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D.13.4.4 splitPolygon
Procedure from library polymake.lib (see polymake_lib).
- Usage:
- splitPolygon (markings); markings list
- Assume:
- markings is a list of integer vectors representing lattice points in
the plane which we consider as the marked points of the convex lattice
polytope spanned by them
- Purpose:
- split the marked points in the vertices, the points on the facets
which are not vertices, and the interior points
- Return:
- list, L consisting of three lists
L[1] : represents the vertices the polygon ordered clockwise
L[1][i][1] = intvec, the coordinates of the ith vertex
L[1][i][2] = int, the position of L[1][i][1] in markings
L[2][i] : represents the lattice points on the facet of the
polygon with endpoints L[1][i] and L[1][i+1]
(i considered modulo size(L[1]))
L[2][i][j][1] = intvec, the coordinates of the jth
lattice point on that facet
L[2][i][j][2] = int, the position of L[2][i][j][1]
in markings
L[3] : represents the interior lattice points of the polygon
L[3][i][1] = intvec, coordinates of ith interior point
L[3][i][2] = int, the position of L[3][i][1] in markings
Example:
| | LIB "polymake.lib";
// the lattice polygon spanned by the points (0,0), (3,0) and (0,3)
// with all integer points as markings
list polygon=intvec(1,1),intvec(3,0),intvec(2,0),intvec(1,0),
intvec(0,0),intvec(2,1),intvec(0,1),intvec(1,2),
intvec(0,2),intvec(0,3);
// split the polygon in its vertices, its facets and its interior points
list sp=splitPolygon(polygon);
// the vertices
sp[1];
==> [1]:
==> [1]:
==> 3,0
==> [2]:
==> 2
==> [2]:
==> [1]:
==> 0,0
==> [2]:
==> 5
==> [3]:
==> [1]:
==> 0,3
==> [2]:
==> 10
// the points on facets which are not vertices
sp[2];
==> [1]:
==> [1]:
==> [1]:
==> 2,0
==> [2]:
==> 3
==> [2]:
==> [1]:
==> 1,0
==> [2]:
==> 4
==> [2]:
==> [1]:
==> [1]:
==> 0,1
==> [2]:
==> 7
==> [2]:
==> [1]:
==> 0,2
==> [2]:
==> 9
==> [3]:
==> [1]:
==> [1]:
==> 1,2
==> [2]:
==> 8
==> [2]:
==> [1]:
==> 2,1
==> [2]:
==> 6
// the interior points
sp[3];
==> [1]:
==> [1]:
==> 1,1
==> [2]:
==> 1
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