中心型时间地图的构建方法与实现
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摘要
中心型时间地图是表达各个点到中心点时间距离的一种有效可视化方法。本文提出一种基于移动最小二乘法的中心型时间地图的构建方法。与以往的研究方法相比,该方法解决了中心型时间地图构建中出现的3个问题:(1)通过距离恒定性等原则解决了时间地图与原地图的尺度一致性问题;(2)通过约束条件的控制解决了转换过程中出现的拓扑错误问题;(3)通过多种可视化方法解决了时间地图变形的可视化表达问题。最后,以2016年度北京市到全国307个市县的真实铁路时间数据为例,构建了以北京市为中心的时间地图,该时间地图以全新的视角展示了北京市与全国各城市间的时间距离关系,并为进一步揭示和挖掘中国铁路交通发展状况的规律和趋势提供了可视化依据。
A central time-space map is an effective method for representing time distance from any positions to a given point on a map.We proposed a new method of generating a central time-space map based on moving least squares(MLS).Compared with other methods,our method solved the following 3 problems:(1)the law of consistency of distance was used to keep the same scale of a time-space map and its original map;(2)we used some constraints to adjust topological errors generated by the process of transformation;(3)many visualization methods were used to represent a time-space map's distortion.Finally,we took real trains' timetable data in China in 2016 as a case study to generate a time-space map with Beijing as the center.The results showed that the time distance relationship between Beijing and other cities from a different perspective and were also helpful for further discovering some knowledge and trends of the development of railway transportation in China.
A central time-space map is an effective method for representing time distance from any positions to a given point on a map.We proposed a new method of generating a central time-space map based on moving least squares(MLS).Compared with other methods,our method solved the following 3 problems:(1)the law of consistency of distance was used to keep the same scale of a time-space map and its original map;(2)we used some constraints to adjust topological errors generated by the process of transformation;(3)many visualization methods were used to represent a time-space map's distortion.Finally,we took real trains' timetable data in China in 2016 as a case study to generate a time-space map with Beijing as the center.The results showed that the time distance relationship between Beijing and other cities from a different perspective and were also helpful for further discovering some knowledge and trends of the development of railway transportation in China.
引文
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[3]余金艳,刘卫东,王亮.基于时间距离的C2C电子商务虚拟商圈分析——以位于北京的淘宝网化妆品零售为例[J].地理学报,2013,68(10):1380-1388.YU Jinyan,LIU Weidong,WANG Liang.Analysis of Virtual Trading Area of C2C E-commerce based on Temporal Distance:A Case Study of 50Cosmetics Retail Stores on TAOBAO in Beijing[J].Acta Geographica Sinica,2013,68(10):1380-1388.
[4]陆军,宋吉涛,梁宇生,等.基于二维时空地图的中国高铁经济区格局模拟[J].地理学报,2013,68(2):147-158.LU Jun,SONG Jitao,LIANG Yusheng,et al.The Simulation of Spatial Distribution Patterns of China's HSR-economic Zones based on the 2D Time-space Map[J].Acta Geographica Sinica,2013,68(2):147-158.
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[8]王丽娜,江南,李响,等.Cartogram表示方法研究综述[J].计算机辅助设计与图形学学报,2017,29(3):393-405.WANG Lina,JIANG Nan,LI Xiang,et al.A Survey of Cartogram[J].Journal of Computer-Aided Design&Computer Graphics,2017,29(3):393-405.
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[15]李文翎,李尚智,黎雅雯,等.基于GIS的广州城市时间地图研究[J].热带地理,2008,28(3):218-222,227.LI Wenling,LI Shangzhi,LI Yawen,et al.A Study on Urban Temporal Map of Guangzhou Based on GIS Based on GIS[J].Tropical Geography,2008,8(3):218-222,227.
[16]HONG S,KIM Y S,YOON J C,et al.Traffigram:Distortion for Clarification via Isochronal Cartography[C]∥Proceedings of the SIGCHI Conference on Human Factors in Computing Systems.Toronto,Ontario,Canada:ACM Press,2014:907-916.
[17]BIES S,VAN KREVELD M.Time-Space Maps from Triangulations[C]∥Proceedings of the 20th International Conference on Graph Drawing.Redmond,WA:Springer,2012:511-516.
[18]ULLAH R,KRAAK M J.An Alternative Method to Constructing Time Cartograms for the Visual Representation of Scheduled Movement Data[J].Journal of Maps,2015,11(4):674-687.
