Delaunay三角形构网的分治扫描线算法

Delaunay三角网作为一种主要的DTM表示法,具有极其广泛的用途。基于分治算法和逐点插入法的合成算法是目前研究较多的用于生成Delaunay三角网的合成算法。简要介绍和评价扫描线算法和分治算法后,提出一种新的基于这两种算法的合成算法。该方法兼顾空间与时间性能,稳定性较高,分别较扫描线算法和分治算法,运行效率和鲁棒性更优。

A New Study of Compound Algorithm Based on Sweepline and Divide-and-conquer Algorithms for Constructing Delaunay Triangulation

As one of the most important DTM model,Delaunay triangulation is widely applied in manifold fields.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 divide-and-conquer and incremental insertion algorithms.This paper simply reviews and assesses sweepline and divide-and-conquer 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.For 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 combined to 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.