Casting with skewed ejection direction revisited

The manufacturing industry has at its disposal a number of processes for constructing objects, including gravity casting, injection molding, stereolithography, NC-machining, deformation, composition, and spray deposition. The survey by Bose and Toussaint [3, 5] gives an overview of geometric problems and algorithms arising in manufacturing processes. Castingis one of the manufacuring processes in which liquified material is poured into a cast that has a cavity formed by two cast parts. After the material hardens, the movable cast part first retracts from the fixed cast part carrying the object with it. Afterwards, the object is ejected from the retracted cast part. In most existing machinery, the retraction and ejection directions are identical, and previous work on this problem has assumed this restriction on casting. Existing technology for injection molding, however, already has the flexibility to accommodate an ejection direction that is different from the retraction direction of the moving cast part. Exploiting this possibility allows to cast more parts, or to cast parts with simpler moulds, and is the subject of the present paper. To simulate the retraction, the fixed cast part will first be removed in a direction opposite to the retraction. Then to simulate the ejection, the remaining cast part will be removed in a direction opposite to the ejection. In our model of casting, the two cast parts are to be removed in two given directions and these directions need not be opposite. Note that the ordering of removal is important. The cast parts should be removed from the object without destroying either cast parts or the object. This ensures that the given object can be mass produced by re-using the same cast parts. The casting process may fail in the removal of the cast parts: if the cast is not designed properly, then one