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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 $\Delta$. 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.
