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Top1. Introduction
Spatial hierarchy is a concept proposed by geographers while studying and expressing the hierarchical structures of geographic entities. Geographers have been engaged in this research for more than a half century. Christaller (1933) proposed the central place theory, which described the form of spatial hierarchy based on the marketing principle, transportation principle and administrative principle. Skinner (1964) investigated the urban hierarchies in Szechwan finding that the hierarchy conformed to Christaller's theory. Following these pioneering researches, a great number of relevant studies about spatial hierarchies have been carried out, such as nations, regions, cities, commercial centres, hospitals and residential care facilities.
Despite the concept of spatial hierarchy is used frequently, the term is somewhat vague. We can difficultly find a strict definition of spatial hierarchy in the early literature, but only from Okabe and Sadahiro (1996). They defined it as ‘a configuration of ranked points which are related by a spatial dominance relation’. In this definition, the ranked points are actually a kind of geographic entities with their own attribute values, such as cities with their populations, residential care facilities with their bed numbers. The spatial dominance relation can be interpreted as the ‘influence’ of the geographic entities and their spatial interactions with each other. For instance, in a three-level hierarchy, central hospitals could be associated with first level points (the highest level), whereas local hospitals could be associated with second level points, and basic health care units with third-level points. Obviously, central hospitals are more dominated than local hospitals and basic health care units. Therefore, it can be interpreted as points with higher ranks are commonly assumed to have all lower level points as well.
The studies of spatial hierarchies have important practical significances in real life, for instance, a study of urban hierarchy helps us to reveal the spatial correlation of urban agglomeration and plan a scientific urban development strategy. A research on facility hierarchy may assist us in understanding the balance of supply and demand of regional facilities and provide us some auxiliary decisions in several aspects, such as facility location and regional service strategy adjustment.
Aroused by the research of Balzer and Deussen on Voronoi Treemaps (Balzer and Deussen, 2005), we try to introduce this information visualisation algorithm into the field of geography to generate a hierarchical layout with spatial information to better visualise and understand the spatial hierarchy.