Surface Fitting using gridfit

Those wishing to model a surface from data in the
form of z(x,y) from scattered or semi-scattered
data have had few options in matlab - mainly
griddata.
Griddata is a valuable tool for interpolation of
scattered data. However it fails when there are
replicates or when the data has many collinear
points. Griddata is also unable to extrapolate
beyond the convex hull of the data unless the 'v4'
option is used, which is slow.
Gridfit solves all of these problems, although it
is not an interpolant. It builds a surface over a
complete lattice, extrapolating smoothly into the
corners. You have control of the amount of
smoothing done, as well as interpolation methods,
which solver to use, etc.
This release allows the user to solve much larger problems using a new tiling option. There is essentially no limit on the size of the suface one builds now, as long as you have dense enough data and enough memory to store the final gridded surface.

Example uses are found in the file gridfit_demo.m,
as well as comparisons to griddata on the same
surfaces.