Application of Convex Hull in Identifying the Types of Urban Land Expansion

Faced with the problem of lacking quantitative approaches to identify the types of urban land expansion, a new method based on the principle of convex hull was presented in this paper, which is to define the types of urban land expansion by the proportion of the area located inside or outside the convex hull of a city's outline. In detail, we first approximated the urban planar outline by selecting finite points from it. The more the amount of points is selected, the more they approximate to the original urban outline. The amount of points selected should be depended on the hardware resources of the computer and the need of the accuracy. Then, the convex hulls of those point sets were respectively constructed by employing our developed algorithms and programs, and the proportions of the area located inside or outside the convex hull are obtained. If the area inside one convex hull is more extensive than the one outside, then the type of urban land expansion of this city belongs to the 'infilling' type, otherwise, the 'extension' type. A case study was presented by using the National Resources and Environmental Database. The result shows that the type of urban land expansion of 29 cities out of the 40 cities in Anhui is the 'infilling' type from 1990 to 2000 and the remaining 11 cities, the 'extension' type. Urban land expansion results in changes of the morphology of urban outline. As indicated 32 cities are more compact from 1990 to 2000 and the other 8 are less compact. Generally, a more compact city has more advantages than a less compact city, so changes of the form of Anhui cities are considered being on a good way.