On Estimation of the Parameters of Gielis Superformula from Empirical Data

Johan Gielis showed that all closed curves might be considered as some sort of deformed ellipses. He gave a superformula to parameterize such shapes. In this study an attempt has been made to estimate the parameters of Gielis' superformula from empirical data. We use an optimum search algorithm on multi-modal surfaces - the Genetic Algorithm- to find the best fit. Randomly scattered starting points have been used for the search of an optimum solution. Some examples are based on simulated data, while the solution of a real problem also may be attempted. It has also been shown that the parameters of the superformula are not uniquely related to the data from which they are estimated. This lack of uniqueness may pose the problems of interpretation of parameters.