On Computing Meshes with Large Smallest Angles

We present a variant of the Delau- nay refinement, method which inherits the theoretical guarantees of the original Delaunay refinement algo- rithm. For a given input domain (a set of points or a planar straight line graph), and a threshold angle �, the Delaunay refinement method computes triangu- lations (meshes) that have all angles at least �. For various input domain types, Delaunay refinement al- gorithm is proven to terminate with correct output for � � 30◦. In practice, the original Delaunay refine- ment algorithm works for values ofas high as 35◦. The new variant of the refinement algorithm termi- nates for larger values of �, as high as 38◦.