  We describe a two-level method for computing a function whose zero-level set
is the surface reconstructed from given points scattered over the surface and
associated with surface normal vectors. The function is defined as a linear
combination of compactly supported radial basis functions (CSRBFs). The method
preserves the simplicity and efficiency of implicit surface interpolation with
CSRBFs and the reconstructed implicit surface owns the attributes, which are
previously only associated with globally supported or globally regularized
radial basis functions, such as exhibiting less extra zero-level sets, suitable
for inside and outside tests. First, in the coarse scale approximation, we
choose basis function centers on a grid that covers the enlarged bounding box
of the given point set and compute their signed distances to the underlying
surface using local quadratic approximations of the nearest surface points.
Then a fitting to the residual errors on the surface points and additional
off-surface points is performed with fine scale basis functions. The final
function is the sum of the two intermediate functions and is a good
approximation of the signed distance field to the surface in the bounding box.
Examples of surface reconstruction and set operations between shapes are
provided.
