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A universal parametrization in B-spline curve and surface interpolation. (English) Zbl 0916.68156
Summary: We propose here a new universal parametrization for B-spline interpolation. The new parametrization is based on the values t i where B-splines N i,k (t) are maximum in case of order k. The resulting interpolation curve X(t) is transformation invariant and more natural looking, in general, than those obtained by other methods. Using a fixed knot vector, t i ’s are independent of interpolating points {P i }, and hence the computation of X(t) can be done more efficiently. In addition, the new method works well in any order k.
MSC:
68U05Computer graphics; computational geometry
41A05Interpolation (approximations and expansions)
41A15Spline approximation