Help with multi-dimensional interpolation?

[Kevin Dressel]

Hey all!

First off, let me apologize for cross-posting, but I'm hoping someone in
these groups can help me out a bit.

I am looking for a way to perform (efficient) interpolation as follows:

Given a set of points with associated coordinates (more than three
dimensions):

a(q,r,s,t,u,v,....)
b(q1,r1,s1,t1,u1,v1,....)
c(q2,r2,s2,t2,u2,v2,....)
d(q3,r3,s3,t3,u3,v3....)
.
.
.
.



and so on, each being equal to some value (i.e., a(q,r,s,t,u,v,....) =
5, b() = 23, etc.), how could I interpolate to solve for point
x(qx,rx,sx,tx,ux,vx,....)?


The problem I am dealing with is a case where each point above is a
summed discrete load derived from individual loads (q,r,s,t,u,v...) that
are multiplied by unique coefficients, i.e. discrete load = q * coef_q +
r * coef_r + s * coef_s + ..... I need to solve for the discrete load
for a point x, in which the unique coefficients are not known.

I've read a bit about Delaunay triangulation techniques, but am still
not certain if it's what I want (or how to implement for that matter).
Primarily, I would like to find a way to interpolate to achieve the
greatest accuracy, which, for the sake of example, would be like taking
the three closest points out of the set of knowns to the unknown point
which also encompasses it.

Any ideas?

Thanks a lot in advance!
Kevin

[Hans-Bernhard Broeker]

Post by Kevin Dressel
First off, let me apologize for cross-posting, but I'm hoping
someone in these groups can help me out a bit.

Cross-posting is usually bad, but sometimes justifiable. But you
cross-posted without limiting the Followup-To to a single group.
That's generally considered inexcusable. Fixed.

Post by Kevin Dressel
I've read a bit about Delaunay triangulation techniques, but am
still not certain if it's what I want (or how to implement for that
matter).

Neither can anybody else be, from the hazy problem description you
gave.

Post by Kevin Dressel
Primarily, I would like to find a way to interpolate to
achieve the greatest accuracy,

Accuracy is impossible to even judge, much less actually achieve,
without knowing what the goal you're trying to hit accurately is. It
seems you don't know what the goal is. Until you do, nobody can
possibly help you.

Post by Kevin Dressel
which, for the sake of example, would
be like taking the three closest points out of the set of knowns to
the unknown point which also encompasses it.

In more than 2 dimensions, you need more than 3 points to define a
region that can encompass a given point. I.e. you need generalized
n-dimensional triangles, a.k.a. "simplices" (plural of "simplex").
And you need a criterion by which to pick one out of a humongous
number of such "triangulations", which nobody outside your problem
domain can help you define.