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Constrained multi-degree reduction with respect to Jacobi norms

Computer Aided Geometric Design, 2016
We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm.
Michael Barton, Rachid Ait-Haddou
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Degree reduction of Bézier curves

Computer-Aided Design, 1991
This is a letter to the editor concerning the paper of \textit{M. A. Watkins} and \textit{A. J. Worsey} [ibid. 20, No. 7, 398-405 (1988; Zbl 0658.65014)]. The autor has found some technical errors in the equations defining the entries of a matrix and its inverse arising from degree reduction of Bézier curves, and proposes a corrected set of equations ...
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Degree reduction of disk Bézier curves

Computer Aided Geometric Design, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Falai Chen, Wu Yang
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Degree reduction of Bézier curves

Computer Aided Geometric Design, 1993
This paper treats the problem of approximating a given Bézier curve of degree \(n\) by another one of degree \(n-1\) in that sense that the maximal Euclidean distance between the two curves is minimized. In contrast to other approaches by \textit{M. A. Watkins} and \textit{A. J. Worsey} [Comput.- Aided Des. 20, No.
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Degree reduction of B-spline curves

Computer Aided Geometric Design, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun-Hai Yong, Shi-Min Hu 0001, Jia-Guang Sun 0001, Xing-Yu Tan   +3 more
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Degree Reduction Approximations

1990
The majority of CAD systems provide some form of parametric curve and surface representation but the precise form of this representation varies considerably. Some systems use simple parametric polynomial curves and surfaces, others provide some form of rational parametric representation.
M. A. Lachance, P. A. Sherar, R. J. Goult   +2 more
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Degree Reduction in Labeled Graph Retrieval

ACM Journal of Experimental Algorithmics, 2015
Within a given collection of graphs, a graph retrieval system may seek all graphs that contain a given graph, or may instead seek all graphs that are contained within a given graph. Although subgraph isomorphism is worst-case exponential, it may be average-case polynomial if graphs are labeled so as to restrict possible correspondences between vertices
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Degree Reduction of B-Spline Curves

1998
This work deals with the problem of degree reducing a B-spline curve without intermediate conversion to Bezier form. Degree elevation for B-spline curves may easily be described in blossom form. We also use blossoms for the degree reduction problem, and set up least squares problems for finding the B-spline coefficients directly.
Hans J. Wolters, G. Wu, Gerald E. Farin
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A unified matrix representation for degree reduction of Bézier curves

Computer Aided Geometric Design, 2004
In this paper, we show the degree reduction of Bézier curves in a matrix representation. Most degree reduction algorithms have been described as a set of recursive equations which are based on the inverse problem of degree elevation.
Namyong Lee, Hasik Sunwoo
exaly   +1 more source

Good degree reduction of Bézier curves using Jacobi polynomials [PDF]

Computers and Mathematics With Applications, 2000
The constrained Chebyshev polynomial is the error function of the best degree reduction of polynomial with C1-continuity. In this paper, we propose the constrained Jacobi polynomial as an alternative error function for good degree reduction. Although the
Kim, H.J., Ahn, Y.J.
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