A universal parametrization in B-spline curve and surface interpolation

Abstract

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.