Firefly Algorithm for Bezier Curve Approximation

A critical problem in many applied fields is to constructthe polynomial curve of a certain degree that approximatesa given set of noisy data points better in the sense of least-squares. This problem arises in a number of areas, suchas Computer-Aided Design & Manufacturing (CAD/CAM), virtual reality, medical imaging, computer animation, andmany others. This paper introduces a new method to solvethis problem through free-form Bezier curves. Our methodapplies a powerful metaheuristic nature-inspired algorithm, called firefly algorithm, introduced recently to solve optimization problems. The paper shows that this new approach can be effectively applied to obtain an optimal approximating Bezier curve to the set of data points with a proper selection of the control parameters. To check the performance of our approach, it has been applied to some illustrative examples of different types, including shapes with complex features such as singularities and self-intersections. Our results show that the method performs very well, being able to yield the best approximating curve with a high degree of accuracy.