Trivariate spline quasi-interpolants based on simplex splines and polar forms

In this work we describe an approximating scheme based on simplex splines on a tetrahedral partition using volumetric data. We use the trivariate simplex B-spline representation of polynomials or piecewise polynomials in terms of their polar forms to construct several differential or discrete quasi interpolants which have an optimal approximation order. (C) 2014 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.