[19]刘瑜,龚咏喜,张晶,等.地理空间中的空间关系表达和推理[J].地理与地理信息科学,2007,23(5):1-7.LIU Yu,GONG Yongxi,ZHANG Jing,et al.Representation and Reasoning of Spatial Relations in Geographical Space[J].Geography and Geo-information Science,2007,23(5):1-7.
[20]沈陈华,王旭姣,司亚莉,等.基于旅行者运动轨迹的时间地图变换[J].地理研究,2015,34(6):1160-1172.SHEN Chenhua,WANG Xujiao,SI Yali,et al.Time-space Map Transformation Based on Travelers'Motion Trajectory[J].Geographical Research,2015,34(6):1160-1172.
[21]SCHAEFER S,MCPHAIL T,WARREN J.Image deformation using moving least squares[J].ACM Transactions on Graphics(TOG),2006,25(3):533-540.
[22]刘婷.移动最小二乘图像变形方法研究[D].大连:大连理工大学,2008.LIU Ting.Study on Image Deformation Based on Moving Least Squares[D].Dalian:Dalian University of Technology,2008.
[23]杜晓荣,平淑文,张永.基于移动最小二乘法的图形图像局部变形技术[J].系统仿真学报,2015,27(4):816-823.DU Xiaorong,PING Shuwen,ZHANG Yong.Graphics and Image Local Deformation Based on Moving Least Squares Method[J].Journal of System Simulation,2015,27(4):816-823.
[24]BENTLEY J L,OTTMANN T A.Algorithms for Reporting and Counting Geometric Intersections[J].IEEE Transactions on Computers,1979,28(9):643-647.
[25]王士君,冯章献,刘大平,等.中心地理论创新与发展的基本视角和框架[J].地理科学进展,2012,31(10):1256-1263.WANG Shijun,FENG Zhangxian,LIU Daping,et al.Basic Perspective and Preliminary Framework for the Theoretical Innovation and Development of Central Place Theory in New Times[J].Progress in Geography,2012,31(10):1256-1263.
[2]靳海攀,郑林,张敬伟.基于时间距离的鄱阳湖生态经济区经济联系变化网络分析研究[J].经济地理,2013,33(6):148-154.JIN Haipan,ZHENG Lin,ZHANG Jingwei.Network Analysis of Economic Contacts Variability in Poyang Lake Ecological Economic Zone based on Travel Time Cost[J].Economic Geography,2013,33(6):148-154.
[3]余金艳,刘卫东,王亮.基于时间距离的C2C电子商务虚拟商圈分析——以位于北京的淘宝网化妆品零售为例[J].地理学报,2013,68(10):1380-1388.YU Jinyan,LIU Weidong,WANG Liang.Analysis of Virtual Trading Area of C2C E-commerce based on Temporal Distance:A Case Study of 50Cosmetics Retail Stores on TAOBAO in Beijing[J].Acta Geographica Sinica,2013,68(10):1380-1388.
[4]陆军,宋吉涛,梁宇生,等.基于二维时空地图的中国高铁经济区格局模拟[J].地理学报,2013,68(2):147-158.LU Jun,SONG Jitao,LIANG Yusheng,et al.The Simulation of Spatial Distribution Patterns of China's HSR-economic Zones based on the 2D Time-space Map[J].Acta Geographica Sinica,2013,68(2):147-158.
[5]王永超,吴晓舜,刘洋,等.基于可达性的沈阳经济区中心地空间结构演变[J].地域研究与开发,2013,32(1):56-60.WANG Yongchao,WU Xiaoshun,LIU Yang,et al,The Evolution of the Structure of Central Places in Shenyang Economic Zone Based on Accessibility[J].Areal Research and Development,2013,32(1):56-60.
[6]BUNGE W.Theoretical Geography[D].Washington:University of Washington,1960.
[7]TOBLER W R.Map Transformations of Geographic Space[D].Washington:University of Washington,1961.
[8]王丽娜,江南,李响,等.Cartogram表示方法研究综述[J].计算机辅助设计与图形学学报,2017,29(3):393-405.WANG Lina,JIANG Nan,LI Xiang,et al.A Survey of Cartogram[J].Journal of Computer-Aided Design&Computer Graphics,2017,29(3):393-405.
[9]BUCHIN K,VAN GOETHEM A,HOFFMANN M,et al.Travel-Time Maps:Linear Cartograms with Fixed Vertex Locations[C]∥Proceedings of the 8th International Conference on Geographic Information Science.Vienna,Austria:Springer International Publishing,2014:18-33.
