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From: Ingo Thies <ingo.thies@gmx.de>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: Plot lines orthogonal to contour lines
Date: Mon, 10 Oct 2011 18:14:16 +0200
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Hi Thomas

> is there a way to plot lines which are orthogonal to the contour
> lines?
> In my case, I want to plot a temperature field by isotherms and heat
> flow lines.

I don't know for sure whether this can be done in gnuplot directly, but 
what you can do ist to extract the contour lines with "set table 
'somefile'", and compute the local derivatives with an external program 
(e.g. you could write a short C code that applies the differential 
quotient method).

If you compute the derivs with respect to some parameter (the contour 
lines are parametric, aren't they?), e.g. the line number as the easiest 
parameter abscissa, for both x and y of the contour line, this gives you 
two derivatives x' and y', both combined would be the tangential vector 
(x',y').

Then compute the orthogonal vector (u,v) = (-y',x') (just think of a 
rotation matrix with a rotation vector of 90 degrees), normalize them to 
unit length, and then you can use them as unit vectors for your isotherms.

HTH,

Ingo