Regina Calculation Engine
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Represents a 2-sphere made from two triangles glued together along their three edges. More...
#include <subcomplex/pillowtwosphere.h>
Public Member Functions | |
PillowTwoSphere * | clone () const |
Returns a newly created clone of this structure. More... | |
Triangle< 3 > * | triangle (int index) const |
Returns one of the two triangles whose boundaries are joined. More... | |
Perm< 4 > | triangleMapping () const |
Returns a permutation describing how the boundaries of the two triangles are joined. 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... | |
Static Public Member Functions | |
static PillowTwoSphere * | formsPillowTwoSphere (Triangle< 3 > *tri1, Triangle< 3 > *tri2) |
Determines if the two given triangles together form a pillow 2-sphere. More... | |
Represents a 2-sphere made from two triangles glued together along their three edges.
The two triangles must be distinct and the three edges of each triangle must also be distinct. Neither of the triangles may be boundary triangles. These two triangless together form an embedded 2-sphere in the triangulation (with the exception that two or three points of the sphere corresponding to the triangles vertices may be identified).
This 2-sphere can be cut along and the two resulting 2-sphere boundaries filled in with 3-balls, and the resulting triangulation has the same number of tetrahedra as the original. If the original 2-sphere was separating, the resulting triangulation will contain the two terms of the corresponding connected sum.
PillowTwoSphere* regina::PillowTwoSphere::clone | ( | ) | const |
Returns a newly created clone of this structure.
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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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static |
Determines if the two given triangles together form a pillow 2-sphere.
tri1 | the first triangle to examine. |
tri2 | the second triangle to examine. |
null
if the given triangles do not form a pillow 2-sphere.
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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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inline |
Returns one of the two triangles whose boundaries are joined.
index | specifies which of the two triangles to return; this must be either 0 or 1. |
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inline |
Returns a permutation describing how the boundaries of the two triangles are joined.
The permutation will map vertices (0,1,2) of triangle(0)
to vertices (0,1,2) of triangle(1)
. The map will represent how the vertices of the triangles are identified by the three edge gluings.
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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 |
A default implementation for detailed output.
This routine simply calls T::writeTextShort() and appends a final newline.
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. |