Andreas von Dziegielewski, Rainer Erbes, and Elmar Schömer (2010)
Conservative swept volume boundary approximation
In: Proceedings of the 14th ACM Symposium on Solid and Physical Modeling, pp. 171–176, New York, NY, USA, ACM. SPM'10 (ISBN: 978-1-60558-984-8).
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.