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D.13.4.1 triangulations
Procedure from library polymake.lib (see polymake_lib).
- Usage:
- triangulations(polygon[,#]); list polygon, list #
- Assume:
- polygon is a list of integer vectors of the same size representing
the affine coordinates of the lattice points
- Purpose:
- the procedure considers the marked polytope given as the convex hull of
the lattice points and with these lattice points as markings; it then
computes all possible triangulations of this marked polytope
- Return:
- list, each entry corresponds to one triangulation and the ith entry is
itself a list of integer vectors of size three, where each integer
vector defines one triangle in the triangulation by telling which
points of the input are the vertices of the triangle
- Note:
- - the procedure calls for its computations the program points2triangs
from the program topcom by Joerg Rambau, Universitaet Bayreuth; it
therefore is necessary that this program is installed in order to use
this procedure; see http://www.rambau.wm.uni-bayreuth.de/TOPCOM/);
- if you only want to have the regular triangulations the procedure should
be called with the string 'regular' as optional argument
- the procedure creates the files /tmp/triangulationsinput and
/tmp/triangulationsoutput;
the former is used as input for points2triangs and the latter is its
output containing the triangulations of corresponding to points in the
format of points2triangs; if you wish to use this for further
computations with topcom, you have to call the procedure with the
string 'keepfiles' as optional argument
- note that an integer i in an integer vector representing a triangle
refers to the ith lattice point, i.e. polygon[i]; this convention is
different from TOPCOM's convention, where i would refer to the i-1st
lattice point
Example:
| LIB "polymake.lib";
// the lattice points of the unit square in the plane
list polygon=intvec(0,0),intvec(0,1),intvec(1,0),intvec(1,1);
// the triangulations of this lattice point configuration are computed
list triang=triangulations(polygon);
==> Evaluating Commandline Options ...
==> ... done.
==> 0
==> 0
triang;
==> [1]:
==> [1]:
==> 1,2,3
==> [2]:
==> 2,3,4
==> [2]:
==> [1]:
==> 1,3,4
==> [2]:
==> 1,2,4
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