Delaunay Refinement by Corner Lopping

Summary

An algorithm for quality Delaunay meshing of 2D domains with curved boundaries is presented. The algorithm uses Ruppert’s “corner lopping” heuristic [MR96b:65137]. In addition to admitting a simple termination proof, the algorithm can accept curved input without any bound on the tangent angle between adjoining curves. In the limit case, where all curves are straight line segments, the algorithm returns a mesh with a minimum angle of arcsin (${1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\sqrt 2$), except “near” input corners. Some loss of output quality is experienced with the use of curved input, but this loss is diminished for smaller input curvature.