Fairing cubic B-spline curves (Q1102694)

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 \textit{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 \textit{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.