Classes | |
struct | regina::NDiscSpec |
Specifies a single normal disc in a normal surface. More... | |
class | regina::NDiscSetTet |
Represents a set of normal discs inside a single tetrahedron. More... | |
class | regina::NDiscSetTetData< T > |
Stores data of type T for every normal disc inside a single tetrahedron. More... | |
class | regina::NDiscSetSurface |
Represents the set of all normal discs forming a normal surface. More... | |
class | regina::NDiscSetSurfaceData< T > |
Stores data of type T for every normal disc within a particular normal surface. More... | |
class | regina::NDiscSpecIterator |
An iterator used for running through all normal discs in a normal surface. More... | |
class | regina::NNormalSurfaceVector |
Stores the vector of a single normal surface in a 3-manifold. More... | |
class | regina::NNormalSurface |
Represents a single normal surface in a 3-manifold. More... | |
class | regina::NNormalSurfaceList |
A packet representing a collection of normal surfaces in a 3-manifold. More... | |
struct | regina::NPrismSpec |
Specifies a single triangular prism in a tetrahedron. More... | |
class | regina::NPrismSetSurface |
Represents the set of prisms defined by slicing along all the quads in a particular normal surface. More... | |
class | regina::NNormalSurfaceVectorANStandard |
An almost normal surface vector using standard triangle-quad-oct coordinates. More... | |
class | regina::NNormalSurfaceVectorMirrored |
A normal surface vector that is mirrored in another coordinate system to avoid frequent lengthy calculations. More... | |
class | regina::NNormalSurfaceVectorQuad |
A normal surface vector using quad coordinates. More... | |
class | regina::NNormalSurfaceVectorStandard |
A normal surface vector using standard triangle-quad coordinates. More... | |
class | regina::NSurfaceFilter |
A packet that accepts or rejects normal surfaces. More... | |
class | regina::NSurfaceSet |
Represents a collection of normal surfaces in a 3-manifold. More... | |
class | regina::NSurfaceSubset |
Represents a subset of a normal surface set. More... | |
class | regina::NXMLFilterReader |
An XML element reader that reads the specific details of a normal surface filter. More... | |
class | regina::NXMLFilterPacketReader |
An XML packet reader that reads a single surface filter. More... | |
class | regina::NXMLNormalSurfaceReader |
An XML element reader that reads a single normal surface. More... | |
class | regina::NXMLNormalSurfaceListReader |
An XML packet reader that reads a single normal surface list. More... | |
class | regina::NSurfaceFilterCombination |
A normal surface filter that simply combines other filters. More... | |
class | regina::NSurfaceFilterProperties |
A normal surface filter that filters by basic properties of the normal surface. More... | |
Functions | |
std::ostream & | regina::operator<< (std::ostream &out, const NDiscSpec &spec) |
Writes the given disc specifier to the given output stream. | |
bool | regina::numberDiscsAwayFromVertex (int discType, int vertex) |
Determines whether or not normal discs of the given type are numbered away from the given vertex. | |
bool | regina::discOrientationFollowsEdge (int discType, int vertex, int edgeStart, int edgeEnd) |
Determines whether or not the natural boundary orientation of a normal disc of the given type follows the given directed normal arc. | |
template<class RayOutputIterator, class FaceOutputIterator> | |
void | regina::createNonNegativeCone (NTriangulation *triangulation, int flavour, RayOutputIterator rays, FaceOutputIterator faces) |
Writes to the given output iterators newly allocated rays and faces representing the cone in the given flavour of coordinate system obtained by setting all coordinates non-negative. | |
NMatrixInt * | regina::makeMatchingEquations (NTriangulation *triangulation, int flavour) |
Creates a new set of normal surface matching equations for the given triangulation using the given flavour of coordinate system. | |
std::ostream & | regina::operator<< (std::ostream &out, const NPrismSpec &spec) |
Writes the given prism specifier to the given output stream. | |
Variables | |
const int | regina::vertexSplit [4][4] |
Lists which vertex splits split which pairs of vertices. | |
const int | regina::vertexSplitMeeting [4][4][2] |
Lists which vertex splits meet which edges. | |
const int | regina::vertexSplitDefn [3][4] |
Lists the vertices which each vertex split splits. | |
const int | regina::vertexSplitPartner [3][4] |
Lists the second vertex with which each vertex is paired under each vertex split. | |
const char | regina::vertexSplitString [3][6] |
Contains strings describing which vertices each vertex split splits. | |
const NPerm | regina::triDiscArcs [4][3] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of triangular normal disc. | |
const NPerm | regina::quadDiscArcs [3][4] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of quadrilateral normal disc. | |
const NPerm | regina::octDiscArcs [3][8] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of octahedral normal disc. |
void regina::createNonNegativeCone | ( | NTriangulation * | triangulation, | |
int | flavour, | |||
RayOutputIterator | rays, | |||
FaceOutputIterator | faces | |||
) |
Writes to the given output iterators newly allocated rays and faces representing the cone in the given flavour of coordinate system obtained by setting all coordinates non-negative.
To rays will be written the extremal rays of this cone, each being a unit vector along a coordinate axis. They will be written in order from the unit vector along the 0th coordinate axis to the last, and will all be of the subclass of NNormalSurfaceVector corresponding to the given flavour of coordinate system.
To faces will be written the vectors perpendicular to the hyperplanes that make up the faces of this cone. Each of these vectors will also be a unit vector along a coordinate axis. These vectors will be written in the same order as the rays, and will all be of class NVectorUnit.
