In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental re...

Abstract We prove quartic convergence of cubic spline interpolation for curves into Riemannian manifolds as the grid size tends to zero. In contrast in Euclidean space, where this result is classical, operator no longer linear. Still, concepts from linear setting may be generalized case, we try use intrinsic formulations and avoid charts much possible.

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...