Construction of a Bivariate \(C^2\) Septic Quasi-interpolant Using the Blossoming Approach
摘要
In this study, we employ a blossoming technique and smoothness criteria to devise a two-step method for creating a \(C^2\) septic spline quasi-interpolant on any given triangulation. This approach ensures an optimal approximation order without the need for coefficient masks associated with smoothness or B-spline basis. To demonstrate the validity of our theoretical findings, we provide numerical experiments.