A new compound algorithm study for delaunay triangulation construction

Delaunay triangulation is always used to construct TIN, and is also widely applied in manifold fields, for it can avoid long and skinny triangles resulting in a nice looking map. A wide variety of algorithms have been proposed to construct delaunay triangulation, such as divide-and-conquer, incremental insertion, trangulation growth, and so on. The compound algorithm is also researched to construct delaunay triangulation, and prevalently it is mainly based on divideand-conquer and incremental insertion algorithms. This paper simply reviews and assesses sweepline and divide-andconquer algorithms, based on which a new compound algorithm is provided after studying the sweepline algorithm seriously. To start with, this new compound algorithm divides a set of points into several grid tiles with different dividing methods by divide-and-conquer algorithm, and then constructs subnet in each grid tile by sweepline algorithm. Finally these subnets are recursively merged into a whole delaunay triangulation with a simplified efficient LOP algorithm. Because topological structure is important to temporal and spatial efficiency of this algorithm, we only store data about vertex and triangle, thus edge is impliedly expressed by two adjacent triangles. In order to fit two subnets merging better, we optimize some data structure of sweepline algorithm. For instance, frontline and baseline of triangulation are integrated into one line, and four pointers point to where maximum and minimum of x axis and y axis are in this outline. The test shows that this new compound algorithm has better efficiency, stability and robustness than divide-and-conquer and sweepline algorithms. Especially if we find the right dividing method reply to different circumstance, its superiority is remarkable.