Curve Fitting Using Conic by Evolutionary Computing

Abstract

Problem statement: A direct method, such as least squares technique is usually used to solve problems involving matching a curve or a surface to a set of data points. The solution obtained by this direct method is precise or very good in approximation, but computationally not very efficient. Thus, in this study, we propose an indirect approach using Particle Swarm Optimization (PSO) technique as an alternative. Approach: As a case study, we use conic curve which satisfy C⁰ continuity to be fitted to a given set of data points. PSO, a soft computing method is employed to optimize the control points and weights which are then used in conic equations. Results: Best fitted conic curve that represents all the given data points is then obtained. Conclusion: We use an indirect technique of soft computing methods, i.e., PSO to fit a curve to a given data set. We believe that other types of soft computing based heuristic procedures may also be used to solve related problems or to find its effectiveness.