Construction of spherical spline quasi-interpolants based on blossoming

Abstract

a b s t r a c tA general theory of quasi-interpolants based on quadratic spherical Powell-Sabin splines on spherical triangulations of a sphere-like surface S is developed by using polar forms.As application, various families of discrete and differential quasi-interpolants reproducing quadratic spherical Bézier-Bernstein polynomials or the whole space of the spherical Powell-Sabin quadratic splines of class C 1 are presented.

Spline Quasi-Interpolation Numerical Methods for Integro-Differential Equations With Weakly Singular Kernels

“…The extremal coefficients µ k (f ) have particular expressions (more details on the construction of dQIs are given in [10,17]). The dQI Q d can be expressed as…”

A C1 composite spline Hermite interpolant on the sphere

“…There are many approaches for fitting scattered data, that range directly from targeting the sphere surface using spherical splines [1][2][3] and references therein. Spherical Bernstein-Bézier splines are fundamental to approximation and data fitting and have gained a lot of attention since they were introduced in Alfeld et al 4 Several techniques are based on spherical splines to solve this type of problem.…”