> 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.nethttp://hobbs-eo.com
Reply by whit3rd●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 Phil Hobbs●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.nethttp://hobbs-eo.com
Reply by Hul Tytus●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
> 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.nethttp://hobbs-eo.com
Reply by Hul Tytus●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 whit3rd●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?
>
> 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 Hul Tytus●September 23, 20202020-09-23
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