Construction of spherical spline quasi-interpolants based on blossoming
The authors study the important problem of fitting scattered data on sphere-like surfaces by means of quasi-interpolation methods. First, some Marsden identities for quadratic spherical Powell-Sabin splines are obtained using blossoms (polar forms). Then the functional coefficients of quasi-interpolating splines are computed by evaluating the blossom values of a chosen local approximation operator at certain points. Various families of discrete and differential quasi-interpolants are constructed that are exact on quadratic spherical Bernstein-Bézier polynomials or on the whole space of spherical Powell-Sabin splines. Error bounds for these methods are presented, along with two numerical examples using data from the Marschner-Lobb test function and from ultrasound images of the human heart.
scientific article; zbMATH DE number 5696569
scientific article