Isothetic polyhedra and monotone boolean formulae

Abstract

We consider the problem of converting boundary representations of isothetic polyhedra into constructive solid geometry (CSG) representations. The CSG representation is a boolean formula based on the halfspaces supporting the faces of the polyhedron. This boolean formula exhibits two important features: no term is complemented (it is monotone) and each supporting halfspace appears in the formula once and only once. In this work we prove that such a representation exists for those cyclic isothetic polyhedra such that for each cyclic deficiency set in the polyhedron it is possible to find out at least either a convex or a concave path of extremal edges which splits the cyclic deficiency set into two subsets.