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Abstract:
We propose a new approach to reconstruct nondiscrete models from gridded volume
samples. As a model, we use quadratic trivariate super splines on a uniform
tetrahedral partition. We discuss the smoothness and approximation properties
of our model and compare to alternative piecewise polynomial constructions. We
observe as a non-standard phenomenon that the derivatives of our splines yield
optimal approximation order for smooth data, while the theoretical error of the
values is nearly optimal due to the averaging rules. Our approach enables
efficient reconstruction and visualization of the data. As the piecewise
polynomials are of the lowest possible total degree two, we can efficiently
determine exact ray intersections with an iso-surface for ray-casting.
Moreover, the optimal approximation properties of the derivatives allow to
simply sample the necessary gradients directly from the polynomial pieces of
the splines. Our results confirm the efficiency of the quasi-interpolating
method and demonstrate high visual quality for rendered isosurfaces.
