Geometry Design Using Function Representation on a Sparse Hierarchical Data Structure. (April 2021)

• Record Type: Journal Article
• Authors: Kambampati, Sandilya; Jauregui, Carolina; Museth, Ken; Kim, H. Alicia
• Is Part Of: Computer aided design. Volume 133(2021)
• Publication Date: 2021-04
• Subjects: function representation -- sparse grids -- optimization -- VDB; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2020.102989
• Languages: English
• ISSNs: 0010-4485

Abstract

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. Graphical abstract: Highlights: Function representation (F-rep) geometries on sparse hierarchical grids using level set functions. Parallel algorithms efficient level set function morphing for solid design. Order or magnitude improvement in performance compared to a reference algorithm. Obtained F-rep file sizes that are an order of magnitude smaller than the corresponding STL (B-rep) files for the same lattice infill designs.