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/spl 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 tetra-hedron of/spl Delta/, the quasi-
interpolating spline is a polynomial of total degree two which provides several advantages …

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 spline is a polynomial of total degree
two which provides several advantages including the efficient computation, evaluation and …