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.

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 multi-core solution as well as a GPU based solution using CUDA. The meshing phase utilizes Delaunay refinement which we carefully modified such that required guarantees are met. The approach is able to handle inputs of very high complexity at desired precision, which we demonstrate on real industrial data sets.

We present a novel technique for approximating the boundary of a swept volume. The generator given by an input triangle mesh is rendered under all rigid transformations of a discrete trajectory. We use a special shader program that creates offset geometry of each triangle on the fly, thus guaranteeing a conservative rasterization and correct depth values. Utilizing rasterization mechanisms and the depth buffer we then get a conservative voxelization of the swept volume (SV) and can extract a triangle mesh from its surface. This mesh is simplified maintaining conservativeness as well as an error bound measured in terms of the one-sided Hausdorff distance. For this we introduce a new technique for tolerance volume computation. The tolerance volume is implicitly given through six 2D-textures residing in texture memory and is evaluated in a special shader program only when needed.