Firefly Algorithm for Polynomial Bézier Surface Parameterization

A classical issue in many applied \elds is to obtain an approximating surface to a given set of data points. Yis problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very o_en, the preferred approximating surface is polynomial, usually described in parametric form. Yis leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very diacult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. Yis paper solves the parameterization problem for polynomial Bézier surfaces by applying the \redy algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address diacult optimization problems. Ye method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.