[comp.graphics] 2D Spline interpolation

gee@dretor.DRETOR.UUCP (Tom Gee see wdf) (10/12/88)

For quite a while now I've been looking throughout "the
literature" for a method of C2 surface interpolation with
irregularly spaced data points.  Although I've found a grand
total of 3 articles on this subject, they have been either
too brief or too technical for me to use.

If anyone could give me some references, hints, helps,
algorithms, etc. to help me here, it would be deeply appreciated.

Thanks!

-----
"If you know what a bubble sort is, |  Thomas Gee
 wipe it from your mind"            |  Aerospace Group
        -- Numerical Methods in C.  |  DCIEM
                                    |  Department of National Defence
               {watmath,utzoo}!dciem!zorac!dretor!gee

rhbartels@watcgl.waterloo.edu (Richard Bartels) (10/19/88)

In article <1068@dretor.DRETOR.UUCP> gee@dretor.UUCP (Tom Gee) writes:
>
>For quite a while now I've been looking throughout "the
>literature" for a method of C2 surface interpolation with
>irregularly spaced data points.

One reference worth noting is:

	An Algorithm for Surface-Fitting with Spline Functions
	P. Dierckx
	IMA Journal of Numerical Analysis
	Vol. 1 (1981) pp. 267-283

-Richard

sinha@caen.engin.umich.edu (SARVAJIT S SINHA) (10/21/88)

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