The resulting lists of extremal rays and faces are guaranteed not to contain any duplicates or redundancies.
triangulation | the triangulation upon which the underlying coordinate system is based. | |
flavour | the flavour of coordinate system to be used; this must be one of the predefined coordinate system constants in NNormalSurfaceList. | |
rays | the output iterator to which the newly allocated extremal rays will be written; this must accept objects of type NRay* . | |
faces | the output iterator to which the newly allocated face perpendiculars will be written; this must accept objects of type NVector<NLargeInteger>* . |
bool regina::discOrientationFollowsEdge | ( | int | discType, | |
int | vertex, | |||
int | edgeStart, | |||
int | edgeEnd | |||
) |
Determines whether or not the natural boundary orientation of a normal disc of the given type follows the given directed normal arc.
Natural boundary orientation is defined by arrays triDiscArcs, quadDiscArcs and octDiscArcs.
discType | the normal disc type under consideration; this should be between 0 and 9 inclusive, as described by the NDiscSpec class notes. | |
vertex | the vertex about which the normal arc runs. | |
edgeStart | the start vertex of the edge to which the normal arc is parallel. | |
edgeEnd | the end vertex of the edge to which the normal arc is parallel. |
NMatrixInt* regina::makeMatchingEquations | ( | NTriangulation * | triangulation, | |
int | flavour | |||
) |
Creates a new set of normal surface matching equations for the given triangulation using the given flavour of coordinate system.
The returned matrix will be newly allocated and its destruction will be the responsibility of the caller of this routine.
Each equation will be represented as a row of the matrix. Each column of the matrix represents a coordinate in the given flavour of coordinate system.
triangulation | the triangulation upon which these matching equations will be based. | |
flavour | the flavour of coordinate system to be used; this must be one of the predefined coordinate system constants in NNormalSurfaceList. |
bool regina::numberDiscsAwayFromVertex | ( | int | discType, | |
int | vertex | |||
) |
Determines whether or not normal discs of the given type are numbered away from the given vertex.
discType | the normal disc type under consideration; this should be between 0 and 9 inclusive, as described by the NDiscSpec class notes. | |
vertex | the vertex under consideration; this should be between 0 and 3 inclusive. |
true
if normal discs of the given type are numbered away from the given vertex, or false
if they are numbered towards the given vertex. std::ostream& regina::operator<< | ( | std::ostream & | out, | |
const NPrismSpec & | spec | |||
) |
Writes the given prism specifier to the given output stream.
The prism specifier will be written as a pair (tetIndex, edge)
.
out | the output stream to which to write. | |
spec | the prism specifier to write. |
std::ostream& regina::operator<< | ( | std::ostream & | out, | |
const NDiscSpec & | spec | |||
) |
Writes the given disc specifier to the given output stream.
The disc specifier will be written as a triple (tetIndex, type, number)
.
out | the output stream to which to write. | |
spec | the disc specifier to write. |
const NPerm regina::octDiscArcs[3][8] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of octahedral normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array octDiscArcs[i]
lists the boundary arcs of the octahedral disc of type i. See NNormalSurface::getOctCoord() for further details.
Note that permutation octDiscArcs[i][j]
will be even precisely when j
is 0, 1, 4 or 5.
octDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. const NPerm regina::quadDiscArcs[3][4] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of quadrilateral normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array quadDiscArcs[i]
lists the boundary arcs of the quadrilateral disc of type i. See NNormalSurface::getQuadCoord() for further details.
Note that permutation quadDiscArcs[i][j]
will be even precisely when j
is even.
quadDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. const NPerm regina::triDiscArcs[4][3] |
Lists in consecutive order the directed normal arcs that form the boundary of each type of triangular normal disc.
Each permutation p represents an arc about vertex p[0]
parallel to the directed edge from p[1]
to p[2]
.
Array triDiscArcs[i]
lists the boundary arcs of the triangular disc of type i. See NNormalSurface::getTriangleCoord() for further details.
Note that every permutation in this array is even.
triDiscArcs(discType, arcIndex)
that essentially looks up the corresponding array. This is necessary because of a bug in gcc 2.95. const int regina::vertexSplit[4][4] |
Lists which vertex splits split which pairs of vertices.
There are three vertex splits, numbered 0,1,2. Each vertex split split the four tetrahedron vertices 0,1,2,3 into two pairs. vertexSplit[i][j]
is the number of the vertex split that keeps vertices i
and j
together.
const int regina::vertexSplitDefn[3][4] |
Lists the vertices which each vertex split splits.
See vertexSplit for details on what a vertex split is. Vertex split number i
splits the vertex pairs vertexSplitDefn[i][0,1]
and vertexSplitDefn[i][2,3]
.
const int regina::vertexSplitMeeting[4][4][2] |
Lists which vertex splits meet which edges.
See vertexSplit for details on what a vertex split is. vertexSplitMeeting[i][j][0,1]
are the numbers of the two vertex splits that meet the edge joining tetrahedron vertices i
and j
.
const int regina::vertexSplitPartner[3][4] |
Lists the second vertex with which each vertex is paired under each vertex split.
See vertexSplit for details on what a vertex split is. Vertex split number i
pairs vertex v
with vertex vertexSplitPartner[i][v]
.
const char regina::vertexSplitString[3][6] |
Contains strings describing which vertices each vertex split splits.
See vertexSplit for details on what a vertex split is. The string describing vertex split number i
is vertexSplitString[i]
and is of the form 02/13
, which in this case is the vertex split that splits vertices 0,2 from vertices 1,3.