Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
A trivariate Powell—Sabin interpolant
Computer Aided Geometric Design
A practical evaluation of popular volume rendering algorithms
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
Quasi-interpolation by quadratic piecewise polynomials in three variables
Computer Aided Geometric Design
A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions
Journal of Approximation Theory
Topology preserving digitization with FCC and BCC grids
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Reconstruction of volume data with quadratic super splines
IEEE Transactions on Visualization and Computer Graphics
Interactive isosurfaces with quadratic C1 splines on truncated octahedral partitions
Information Visualization - Special issue on Visualization and Data Analysis 2011
Multivariate normalized Powell-Sabin B-splines and quasi-interpolants
Computer Aided Geometric Design
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We describe an approximating scheme for the smooth reconstruction of discrete data on volumetric grids. A local quasi-interpolation method for quadratic C^1-splines on uniform tetrahedral partitions is used to achieve a globally smooth function. The Bernstein-Bezier coefficients of the piecewise polynomials are thereby directly determined by appropriate combinations of the data values. We explicitly give a construction scheme for a family of quasi-interpolation operators and prove that the splines and their derivatives can provide an approximation order two for smooth functions. The optimal approximation of the derivatives and the simple averaging rules for the coefficients recommend this method for high quality visualization of volume data. Numerical tests confirm the approximation properties and show the efficient computation of the splines.