基于不规则三角网的数字地形生成与简化算法研究
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摘要
随着数字地球概念的提出及虚拟现实技术广泛应用,三维地形模型作为其中不可缺少的组成部分,扮演着越来越重要的角色。它是建立虚拟地形环境的“骨架”,是对复杂地形进行分析和研究的基础,是绘制逼真地形环境场景、准确表达空间信息相关关系以及空间分析结果可视化的前提。由于三维地形场景的生成一般基于真实的地形数据和高分辨率的遥感影像,对于大规模地形场景的显示来说,如此庞大的数据量使得图形工作平台无法进行实时的显示。针对大规模地形场景的绘制问题,国内外的学者进行了大量的研究,其工作重点集中在TIN的生成技术和多分辨率地形模型上。
本文主要研究了三维地形模型建模的基本理论与方法,总结了前人在地形模型建模方面所作的工作。针对逐点插入算法在构建TIN地形模型时效率低的问题,提出了一种基于“虚拟网格”划分的VG-逐点插入法,并给出了一种优化离散点插入顺序的方法,减少了点插入过程中需查找的三角形数目和需要重构的三角形个数。VG-逐点插入算法使时间复杂度由原来( )O n2降低到了O (n log n),实现了TIN地形模型的快速建立。同时研究、对比了各种构造多分辨率地形模型的算法,针对常用的PM算法存在的时间效率低、部分拓扑关系不能有效保持的问题,将二次误差测度与顶点的法向锥半角相结合作为网格简化准则,代替了原PM算法中的能量方程;选择折叠边其中的一个顶点作为边折叠后新顶点的位置,提出了一种改进的PM算法。改进后的算法不仅降低了原算法的复杂度,而且消除了累进网格的二义性。同时还对简化过程中各种可能产生的拓扑错误进行了判断并给出有效的解决方法。在算法的改进过程中还对边界边、边界点进行了合理的处理,使得算法更具有普遍性;采用最小堆进行对边折叠误差进行排序,降低了时间复杂度。最后采用太行山某区域地形数据验证了TIN地形模型生成算法的可行性和高效性,并验证了改进后的PM算法不仅效率高而且生成的简化网格质量好,为地形模型在实际中应用提供了前提。
With the present of digital-earth concept and comprehensive application of virtual reality technology, Three-Dimension Terrain Model (3D terrain model) as an indispensable part of those is playing a more important role. 3D terrain model is the“framework”of modeling Virtual Terrain Environment (VTE), and it is the basis of analysing and researching on the complicated terrain, and it is also the premise of rendering real terrain scene, exactly expressing the space information correlativity and visualizing spatial analysis result. Establishing 3D terrain model generally based on the real terrain data and high resolution satellite images. The quantity of data is so large that graphics platform can not display large-scale terrain in real-time. In order to solve this problem, researchers have done a lot of work. And most of these work focuses on the creation of irregular triangle network (TIN) and multiresolution terrain models.
This paper studies and summarizes the fundamental theories and methods of establishing 3D terrain model. Focusing on the problem of inefficiency about the traditional incremental inserting algorithm, this paper presents VG-incremental inserting algorithm based on the Virtual Grid and provides a new method of optimizing the insertion sequence about the discrete points. As a result, the triangular numbers to be searched and reconstructed can be reduced. The VG-incremental inserting algorithm decreases the time complexity from ( )O n2 to O (n log n) and realizes the TIN terrain model more quickly. All kinds of modeling multiresolution terrain model algorithms are studied and contrasted as well. Aiming at the problems of time inefficiency and some topological characteristic can’t be maintained effectively in traditional PM algorithm, an improved PM algorithm is presented through combining quadric error metrics and half angle of vertex normal cone as the rule of mesh simplification to repalce original energy equation of PM algorithm and choosing one vertex of collapse edge as the new vertex position. The improved PM algorithm not only reduces the algorithmic complexity,but also eliminates the ambiguity of progressive mesh, at the same time, recommends how to judge and solve all kinds of the topological characteristics in process of mesh simplification. Furthermore, the method for dealing with the boundary vertexes and edges along with the smallest stack to rank the folded error were used for improving the time efficiency and universal application of the algorithm. The feasibility and the high-efficiency of the algorithm for establishing TIN terrian model as well as the good performance in the efficiency and quality of the improved PM algorithm has been confirmed by the experiments on certain area terrain data of TaiHang mountain. All of this providing the premise for the application of terrain model in practice.
