Geometric and computational aspects of manufacturing processes

A survey is presented on the geometric and computational aspects of molding, gravity casting, stereolithography, and laser sculpting. Emphasis is placed on the two fundamental questions that arise concerning every type of manufacturing process: (a) Given an object, can it be constructed using a particular process? (b) Given that an object can be built using a particular process, what is the best way to construct the object? The techniques surveyed in this paper answer the above questions for several mathematical (geometric) models of the actual manufacturing processes used in industry