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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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