Function Representation Based Analytic Shape Hollowing Optimization

Abstract We present a function representation based analytic optimization framework for shape hollowing problem to achieve various functionalities. A compact description of model with cavities is constructed by introducing a field function, which could handle geometry and topology changes of interior shapes effortlessly without both local and global self-intersections. The variation of cavities is permitted in the entire interior volume without restrictions of skeletons and topology changes. Moreover, the function representation inherently defines smooth and accurate shapes that are independent of mesh resolution. Last but not least, the analytic derivatives of variables in gradient based optimization can be directly executed on the function representation without remeshing. Benefiting from the proposed function representation, our method provides an efficient and controllable framework to represent, analyze and optimize shape with cavities directly on functions. Various experiments have shown that our approach can obtain smooth and effective cavities that well predict the physical properties of fabricated models.