Fast Sizing Calculations for Meshing

Provably correct algorithms for meshing difficult domains in three dimensions have been recently developed in the literature. These algorithms handle the problem of sharp angles (< / 2) between segments and between facets by constructing protective collars around these regions. The collars are approximately sized according to the local fea- ture sizeof the input. With the eventual goal of developing time-efficient algorithms for the same mesh generation problems, we give a method for estimating the feature size of a 3D piecewise-linear-complex of size n on domain in time O(nlog + m), where is the spread of the in- put. The linear term m 2 O( R 1/lfs3) is bounded above by the output size of a quality generated mesh. Our algo- rithm is based on early termination of the Sparse-Voronoi- Refinement (SVR) meshing algorithm, which is not guar- anteed to terminate in the presence of sharp angles.