Robust geometric methods for surface modeling and manufacturing

We investigate methods to aid in the process of going from a conceptual shape of a part to its physical realization. We present contributions to the “design for manufacture” problem in two major areas: surface model representation and process planning for layered manufacturing. In surface modeling, the focus is on subdivision surfaces and the analysis of their continuity behavior. We present a new algorithm for the exact evaluation of piecewise smooth Loop and Catmull-Clark surfaces near user-defined sharp features. This algorithm aids in the geometric process planning of subdivision surfaces for manufacturing. On the process planning side, we have developed an approach to layered manufacturing that produces parts with thin, dense walls filled with a loose web-like interior to reduce material usage and accelerate build times. The key algorithm in this process generates a conservative offset of a polyhedral surface by generating a stack of 2D slice contours, calculating individual offset contours, and forming appropriate Boolean combinations of these contours. We describe a numerically robust algorithm for constructing the generalized Voronoi diagram of polygonal slice contours which is then used to generate clean offset contours for each slice, which are combined between layers to create the conservative 3D offset surface.

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