Abstract :
A very important issue in many applied fields is to construct the fitting curve that approximates a given set of data points optimally in the sense of least-squares. This problem arises in a number of areas, such as computer-aided design and manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Since the problem consists of minimizing the least-squares fitting error, it can be formulated as an optimization problem. Unfortunately, it is also a highly nonlinear, over-determined, multivariate continuous optimization problem. As a consequence, classical mathematical methods cannot solve it in its generality. Clearly, there is a need for more general techniques to tackle this issue. A critical step in this process is to obtain a suitable parameterization of the data points. In this context, this paper introduces a new method to obtain an optimal solution for the parameterization problem of the least-squares fitting Bézier curve. Our approach is based on a powerful nature-inspired optimization method called bat algorithm, which has been recently introduced to solve hard continuous optimization problems. In spite of these remarkable features for optimization, the bat algorithm has never been applied in the context of data fitting for geometric modeling or computer graphics. To analyze the performance of this approach, it has been applied to some simple yet illustrative examples of Bézier curves with satisfactory results.
