Memetic Electromagnetism Algorithm for Finite Approximation with Rational Bézier Curves

The problem of obtaining a discrete curve approximation to data points appears recurrently in several real-world fields, such as CAD/CAM (construction of car bodies, ship hulls, airplane fuselage), computer graphics and animation, medicine, and many others. Although polynomial blending functions are usually applied to solve this problem, some shapes cannot yet be adequately approximated by using this scheme. In this paper we address this issue by applying rational blending functions, particularly the rational Bernstein polynomials. Our methodology is based on a memetic approach combining a powerful metaheuristic method for global optimization (called the electromagnetism algorithm) with a local search method. The performance of our scheme is illustrated through its application to four examples of 2D and 3D synthetic shapes with very satisfactory results in all cases.