The Gielis superformula describes almost any closed curve in terms of deformed circle or ellipse. It has found many applications in design problems. By varying the parameters of the Gielis superformula or deforming a circle by different types of functions one can generate fascinating 2D or 3D figures. However, given a figure, it is not easy to obtain the parameters that generate the figure. Thus, reverse engineering to obtain the Gielis formula is indeterminate. The present study generates some interesting 2D shapes and makes an attempt to get back the parameters by two methods of global optimization—simulated annealing and particle swarm. It has been found that while the enterprise of fitting the curve to the given shapes (closed curves) is commendably successful, the parameters that generated those curves could not be reliably estimated. It shows that while the ‘formula to geometric shape’ has uniqueness, ‘the shape to the formula’ has nonunique solutions.

Computational Mathematics Journal, Logistic Regression Models, Business Management, Decision Theory, Logistic Regression Programs, SPSS Nonlinear Program, Proportional Reductions, Statistical Aanalysis Software Package, Statistical Software SPSS, Squared Pearson Correlation .