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From: Karl Ratzsch <mail.kfr@gmx.net>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: set range for second independent variable in special file '++'
Date: Fri, 24 Mar 2017 13:15:06 +0100
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Am 20.03.2017 um 20:38 schrieb Ethan A Merritt:
> Ethan A Merritt wrote:
>> Karl Ratzsch wrote:
>>> It seems I can only specify one independent variable with range for
>>> '++'. Is that so?
>>
>> Yes, but...
>> That's mostly because it's not clear how one could use it.
>> If you have an example of a type of plot that this would allow,
>> I'd be happy to look into adding it.

Hm, there are many, i think. The special filename "++" at the moment
always directly maps the second independent variable to the y axis, but
it could easily be meant to be sth else. Of course one can scale the
values to the wanted sampling range in the "using" specifier, but you
need a number of additional variables and it makes the script hard to read.

Any kind of circular object would be an example, or generally a 3D plot
with a coordinate transformation.

Parametric mode is an alternative, but I think I'm not the only one who
tries to avoid it because of the ugly syntax. ;-)

>>> I want to plot a ribbon wound on a cylindrical core (not actually such a
>>> boring one, but nevermind).

>> set parametric
>> splot radius*sin(u), radius*cos(u), (rise*u-v)
>> set isosample 100, 10
>  set hidden3d
>  replot

Here's the actual plot I wanted to make, now using parametric mode. It's
a short electric coil with a large volume of constant magnetic flux density.

a=-0.012   # zero for even coil width
n=9.	   # windings
l=20.;r=8. # lenght and radius
d=0.5      # distance between windings

#PRIVALOV, DVINSKIKH, VIETH, 1996, JMagRes A, 123, 157-160
k(n,a) = l/2 / (pi*n + a*pi**2*n**2) # normalise height to l
s(th,a) = k(n,a) * (th + a*th*abs(th)) # conductor center
h1(th,a) = (s(th+2*pi,a) + s(th,a))/2  - d/2 # edge 1
h2(th,a) = (s(th-2*pi,a) + s(th,a))/2  + d/2 # edge 2

set param
set xr[-r:r]; set yr[-r:r]
set urange [-n*pi:n*pi]
set vrange [0:1]
set isosample 1000,8
set hidden3d
set view equal xyz
set xyplane 0
splot r*cos(u),r*sin(u),h1(u,a)*v/2 + h2(u,a)*(1-v)/2