Parallelism-Oriented Dynamic Incremental Delaunay Triangulation Algorithm

Abstract

Delaunay triangulation is a main topic in computer graphics. Various types of new requirements have appeared during the development of parallel triangulation algorithms, e.g., updating the triangulation incrementally given a set of increasing points. Existing incremental triangulation algorithms do not support for inserting points outside of the triangulation. This paper proposes the expansion of triangulation and designs an incremental triangulation algorithm TID (truly incremental Delaunay) supporting for inserting any number of points with any distribution into an existing triangulation for any time. TID is designed to produce a unique triangulation result for any distribution of points. Experimental evaluation results on TID show that TID has higher computational efficiency than existing algorithms and introduces low computational overhead. In addition, TID has already been used in parallel triangulation algorithm as local triangulation algorithm.