Robust delaunay triangulation for domain with acute angles

A new algorithm is presented to automatic generate conforming Delaunay triangulation of non-manifold geometric domains with acute angles. The algorithm is based on Delaunay refinement technique, which often failed to terminate when there are small angles in input geometry. By assigning proper weights to vertices on sharp-angled elements and take place Delaunay triangulation with weighted Delaunay triangulation, the algorithm can accept any inputs without any bound on angle and without setting any protected area and adding any new vertices near the sharp-angled elements. The algorithm also guarantees bounded circumradius to shortest edge length for all elements except the ones near small input angles. A simple terminator proof and some results are also presented.