Multistage trivariate surfaces (Q801628)

The paper discusses interpolants to arbitrarily spaced data in 3 or more dimensions. A ''multistage method'' is defined by the following procedure: (1) interpolate to the arbitrarily placed data with a general method, (2) then evaluate this general method over a coarse rectilinear grid to provide data for a tensor product method, and (3) render the surface by evaluating the tensor product over a fine grid. The rationale for algorithms like this is the fact that interpolants from step 1 may be expensive to compute for large data sets (as are often needed for rendering). Thus a reasonably small number is extracted from 1 to produce a ''cheap'' surface 2.