What plotting software to use: 2D polar plot with unique data - matlab

Question

I have my (example) data in the following format:
R_min R_max θ_min θ_min Zones
0 260 0 1.57 114
260 270 0 1.57 106
270 320 0 1.57 107
As you can see, I have "zones" (areas) that are created from R_min to R_max that sweep from theta_min to theta_max. Each row of data represents an area that I want to plot with a corresponding color based on the zone number. In this simple case, the data I show above would look like the following picture:
What plotting software should I use to accomplish this? I have been investigating the following options:
MATLAB. I am having trouble finding exactly what I need, but have found features like http://www.mathworks.com/help/symbolic/mupad_ref/plot-density.html?searchHighlight=plot%3A%3Adensity
Gnuplot. My issue with Gnuplot is the lack of documentation.
Are there other programs or a better way to compile my data to make my task-at-hand doable?
My real data set has thousands of rows of data and not nearly as simple as a quarter circle rainbow.

Answer 1

Here is one possible solution with gnuplot. That uses the circles plotting style to draw the overlapping wedges at the origin with a specified radius. That requires you to have your data sorted by descending maximum radius, and that you have no gaps.
Here is a possible script:
set xrange [0:350]
set yrange [0:350]
set size ratio -1
set style fill solid noborder
set palette defined (106 'blue', 107 'yellow', 114 'magenta')
set cbrange [106:114]
unset colorbox
plot 'test.txt' using (0):(0):2:($3*180/pi):($4*180/pi):5 with circles linecolor palette notitle
with the result (with 4.6.4):
Some more remarks:
The radius of the circles is given in units of the x-axis, but the y-axis isn't adapted accordingly. That's why you must set both xrange, yrange and even the ratio of the two axes with set size ratio -1.
Using the palette for coloring is one option, other options like using linecolor variable or linecolor rgb variable, are explained e.g. in gnuplot candlestick red and green fill.
On Unix systems, the sorting could also be done on-the-fly with e.g.
plot '< sort -r test.txt' ...

Answer 2

It's actually easy to do that with Matlab using simple trigonometry and the fill function:
% R_min R_max θ_min θ_min Zones
data = [
0 260 0 1.57 114
260 270 0 1.57 106
270 320 0 1.57 107];
% Define a color table, indexed by the "Zones" column
colors = {};
colors{114} = [1.0 0.0 0.5];
colors{106} = [0.7 0.0 1.0];
colors{107} = [1.0 1.0 0.0];
% Define the resolution of the plot (more points = more round)
nPoints = 100;
clf;
hold on;
for i = 1:size(data, 1)
% Extract the data from the i'th row. There's no need for this, you
% could access it directly below, but it makes the code more clean. :)
r_min = data(i,1);
r_max = data(i,2);
theta_min = data(i,3);
theta_max = data(i,4);
color = data(i, 5);
% First, get the sine and cosine between theta_min and theta_max
sin_theta = sin(linspace(theta_min, theta_max, nPoints));
cos_theta = cos(linspace(theta_min, theta_max, nPoints));
% Now, draw a semi-circle with radius = r_min and merge this
% semi-circle with another with radius = r_max, but reversed, so that
% it begins where the previous semi-circle ended.
x = [sin_theta * r_min sin_theta(end:-1:1) * r_max];
y = [cos_theta * r_min cos_theta(end:-1:1) * r_max];
% Draw the polygon.
fill(x,y, colors{color}, 'EdgeColor', colors{color});
end
hold off;
axis equal;
grid;
maxRadius = max(data(:,2));
axis([-maxRadius maxRadius -maxRadius maxRadius]);
Result: