{'fraction_non_alphanumeric': 0.019230769230769232, 'fraction_numerical': 0.0, 'mean_word_length': 5.18125, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Analysis of Surface Changes by Tessellations Analysis of Surface Changes by Tessellations

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.