Size Competitive Meshing Without Large Angles

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.

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Gary L. Miller, Todd Phillips, Donald Sheehy
• Keywords: ICALP 2007, Input, Optimal Size Mesh, Theoretical Computer Science, Triangulation