A bat algorithm for polynomial Bèzier surface parameterization from clouds of irregularly sampled data points

This paper presents a novel method for polynomial Bézier surface parameterization from clouds of irregularly sampled data points. This problem is a crucial step in surface reconstruction for reserve engineering, a field with very important applications in many industrial and technological domains such as computer-aided design (CAD), computer aided manufacturing (CAM), virtual reality, computer graphics, medical imaging, computer animation, and many others. Regrettably, it is also a high-dimensional, nonlinear, over-determined, continuous optimization problem. As a consequence, classical mathematical methods fail to solve it in its generality. Our approach is based on a powerful nature-inspired optimization method called bat algorithm, which has been recently proposed to solve hard continuous optimization problems. To analyze the performance of our approach, it has been applied to three illustrative examples of irregularly sampled Bézier surfaces. The numerical and visual results confirm the excellent performance of this method even for clouds of strong irregular patterns, a very challenging issue for many other optimization techniques.