Trivariate near-best blending spline quasi-interpolation operators
This paper deals with the construction of trivariate quasi-interpolation operators based on the blending of univariate B-spline and bivariate box-spline quasi-interpolation operators. The proposed quasi-interpolation method can be used for building non-discrete models from discrete data on volumetric grids, as required, for example, in scientific visualization, medical imaging, or computer graphics. The coefficients of the proposed linear functionals are computed to minimize an objective function constructed from the Bernstein-Bézier coefficients of the fundamental function of the resulting operator. In the case of blending \(C^1\) quadratic B-splines and box-splines, it is shown that the minimization problem has infinitely many solutions depending on a parameter. Further, a specific value of the parameter is determined numerically that yields very favorable results. The paper also treats the case of blending the quartic B-spline with each of the quartic box-splines \(M_{2,1}\) and \(M_{1,2}\). The corresponding minimization problem now has a unique solution, which is computed exactly.
scientific article; zbMATH DE number 6871986
scientific article