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D.13.4.4 splitPolygon
Procedure from librarypolymake.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
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 |