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Title: Iterative sequential bat algorithm for free-form rational Bézier surface reconstruction

Authors: Andrès Iglesias; Akemi Gálvez; Marta Collantes

Addresses: Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, 274-8510, Funabashi, Japan; Department of Applied Mathematics and Computational Sciences, University of Cantabria, E.T.S.I. Caminos, Canales y Puertos, Avda. de los Castros, s/n, 39005, Santander, Spain ' Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, 274-8510, Funabashi, Japan; Department of Applied Mathematics and Computational Sciences, University of Cantabria, E.T.S.I. Caminos, Canales y Puertos, Avda. de los Castros, s/n, 39005, Santander, Spain ' Department of Applied Mathematics and Computational Sciences, University of Cantabria, E.T.S.I. Caminos, Canales y Puertos, Avda. de los Castros, s/n, 39005, Santander, Spain

Abstract: Surface reconstruction is an important issue in many areas: CAD/CAM (reverse engineering for automotive, aerospace and shipbuilding industries), rapid prototyping, biomedical engineering (customised prosthesis, medical implants), medical imaging (computer tomography, magnetic resonance), and others. A classical approach in the field is to consider free-form polynomial surfaces. However, the polynomial scheme cannot replicate many shapes such as the quadrics. In this paper, we overcome this limitation by using rational Bézier surfaces. This rational case is more complicated than the polynomial one, leading to a difficult over-determined nonlinear continuous optimisation problem. Our approach is based on a powerful bio-inspired technique called bat algorithm, sequentially applied in our method to compute the data parameters and weights. This process is performed iteratively with the output of each bat algorithm as the input of the next one, and so on. Then, the poles are computed by SVD least squares approximation. Our method has been applied to three illustrative examples with remarkable results. It can recover the underlying shape of complicated surfaces with good accuracy for data points affected by measurement noise and irregular sampling. Comparative work with common approaches in the field shows that our method outperforms them for all instances in this paper.

Keywords: surface reconstruction; free-form shapes; rational Bézier surface; reverse engineering; bat algorithm.

DOI: 10.1504/IJBIC.2018.090093

International Journal of Bio-Inspired Computation, 2018 Vol.11 No.1, pp.1 - 15

Available online: 23 Feb 2018 *

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