Geometric aspects of the casting process

Manufacturing is the process of converting raw materials into useful products. Among the most important manufacturing processes, casting is a commonly used manufacturing process for plastic and metal objects. The industrial casting process consists of two stages. First, liquid is filled into a cavity formed by two cast parts. After the liquid has hardened, one cast part retracts, carrying the object with it. Afterwards, the object is ejected from the retracted cast part. In both retraction and ejection steps, the cast parts and the object should not be damaged, so that the quality of final object is guaranteed and the cast parts can be reused to produce another object. This mode of production is called ``mass production''. Due to the geometric nature of the casting process, many geometric problems arise in the automation of casting. The problems we address here concern this aspect: Given a 3-dimensional object, is there a cast for it whose parts can be removed after the liquid has solidified? An object for which this is the case is called castable. We consider the castability problem in three different casting models with a two-part cast. In the first casting model, two parts must be removed in opposite directions. There are two cases depending on whether the removal direction is specified in advance or not. The second model is identical to the first casting model, except that the cast machinery has a certain level of uncertainty in its directional movement. In the third model, the two cast parts are to be removed in two given directions and these directions need not be opposite. For all three casting models, we give complete characterizations of castability, and obtain algorithms to verify these conditions for polyhedral parts. In manufacturing, features of an object imply manufacturing information, which facilitates the process of analyzing manufacturability and the automated design of a cast for the object. A small hole or a depression on the boundary of an object, for example, restricts the set of removal directions for which this object is castable, since the portion of the cast in the hole or in the depression must be removed from the object without breaking the object. We define a geometric feature, the cavity, which is related to the castability of objects, and provide algorithms to extract it from objects