Complexity measurement of line element on nautical chart considering local difference

doi:10.11947/j.AGCS.2022.20210129

Abstract

Abstract: The existing line-element-complexity-measurement methods are usually to calculate the overall complexity of a single line element, which cannot consider the differences of line element in different regions. Therefore, we present a complexity measurement method of line element on nautical chart considering local difference. Firstly, the correlation between the length of edge in triangle network and the complexity of the line elements is analyzed. Then, the complex field of line elements on nautical chart is obtained by the steps of constructing constrained Delaunay triangulation, calculating the data point complexity of line elements and interpolating. Finally, we choose two groups of typical nautical charts as experimental data, and verify the rationality of this method by several statistical experiments. The experimental results show that:the proposed method, considering local differences, can define the complexity of line elements on nautical chart better, which also can accurately and quantitatively evaluate the complexity of line elements in each region.

Key words: nautical chart, line element, complexity, constrained Delaunay triangulation

CLC Number:

P208

WEI Hongcheng, ZHANG Lihua, TANG Lulu, DONG Jian, LI Gaixiao, YUAN Hao. Complexity measurement of line element on nautical chart considering local difference[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(9): 1959-1968.

References

[1] 王厚祥, 李进杰.海图制图综合[M]. 北京:测绘出版社, 1999. WANG Houxiang, LI Jinjie. Generalization of nautical charts[M]. Beijing:Surveying and Mapping Press, 1999.
[2] 刘欢, 谢三德, 王芳. 海岸线自动综合方法综述[J]. 测绘科学技术学报, 2010, 27(3):225-228. LIU Huan, XIE Sande, WANG Fang. Study on the method of automatic cartographic generalization of coastline[J]. Journal of Geomatics Science and Technology, 2010, 27(3):225-228.
[3] 刘颖, 翟京生. 海岸线形态的表达与自动综合[J]. 测绘与空间地理信息, 2005, 28(4):78-81. LIU Ying, ZHAI Jingsheng. The research on pattern presentation and automatic generalization of coastlines[J]. Geomatics & Spatial Information Technology, 2005, 28(4):78-81.
[4] 陈惠荣, 彭认灿, 郑义东, 等. 以弯曲骨架线为化简指标的海岸线综合方法[J]. 武汉大学学报(信息科学版), 2011, 36(12):1418-1422. CHEN Huirong, PENG Rencan, ZHENG Yidong, et al. Coastline generalization based on skeleton line of curve bends[J]. Geomatics and Information Science of Wuhan University, 2011, 36(12):1418-1422.
[5] 张立华, 唐露露, 贾帅东, 等. 多条海岸线协同化简的层次化三角网分区法[J]. 测绘学报, 2019, 48(4):520-531.DOI:10.11947/j.AGCS.2019.20180382. ZHANG Lihua, TANG Lulu, JIA Shuaidong, et al. A collaborative simplification method for multiple coastlines based on the hierarchical triangulation network partition[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(4):520-531. DOI:10.11947/j.AGCS.2019.20180382.
[6] 杜佳威, 武芳, 李靖涵, 等. 一种河口湾海岸线渐进化简方法[J]. 测绘学报, 2018, 47(4):547-556.DOI:10.11947/j.AGCS.2018.20170440. DU Jiawei, WU Fang, LI Jinghan, et al. A progressive simplification method for the estuary coastline[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(4):547-556. DOI:10.11947/j.AGCS.2018.20170440.
[7] 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. 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.
[8] 国家质量技术监督局. 中国航海图编绘规范:GB 12320-1998[S]. 北京:中国标准出版社, 1999. State Bureau of Quality and Technical Supervision of the People's Republic of China. Specifications for Chinese nautical charts:GB 12320-1998[S]. Beijing:Standards Press of China, 1999.
[9] 武芳, 巩现勇, 杜佳威. 地图制图综合回顾与前望[J]. 测绘学报, 2017, 46(10):1645-1664.DOI:10.11947/j.AGCS.2017.20170287. WU Fang, GONG Xianyong, DU Jiawei. Overview of the research progress in automated map generalization[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10):1645-1664. DOI:10.11947/j.AGCS.2017.20170287.
[10] 李成名, 郭沛沛, 殷勇,等. 一种顾及空间关系约束的线化简算法[J]. 测绘学报, 2017, 46(4):498-506.DOI:10.11947/j.AGCS.2017.20160546. LI Chengming, GUO Peipei, YIN Yong, et al. A line simplification algorithm considering spatial relations between two lines[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(4):498-506. DOI:10.11947/j.AGCS.2017.20160546.
[11] 程绵绵, 孙群, 徐立, 等. 面轮廓线相似性和复杂性度量及在化简中的应用[J]. 测绘学报, 2019, 48(4):489-501.DOI:10.11947/j.AGCS.2019.20180124. CHENG Mianmian, SUN Qun, XU Li, et al. Polygon contour similarity and complexity measurement and application in simplification[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(4):489-501. DOI:10.11947/j.AGCS.2019.20180124.
