关键词: 城市；空间相互作用；Voronoi图；理论模型

Abstract:

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.

Key words: city, spatial interaction, theoretic model, Voronoi diagram