Size competitive meshing without large angles

Authors:
Gary L. Miller;Todd Phillips;Donald Sheehy
Affiliations:
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA;Computer Science Department, Carnegie Mellon University, Pittsburgh, PA;Computer Science Department, Carnegie Mellon University, Pittsburgh, PA
Venue:
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Year:
2007

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Abstract

We present a new meshing algorithm for the plane, Overlay Stitch Meshing (OSM), accepting as input an arbitrary Planar Straight Line Graph and producing a triangulation with all angles smaller than 170°. The output triangulation has competitive size with any optimal size mesh having equally bounded largest angle. The competitive ratio is O(log(L/s)) where L and s are respectively the largest and smallest features in the input. OSM runs in O(n log(L/s) +m) time/work where n is the input size and m is the output size. The algorithm first uses Sparse Voronoi Refinement to compute a quality overlay mesh of the input points alone. This triangulation is then combined with the input edges to give the final mesh.