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Fairing cubic B-spline curves. (English) Zbl 0644.65007

This paper is concerned with numerical algorithms for locally fairing cubic B-spline curves in order to obtain a fine curvature plot. A mathematical definition of relative fairness of curves is given in terms of the value of the third derivative step discontinuity. The methods discussed are based on J. A. Kjellander’s approach to fairing a piecewise cubic curve [Smoothing of cubic parametric splines, Comput. Aided Des. 15, 175-179 (1983)] and on the inversion of W. Boehm’s knot inserting algorithm for B-spline curves [Inserting new knots into B- spline curves, Comput. Aided Des. 12, 199-201 (1981)]. Three kinds of knot removal algorithms for fairing are studied with their advantages and difficulties in various cases. Some numerical examples are considered and comparison with other methods is drawn.
Reviewer: V.V.Kobkov

MSC:

65D07 Numerical computation using splines
65D10 Numerical smoothing, curve fitting
53A04 Curves in Euclidean and related spaces
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[1] Boehm, W., Inserting new knots into B-spline curves, Cad, 12, 199-201, (1981)
[2] Boehm, W.; Farin, G.; Kahmann, J., A survey of curve and surface methods for CAGD, Computer aided geometric design, 1, 1-60, (1984) · Zbl 0604.65005
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