Abstract
Surface reconstruction is a very important problem in fields such as geometric modeling and processing, and CAD/CAM. Most of the methods proposed to solve this problem rely on parametric polynomial schemes. However, there are shapes that cannot be described by using a strictly polynomial approach. In this paper we introduce a new method to address the surface reconstruction problem from scattered data points through rational Bézier surfaces. Our approach is based on the combination of simulated annealing, the natural neighbor interpolation method, and least-squares minimization to perform data parameterization, data fitting, and weight computation. Some computer experiments carried out for both organized and unorganized data sets show the good performance of our approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Foley, T.A.: Interpolation and approximation of 3-D and 4-D scattered data. Comput. Math. Appl. 13(8), 711–740 (1987)
Gálvez, A., Cobo, A., Puig-Pey, J., Iglesias, A.: Particle swarm optimization for Bézier surface reconstruction. In: Bubak, M., Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2008. LNCS, vol. 5102, pp. 116–125. Springer, Heidelberg (2008). doi:10.1007/978-3-540-69387-1_13
Gálvez, A., Iglesias, A.: Particle swarm optimization for non-uniform rational B-spline surface reconstruction from clouds of 3D data points. Inf. Sci. 192, 174–192 (2012)
Gálvez, A., Iglesias, A.: Firefly algorithm for polynomial Bézier surface parameterization. J. Appl. Math. 2013, 1–9 (2013)
Gálvez, A., Iglesias, A., Cabellos, L.: Cuckoo search with Lévy flights for weighted Bayesian energy functional optimization in global-support curve data fitting. Sci. World J. 2014, 1–11 (2014). Article ID 138760
Greiner, G., Hormann, K.: Interpolating and approximating scattered 3D-data with hierarchical tensor product B-splines. In: Surface Fitting and Multiresolution Methods, pp. 163–172. Vanderbilt University Press (1997)
Iglesias, A., Gálvez, A.: Nature-inspired swarm intelligence for data fitting in reverse engineering: recent advances and future trends. Stud. Comput. Intell. 637, 151–175 (2016)
Iglesias, A., Gálvez, A., Collantes, M.: Bat algorithm for curve parameterization in data tting with polynomial Bézier curves. In: Proceedings of Cyberworlds 2015, Visby, Sweden, pp. 107–114. IEEE Computer Society Press, Los Alamitos (2015)
Iglesias, A., Gálvez, A., Loucera, C.: A simulated annealing approach for data fitting with Bézier surfaces. In: Proceedings of International Conference on Intelligent Information Processing, Security and Advanced Communication, IPAC 2015, pp. 4:1–4:6. ACM Press (2015)
Iglesias, A., Gálvez, A., Loucera, C.: Two simulated annealing optimization schemas for rational Bézier curve fitting in the presence of noise. Math. Problems Eng. 2016, 1–17 (2016). Article ID 8241275
Ingber, L.: Adaptive simulated annealing (ASA): lessons learned. Control Cybern. 25, 33–54 (1996)
Johnson, S.G.: The NLopt nonlinear optimization package. http://ab-initio.mit.edu/nlopt
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated annealing. In: van Laarhoven, P.J.M., Aarts, E.H.L. (eds.) Simulated Annealing: Theory and Applications, pp. 7–15. Springer, Dordrecht (1987)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087 (1953)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)
Sarkar, B., Menq, C.H.: Smooth-surface approximation and reverse engineering. Comput. Aided Des. 23(9), 623–628 (1991)
Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)
Sibson, R.: A brief description of natural neighbor interpolation. In: Barnet, V. (ed.) Interpreting Multivariate Data, pp. 21–36. Wiley, Chichester (1981)
Zhao, H.K., Osher, S., Merriman, B., Kang, M.: Implicit, nonparametric shape reconstruction from unorganized points using a variational level set method. Comput. Vis. Image Underst. 80, 295–319 (1998)
Acknowledgments
This work has been supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under grants TEC2013-47141-C4-R (RACHEL) and #TIN2012-30768 (Computer Science National Program) and Toho University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Loucera, C., Iglesias, A., Gálvez, A. (2017). Simulated Annealing and Natural Neighbor for Rational Bézier Surface Reconstruction from Scattered Data Points. In: Del Ser, J. (eds) Harmony Search Algorithm. ICHSA 2017. Advances in Intelligent Systems and Computing, vol 514. Springer, Singapore. https://doi.org/10.1007/978-981-10-3728-3_35
Download citation
DOI: https://doi.org/10.1007/978-981-10-3728-3_35
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3727-6
Online ISBN: 978-981-10-3728-3
eBook Packages: EngineeringEngineering (R0)