地图投影经纬网构形规律研究
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摘要
针对地图投影的经纬网构形存在怎样的规律问题,该文在论述常规地图投影具有一条中央直经线,投影的经纬网具有镜射变换特点的基础上,对地图平面上的经纬网、中央经线及其类型、地图投影的不同空间结构的经线族、纬线族进行了数学表达。通过引入无穷大数学的相关概念,阐释了地图投影的拓扑不变性。在定义若干经线族和纬线族的基础上,应用不同经线族和纬线族组合成常规地图投影和具有跨极中央经线的混合型地图投影的原理,对经纬网的构形规律进行了描述和解释。
Aiming at the problem of the configuration of the meridian and latitude network of the map projection,and on the basis of the fact that the conventional map projection has a central straight line and the projected meridian and latitude network has the characteristics of mirror transformation,this paper gave mathematical expression on meridian and latitude network,central meridian and its type,different spatial structures of the latitude and meridian groups in map projection.The concepts of infinite mathematics were introduced to explain the topological invariance of map projection.On basis of the definition of several meridian and latitude groups,and based on the theory that different latitude and meridian groups can combine to form conventional map projection and hybrid map projection with transcentral meridians,the configuration law of the latitude and meridian network was described and explained.
Aiming at the problem of the configuration of the meridian and latitude network of the map projection,and on the basis of the fact that the conventional map projection has a central straight line and the projected meridian and latitude network has the characteristics of mirror transformation,this paper gave mathematical expression on meridian and latitude network,central meridian and its type,different spatial structures of the latitude and meridian groups in map projection.The concepts of infinite mathematics were introduced to explain the topological invariance of map projection.On basis of the definition of several meridian and latitude groups,and based on the theory that different latitude and meridian groups can combine to form conventional map projection and hybrid map projection with transcentral meridians,the configuration law of the latitude and meridian network was described and explained.
引文
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[2]钟业勋,童新华,韦清嫄,等.地图投影的拓扑学原理[J].桂林理工大学学报,2014,34(3):510-514.(ZHONG Yexun,TONG Xinhua,WEI Qingyuan,et al.Topologic principle in mapping projection[J].Journal of Guilin University of Technology,2014,34(3):510-514.)
[3]胡毓钜,龚剑文.地图投影[M].2版.北京:测绘出版社,1992.(HU Yuju,GONG Jianwen.Map projections[M].2nd ed.Beijing:Surveying and Mapping Press,1992.)
[4]钟业勋,胡宝清.数理地图学:地图学及其数学原理[M].2版.北京:测绘出版社,2017.(ZHONG Yexun,HU Baoqing.Mathematical cartography:cartography and its mathematical elements[M].2nd ed.Beijing:Surveying and Mapping Press,2017.)
[5]刘佳奇,钟业勋,胡宝清,等.基于镜射变换的地图投影新定义体系[J].黑龙江工程学院学报,2017,31(3):1-4.(LIU Jiaqi,ZHONG Yexun,HU Baoqing.New definitions system of map projection based on reflex transformation[J].Journal of Heilongjiang Institute of Technology,2017,31(3):1-4.)
[6]钟业勋,胡毓钜,乔俊军.地图投影的科学美和艺术美[J].海洋测绘,2012,32(2):75-78.(ZHONG Yexun,HU Yuju,QIAO Junjun.Beauty of science and art in map projection[J].Hydrographic Surveying and Charting,2012,32(2):75-78.)
[7]钟业勋,胡毓钜,童新华.基于不同经纬线类型组合的地图投影新定义[J].海洋测绘,2012,32(6):13-16.(ZHONG Yexun,HU Yuju,TONG Xinhua.The new definition of map projections based on different types of meridian and parallel combination[J].Hydrographic Surveying and Charting,2012,32(6):13-16.)
[8]毋河海.GIS与地图信息综合基本模型与算法[M].武汉:武汉大学出版社,2010.(WU Hehai.GIS and map generalization models&algorithms[M].Wuhan:Wuhan University Press,2010.)
[9]张铁声.相似论:相似·同构·认知[M].南京:江苏科技出版社,1995.(ZHANG Tiesheng.Similarity theory:smilarity·isomorphism·cognition[M].Nanjing:Jiangsu Science and Technology Press,1995.)
[10]汪信砚.科学价值论[M].桂林:广西师范大学出版社,1995.(WANG Xinyan.Scientific axiology[M].Guilin:Guangxi Normal University Press,1995.)
[11]汪罗淼,严虹,廖义琴.几何学概论[M].北京:清华大学出版社,2011.(WANG Luomiao,YAN Hong,LIAO Yiqin.Introduction to geometry[M].Beijing:Tsinghua University Press,2011.)
[12]谷超豪.数学词典[M].上海:上海辞书出版社,1992.(GU Chaohao.Mathmetical dictonary[M].Shanghai:Dictonary Press of Shanghai,1992.)
[13]吴迪,钟业勋,胡宝清,等.系列世界地图的经纬网数学模型研究[J].海洋测绘,2018,38(2):61-65.(WU Di,ZHONG Yexun,HU Baoqing,et al.Structural character of meridian and parallel and its mathematical model of world maps[J].Hydrographic Surveying and Charting,2018,38(2):61-65.)
[14]钟业勋,冯可君.关于地图投影存在变形的数学分析与几何证明[J].地图,1993(2):11-13.(ZHONG Yexun,FENG Kejun.Mathematical analysis and geometric proof of deformation of map projection[J].Map,1993(2):11-13.)
[15]伽莫夫G.从一到无穷大:科学中的事实和臆测[M].暴永宁,译.北京:科学出版社,2017.(GAMOW G.From one to infinitely great:fact and conjecture in sciences[M].BAO Yongning,translation.Beijing:Scentific Press,2017.)
[16]胡毓钜,龚剑文.地图投影图集[M].3版.北京:测绘出版社,2006.(HU Yuju,GONG Jianwen.Map Projections[M].3rd ed.Beijing:Surveying and Mapping Press,2006.)
[17]郝晓光.新编世界地图:历史与科学的交融[R].[出版地不详]:[出版者不详],2015.(HAO Xiaoguang.The new world map:the blend of history and science[R].[S.l.]:[s.n.],2015.)
[18]郝晓光,徐汉卿,刘根友,等.系列世界地图[J].大地测量与地球动力学,2003,23(2):111-116.(HAO Xiaoguang,XU Hanqing,LIU Genyou,et al.A series of world map[J].Crustal Deformation and Earthquake,2003,23(2):111-116.)