本文主要研究了三维地形模型建模的基本理论与方法,总结了前人在地形模型建模方面所作的工作。针对逐点插入算法在构建TIN地形模型时效率低的问题,提出了一种基于“虚拟网格”划分的VG-逐点插入法,并给出了一种优化离散点插入顺序的方法,减少了点插入过程中需查找的三角形数目和需要重构的三角形个数。VG-逐点插入算法使时间复杂度由原来( )O n2降低到了O (n log n),实现了TIN地形模型的快速建立。同时研究、对比了各种构造多分辨率地形模型的算法,针对常用的PM算法存在的时间效率低、部分拓扑关系不能有效保持的问题,将二次误差测度与顶点的法向锥半角相结合作为网格简化准则,代替了原PM算法中的能量方程;选择折叠边其中的一个顶点作为边折叠后新顶点的位置,提出了一种改进的PM算法。改进后的算法不仅降低了原算法的复杂度,而且消除了累进网格的二义性。同时还对简化过程中各种可能产生的拓扑错误进行了判断并给出有效的解决方法。在算法的改进过程中还对边界边、边界点进行了合理的处理,使得算法更具有普遍性;采用最小堆进行对边折叠误差进行排序,降低了时间复杂度。最后采用太行山某区域地形数据验证了TIN地形模型生成算法的可行性和高效性,并验证了改进后的PM算法不仅效率高而且生成的简化网格质量好,为地形模型在实际中应用提供了前提。
With the present of digital-earth concept and comprehensive application of virtual reality technology, Three-Dimension Terrain Model (3D terrain model) as an indispensable part of those is playing a more important role. 3D terrain model is the“framework”of modeling Virtual Terrain Environment (VTE), and it is the basis of analysing and researching on the complicated terrain, and it is also the premise of rendering real terrain scene, exactly expressing the space information correlativity and visualizing spatial analysis result. Establishing 3D terrain model generally based on the real terrain data and high resolution satellite images. The quantity of data is so large that graphics platform can not display large-scale terrain in real-time. In order to solve this problem, researchers have done a lot of work. And most of these work focuses on the creation of irregular triangle network (TIN) and multiresolution terrain models.
This paper studies and summarizes the fundamental theories and methods of establishing 3D terrain model. Focusing on the problem of inefficiency about the traditional incremental inserting algorithm, this paper presents VG-incremental inserting algorithm based on the Virtual Grid and provides a new method of optimizing the insertion sequence about the discrete points. As a result, the triangular numbers to be searched and reconstructed can be reduced. The VG-incremental inserting algorithm decreases the time complexity from ( )O n2 to O (n log n) and realizes the TIN terrain model more quickly. All kinds of modeling multiresolution terrain model algorithms are studied and contrasted as well. Aiming at the problems of time inefficiency and some topological characteristic can’t be maintained effectively in traditional PM algorithm, an improved PM algorithm is presented through combining quadric error metrics and half angle of vertex normal cone as the rule of mesh simplification to repalce original energy equation of PM algorithm and choosing one vertex of collapse edge as the new vertex position. The improved PM algorithm not only reduces the algorithmic complexity,but also eliminates the ambiguity of progressive mesh, at the same time, recommends how to judge and solve all kinds of the topological characteristics in process of mesh simplification. Furthermore, the method for dealing with the boundary vertexes and edges along with the smallest stack to rank the folded error were used for improving the time efficiency and universal application of the algorithm. The feasibility and the high-efficiency of the algorithm for establishing TIN terrian model as well as the good performance in the efficiency and quality of the improved PM algorithm has been confirmed by the experiments on certain area terrain data of TaiHang mountain. All of this providing the premise for the application of terrain model in practice.
引文
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[2]邸凯昌著.空间数据发掘与知识发现.武汉:武汉大学出版社[M], 2000.
[3]石云,孙玉方,左春.空间数据采掘的研究与发展[J].计算机研究与发展,1999,36(11): 1301-1308.
[4]高俊.地理空间数据可视化[J].测绘工程,2000,9(3):1-7.
[5]林珲,龚建华.虚拟地理环境[M].高等教育出版社,2001.
[6] Gahengan M. Four barrier to the development of effective explorary visualization tools for geoscience. Int. J. Geographical Information Systems,1999,13 (4): 289-309.
[7]马小虎.一种基于图的平面点集Delaunay三角剖分算法[J].中国图像图形学报,1997,2(1):7-11.
[8] Lee D. T. Schachter B. J. Tow Algorithms For Constructing a Delaunay Triangulation.Int J of Computer and Information Science,1980,9(3):219-243.
