Abstract
An algorithmic approach to degree elevation of NURBS curves is presented. The new algorithms are based on the weighted blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (a) decompose the NURBS curve into piecewise rational Bézier curves, (b) elevate the degree of each rational Bézier piece, and (c) compose the piecewise rational Bézier curves into NURBS curve.
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References
P. J. Barry, An Introduction to Blossoming, in: R. N. Goldman, T. Lyche, Ed.,Knot Insertion and Deletion Algorithms for B-spline Curves and Surface, (SIAM, 1993), 1–10.
G. Farin,Curves and surfaces for computer aided geometric design: A practical guide, Academic Press, San Diego, 1993.
L. Piegl and W. Tiller,The NURBS Book, Springer-Verlag, 1995.
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This work was supported by Korea Research Foundation Grant(KRF-99-015-DP0037).
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Lee, BG., Park, Y. Degree elevation of nurbs curves by weighted blossom. Korean J. Comput. & Appl. Math. 9, 151–165 (2002). https://doi.org/10.1007/BF03012346
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DOI: https://doi.org/10.1007/BF03012346