## Algorithm for Rapidly Generating Digital Terrain Model Based on Quad-tree

**XIE Chuan jie 1) , WAN Hong tao 2) 1) (State Key Lab. of Resources and Environment Information Systems, The Institute of Geography Science and Resources, CAS, Beijing 100101) 2) (Institute of Reniote Sensing Applications,**

In this paper, an algorithm to generate digital terrain model rapidly is presented. The algorithm is based on the constrained delaunay triangulation(CDT) algorithm. The algorithm achieves a high performance by efficient managing data for the digital terrain model by quad tree, and by reducing the calculation of the algorithm by quad tree. At first, the discrete points of the digital terrain model are distributed to different leaf nodes of the quad tree; then, the points in the leaf node of quad tree are triangulated by delaunay triangulation algorithm; at Last, meshes in the nodes which are neighborhood in space are coalesced together to generate a new smooth mesh. The algorithm is high performance because in the coalition which only need to deal with the points in the hull of the mesh in each node of quad tree. Moreover, the constrained edges and constrained polygons can be integrated to the mesh quickly by using quad tree structure. In the paper, the test results of the algorithm and the analysis to the test results are also presented. Moreover, a test picture of the algorithm is illustrated. In the last part of the paper, the time cost analysis of the algorithm and the spatial characteristics analysis of the algorithm are presented. The test results show that the algorithm not only has excellent performance but also is robust. The time cost analysis of the algorithm shows that the expected time of the algorithm is O(n log( n )), and the analysis of the spatial characteristics of the algorithm shows that algorithm can be adaptive to different spatial distributed situation of the points set to be triangulated. Meanwhile, the constrained edges and the constrained polygons can be integrated into the triangulated mesh efficiently with the help of quad tree structure of the algorithm.

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