[9] Sapidis N. , Perucchio R. ,Delaunay triangulation of arbitrarily shaped planar domains. GAGD. 1991,8(6):421-437.
[10] Watson D. F. Computing the n-dimentional Delaunay tessellation with application to Voronoi polutopes. The Computer J,1981,24(2):162-166.
[11] Daniel K. Blandford,Guy E. Blelloch,Clemens Kadow. Engineering a Compact Parallel Delaunay Algorithm in 3D. ACM Symposium on Computational Geometry (SoCG), June 2006,pages:292-300.
[12] Lawson C. L., A software for C surface interpolation. In: Rice J R. ed. Mathematical Software III. New York, Academic press: 1997,219-242.
[13] Floriani. L. D. Puppo. E. An on-line Algorithm for Constrained Delaunay Triangulation. GAGIP: Graphical Mofels and Image Processing. 1992,54(3):290-300.
[14]袁翰,李伟波,陈婷婷.对构建Delaunay三角网中凸壳算法的研究与改进[J].计算机工程,2007,33(7):70-72.
[15]徐道柱,刘海砚.Delaunay三角网建立的改进算法[J].测绘与空间地理信息,2007,30(1): 38-41.
[16]蒲浩,宋占峰,詹振炎.快速构建三角网数字地形模型方法的研究[J].中国铁道科学,2002, (12):10-105.
[17]徐道柱,刘海砚.Delaunay三角网建立的改进算法[J].测绘与空间地理信息,2007,30(1) :38-41.
[18]武晓波,王世新,肖春生.一种生成Delaunay三角网的合成算法[J.遥感学报,2000,4(1):32-35.
[19]徐青,常歌,杨力.基于自适应分块的TIN三角网建立算法[J].中国图象图形学报,2000,5(A):461-465
[20] V.J.D.Tsai.Delaunay Triangulation in TIN Creation:an overview and a linear-time algorithm . Int.J. of Gis,1993,7(6):501-524.
[21]何俊,戴浩,谢永强,刘宝生.一种改进的快速Delaunay三角网三角剖分算法[J].系统仿真学报,2006,18(11):3055-3057.
[22] Shamos M. and Hoey D..Closet-point problem.Processing of the 16th Annnual IEEE Symposium on Foundation of Computer Science.1975,151-162.
[23]石松,朱泉锋,唐丽.四叉树高效Delaunay三角网生成算法[J].计算机工程,2005,31(18): 87-89.
[24]贾瑞生,姜岩,孙红梅,葛平俱.三维地形建模与可视化研究[J].系统仿真学报,2006,18:330-332.
[25]何晖光,田捷,张晓鹏等.网格化简综述[J].软件学报,2002,13(12):2215-2224.
[26] Rossignac,J.,Borrel,P.Multi-Resolution 3D approximation for rendering complex scenes. In: Falcidieno,B.,Kunii, T.L.,eds. Proceedings of the 2nd Conference Modeling in Computer Graphics: Methods and Applications. Berlin: Springer-Verlag, 1993, 453-465.
[27] Coral C. M. et al., Modeling the integration lf light between diffuse surface. In: Proc. Of SIGGRAPH’84. New York: The Assoc. Computing Machinery, INC.1984, 213-222.
[28]沈沉,沈向洋,马颂德.基于图像的光照模型研究综述[J].计算机学报,2000,23(12): 1261-1269.
[29] Zhou Kun,Pan Zhigeng,Shi Jiaoying. A new mesh simplification based on triangle collapse. Journal of Automation,1999,25(1):1-8 (in Chinese).
[30] Schroeder W.et al. Dcimation of triangules meshes. Computer Graphics.1999,26(2):65-68.
[31] Lindstrom P. et al., Real-time Continuous level of Detail Rendering of Height Fields. In: proc. IEEE Visualization’98. 1998,279-286.
[32] Kalvin, A.D., Taylor, R.H. Superfaces: polygonal mesh simplification with bounded error. IEEE Computer Graphics and Applications,1996,16(3):64-77.
[33] Li Jie,Tang Zesheng. Realtime continuous level of detail rendering for 3D complex models. In: Shi Jiaoying, ed. Proceedings of the CAD&Graphics’97. Shenzhen: International Academic Publishers,1997. 101-106.
[34] Li Jie, Tang Zesheng. An improved greedy algorithm for simplification of triangular meshes. In: Shi Jiaoying,ed. Proceedings of the CAD&Graphics’97. Shenzhen: International Academic Publishers,1997. 119-122.
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