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.

在这项研究中，我们介绍了使用稀疏和动态体素数据结构体动态B +树（VDB）进行基于有效功能表示（F-rep）的几何设计的新算法。水平设置方法用作F-rep方法。具体来说，我们针对边界点开发了快速扫掠方法，以对水平设置的表面速度进行扩展，以在此类稀疏和动态数据结构上进行有效的几何优化。为了进行基准测试，我们内部开发了一个水平集方法，使用了密集数据结构上的最新算法，以此作为参考。OpenVDB是一个开源库，用于存储和修改稀疏和动态体素数据。我们的结果表明，所开发的方法比参考方法快一个数量级，同时仅消耗一小部分内存。