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From: gwyn@brl-tgr.ARPA (Doug Gwyn )
Newsgroups: net.math
Subject: Re: curve fitting (maybe)
Message-ID: <4735@brl-tgr.ARPA>
Date: Wed, 19-Sep-84 15:28:50 EDT
Article-I.D.: brl-tgr.4735
Posted: Wed Sep 19 15:28:50 1984
Date-Received: Tue, 25-Sep-84 20:25:37 EDT
References: <1197@cwruecmp.UUCP>
Organization: Ballistics Research Lab
Lines: 18

Judging by your diagram, you appear to want to take the existing
data as samples of some vector field and then interpolate to find
the field value at a given point.

Without some conditions on the vector field there is of course no
single solution to this problem.

The diagram also shows multiple field values at a point.  This
implies "least squares" style fitting would be appropriate.  To
make this work I think there would have to be some implied order
to the points.

As a rough approximation, how about making the vector at the test
point the weighted average of all known vectors, with the weights
such that the nearest point (using Euclidean metric) scales the
"range" of the weight and the total weights sum up to 1.  E.g.
except right at a data point, a Gaussian function of distance from
the test point could be used.