The Alternative Snake - and Other Animals

In this paper I introduce a new way of generating and describing shapes which was largely inspired by reading D'Arcy Thompson's classic "On Growth and Form" [1]. There are suggestive parallels between my system and "coupled oscillation" models of handwriting [2] and locomotion [3]. Like many others the system involves a mapping from a space of "implicit parameters" to the space of observables. I limit discussion to the simplest case in which a single parameter G is mapped into 2-D Euclidean space by two Fourier series x(Q),y(Q) whose coefficients may be restricted or cross-constrained in various ways. One application to computer vision is in defining "snakes" - contour models which are fitted to image data by gradient-climbing techniques [4,5]. I