This paper describes a geometric algorithm for automated design of multi-stage molds for manufacturing multi-material objects. In multi-stage molding process, the desired multi-material object is produced by carrying out multiple molding operations in a sequence, adding one material in the target object in each mold-stage. We model multi-material objects as an assembly of single-material components. Each mold-stage can add only one type of material. Therefore, we need a sequence of mold-stages such that (1) each mold-stage only adds one single-material component either fully or partially, and (2) the molding sequence completely produces the desired object. In order to find a feasible mold-stage sequence, our algorithm decomposes the multi-material object into a number of homogeneous components to find a feasible sequence of homogeneous components that can be added in a sequence to produce the desired multi-material object. Our algorithm starts with the final object assembly and considers removing components either completely or partially from the object one-at-a-time such that it results in the previous state of the object assembly. If a component can be removed from the target object leaving the previous state of the object assembly a connected solid then we consider such decomposition a valid step in the stage sequence. This step is recursively repeated on new states of the object assembly until the object assembly reaches a state where it only consists of one component. When an object-decomposition has been found that leads to a feasible stage sequence, the gross mold for each stage is computed and decomposed into two or more pieces to facilitate the molding operation. We expect that our algorithm will provide a step towards automating the design of multi-stage molds and therefore will help in reducing the mold design lead-time for multi-stage molds.
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