Polycube Optimization and Applications: From the Digital World to Manufacturing

In this thesis, after a summary of the state-of-the-art methods to compute polycube mappings, we study a possible optimization of the polycubes structure and two potential uses of that. We start from a polycube corners alignment, to improve the polycube-based mesh structure in terms of coarse surface and volume block decomposition. Then, we present an automatic method to enhance the elements quality of a polycube-based hex-mesh, via a selective padding strategy that improves the mesh quality only where it is needed. In closing, we move from the digital environment to the manufacturing one, to introduce a method for the decomposition of digital shapes, for fabrication purposes, by using a polycube-induced partitioning. The key idea of this thesis is exploring the polycube world from different points of view, by moving from the purely digital world to the more concrete one of the fabrication.