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首页> 外文期刊>Computers, Environment and Urban Systems >Comparison Of Region Approximation Techniques Based On Delaunay Triangulations And Voronoi Diagrams
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Comparison Of Region Approximation Techniques Based On Delaunay Triangulations And Voronoi Diagrams

机译：基于Delaunay三角剖分和Voronoi图的区域逼近技术的比较

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Region approximation techniques based on constructions from sample data points, i.e. points whose position is known and which are known to be inside or outside the region of interest, can be advantageous in a variety of applications. This paper compares two different constructions and presents results from a Monte Carlo model that shows that the construction based on mid points of edges in a Delaunay trian-gulation produces the lowest errors. These errors are some 10% less than those produced by the Voronoi diagram construction which appears to be more widely used at present. A consideration of the basic geometries of the different constructions leads to an expression for approximating the expected error in the case of a random point distribution. The expression takes the form E_(RMS) = k_d [S/4 + (l_o~2)/(32S) (((l_c~2)/(l_o~2)) - 1)], where S is the average point spacing, l_o is the length of region boundary being approximated (the optimum length for the construction), and l_c the length of the constructed line approximating the boundary. The constant k_d accounts for the non-uniform spacing of the points in the distribution and has a value of about 1.1 for a random distribution. Predictions from this expression agree well with the results from the Monte Carlo model. The case of finite as well as infinite radius of curvature is considered and some possible improvements on the constructions modelled are suggested.
机译：基于来自样本数据点（即，其位置已知并且已知在感兴趣区域的内部或外部）的点的构造的区域近似技术在各种应用中可能是有利的。本文比较了两种不同的构造，并给出了蒙特卡洛模型的结果，该结果表明，基于Delaunay trian-gulation的边中点的构造产生的误差最小。这些误差比Voronoi图构造所产生的误差小10％，而Voronoi图构造目前似乎已被广泛使用。考虑到不同构造的基本几何形状，得出了一种在随机点分布的情况下近似预期误差的表达式。表达式的形式为E_（RMS）= k_d [S / 4 +（l_o〜2）/（32S）（（（l_c〜2）/（l_o〜2））-1）]，其中S是平均点间距，l_o是近似区域边界的长度（构造的最佳长度），l_c是近似边界的构造线的长度。常数k_d解释了分布中点的不均匀间距，对于随机分布，其值约为1.1。该表达式的预测与蒙特卡洛模型的结果非常吻合。考虑了有限曲率半径和无限曲率半径的情况，并提出了对建模结构的一些可能的改进。

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