An Electromagnetism-Based Global Optimization Approach for Polynomial Bezier Curve Parameterization of Noisy Data Points

This paper concerns the problem of fitting curves to data points, a classical optimization problem in Computer-Aided Geometric Design (CAGD) and CAD/CAM. This issue plays an important role in real-world problems such as the construction of car bodies, ship hulls, airplane fuselage, and other free-form objects. A typical example comes from reverse engineering where free-form shapes are extracted from clouds of scanned data points. In this paper we address this issue by applying a nature-inspired method, called electromagnetism algorithm, introduced recently to solve global optimization problems. The method is based on the interaction among particles endowed with electric charge and subjected to an attraction-repulsion mechanism in order to move the sample points towards the optimality. This algorithm is applied to compute a proper parameterization of noisy data points in order to fit Bezier curves to given sets of irregularly sampled data points. Some illustrative examples for both open and closed 2D and 3D curves show the good performance of our approach.