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Discrete Variational Calculus for B-Spline Curves
Mathematics in Computer Science, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Zhao, Elizabeth L. Mansfield
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Degree elevation of B-spline curves
Computer Aided Geometric Design, 1984An algorithm is presented which expresses any given linear combination of B-splines of order k as a linear combination of B-splines of order \(k+1\). This algorithm consists of two parts: (1) A simple representation of the curve by a sum of B-splines of order \(k+1\), and (2) a representation of these splines on a common node vector by inserting new ...
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Algorithm for degree reduction of B-spline curves
Computer-Aided Design, 1995This paper presents -- in continuation of the authors' previous work on degree elevation [ibid. 19, No. 9, 485-498 (1987; Zbl 0655.65012)] -- an algorithm for degree reduction of a given \(B\)-spline-curve. The three main steps of the new algorithm are: Decomposition of the given \(B\)- spline into Bézier pieces; degree reduction of each Bézier piece ...
Les A. Piegl, Wayne Tiller
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The redefinition of B-spline curve
The International Journal of Advanced Manufacturing Technology, 2011This paper proposes a new formula of B-spline curve. The new formula generates exact same shape as that of the original B-spline curve formula but has different basic functions and knot vector. This formula requires the number of knots to be the same as the number of control points.
Jung, HB, Kim, K
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1995
In this chapter we define nonrational B-spline curves and surfaces, study their properties, and derive expressions for their derivatives. For brevity we drop the word nonrational for the remainder of this chapter. The primary goal is to acquire an intuitive understanding of B-spline curves and surfaces, and to that end the reader should carefully study
Les Piegl, Wayne Tiller
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In this chapter we define nonrational B-spline curves and surfaces, study their properties, and derive expressions for their derivatives. For brevity we drop the word nonrational for the remainder of this chapter. The primary goal is to acquire an intuitive understanding of B-spline curves and surfaces, and to that end the reader should carefully study
Les Piegl, Wayne Tiller
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1974
Publisher Summary An example of a highly successful computerized design system is Systeme UNISURF, which was developed by P.Bezier at Regie Renault. The essence of the success of Bezier's system is that it combines modern approximation theory and geometry in a way that provides the designer with computerized analogs of his conventional design and ...
William J. Gordon, Richard F. Riesenfeld
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Publisher Summary An example of a highly successful computerized design system is Systeme UNISURF, which was developed by P.Bezier at Regie Renault. The essence of the success of Bezier's system is that it combines modern approximation theory and geometry in a way that provides the designer with computerized analogs of his conventional design and ...
William J. Gordon, Richard F. Riesenfeld
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Uniform trigonometric polynomial B-spline curves
Science in China Series F Information Sciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yonggang Lü, Guozhao Wang, Xunnian Yang
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