Accurate Geographical Distance Field Generation on the Ellipsoidal Earth and Its Application
ISBN 978-85-88783-11-9
Authors
1Hai, H.; 2Huiping, J.; 3Yanlan, W.; 4Hui, Y.
1WUHAN UNIVERSITY Email: huhai@whu.edu.cn
2WUHAN UNIVERSITY Email: jianghuiping@whu.edu.cn
3ANHUI UNIVERSITY
4WUHAN UNIVERSITY
Abstract
Along with the quickened pace of the globalization process, the requirements for spatial analysis at large scale are growing more and more urgent. The traditional method of ellipsoidal spatial analysis is to project the initial data on earth’s surface to the Euclidean plane and simulate approximately through Euclidean geometry. However, as the research range gradually expands from some local areas, e.g., cities and towns, to continental or global areas, the simulation is bound to face some challenges. On the one hand, as earth’s surface is a anisotropic irregular ellipsoidal surface, the veracity of spatial analysis based on isotropic Euclidean plane cannot be guaranteed because of the large errors of computation; on the other hand, as the quantities of data involved in spatial analysis at the global scale keeps accumulating dramatically, the vector algorithms based on Euclidean geometry are subject to having trouble in complex spatial computation, which results in relatively high time complexity. The present method is based on map algebra and combines the raster and vector methods. According to the raster-based geographical distance transformation, a raster bucket, a customized data structure, is applied to conduct the distance transformation based on both the raster and vector methods at the geodesic scale, which maintains the positioning accuracy of vector method as well as the neighborhood effect among cells of raster method. The computational efficiency of this raster&vector-based geographical distance transformation is O(m) where m is the number of pixels in the image, i.e., grid resolution, which is irrelevant to the quantity and morphology of spatial objects, therefore, this algorithm can control the positioning error around 0.001 m within several thousand kilometers range of span and consequently create the distance field in the geodesic metric system with a fairly high degree of accuracy. Products of the transformation mainly include 3 raster matrices: ①the raster matrix of spatial distances: each element is the nearest geodesic distance between the center of each cell and the correspondingly nearest spatial object; ②the raster matrix of source objects: the codes of the correspondingly nearest spatial object; ③the raster matrix of source coordinates: the geodetic coordinates of the correspondingly nearest point on the source spatial object. Compared with the previous raster-based method, the raster&vector-based method proposed presently reduces the dependence on grid resolution significantly, which is capable of computing an accurate result just like vector method under an easy condition of fairly low grid resolution. A series of basic products of ellipsoidal spatial analysis can be generated via the accurate distance field on the ellipsoidal surface. As regards the massive data with arbitrary complex morphology, this method is capable of rapidly computing the ellipsoidal buffers, Voronoi diagrams, Delaunay triangulation net, central axis, skeleton lines, etc., which has been applied to the solution of accurate maritime delimitation. As a kind of space-oriented computing tool at a large scale, the geographical distance field is capable of shifting a large proportion of spatial analysis algorithms from the Euclidean plane to the earth ellipsoidal surface without loss of accuracy, thus playing a crucial role in suitable allocation and utilization of resources through Tobler's First Law of Geography (TFL). In conclusion, the method will have a broad prospect of application for Digital Earth.