Determining the castability of simple polyhedra

A polyhedron P is castable if its boundary can be partitioned by a plane into two polyhedral terrains. Such polyhedra can be manufactured easily using two cast parts. Assuming that the cast parts are removed by a single translation each, it is shown that for a simple polyhedron with n vertices, castability can be decided in O(n2logn) time and linear space using a simple algorithm. Furthermore, a more complicated algorithm solves the problem in O(n3/2+&egr;) time and space, for any fixed &egr;>0. In the case where the cast parts are to be removed in opposite directions, a simple O(n2) time algorithm is presented. Finally, if the object is a convex polyhedron and the cast parts are to be removed in opposite directions, a simple O(nlog2n) algorithm is presented.