Mathematical morphology for design and manufacturing

In general geometric models, the design of objects is usually separated from the manufacture. Some advanced models give solutions to some of the derived problems but lack a related model of representation. The proposed model addresses the process of designing objects by assimilation of the machining process. It is based on set theory and mathematical morphology and no operation between solids or surfaces is done. Mathematical morphology describes geometric shapes from simpler ones. Sets represent object shapes in a nn-dimensional space and morphological operations represent geometric relationships between the points in the sets. An analogy between the design and the machining processes can be established: in the machining, the geometry of an object (piece) is also described by the geometry of another object (tool). Specifically, the specification of pieces and tools can be achieved through the use of new operations describing geometric processes of cutting and reconstruction (erosion and dilation respectively, in morphological terms). For manufacturing purposes, the new morphologic operations must be restricted to support an order that will represent the tool trajectory. As a result, the model is generic (as it can be extended to any other tool shape), robust (the set theory avoids special cases or incorrect solutions) and directly displayable.