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An automatic algorithm for fairing B-spline curves of general order
is presented. This work was motivated by a method of Farin and Sapidis about
fairing planar cubic B-spline curves by subsequently removing and reinserting
knots. Instead our new algorithm is based on the idea of subsequently
changing one control point of a given B-spline curve so that the new curve
minimizes the integral of the squared -th derivative of the B-spline curve.
How to proceed, if a tolerance is given and must be kept, is also discussed.
Key words: B-spline curves; knot removal; knot insertion;
strain energy; energy integral; fairing; smoothing; distance tolerance. |