利用可控分形插值实现海岸线多分辨率可视化
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摘要
为了实现海岸线弯曲特征保持的多分辨率可视化,提出一种基于可控分形插值的海岸线多分辨率可视化方法.首先对海岸线进行弯曲特征划分,将不可控的整体分形插值变换为以弯曲为单元的分段插值组合;然后利用一维随机中点移位法对各弯曲单元进行分形插值,并利用各弯曲单元的几何特征对分形插值函数的主要参量进行约束控制;最后建立分形次数与分辨率之间的函数关系,实现海岸线弯曲特征保持的多分辨率可视化.实验结果表明,该方法能够实现海岸线从低分辨率到高分辨率的多分辨率可视化重建,并能有效地保持海岸线的弯曲特征和随机分形特征.
To implement multi-resolution visualization of coastline with its bending characteristics preserved,this paper proposes a multi-resolution visualization method for coastline based on the controlled fractal interpolation.First,the coastline is divided into several parts based on its bending characteristics,which can change the uncontrollable general fractal interpolation into a combination of several piecewise interpolation units.Second,the one dimensional random midpoint displacement method is taken to do fractal interpolation for each bending unit,and the main parameters of the fractal interpolation function are controlled by the geometrical characteristics of each bending unit.At last,by establishing a function relation between the number of fractal interpolation and the resolution,the multi-resolution visualization of coastline is implemented by this controlled fractal interpolation.The experiments show that this method can realize multi-resolution visualization reconstruction of coastline from low resolution to high resolution,and can effectively maintain the bending characteristics and random fractal characteristics of coastline.
To implement multi-resolution visualization of coastline with its bending characteristics preserved,this paper proposes a multi-resolution visualization method for coastline based on the controlled fractal interpolation.First,the coastline is divided into several parts based on its bending characteristics,which can change the uncontrollable general fractal interpolation into a combination of several piecewise interpolation units.Second,the one dimensional random midpoint displacement method is taken to do fractal interpolation for each bending unit,and the main parameters of the fractal interpolation function are controlled by the geometrical characteristics of each bending unit.At last,by establishing a function relation between the number of fractal interpolation and the resolution,the multi-resolution visualization of coastline is implemented by this controlled fractal interpolation.The experiments show that this method can realize multi-resolution visualization reconstruction of coastline from low resolution to high resolution,and can effectively maintain the bending characteristics and random fractal characteristics of coastline.
引文
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[16]Wang Hongyong,Fan Zhaolei.Analytical characteristics of fractal interpolation functions with function vertical scaling factors[J].Acta Mathematica Sinica,2011,54(1):147-158(in Chinese)(王宏勇,樊昭磊.具有函数纵向尺度因子的分形插值函数的分析特性[J].数学学报,2011,54(1):147-158)
[17]Metzler W,Yun C H.Construction of fractal interpolation surfaces on rectangular grids[J].International Journal of Bifurcation and Chaos,2011,20(12):4079-4086
[18]Wu Hehai.Application of extended fractal dimension in map generalization[J].Science of Surveying and Mapping,2010,35(4):10-13(in Chinese)(毋河海.扩展分维在地图信息综合中的应用[J].测绘科学,2010,35(4):10-13)
[19]Huang Yafeng,Ai Tinghua,Liu Yaolin,et al.Geographic-feature oriented ria coastline simplification[J].Acta Geodaetica et Cartographica Sinica,2013,42(4):595-601(in Chinese)(黄亚锋,艾廷华,刘耀林,等.顾及地理特征保持的溺谷海岸线化简算法[J].测绘学报,2013,42(4):595-601)
[20]Wang Qiao,Wu Jitao.The research on fractal method of determining reduced length of cartographic lines[J].WTUSM Bulletin of Science and Technology,1996(3):5-7(in Chinese)(王桥,吴纪桃.地图上曲线长度归算的分形方法研究[J].武测科技,1996(3):5-7)
[21]Ai Tinghua,Guo Renzhong,Liu Yaolin.A binary tree representation of curve hierarchical structure in depth[J].Acta Geodaetica et Cartographica Sinica,2001,30(4):343-348(in Chinese)(艾廷华,郭仁忠,刘耀林.曲线弯曲深度层次结构的二叉树表达[J].测绘学报,2001,30(4):343-348)
[22]Beckett P.Cartographic generalization[J].The Cartographic Journal,1977,14(1):49-55
[2]Secchi P,Vantini S,Zanini P.Hierarchical independent component analysis:a multi-resolution non-orthogonal data-driven basis[J].Computational Statistics&Data Analysis,2016,95:133-149
