Quasi-interpolation by quadratic C1-splines on truncated octahedralpartitions

摘要

We describe an approximating scheme for the smooth reconstruction of discrete data onvolumetric grids. A local quasi-interpolation method for quadratic C1-splines on uniformtetrahedral partitions is used to achieve a globally smooth function. The Bernstein-Beziercoefficients of the piecewise polynomials are thereby directly determined by appropriatecombinations of the data values. We explicitly give a construction scheme for a family ofquasi-interpolation operators and prove that the splines and their derivatives can providean approximation order two for smooth functions. The optimal approximation of thederivatives and the simple averaging rules for the coefficients recommend this methodfor high quality visualization of volume data. Numerical tests confirm the approximationproperties and show the efficient computation of the splines.