MPI-I-2003-4-006

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 $\Delta$. 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 $\Delta$ , the spline is a polynomial of total degree two which provides several advantages including the e cient computation, evaluation and visualization of the model. We apply Bernstein-B{\´e}zier techniques wellknown in Computer Aided Geometric Design to compute and evaluate the trivariate spline and its gradient. With this approach the volume data can be visualized e ciently e.g. with isosurface ray-casting. 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 e ciency of the method and demonstrate a high visual quality for rendered isosurfaces.

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Das Paper war damals submitted, so da"s ich es nicht "offentlich machen wollte, der Report diente in erster Linie dem Jahresbericht und der Fachbeiratsbegehung