Interleaving Delaunay Refinement and Optimization for 2D Triangle Mesh Generation

We address the problem of generating 2D quality triangle meshes from a set of constraints provided as a planar straight line graph. The algorithm first computes a constrained Delaunay triangulation of the input set of constraints, then interleaves Delaunay refinement and optimization. The refinement stage inserts a subset of the Voronoi vertices and midpoints of constrained edges as Steiner points. The optimization stage optimizes the shape of the triangles through the Lloyd iteration applied to Steiner points both in 1D along constrained edges and in 2D after computing the bounded Voronoi diagram. Our experiments show that the proposed algorithm inserts fewer Steiner points than Delaunay refinement alone, and improves over the mesh quality.