdgeMapping()).
The images of 2 and 3 under the permutations that are returned have the following properties. In each tetrahedron, the images of 2 and 3 under this map form a directed edge of the tetrahedron (running from the image of vertex 2 to the image of vertex 3). For any given edge of the triangulation, these corresponding directed edges together form an ordered path within the triangulation that circles the common edge of the triangulation (like an edge link, except that it is not near to the edge and so might intersect itself). Furthermore, if we consider the individual tetrahedra in the order in which they appear in the list NEdge::getEmbeddings(), these corresponding directed edges appear in order from the start of this path to the finish (for internal edges this path is actually a cycle, and the starting point is arbitrary).
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
edge  the edge of this tetrahedron to examine. This should be between 0 and 5 inclusive. 

inline 
A deprecated alias for getTriangle().
This routine returns the triangle in the triangulation skeleton corresponding to the given face of this tetrahedron. See getTriangle() for further details.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive, where face i lies opposite vertex i . 

inline 
A deprecated alias for getTriangleMapping().
This routine examines the given face of this tetrahedron, and returns a mapping from the "canonical" vertices of the corresponding triangle of the triangulation to the matching vertices of this tetrahedron. See getTriangleMapping() for further details.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive. 

inline 
Returns the triangle in the triangulation skeleton corresponding to the given face of this tetrahedron.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive, where face i lies opposite vertex i . 

inline 
Examines the given face of this tetrahedron, and returns a mapping from the "canonical" vertices of the corresponding triangle of the triangulation to the matching vertices of this tetrahedron.
In detail: Suppose two faces of two tetrahedra are identified within the overall triangulation. We call this a single "triangle of the triangulation", and arbitrarily label its vertices (0,1,2). This routine then maps the vertices (0,1,2) of this triangle of the triangulation to the individual vertices of this tetrahedron that make up the given face.
Because we are passing the argument face, we already know which vertices of this tetrahedron are involved. What this routine tells us is the order in which they appear to form the overall face of the triangulation.
As a consequence: Consider some pair of tetrahedron faces that are identified together as a single triangle of the triangulation, and choose some i from the set {0,1,2}. Then the vertices getTriangleMapping(...)[i]
of the individual tetrahedra are identified together, since they both become the same vertex of the same triangle of the triangulation (assuming of course that we pass the correct face number in each case to getTriangleMapping()).
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
face  the face of this tetrahedron to examine. This should be between 0 and 3 inclusive. 

inline 
Returns the triangulation to which this tetrahedron belongs.

inline 
Returns the vertex in the triangulation skeleton corresponding to the given vertex of this tetrahedron.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
vertex  the vertex of this tetrahedron to examine. This should be between 0 and 3 inclusive. 

inline 
Returns a permutation that maps 0 to the given vertex of this tetrahedron, and that maps (1,2,3) to the three remaining vertices in the following "orientationpreserving" fashion.
The images of (1,2,3) under this permutation imply an orientation for the tetrahedron face opposite the given vertex. These orientations will be consistent for all tetrahedra containing the given vertex, if this is possible (i.e., if the vertex link is orientable).
Note that there are still arbitrary decisions to be made for the images of (1,2,3), since there will always be three possible mappings that yield the correct orientation.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.
vertex  the vertex of this tetrahedron to examine. This should be between 0 and 3 inclusive. 
bool regina::NTetrahedron::hasBoundary  (  )  const 
Determines if this tetrahedron has any faces that are boundary triangles.
true
if and only if this tetrahedron has any boundary triangles.

inline 
Returns the index of this tetrahedron in the underlying triangulation.
This is identical to calling getTriangulation()>tetrahedronIndex(this)
.
Note that tetrahedron indexing may change when a tetrahedron is added or removed from the underlying triangulation.
void regina::NTetrahedron::isolate  (  ) 
Undoes any face gluings involving this tetrahedron.
Any other tetrahedra involved will be automatically updated.
void regina::NTetrahedron::joinTo  (  int  myFace, 
NTetrahedron *  you,  
NPerm4  gluing  
) 
Joins the given face of this tetrahedron to another tetrahedron.
The other tetrahedron involved will be automatically updated.
Neither tetrahedron needs to belong to a triangulation (i.e., you can join tetrahedra together before or after calling NTriangulation::addTetrahedron()). However, if both tetrahedra do belong to a triangulation then it must be the same triangulation.
myFace  the face of this tetrahedron that will be glued to the given other tetrahedron. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 
you  the tetrahedron (possibly this one) that will be glued to the given face of this tetrahedron. 
gluing  a permutation describing the mapping of vertices by which the two tetrahedra will be joined. Each vertex v of this tetrahedron that lies on the given face will be identified with vertex gluing[v] of tetrahedron you . In addition, the face of you that will be glued to the given face of this tetrahedron will be face number gluing[myFace] . 

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.

inline 
Returns the orientation of this tetrahedron in the triangulation.
The orientation of each tetrahedron is always +1 or 1. In an orientable component of a triangulation, adjacent tetrahedra have the same orientations if one could be transposed onto the other without reflection, and they have opposite orientations if a reflection would be required. In a nonorientable component, orientations are still +1 and 1 but no further guarantees can be made.
As of Regina 4.90, if the skeletal information for the triangulation has not been computed then this will be done automatically. There is no need for users to explicitly recompute the skeleton themselves.

inline 
Sets the text description associated with this tetrahedron.
Note that descriptions need not be unique, and may be empty.
desc  the new description to assign to this tetrahedron. 

inherited 
Returns the output from writeTextShort() as a string.
__str__()
function.

inlineinherited 
A deprecated alias for str(), which returns the output from writeTextShort() as a string.

inlineinherited 
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
NTetrahedron* regina::NTetrahedron::unjoin  (  int  myFace  ) 
Unglues the given face of this tetrahedron from whatever is joined to it.
The other tetrahedron involved (possibly this one) will be automatically updated.
myFace  the face of this tetrahedron whose gluing we will undo. This should be between 0 and 3 inclusive, where face i is opposite vertex i of the tetrahedron. 

virtual 
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be humanreadable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out  the output stream to which to write. 
Reimplemented from regina::ShareableObject.

inlinevirtual 
Writes this object in short text format to the given output stream.
The output should be humanreadable, should fit on a single line, and should not end with a newline.
out  the output stream to which to write. 
Implements regina::ShareableObject.

friend 
Allow access to private members.