## A class of general quartic spline curves with shape parameters.(English)Zbl 1221.65040

A general method to generate quartic splines with a non-uniform knot vector from four consecutive subintervals (i.e., four control points) are presented. The splines have $$C^{2}$$ continuity at simple knots and include the cubic non-unifrom B-spline as a special case. Piecewise quartic spline curves with three local parameters based on the given splines, which have $$C^2 \cap G^3$$ continuity, are presented. The spline curves can be used as interpolate sets of $$C^2$$ continuous points without solving a linear system. The effects of local adjustments via three shape parameters on the shape of the quartic spline curves are illustrated.

### MSC:

 65D07 Numerical computation using splines 41A15 Spline approximation 65D17 Computer-aided design (modeling of curves and surfaces) 65D05 Numerical interpolation
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### References:

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