[12] FALOUTSOS C, KAMEL I. Beyond uniformity and independence:analysis of R-trees using the concept of fractal dimension[C]//Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems-PODS'94. Minneapolis, Minnesota, USA:ACM Press, 1994:4-13.
[13] WILLIAMS H. Chaos and fractals, new frontiers of science[J]. The Mathematical Gazette, 2006, 90(519):562.
[14] MA Ding, JIANG Bin. A smooth curve as a fractal under the third definition[J]. Cartographica:the International Journal for Geographic Information and Geovisualization, 2018, 53(3):203-210.
[15] 高义, 苏奋振, 周成虎, 等. 基于分形的中国大陆海岸线尺度效应研究[J]. 地理学报, 2011, 66(3):331-339. GAO Yi, SU Fenzhen, ZHOU Chenghu, et al. Scale effects of China mainland coastline based on fractal theory[J]. Acta Geographica Sinica, 2011, 66(3):331-339.
[16] 刘孝贤, 赵青. 基于分形的中国沿海省区海岸线复杂程度分析[J]. 中国图象图形学报, 2004, 9(10):1249-1257. LIU Xiaoxian, ZHAO Qing. Analysis on the complication-degree for coast line of the Chinese provinces along the sea based on the fractal theory[J]. Journal of Image and Graphics, 2004, 9(10):1249-1257.
[17] 肖天元, 刘鹏程, 艾廷华, 等. 一种傅里叶信息度量的曲线分形描述与多尺度表达方法[J]. 武汉大学学报(信息科学版), 2020, 45(1):119-125. XIAO Tianyuan, LIU Pengcheng, AI Tinghua, et al. A fractal description and multi-scale expression method of Fourier information metrics[J]. Geomatics and Information Science of Wuhan University, 2020, 45(1):119-125.
[18] 刘鹏程, 艾廷华, 毕旭. 傅立叶级数支持下的等高线多尺度表达模型[J]. 武汉大学学报(信息科学版), 2013, 38(2):221-224. LIU Pengcheng, AI Tinghua, BI Xu. Multi-scale representation model for contour based on Fourier series[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2):221-224.
[19] 何爱玲, 王力加, 郭晶鑫, 等. 二维图形复杂度计算与叶片轮廓复杂性分析[J]. 数学计算, 2014,3(3):89-95. HE Ailing, WANG Lijia, GUO Jingxin, et al. Complexity computation of two-dimensional graphics and complexity analysis of leaf contour[J]. Mathematical Computation, 2014,3(3):89-95.
[20] 刘慧敏, 邓敏, 徐震, 等. 线要素几何信息量度量方法[J]. 武汉大学学报(信息科学版), 2014, 39(4):500-504. LIU Huimin, DENG Min, XU Zhen, et al. Geometric information content measurement of individual line feature[J]. Geomatics and Information Science of Wuhan University, 2014, 39(4):500-504.
[21] 艾廷华, 郭仁忠, 陈晓东. Delaunay三角网支持下的多边形化简与合并[J]. 中国图象图形学报, 2001, 6(7):703-709. AI Tinghua, GUO Renzhong, CHEN Xiaodong. Simplification and aggregation of polygon object supported by delaunay triangulation structure[J]. Journal of Image and Graphics, 2001, 6(7):703-709.
[22] 邵春丽, 胡鹏, 黄承义, 等. Delaunay三角网的算法详述及其应用发展前景[J]. 测绘科学, 2004, 29(6):68-71, 5. SHAO Chunli, HU Peng, HUANG Chengyi, et al. The expatiation of Delaunay algorithms and a promising direction in application[J]. Science of Surveying and Mapping, 2004, 29(6):68-71, 5.
[23] 艾廷华, 郭仁忠. 支持地图综合的面状目标约束Delaunay三角网剖分[J]. 武汉测绘科技大学学报, 2000, 25(1):35-41. AI Tinghua, GUO Renzhong. A constrained delaunay partitioning of areal objects to support map generalization[J]. Journal of Wuhan Technical University of Surveying and Mapping (Wtusm), 2000, 25(1):35-41.
[24] 艾廷华, 郭仁忠. 基于约束Delaunay结构的街道中轴线提取及网络模型建立[J]. 测绘学报, 2000, 29(4):348-354. AI Tinghua, GUO Renzhong. Extracting center-lines and building street network based on constrained delaunay triangulation[J]. Acta Geodaetica et Cartographica Sinica, 2000, 29(4):348-354.
[25] 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. 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.
[26] 朱求安, 张万昌, 余钧辉. 基于GIS的空间插值方法研究[J]. 江西师范大学学报(自然科学版), 2004, 28(2):183-188. ZHU Qiuan, ZHANG Wanchang, YU Junhui. The spatial interpolations in GIS[J]. Journal of Jiangxi Normal University (Natural Science Edition), 2004, 28(2):183-188.
[27] 邓晓斌. 基于ArcGIS两种空间插值方法的比较[J]. 地理空间信息, 2008, 6(6):85-87. DENG Xiaobin. Comparison between two space interpolation methods based on ArcGIS[J]. Geospatial Information, 2008, 6(6):85-87.
[28] SIBSON R. A vector identity for the Dirichlet tessellation[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1980, 87(1):151-155.
[29] BELIKOV V V, IVANOV V D, KONTOROVICH V K, et al. The non-sibsonian interpolation:a new method of interpolation of the values of a function on an arbitrary set of points[J]. Computational Mathematics and Mathematical Physics, 1997,37(1):11-17.
[30] 周小平, 周瑞忠. 基于Voronoi图的新型几何插值及其与传统代数插值方法的比较[J]. 岩石力学与工程学报, 2005, 24(1):133-138. ZHOU Xiaoping, ZHOU Ruizhong. New geometric interpolation method based on voronoi diagram and the comparison with traditionalalgebraic method[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(1):133-138.
[31] 王兆清, 冯伟. 自然单元法研究进展[J]. 力学进展, 2004, 34(4):437-445. WANG Zhaoqing, FENG Wei. Advances in natural element method[J]. Advances in Mechanics, 2004, 34(4):437-445.
[32] 刘立珍. 基于自然单元法的渗流分析[D]. 北京:清华大学, 2011. LIU Lizhen. Seepage analysis based on natural element method[D]. Beijing:Tsinghua University, 2011.