A Comparative Study on Fitting of Gielis Curves by Classical versus Generalized Simulated A.pdf

A Comparative Study on Fitting of Gielis Curves by Classical versus Generalized Simulated Annealing Methods SK Mishra Dept. of Economics NEHU, Shillong (India) Introduction: The Gielis superformula 1 n n (n1 ) 1 m 2 1 m 3 r( ) f ( ).a cos( 4 ) b sin( 4 ) f ( ).g ( ) ; a, b, m 0 … (1) describes almost any closed curve in terms of the deformed circle (or ellipse), g ( ), and another function, f ( ), and their parameters (Gielis, 2003; Gielis and Gerats, 2004). The function f ( ) may be considered as a modifier of the Gielis function, g ( ) . Estimation of Gielis Parameters: For a scientific purpose, Gielis parameters need to be estimated from empirical data. Presently, we are concerned with the possibilities of the same. Let the n true points be [z (x , y ); i 1, 2, ...,n] , of which the corresponding observed values i i i are z (x , y ) , possibly with errors of measurement and displacement of origin by (c , c ) , i i x y unknown to us. Let (c , c ) be the approximate or assum