Exact and Efficient Polyhedral Envelope Containment Predicate

The computation of distances between surfaces is a basic building block in geometry processing. In particular, the computation of the Hausdorff distance between an individual triangle T and a triangle mesh M is often used by meshing and remeshing algorithms (eg,[Cheng et al. 2019; Hu et al. 2020, 2018]) to ensure geometric preservation up to a small distance ϵ. This distance allows algorithms to smooth out small details, fill small gaps, remove noise, and perform other operations to generate a high quality mesh, while at the same time bounding the geometrical approximation error. This bound is used, for example, in graphics applications to ensure sub pixels accuracy, or in finite element analysis to bound the error on the solution.

Aug 1, 2020 1:00 PM