resistive panel

Well, mathematically, it's an application of conformal mapping; the key algorithms use a Schwartz-Christoffel transformation for the corners. So, Morse and Feshbach, _Methods_of_Theoretical_Physics_ has the method, around page 445 of volume I. Then with the plate shape tamed, you just solve Laplace's equation, with the boundary conditions, and reverse the transformation.

Thanks for the directions Whit.

Hul

whit3rd wrote:

"then a miracle occurs"

Phil - I was thinking along the same lines you mentioned but a bit more so. The simplicty of a flat panel does make methods for 3 dimensional surfaces seem excessive. I'm hoping to find something similar to calculating position from a knowledge of 2 distances. The hooker being that distances on the panel would be curved, so some code is required for corrections. If you or anyone else have any suggestions along these lines, please mention them.

Hul

Phil Hobbs wrote:

Conformal mapping is inherently a 2D method because it relies on complex-variable calculus--it maps one region of the complex plane into another. If the geometry is sufficiently simple, it can do magic on Laplace's equation problems. It's also useful numerically.

It would be easier to help if you could give more details about the panel--all you've said about it is that it's resistive and is connected at multiple points on its edges.

One fairly general approach would be to use the relaxation method to calculate the response for various source positions, fit a 2-D polynomial or a 2-D spline, and use that. (Numerical Recipes has a pretty good discussion of surface fitting.)

Cheers

Phil Hobbs

That's a tad ugly, but do-able. Even uglier would be an 'exact' conformal solution with an equation-solve element that does least-entropy fitting to X,Y, and source value. The desired solution is a single-point current source, or voltage source, I hope?

Before I did the relaxation method, I'd wonder if ultrasound time-of-flight is easier. Heck, I'd wonder if attack-the-prototype with probes, on a grid, is easier.

What have you got against relaxation? Summer's just over, dude, no reason to rush back into things. ;)

Cheers

Phil Hobbs