In this paper we study the approximation power, the existence of a normalized B-basis and the structure of a degree-raising process for spaces of the form span < 1, x,..., x^(n-2), u( x), v( x) >, requiring suitable assumptions on the functions u and v. The results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of CAGD
Abstract. This paper is concerned with the problem of existence of monotone and/or convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality k < n -k. The theorems presented here are useful in developing algorithms for the construction of shape-preserving splines interpolating arbitrary sets of data points. Earlier results of McAllister, Passow and Roulier can be deduced from those given in this paper.
This article describes a general-purpose method for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions. Examples of applications of the related Fortran code are periodic shape-preserving spline interpolation and the construction of visually pleasing closed curves.
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