Anyone know where to find a description of the method for determing the position of a voltage source on a resistance plate that is connected at multiple points on the edges? Or source code maybe? Hul
resistive panel
Started by ●September 23, 2020
Reply by ●September 23, 20202020-09-23
On Wednesday, September 23, 2020 at 5:02:37 PM UTC-7, Hul Tytus wrote:> Anyone know where to find a description of the method for determing the > position of a voltage source on a resistance plate that is connected at > multiple points on the edges? Or source code maybe? > > HulWell, 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.
Reply by ●September 24, 20202020-09-24
Thanks for the directions Whit. Hul whit3rd <whit3rd@gmail.com> wrote:> On Wednesday, September 23, 2020 at 5:02:37 PM UTC-7, Hul Tytus wrote: > > Anyone know where to find a description of the method for determing the > > position of a voltage source on a resistance plate that is connected at > > multiple points on the edges? Or source code maybe? > > > > Hul> 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.
Reply by ●September 24, 20202020-09-24
On 2020-09-24 06:29, Hul Tytus wrote:> Thanks for the directions Whit. > > Hul > > whit3rd <whit3rd@gmail.com> wrote: >> On Wednesday, September 23, 2020 at 5:02:37 PM UTC-7, Hul Tytus wrote: >>> Anyone know where to find a description of the method for determing the >>> position of a voltage source on a resistance plate that is connected at >>> multiple points on the edges? Or source code maybe? >>> >>> Hul > >> 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."then a miracle occurs" <-- I think Whit could be more explicit here. ;) Analytical conformal mapping is generally hard unless the transformation is simple, such as mapping the upper half plane onto a circular disc. Every corner in the domain gives rise to a fractional power term in the integrand, which is a bear. A simple 2D Laplace solver that you can code up very quickly is the relaxation method, where you divide the domain up into a square grid, and on each iteration replace the voltage at each point with the average of its four nearest neighbours. There are lots of faster methods, but that one works fine and is sure easy. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Reply by ●September 24, 20202020-09-24
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 <pcdhSpamMeSenseless@electrooptical.net> wrote:> On 2020-09-24 06:29, Hul Tytus wrote: > > Thanks for the directions Whit. > > > > Hul > > > > whit3rd <whit3rd@gmail.com> wrote: > >> On Wednesday, September 23, 2020 at 5:02:37 PM UTC-7, Hul Tytus wrote: > >>> Anyone know where to find a description of the method for determing the > >>> position of a voltage source on a resistance plate that is connected at > >>> multiple points on the edges? Or source code maybe? > >>> > >>> Hul > > > >> 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.> "then a miracle occurs" <-- I think Whit could be more explicit here. ;)> Analytical conformal mapping is generally hard unless the transformation > is simple, such as mapping the upper half plane onto a circular disc. > Every corner in the domain gives rise to a fractional power term in the > integrand, which is a bear.> A simple 2D Laplace solver that you can code up very quickly is the > relaxation method, where you divide the domain up into a square grid, > and on each iteration replace the voltage at each point with the average > of its four nearest neighbours.> There are lots of faster methods, but that one works fine and is sure easy.> Cheers> Phil Hobbs> -- > Dr Philip C D Hobbs > Principal Consultant > ElectroOptical Innovations LLC / Hobbs ElectroOptics > Optics, Electro-optics, Photonics, Analog Electronics > Briarcliff Manor NY 10510> http://electrooptical.net > http://hobbs-eo.com
Reply by ●September 25, 20202020-09-25
On 2020-09-24 18:56, Hul Tytus wrote:> 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.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.> 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.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 -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Reply by ●September 25, 20202020-09-25
On Friday, September 25, 2020 at 1:33:25 AM UTC-7, Phil Hobbs wrote:> On 2020-09-24 18:56, Hul Tytus wrote:> > 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.> 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.)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.
Reply by ●September 26, 20202020-09-26
On 2020-09-25 21:34, whit3rd wrote:> On Friday, September 25, 2020 at 1:33:25 AM UTC-7, Phil Hobbs wrote: >> On 2020-09-24 18:56, Hul Tytus wrote: > >>> 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. > >> 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.) > > 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 -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
