A new objective function for the recovery of Gielis curves

Abstract

The superformula generates curves called Gielis curves, which depend on a small number of input parameters. Recovering parameters generating a curve that adapts to a set of points is a non-trivial task, thus methods to accomplish it are still being developed. These curves can represent a great variety of forms, such as living organisms, objects and geometric shapes. In this work we propose a method that uses a genetic algorithm to minimize a combination of three objectives functions: Euclidean distances from the sample points to the curve, from the curve to the sample points and the curve length. Curves generated with the parameters obtained by this method adjust better to real curves in relation to the state of art, according to observational and numeric comparisons.