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 …