Geometry Design Using Function Representation on a Sparse Hierarchical Data Structure

Abstract In this study, we introduce new algorithms for efficient function representation (F-rep) based geometric design using the sparse and dynamic voxel data structure Volumetric Dynamic B+ tree (VDB). The level set method is used as the F-rep method. Specifically, we develop the Fast Sweeping Method for boundary points to level set surfaces velocity extension for efficient geometry optimization on such sparse and dynamic data structures. For benchmarking, we developed a level set method in-house, using state of the art algorithms on a dense data structure, which we use as a reference. OpenVDB, which is an open source library, is used to store and modify the sparse and dynamic voxel data. Our results show that the developed method is up to an order of magnitude faster than the reference method, while only consuming a small fraction of the memory. Finally, we apply the level set method using the sparse and dynamic data structure for lattice infill designs, where we show that the sparse F-rep geometry file is more than an order of magnitude smaller in size than a conventional boundary representation (B-rep) formats such as a stereolithography (STL) file.

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