[3]van Oosterom P,Meijers M.Vario-scale data structures supporting smooth zoom and progressive transfer of 2D and 3D data[J].International Journal of Geographical Information Science,2014,28(3):455-478
[4]Reniers D,van Wijk J,Telea A.Computing multiscale curve and surface skeletons of genus 0 shapes using a global importance measure[J].IEEE Transactions on Visualization and Computer Graphics,2008,14(2):355-368
[5]Cao Zhenzhou,Li Manchun,Cheng Liang,et al.Algorithm of generating multi-resolution curves for progressive transmission over the Internet[J].Journal of Computer Applications,2013,33(3):688-690+694(in Chinese)(操震洲,李满春,程亮,等.适用于网络渐进传输的多分辨率曲线生成算法[J].计算机应用,2013,33(3):688-690+694)
[6]Nie Junlan,Zhang Jikai,Liu Shuo,et al.Enum-quadtree based multi-resolution geometry image rendering method[J].Journal of Computer-Aided Design&Computer Graphics,2013,25(7):988-995(in Chinese)(聂俊岚,张继凯,刘硕,等.基于枚举四叉树的多分辨率几何图像绘制方法[J].计算机辅助设计与图形学学报,2013,25(7):988-995)
[7]Ai Tinghua,Cheng Jianguo.Key issues of multi-scale representation of spatial data[J].Geomatics and Information Science of Wuhan University,2005,30(5):377-382(in Chinese)(艾廷华,成建国.对空间数据多尺度表达有关问题的思考[J].武汉大学学报:信息科学版,2005,30(5):377-382)
[8]Yang Yan,Ji Xiaogang,Li Qingzhong,et al.Multiresolution compliance for quasi-uniform cubic B-spline curves[J].Machine Design and Research,2014,30(1):1-4(in Chinese)(杨艳,纪小刚,李庆忠,等.准均匀三次B样条曲线的多分辨率光顺[J].机械设计与研究,2014,30(1):1-4)
[9]Gao Min,Zheng Hongchan.Multiresolution representation of freedom curves based on reverse B-spline of degree three subdivision scheme[J].Scientia Sinica Informationis,2013,43(7):895-906(in Chinese)(高敏,郑红婵.基于三次B样条逆向细分的自由曲线的多分辨率表示[J].中国科学:信息科学,2013,43(7):895-906)
[10]Zhao Gang,Wang Aizeng,Mu Guowang.Wavelet-based automatic fairing algorithm for non-uniform B-spline curve[J].Journal of Computer-Aided Design&Computer Graphics,2010,22(11):1925-1931(in Chinese)(赵罡,王爱增,穆国旺.基于小波的非均匀B样条曲线自动光顺算法[J].计算机辅助设计与图形学学报,2010,22(11):1925-1931)
[11]Shu X,Pan L,Wu X J.Multi-scale contour flexibility shape signature for Fourier descriptor[J].Journal of Visual Communication and Image Representation,2015,26(c):161-167
[12]Wang Qiao.Fractal interpolation of map curve[J].WTUSM Bulletin of Science and Technology,1995(4):8-13(in Chinese)(王桥.地图曲线的分形插值[J].武测科技,1995(4):8-13)
[13]Barnsley M F.Fractal functions and interpolation[J].Constructive Approximation,1986,2(1):303-329
[14]Lu Lin,Wu Jitao,Liu Zhongkan.A new multi-resolution interpolation based on the variance of geographic curve[J].Acta Geodaetica et Cartographica Sinica,2004,33(4):352-355(in Chinese)(卢林,吴纪桃,柳重堪.基于等高线统计特性的多分辨率插值方法[J].测绘学报,2004,33(4):352-355)
[15]Zhang Huaguo,Huang Weigen,Zhou Changbao.A new fractal interpolation approach for geographic curve[J].Acta Geodaetica et Cartographica Sinica,2002,31(3):255-261(in Chinese)(张华国,黄韦艮,周长宝.一种新的地理线要素分形插值方法[J].测绘学报,2002,31(3):255-261)
[16]Wang Hongyong,Fan Zhaolei.Analytical characteristics of fractal interpolation functions with function vertical scaling factors[J].Acta Mathematica Sinica,2011,54(1):147-158(in Chinese)(王宏勇,樊昭磊.具有函数纵向尺度因子的分形插值函数的分析特性[J].数学学报,2011,54(1):147-158)
[17]Metzler W,Yun C H.Construction of fractal interpolation surfaces on rectangular grids[J].International Journal of Bifurcation and Chaos,2011,20(12):4079-4086
[18]Wu Hehai.Application of extended fractal dimension in map generalization[J].Science of Surveying and Mapping,2010,35(4):10-13(in Chinese)(毋河海.扩展分维在地图信息综合中的应用[J].测绘科学,2010,35(4):10-13)
[19]Huang Yafeng,Ai Tinghua,Liu Yaolin,et al.Geographic-feature oriented ria coastline simplification[J].Acta Geodaetica et Cartographica Sinica,2013,42(4):595-601(in Chinese)(黄亚锋,艾廷华,刘耀林,等.顾及地理特征保持的溺谷海岸线化简算法[J].测绘学报,2013,42(4):595-601)
[20]Wang Qiao,Wu Jitao.The research on fractal method of determining reduced length of cartographic lines[J].WTUSM Bulletin of Science and Technology,1996(3):5-7(in Chinese)(王桥,吴纪桃.地图上曲线长度归算的分形方法研究[J].武测科技,1996(3):5-7)
[21]Ai Tinghua,Guo Renzhong,Liu Yaolin.A binary tree representation of curve hierarchical structure in depth[J].Acta Geodaetica et Cartographica Sinica,2001,30(4):343-348(in Chinese)(艾廷华,郭仁忠,刘耀林.曲线弯曲深度层次结构的二叉树表达[J].测绘学报,2001,30(4):343-348)
[22]Beckett P.Cartographic generalization[J].The Cartographic Journal,1977,14(1):49-55