On the separation of a polyhedron from its single-part mold

摘要

Casting is a manufacturing process where liquid material is poured into a mold having the shape of a desired product. After the material solidifies, the product is pulled out of the mold. We study the case in which the mold is made of a single part and the object to be produced is a three-dimensional polyhedron. Objects that can be produced this way are called castable with a single-part mold. A direction in which the object can be removed without breaking the mold is called a valid pull-out direction. We give an algorithm that decides whether a given polyhedron with n facets is castable with a single-part mold, and if so indicates how to orient the polyhedron in the mold and a direction in which the product can be pulled out without breaking the mold. Our algorithm runs in O(n) time. The best previously known algorithm for this problem runs in O(n2) time.