[10]KAISER C,WALSH F,FARMER C J Q,et al.Usercentric time-distance representation of road networks[C]∥Proceedings of the 6th International Conference on Geographic Information Science.Berlin Heidelberg:Springer,2010:85-99.
[11]AXHAUSEN K W,DOLCI C,FR?HLICH P,et al.Constructing Time-Scaled Maps:Switzerland from 1950to2000[J].Transport Reviews,2008,28(3):391-413.
[12]SHIMIZU E,INOUE R.A New Algorithm for Distance Cartogram Construction[J].InternationalJournalofGeographical Information Science,2009,23(11):1453-1470.
[13]AHMED N,MILLER H J.Time-Space Transformations of Geographic Space for Exploring,Analyzing and Visualizing Transportation Systems[J].Journal of Transport Geography,2007,15(1):2-17.
[14]何亚坤,艾廷华,禹文豪.等时线模型支持下的路网可达性分析[J].测绘学报,2014,43(11):1190-1196.DOI:10.13485/j.cnki.11-2089.2014.0183.HE Yakun,AI Tinghua,YU Wenhao.Accessibility Analysis of Road Network Supported by Isochrone Model[J].Acta Geodaetica et Cartographica Sinica,2014,43(11):1190-1196.DOI:10.13485/j.cnki.11-2089.2014.0183.
[15]李文翎,李尚智,黎雅雯,等.基于GIS的广州城市时间地图研究[J].热带地理,2008,28(3):218-222,227.LI Wenling,LI Shangzhi,LI Yawen,et al.A Study on Urban Temporal Map of Guangzhou Based on GIS Based on GIS[J].Tropical Geography,2008,8(3):218-222,227.
[16]HONG S,KIM Y S,YOON J C,et al.Traffigram:Distortion for Clarification via Isochronal Cartography[C]∥Proceedings of the SIGCHI Conference on Human Factors in Computing Systems.Toronto,Ontario,Canada:ACM Press,2014:907-916.
[17]BIES S,VAN KREVELD M.Time-Space Maps from Triangulations[C]∥Proceedings of the 20th International Conference on Graph Drawing.Redmond,WA:Springer,2012:511-516.
[18]ULLAH R,KRAAK M J.An Alternative Method to Constructing Time Cartograms for the Visual Representation of Scheduled Movement Data[J].Journal of Maps,2015,11(4):674-687.
[19]刘瑜,龚咏喜,张晶,等.地理空间中的空间关系表达和推理[J].地理与地理信息科学,2007,23(5):1-7.LIU Yu,GONG Yongxi,ZHANG Jing,et al.Representation and Reasoning of Spatial Relations in Geographical Space[J].Geography and Geo-information Science,2007,23(5):1-7.
[20]沈陈华,王旭姣,司亚莉,等.基于旅行者运动轨迹的时间地图变换[J].地理研究,2015,34(6):1160-1172.SHEN Chenhua,WANG Xujiao,SI Yali,et al.Time-space Map Transformation Based on Travelers'Motion Trajectory[J].Geographical Research,2015,34(6):1160-1172.
[21]SCHAEFER S,MCPHAIL T,WARREN J.Image deformation using moving least squares[J].ACM Transactions on Graphics(TOG),2006,25(3):533-540.
[22]刘婷.移动最小二乘图像变形方法研究[D].大连:大连理工大学,2008.LIU Ting.Study on Image Deformation Based on Moving Least Squares[D].Dalian:Dalian University of Technology,2008.
[23]杜晓荣,平淑文,张永.基于移动最小二乘法的图形图像局部变形技术[J].系统仿真学报,2015,27(4):816-823.DU Xiaorong,PING Shuwen,ZHANG Yong.Graphics and Image Local Deformation Based on Moving Least Squares Method[J].Journal of System Simulation,2015,27(4):816-823.
[24]BENTLEY J L,OTTMANN T A.Algorithms for Reporting and Counting Geometric Intersections[J].IEEE Transactions on Computers,1979,28(9):643-647.
[25]王士君,冯章献,刘大平,等.中心地理论创新与发展的基本视角和框架[J].地理科学进展,2012,31(10):1256-1263.WANG Shijun,FENG Zhangxian,LIU Daping,et al.Basic Perspective and Preliminary Framework for the Theoretical Innovation and Development of Central Place Theory in New Times[J].Progress in Geography,2012,31(10):1256-1263.