Visualization of Volume Data with Quadratic Super Splines

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 efficient
computation, evaluation and visualization of the model. We apply
Bernstein-B\'ezier techniques well-known in Computer Aided Geometric
Design to compute and evaluate the trivariate spline and its gradient.
With this approach the volume data can be visualized efficiently 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 efficiency of the method and demonstrate a high visual
quality for rendered isosurfaces.