Gnuplot in Polar Coordinates

[adamwest]

I am brand new to Gnuplot and am having a problem trying to figure out how to graph in Polar Coordinates for a school assignment. What bothers me is we didn't go over other coordinate systems like Polar or Parametric at all for Gnuplot, and the internet tutorials I find seem to assume some basic knowledge and just tell me to do "set polar".

1. The problem I am trying to solve:

The electron density around a particular molecule centered at the origin is described by

n(r,theta) = [cos(r)]^2 * {1+[cos(theta)]^2} * exp(-r^2/25)

where r and theta are usual polar coordinates [e.g., (x,y) = (r*cos(theta),r*sin(theta))].

Write a gnuplot script elec.gpl that generates a surface plot of this function on a domain of x=-5..5 and y=-5..5. Set your script so that

gnuplot> elec.gpl

generates the plot as a postscript file called "elec.ps"

Homework Equations

None, just miscellaneous commands listed below

The Attempt at a Solution

set terminal png enhanced
set output 'elec.ps'
set polar
set angle degrees
set title 'Electron Density Around Molecule'
set xrange[-5:5]
set yrange[-5:5]
set grid
set grid polar
plot (cos(x))^2 *(1+(cos(y))^2)*exp(-x^2/25)
quit


I have tried changing x to r, y to t, y to theta, etc. I simply can't figure out how Gnuplot wants me to define polar coordinate inputs. Is there a way to redefine x as r*cos(theta) and y as r*sin(theta) and then let me set inputs and ranges for r and theta? I bet the answer is something obvious because Gnuplot is REALLY easy to use for rectangular coordinates.

Thank you for your help! :)

 

[KataKoniK]

Hello!

I can understand your frustration with trying to graph in polar coordinates using Gnuplot. It can be confusing if you are not familiar with it. Here are a few tips that might help you out:

1. As you mentioned, you can redefine x and y as r*cos(theta) and r*sin(theta) respectively. This can be done using the "using" keyword in your plot command. For example, your plot command can look like this: plot 'datafile' using (r*cos(theta)):(r*sin(theta)):(expression) with lines.

2. Another way to plot in polar coordinates is to use the "parametric" plot command. This allows you to specify the equations for both r and theta in terms of a parameter t. For your case, it would look like this: plot [t=0:360] (t):(expression) with lines.

3. You can also set the ranges for r and theta in your plot command. For example, if you want to plot for r=0 to 5 and theta=0 to 360, your plot command would look like this: plot [r=0:5] [theta=0:360] (expression) with lines.

I hope these tips help you out in solving your problem. If you need more help, feel free to ask! Best of luck with your assignment.