伪形心多边形形心距离计算方法A centroidal distance calculation method of polygons based on assumed centroid
朱钰;王伟;章传银;
摘要(Abstract)：
针对多边形形心距离计算过程中存在的形心位于多边形外的问题,该文提出伪形心的概念,通过三角剖分的方式,计算多边形边界到多边形形心距离最小的点,将形心合理地平移到边界上,进而计算多边形形心距离。针对伪形心存在于邻接边的特殊情况,又提出将形心平移到多边形主骨架线上的改进算法。该文提出的算法简单,易于实现,适用性强,进一步扩展了多边形形心距离计算的思路。
关键词(KeyWords)： 伪形心;三角剖分;主骨架线;形心距离
基金项目(Foundation): 国家自然科学基金项目(41304009,41374081)
作者(Authors): 朱钰;王伟;章传银;
DOI: 10.16251/j.cnki.1009-2307.2018.02.002
参考文献(References)：
- [1]闫浩文,王明孝,王中辉.计算几何:空间数据处理方法[M].北京:科学出版社,2012.(YAN Haowen,WANG Mingxiao,WANG Zhonghui.Computation geometry:spatial data processing method[M].Beijing:Science Press,2012.)
- [2]毛定山,崔先国,李行,等.求解简单多边形间最小距离的一个线性时间算法[J].中国图象图形学报,2008,13(12):2400-2408.(MAO Dingshan,CUI Xianguo,LI Xing,et al.An algorithm for computing the minimal distance between two polygons in linear time[J].Journal of Image and Graphics,2008,13(12):2400-2408.)
- [3]杨春成,张清浦,田向春,等.顾及几何形状相似性的简单多边形最近距离计算方法[J].测绘学报,2004,33(4):311-318.(YANG Chuncheng,ZHANG Qingpu,TIAN Xiangchun,et al.A closest distance computation method for simple polygons considering geometry shape similarity[J].Acta Geodaetica et Cartographica Sinica,2004,33(4):311-318.)
- [4]陈涛,艾廷华.多边形骨架线与形心自动搜寻算法研究[J].武汉大学学报(信息科学版),2004,29(5):443-446.(CHEN Tao,AI Tinghua.Automatic extraction of skeleton and center of area feature[J].Geomatics and Information Science of Wuhan University,2004,29(5):443-446.)
- [5]田耀永,任世霞.AutoCAD多边形形心解算的新方法:二分无限逼近法原理及应用[J].科技创新与生产力,2012(1):84-86.(TIAN Yaoyong,REN Shixia.New methods of AutoCAD centroid calculating of polygon:principle and application of half infinite approximation[J].Technology Innovation and Productivity,2012(1):84-86.)
- [6]姜永发,张书亮,兰小机,等.长对角线法实现GIS中矢量地图面状地物汉字注记的自动配置[J].武汉大学学报(信息科学版),2005,30(6):544-548.(JIANG Yongfa,ZHANG Shuliang,LAN Xiaoji,et al.Automatic placement of GIS vector map annotation in area feature by long-diagonal[J].Geomatics and Information Science of Wuhan University,2005,30(6):544-548.)
- [7]HEAM D D,BAKER M P.Computer graphics with OpenGL[M].Beijing:Tsinghua University Press,2006.
- [8]魏士春,张红日,苏奋振,等.基于ArcGIS的面状要素中轴线提取方法研究[J].地理空间信息,2007,5(2):45-47.(WEI Shichun,ZHANG Hongri,SU Fenzhen,et al.Method for medical axis extraction based on ArcGIS[J].Geospatial Information,2007,5(2):45-47.)
- [9]CHOI H I,CHOI S W,MOON H P,et al.New algorithm for medial axis transform of plane domain[J].Graphical Models and Image Processing,1997,59(6):463-483.
- [10]SHAKED D,BERUCKSTEIN A M.The curve axis[J].Computer Vision and Image Understanding,1996,63(2):367-369.
- [11]王中辉,闫浩文.多边形主骨架线提取算法的设计与实现[J].地理与地理信息科学,2011,1(1):42-48.(WANG Zhonghui,YAN Haowen.Design and implementation of an algorithm for extraction the main skeleton lines of polygons[J].Geography and Geo-Information Science,2011,1(1):42-48.)
- [12]汤立东.计算几何中LR可视化问题研究[D].大连:大连海事大学,2010.(TANG Lidong.The research of LR visibility polygon in computational geometry[D].Dalian:Dalian Maritime University,2010.)
- [13]周雅洁,刘英,张晶伟.基于局部可见点进行的凹多边形凸分解算法[J].武汉大学学报(工学版),2004,37(2):85-87.(ZHOU Yajie,LIU Ying,ZHANG Jingwei.A poygon convex decomposition algorithm based on partial visible point[J].Engineering Journal of Wuhan University,2004,37(2):85-87.)