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D.13.1.10 splitPolygon

Procedure from library polymake.lib (see polymake_lib).

splitPolygon (markings); markings list

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

split the marked points in the vertices, the points on the facets which are not vertices, and the interior points

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),
// split the polygon in its vertices, its facets and its interior points
list sp=splitPolygon(polygon);
// the vertices
// the points on facets which are not vertices
// the interior points