Paolo Costantini

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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, 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(More)
Rational re-parameterizations of a polynomial curve that preserve the curve degree and [0,1] parameter domain are characterized by a single degree of freedom. The “optimal” re-parameterization in this family (that comes closest under the L2 norm to arc-length parameterization) can be identified by solving a quadratic equation, but may exhibit too much(More)
In this paper we present a new local method for constructing a C1 function which interpolates triangulated scattered data sets. This function is made up by polynomial triangular macro-elements of adaptive degree, which are an extension of the Clough–Tocher cubic elements and tend to the interpolating planar triangular interpolant as the degrees tend to(More)
We propose a local method for the construction of differentiable functions which interpolate a set of gridded data and are monotonicity preserving, that is increasing or decreasing exactly where the data are, The scheme is based upon the boolean sum of cubic interpolating operators, which blend together shape-preserving, one dimensional, interpolating(More)