Can we enhance Delaunay triangulations? This paper introduces sink insertion, a new technique for improving the mesh quality of Delaunay triangulations. It compares sink insertion with the conventional circumcenter insertion technique. Sink insertion seeks to create meshes more robust for numerical applications. The sink insertion is compared with the conventional circumcenter insertion technique under three scheduling regimes: incremental, in blocks, and in parallel. It is a crucial technique when generating meshes. It works well for Delaunay triangulations. Sink insertion enhances mesh quality. Justification for sink insertion is given in terms of mesh quality, numerical robustness, running time, and ease of parallelization. Sink insertion techniques offer improvements for meshing problems.
The International Journal of Foundations of Computer Science is dedicated to theoretical foundations of computer science. This paper fits the scope of the journal by presenting and evaluating a novel approach for mesh improvement in Delaunay triangulations. The technique’s algorithmic properties, numerical robustness, and parallelization potential are relevant to the journal’s readership of researchers in theoretical computer science.