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Abstract

We develop a new approach to reconstruct non-discrete models from
gridded volume samples. As a model, we use quadratic trivariate super
splines on a uniform tetrahedral partition . The approximating splines
are determined in a natural and completely symmetric way by averaging
local data samples, such that appropriate smoothness conditions are
automatically satisfied. On each tetrahedron of , the
quasi-interpolating spline is a polynomial of total degree two which
provides several advantages including efficient computation,
evaluation and visualization of the model. We apply Bernstein-B´ezier
techniques well-known in CAGD to compute and evaluate the trivariate
spline and its gradient. With this approach the volume data can be
visualized efficiently e.g. with isosurface raycasting. Along an
arbitrary ray the splines are univariate, piecewise quadratics and
thus the exact intersection for a prescribed isovalue can be easily
determined in an analytic and exact way. Our results confirm the
efficiency of the quasi-interpolating method and demonstrate high
visual quality for rendered isosurfaces.