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Abstract:
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. 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 of smooth functions.
The constants of the corresponding error bounds are given explicitly.
Numerical tests confirm the results and the efficiency
of the method.
