Original Articles

Analysis of the Principle and Evolvement of the Theoretic Models of Urban Spatial Interaction

  • 1. College of Environment and Planning| Henan University| Kaifeng 475004| China|
    2. Institute of Sino-Australia Geographic Information Analysis and Applications| Henan University| Kaifeng 475004| China

Online published: 2009-07-25


The theory of urban spatial interaction is an important basic theory in urban geography. For the theoretic models come from occident, our country correspondingly lags and research mainly on there demonstration, more research should be done in theory. This paper analyzes the principle of the noted theoretic models of urban spatial interaction. Considering breaking-point model has been applied widely and verified in practice. Its limitation, evolvement and expanded form were principally studied.Reily put forward Law of Gravitation on Zero-Sale in 1931 according to Newton’s Law of Gravitation. Converse expanded the theory, brought forward Breaking Point Theory and gave the computational formula in 1949. Because the theory just gives only one breaking point between two cities, many methods for partitioning space are used, for instance, making vertical line through the breaking point on the linked line between the two nearby cities and linking the nearby breaking points with smooth lines. In fact, , these are not feasible and not rigorous. Other conventional theoretic models of urban international action, including Gravitation Model and Potential Model, also have obvious limitations.
  Although geographical boundary is usually fuzzy and uncertain, it is still valuable in theory and actual application if we can find an advantageous and correct method for delimiting the urban abstracted regions. Considering Voronoi diagram’s geometric particularities, the rationality for dividing up space and the solvability by computer, some researchers tried to apply it in expanding and validating classical Breaking Point Theory. The method of compartmentalizing urban influential space based on ordinary Voronoi diagram ignores urban compositive strength, and the method based on weighted Voronoi diagram doesn’t take the geographical principle into account. The scientific meaning and rationality is demonstrated in theory about integrating breaking-point model and Voronoi diagram. The expanded breaking points model shows that in a well-proportioned plane, the boundary between two city’s abstracted regions is the vertical bisector of the connected line with them if the cities’ weights are equal; the boundary is an arc if the weights are not equal; the orbit of all the breaking points in the plane forms ordinary Voronoi diagram and weighted Voronoi diagram accordingly; and each city’s weight equals to the square root of its central strength value in the second situation.
  Apocalypses can be received from analyzing the principle and evolvement of the theoretic models of urban spatial interaction, which geography is an intersecting and practicing subject which sets the complicated natural and human phenomenon as studying objects, it is necessary that geography should use the new theories, techniques and methods for reference, which is the keys for developing itself.

Cite this article

YAN Weiyang1,2| WANG Fazeng1| QIN Yaochen1 . Analysis of the Principle and Evolvement of the Theoretic Models of Urban Spatial Interaction[J]. PROGRESS IN GEOGRAPHY, 2009 , 28(4) : 511 -518 . DOI: 10.11820/dlkxjz.2009.04.005


[1]   许学强,周一星,宁越敏. 城市地理学. 北京:高等教育出版社,2003.

[2]   毋河海. 地图数据库系统. 北京:测绘出版社,2000.

[3]   秦耀辰. 区域系统模型原理及其应用. 北京:科学出版社,2005.

[4]   戴特奇,金风君,王娇娥. 空间相互作用与城市关联网络演进. 地理科学进展,2005,24(2):80-89.

[5]   张伟,顾朝林. 城市与区域规划模型系统. 南京:东南大学出版社,2000.

[6]   刘科伟. 城市空间影响范围与城市经济区划问题探讨:以山西省为例. 西北大学学报: 自然科学版,1995,25(2):129-134.

[7]   李红启. 基于Wilson模型的物流空间相互作用. 经济地理,2008,28(4):588-591.

[8]   王新生,余瑞林,姜友华. 基于道路网络的商业网点市场域分析. 地理研究,2008,27(1):85-92.

[9]   薛领,杨开忠. 基于空间相互作用模型的商业布局:以北京市海淀区为例. 地理研究,2005,24(2):265-272.

[10] Reilly W J. Methods for the study of retail relationship. University of Texas Bulletin, 1929,(2944): 164.

[11] Converse P D. New laws of retail gravitation. Journal of Marketing, 1949,(14): 379-384.

[12] Wilson A G. A statistical theory of spatial distribution models. Transportation Res., 1967,1: 253-269.

[13] 王铮,丁金宏. 理论地理学. 北京:科学出版社,2000.

[14] 周培德. 计算几何:算法分析与设计. 北京:清华大学出版社,2000, 88-132.

[15] 郭仁忠. 空间分析. 武汉:武汉大学出版社,2001.

[16] Li C, Chen J, Li Z. A Raster-based method for computing voronoi diagrams of spatial objects using dynamic distance transformation. International Journal of Geographical Information Science,1999,13: 209-225.

[17] 张有会. 线段加权的Voronoi图.计算机学报, 1995,18(11):822-829.

[18] 胡鹏,游涟,杨传勇, 等. 地图代数. 武汉:武汉大学出版社,2002.

[19] 王新生,郭庆胜,姜友华. 一种用于界定经济客体空间影响范围的方法:Voronoi图. 地理研究,2000,19(3):312-315.

[20] 王新生,李全,郭庆胜, 等. Voronoi图的扩展、生成及其应用于界定城市空间影响范围. 华中师范大学学报 (自然科学版),2002,36(1):107-111.

[21] 郭庆胜,闫卫阳,李圣权. 中心城市影响范围的近似性划分. 武汉大学学报(信息科学版),2003,28(5):596-599.

[22] 闫卫阳,郭庆胜,李圣权. 基于加权Voronoi图的城市经济区划分方法探讨. 华中师范大学学报(自然科学版),2003,37(4):567-571.

[23] 闫卫阳,秦耀辰,郭庆胜, 等. 城市断裂点理论的扩展、验证及应用. 人文地理,2004,(2):12-16.

[24] 吴殿廷. 区域经济学. 北京:科学出版社,2003.

[25] 闫卫阳. 城市体系空间布局的模型化与智能化方法研究. 武汉大学博士学位论文,2004.

[26] Golledge R G. Path selection and route preference in human navigation: A progress report//Frank A U, Kuhn W. Spatial Information Theory. New York: Springer, 1995, 207-222.

[27] Okabe A, et al. Spatial Tessellation: Concepts and Applications of Voronoi Diagrams. 2nd edn. Chichester: John Wiley, 2000, 1-671.