本文關(guān)鍵詞： 歐氏距離 馬氏距離 多高斯 Voronoi圖 一對(duì)多關(guān)系　出處：《地理與地理信息科學(xué)》2016年03期 　論文類型：期刊論文

【摘要】：Voronoi圖作為一種重要的幾何結(jié)構(gòu),不僅是計(jì)算幾何研究的重要內(nèi)容,還是地理空間分析的有力工具,在科學(xué)與工程領(lǐng)域應(yīng)用廣泛。針對(duì)傳統(tǒng)歐氏距離條件下Voronoi圖生長(zhǎng)元權(quán)值大小等同、生長(zhǎng)元與Voronoi圖數(shù)據(jù)結(jié)構(gòu)一對(duì)一關(guān)系的局限性,該文以高斯分布的統(tǒng)計(jì)距離為切入點(diǎn),利用馬氏距離作為Voronoi圖生成距離測(cè)度,提出一種新的Voronoi圖,即多高斯Voronoi圖(MGVD)。MGVD不但囊括了歐氏距離作用下產(chǎn)生的普通Voronoi圖與加權(quán)Voronoi圖,而且將生長(zhǎng)元與Voronoi圖數(shù)據(jù)結(jié)構(gòu)的一對(duì)一關(guān)系拓展為空間的一對(duì)多關(guān)系,表現(xiàn)出單個(gè)空間生長(zhǎng)元的多個(gè)Voronoi圖存在。最后,通過模擬實(shí)驗(yàn)驗(yàn)證了該方法的可行性。
[Abstract]:The Voronoi map is an important geometric structure, is not only an important part of research in computational geometry, is a powerful tool for the analysis of geographic space, widely used in the fields of science and engineering. The traditional Euclidean distance under the condition of Voronoi growth element weights equal growth element and Voronoi graph data structure is a one-to-one relationship limitation. In this paper, the statistical distribution of Gauss distance as the starting point, use the Mahalanobis distance as the distance measure to generate Voronoi diagram, this paper proposes a new Voronoi map, which Gauss Voronoi (MGVD).MGVD not only include the ordinary Voronoi diagram Voronoi diagram and generate Euclidean distance under the action, and the growth of yuan and the relationship between development of one to many relationships for spatial data structures of Voronoi, showing a number of Voronoi yuan in the presence of a single space growth chart. Finally, the simulation results verify the feasibility of the method.

【作者單位】： 中國(guó)礦業(yè)大學(xué)(北京)地球科學(xué)與測(cè)繪工程學(xué)院;
【基金】：中央高校基本科研業(yè)務(wù)費(fèi)專項(xiàng)資金項(xiàng)目(2010YD06)
【分類號(hào)】：P208
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本文編號(hào)：1506134