V F m Voronoi a m Voronoi 3 Voronoi [1 10] [1] [7-8] d A = D AB / 1+ 姨 P A /P B 6 v = V-min A new_max A -new_min A + new_min A 3 7 max A -

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1 30 7 Vol.30 No ECONOMIC GEOGRAPHY Jul : (2010) Voronoi GIS 1990 Voronoi TU984.2 A 1 [1] 1.1 [2-8] 6 1 [2-6] x ij* = x ij-x j 1 [5] S j x ij* x ij j i x j S j j Rd [2] 2 V [9-11] Voronoi Voronoi SPSS Voronoi Voronoi 1990 V = Σa m F m 2 m = ; BAH31B KZCX2- YW k

2 V F m Voronoi a m Voronoi 3 Voronoi [1 10] [1] [7-8] d A = D AB / 1+ 姨 P A /P B 6 v = V-min A new_max A -new_min A + new_min A 3 7 max A -min A d v A d B A B D AB A B v P A P B maxa mina new_maxa new_mina 1.2 Voronoi Voronoi Voronoi d A /d B = 姨 P A /P B 7 Voronoi 2 Voronoi 2.1 Voronoi [9] Pearce Voronoi ordinary Voronoi diagram [15] Voronoi Boots South Voronoi higher order multiplicatively weighted Voronoi polygons [16] Voronoi ( additively weighted Voronoi diagram ) Voronoi Voronoi Voronoi P i= i 1 2 n n w i i= 1 2 n n 2.2 [17-18 ] d p w p = 1 i w i1 d p i - w i2 i = 1 2 n 4 w i1 > 0 w i2 Voronoi w i2 =0 Voronoi /km 2 Voronoi 5 v p n i w = i 疑疑 P d p p i < d p p i 疑 i = 1 2 n 5 i = j w i w j Voronoi 45.4 km % Voronoi Voronoi

3 Tab.1 The central intensity and the change of ranking of the cities in Heilongjiang province Okabe Sadahiro [19] Voronoi Voronoi Voronoi

4 Voronoi Voronoi 1 Voronoi 2 Voronoi Fig.1 The influential area of central cities based on weighted Voronoi diagram Voronoi Fig.3 The division of urban economic regions in Heilongjiang based on weighted Voronoi diagram Fig The merged influential area of central cities based on weighted Voronoi diagram Tab.2 2 The planning of urban economic region in urban system planning of Heilongjiang province

5 [2] 46(2) Voronoi [3] (4) [4] [J] (3) [5] Voronoi (12) [6] Voronoi 1996(11) [7] [8] Okabe A Boots B Sugihara K.Nearest neighborhood operations with generalized Voronoi diagram[j]. International Journal of Geo- graphical Information Systems 1994(8) parison with census data [J]. Computer [10] - Voronoi [J] (3) [11]. [J]. ) [12] [J] (2) [13] (1) Diagrams [M]. Chichester JohnWiley comparison with census data [J]. Computer Urban Systems (5) [16] Boots B N order Retailing (4) [17].. [J] [J]... [J].. [J]. [M]. [9] Pearce J.Techniques for defining school catchments areas for com- Systems (5) Environment and Urban Voronoi ( (4).. [J]. [14] Okabe. Spatial Tessellation:concepts and applications of Voronoi [15] Pearce J. Techniques for defining school catchment areas for Environment and South R. Modeling retail trade areas using higher multiplicatively weighted Voronoi diagram s[j]. Journal of [M] [18]. Voronoi [J] (11) [19] Okabe A Sadahiro Y. An illusion of spatial hierarchy spatial [1]. [M]. hierarchy in a random configuration[j]. Environment and Planning A

6 THE CHANGE OF URBAN ECONOMIC INFLUENCE REGIONS IN HEILONGJ IANG PROVINCE SINCE 1990 HUANG Jian - yi 1,2,ZHANG Ping - yu 3,LIU Yi 1 (1.Institute of Geographic Sciences and Natural Resource Research,CAS,Beijing ,China;2. Graduate School of the Chinese Academy of Sciences,Beijing ,China;3. Northeast Institute of Geography and Agricultural Ecology,CAS,Changchun ,Jilin,China) Abstr act: The work to define spatial relationship among urban economic influence regions is a quite difficult issue,but an important job to urban geography and urban planning. Because of the dynamic development of the urban economy,the urban economic influence regions will change with the development of city economic power. Based on the development trends of the urban economic influence region,making the division of the urban economic regions has an important significance. At first this paper analyzes the existing methods for the division of urban economic regions. Considering weighted Voronoi diagram s geometric particularity,the rationality for dividing up space and the solvability by computer,the paper calculates the central intensity of the cities in Heilongjiang province by using the factor analysis method in SPSS software, then establishes multiplicatively weighted Voronoi diagram based on the breaking points, taking the central intensity as vertex weight, and at last divides the urban economic influence regions in 1990 and 2006.From the central intensity of the city, we can found that the ranking of most cities have not changed a lot, but the ranking of Daqing has raised quickly. The result of the weighted Voronoi diagram division shows that the whole pattern of the economic influence region in Heilongjiang has not changed much,but the cities in the south of the Heilongjiang province have developed quickly,especially the cities along the railway of Suiman, and the influence regions of the cities in the south are expanding to the north gradually. This has a closely relationship with the economic development trends of Heilongjiang province, whilst in the local regions,the economic influence regions of some cities have changed dramatically, the urban economic influence regions of Daqing and Mudanjiang are expanding,while the influential regions of Qiqihaer and Jiamusi are shrinking, causing by the change of the city economic power.based on the factual situations of social-economic development in Heilongjiang province,the paper makes the division of urban economic regions of Heilongjiang province, in order to provide reference for decision-making in the future regional planning in Heilongjiang. Key words: urban economic influence region;factor analysis;weighted Voronoi diagram;heilongjiang 1984 E- mail huangjy84@163.com

1556 地理科学进展 30 卷他关于农村住房结构与抗震性能的研究, 则多是从工程抗灾的角度, 研究某种构造类型的房屋, 力图找到传统房屋的结构失误和新建房屋中存在的问 [

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