A Shape Definition for Geographic Applications Based on Edge, Elongation, and Perforation

An expanded definition for measuring shape in a geographic context is presented. Shape analysis is important in many geographic contexts such as studying the effects of urban development, measuring geographic characteristics of drainage basins, and examining the patterns of geologic formations. This research implements and tests an approach to expand the current mathematical definition of shape and to measure shape for geographic applications, called the trivariate shape definition. The expanded definition involves identifying three characteristics to define shape: edge, elongation, and perforation. Indices to measure these characteristics were identified and applied to two different data sets. Analysis of results from these data sets suggests that the trivariate index clustered groups of objects based on shape similarity. The trivariate approach provides more flexibility to measure shape by relying on a more specific definition of shape.