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From: sinha@caen.engin.umich.edu (SARVAJIT S SINHA)
Newsgroups: comp.graphics
Subject: Re: 2D Spline interpolation
Summary: 2D-spline scattered-data interpolation references:
Message-ID: <3f2e5938.14dd5@sight.engin.umich.edu>
Date: 21 Oct 88 03:00:00 GMT
References: <1068@dretor.DRETOR.UUCP>
Distribution: na
Organization: U of M Engineering, Ann Arbor, Mich.
Lines: 42


My thesis is going to be on this, so I can point you to the
relevant articles:
The place to start, and get the theory overview is in 

author = "L. L. Schumaker",
title = "Fitting Surfaces to scattered data",
booktitle = "Approximation Theory II",
pages = {203-268},
year = 1979,
editors are: GGLorentz, CKChui, LLSchumaker
publisher: Academic Press

You can get theoretical by tracing the references therein.

Larry presents the thin plate spline (whose basis function
looks like      2
               r log(r),
where
                        2        2
         r = sqrt((x-x ) + (y-y )  )
                      i        i
He also presents the set of linear equations to solve
for the coefficients of the spline, assuming one of these
basis functions at each knot(data point).

Also see:
@article{Franke82,
author = "R. Franke",
title = "Scattered Data Interpolation: Tests of some methods",
journal = "Mathematics of Computation",
volume = 38,
pages = {181-200},
year = 1982,
month = "Jan."}

Franke compares various methods to solve your problem.

Hope this helps,
If you need more info, email me @ sinha@caen.engin.umich.edu


Sarvajit Sinha @ University of Michigan