Abstract
Curves consisting of just one polynomial or rational segment are often inadequate. Their shortcomings are:
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a high degree is required in order to satisfy a large number of constraints; e.g., (n-1)-degree is needed to pass a polynomial Bé curve through n data points. However, high degree curves are inefficient to process and are numerically unstable;
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a high degree is required to accurately fit some complex shapes;
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single-segment curves (surfaces) are not well-suited to interactive shape design; although Bé curves can be shaped by means of their control points (and weights), the control is not sufficiently local.
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© 1997 Springer-Verlag Berlin Heidelberg
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Piegl, L., Tiller, W. (1997). B-Spline Basis Functions. In: The NURBS Book. Monographs in Visual Communication. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59223-2_2
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DOI: https://doi.org/10.1007/978-3-642-59223-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61545-3
Online ISBN: 978-3-642-59223-2
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