A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
An explicit basis for C1 quartic by various bivariate splines
SIAM Journal on Numerical Analysis
A trivariate Powell—Sabin interpolant
Computer Aided Geometric Design
The generic dimension of the space of C1 splines of degree d≥8 on tetrahedral decompositions
SIAM Journal on Numerical Analysis
On dimension and existence of local bases for multivariate spline spaces
Journal of Approximation Theory
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Interactive ray tracing for isosurface rendering
Proceedings of the conference on Visualization '98
Accelerating volume rendering with quantized voxels
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
A practical evaluation of popular volume rendering algorithms
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Developments in bivariate spline interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Volume Graphics
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Smooth approximation and rendering of large scattered data sets
Proceedings of the conference on Visualization '01
Triquadratic Reconstruction for Interactive Modelling of Potential Fields
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
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
Reconstruction of volume data with quadratic super splines
IEEE Transactions on Visualization and Computer Graphics
Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
An explicit quasi-interpolation scheme based on C 1 quartic splines on type-1 triangulations
Computer Aided Geometric Design
Quadratic spherical spline quasi-interpolants on Powell--Sabin partitions
Applied Numerical Mathematics
A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions
Journal of Approximation Theory
Quasi-interpolation by quadratic C1-splines on truncated octahedral partitions
Computer Aided Geometric Design
Construction of spherical spline quasi-interpolants based on blossoming
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
A quasi-interpolation method for quadratic piecewise polynomials in three variables is described which can be used for the efficient reconstruction and visualization of gridded volume data. The Bernstein-Bézier coefficients of the splines are immediately available from the given data values by applying a local averaging, where no prescribed derivatives are required. Since the approach does not make use of a particular basis or a subset spanning the spline spaces, we analyze the smoothness properties of the trivariate splines. We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives for smooth functions. The constants of the corresponding error bounds are given explicitly. Numerical tests confirm the results and the efficiency of the method.