Comparison of Plane Forms

摘要

Nonlinear two-dimensional grid transformations are used to compare plane figures. The method is based on the identification of homologous points, and thus can be considered as a bidimensional extension of ordinary curvilinear regression, but is here approached from the point of view of cartography. All of the techniques illustrated by Thompson in 1917 can be mimicked by the computer program. Extensions of the method, based on the derivatives of the transformations, permit the determination of the axes of principal change, and also suggest numerical measures for the degree of similarity of topologically equivalent figures. Applications are illustrated in biology and geography, and more general uses are suggested.