Abstract
NURBS (Non-uniform rational B-splines) has become the industry standard tools for the representation, design and data exchange of geometric information to be processed and used by computers because of their useful geometrical properties. The problem of the parameterization of data points in NURBS curve/surface has been considered by several of researchers. We propose in this paper a new parameterization method for NURBS approximation. The current methods of parameterization such as centripetal method uses only the previous knot vector to calculate the recent knot. In this paper, we give a new parameterization method based on the correlation of the nodes. This approach inherits the advantages of the relation and position of the knots.
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Jung, H.B., Kim, K.: A New Parameterization Method for NURBS Surface Interpolation. Int. J. Adv. Manuf. Technol. 16, 784–790 (2000)
Joken, S., Naoya, I.: Geometrically local isotropic independence and numerical analysis of the Mahalanobis metric in vector space. Pattern Recognition Letters, 709–716 (2010)
Mohamed, N., Atef, H., Sawssen, J., Christiane, W.: NURBS Skeleton: A New Shape Representation Scheme Using Skeletonization and NURBS Curves Modeling, pp. 197–205. Springer, Heidelberg (2011)
Shamsuddin, S.M., Ahmed, M.A.: A Hybrid Parameterization Method for NURBS. In: Proc. of the international Conference on Computer Graphics, Imaging and Visualization (CGIV 2004), pp. 15–20. IEEE Computer Society, Washington, DC (2004)
Farin, G.: From Conics to NURBS: A Tutorial and Survey. IEEE Comput. Graph. Appl. 12, 78–86 (1992)
Choong-Gyoo, L.: A universal parameterization in B-spline curve and surface interpolation. Computer Aided Geometric Design 16, 407–422 (1999)
Lee, E.T.Y.: A Treatment of Conics in Parametric Rational Bezier Form, Boeing document, Boeing, Seattle, Wash. (February 1981)
Adi, D.I.S., Shamsuddin, S.M., Hashim, S.Z.M.: NURBS Curve Approximation using Particle Swarm Optimization. In: Seventh International Conference on Computer Graphics, Imaging and Visualization, pp. 73–79. IEEE Computer Society (2010)
Piegl, L., Tiller, W.: The NURBS book, 2nd edn. Springer-Verlag New York, Inc. (1997)
Godse, A.P., Gods, D.A.: Computer Graphics And Multimedia (2009)
Genichi, T., Rajesh, T.: The Mahalanobis-Taguchi strategy: a pattern technology system (2002)
Daviv, F.R.: An Introduction to NURBS. An Imprint of Elsevier (2001)
Lee, E.T.: Choosing nodes in parametric curve interpolation. Comput., 363–370 (1989)
Teknomo, K.: Similarity Measurement (2006)
Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design. A.K. Peters, Ltd. (1993)
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Jalel, S., Naouai, M., Hamouda, A., Jebabli, M. (2012). NURBS Parameterization: A New Method of Parameterization Using the Correlation Relationship between Nodes. In: Carrasco-Ochoa, J.A., Martínez-Trinidad, J.F., Olvera López, J.A., Boyer, K.L. (eds) Pattern Recognition. MCPR 2012. Lecture Notes in Computer Science, vol 7329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31149-9_22
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DOI: https://doi.org/10.1007/978-3-642-31149-9_22
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