Fitting an Origin-Displaced Logarithmic Spiral to Empirical Data by Differential Evolution Method of Global Optimization

Abstract:     
Logarithmic spirals are abundantly observed in nature. To obtain the parameters of such spirals, curve-fitting may be required. However, the usual procedure of curve-fitting fails miserably in this regard. The difficulties become much more intense when the observed points z = (x,y) are not measured from their origin (0, 0), but shifted away from the origin by (cx, cy). This paper intends to devise a method to fit a logarithmic spiral to empirical data measured with a displaced origin. The best fit has been obtained by the differential evolution method of global optimization.

Keywords: Logarithmic spiral, Shift in origin, Box algorithm, Differential evolution method, Global optimization

Accepted Paper Series