High Precision Conservative Surface Mesh Generation for Swept Volumes

We present a novel, efficient, and flexible scheme to generate a high-quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the one-sided Hausdorff distance of the generated mesh to the swept volume is upper bounded by a user defined tolerance. Exploiting this tolerance the algorithm generates a mesh that is adapted to the local complexity of the swept volume boundary, keeping the overall output complexity remarkably low. The algorithm is two-phased: the actual sweep and the mesh generation. In the sweeping phase, we introduce a general framework to compute a compressed voxelization. The phase is tailored for an easy application of parallelization techniques. We show this for our exemplary implementation and provide a multicore solution, as well as a GPU-based solution using CUDA. For the meshing phase we utilize and extend the well known Delaunay refinement such that it generates an adaptive conservative approximation that obeys the user defined upper bound on the one-sided Hausdorff distance to the swept volume. The approach is able to handle inputs of high complexity and compute an approximation with a very high precision, which we demonstrate on real industrial data sets.