Analysis of Surface Changes by Tessellations Yukio

This paper develops a method for analyzing the change of surface, a continuous function defined over the two-dimensional space. The surface change is represented by a scalar field in a spatio-temporal region. The region is divided into subregions called hills and waves which are based on the local form of the surface. They are both threedimensional tessellations of the spatio-temporal region, and provide an overview of the surface change. To summarize the tessellations, four operations are proposed: section, projection, fusion, and graph representation. They extract useful information from tessellations to describe the structure of surface change. To test the validity of the method, the change of a retail cluster in Shinjuku and Shibuya area in Tokyo is analyzed. The empirical study yields some interesting findings that help us understand changes in the spatial structure of retailing.