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How to create a quiver plot with logarithmic scaled arrows

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Hey, I have a vector field with a large dynamic range; therefore the only way to properly see it in a quiver plot is if the length of the vectors will scale logarithmic instead of linearly.
As far as I know, there is no built in way to do it. Manually take the log before calling quiver will not work as it will change the angles, and therefore the quiver plot will be wrong.
I tried searching online but couldn't a way to do it, anyone knows one?
Another option is starting with the matlab built in quiver plot code and manually making another function that fixes it, is there anyway to get it?
  2 Comments
Chad Greene
Chad Greene on 7 Mar 2016
Interesting problem. The code for quiver is viewable. Type
open quiver
and it should be relatively painless to manually hack the length scaling.
Yoav Romach
Yoav Romach on 7 Mar 2016
Thanks! Didn't know it was that simple to open the code for matlab functions :)
Unfortunately, it did not help me; taking a look at the code, the important lines are just these two:
h = matlab.graphics.chart.primitive.Quiver;
set(h,'Parent',parax,'Color_I',c,'LineStyle_I',ls,pvpairs{:});
pvpairs is simply the x,y,u,v data, so it seems that the behavior is hard-coded into a primitive "Quiver" chart type :\
Any other ideas?

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Accepted Answer

Star Strider
Star Strider on 7 Mar 2016
I’m not certain what you’re plotting, so I’m guessing here.
This is one approach:
t = linspace(1E-3, 6*pi);
x = t .* cos(t) + 2;
y = t.* sin(t) + 2;
dx = gradient(x);
dy = gradient(y);
figure(1)
quiver(x, y, dx, dy) % Retain Scaling
grid
axis equal
log_dx = log(hypot(dx,dy)) .* (dx);
log_dy = log(hypot(dx,dy)) .* (dy);
figure(2)
quiver(x, y, log_dx, log_dy, 0) % Log Arrows, No Scaling
grid
axis equal
  6 Comments
Arthur Ku
Arthur Ku on 22 Sep 2018
Edited: Arthur Ku on 22 Sep 2018
Very nice, Yoav!
I tested this out with a few point charges and it looks great when superimposed on a contour plot. Thank you both for your solutions. As Star Strider said, this would be great on File Exchange.
Yoav Romach
Yoav Romach on 15 Oct 2018
Edited: Star Strider on 15 Oct 2018
Thanks Arthur.
About two years later, I added it to file exchange with some additional commenting (but no significant code changes). If people will report bugs, I'll try to fix them.
Hopefully it'll help people :)

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More Answers (1)

Angelo Hafner
Angelo Hafner on 15 Mar 2019
Edited: Angelo Hafner on 15 Mar 2019
Just enter the u,v,w components in the function log_cv... The function returns the log components of the vector [u,v,w]...
function [log_ax,log_ay,log_az] = log_cv(u,v,w)
r = sqrt(u.^2 + v.^2 + w.^2);
rho = sqrt(u.^2 + v.^2);
t = atan2(rho,w);
f = atan2(v,u);
log_ax = log10(r) .* sin(t) .* cos(f);
log_ay = log10(r) .* sin(t) .* sin(f);
log_az = log10(r) .* cos(t);
end
  1 Comment
Yoav Romach
Yoav Romach on 16 Mar 2019
Hey Angelo,
This was answered two years ago, and I created a function to solve it, see above.
Your function would not work properly if r will be smaller than 1 (I mean it will work, but will mess up the quiver).

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