how to display three one dimensional vectors as a 2 dimensional image

Hi, This should be simple. I think there must be a very easy way to do this but I cannot figure it out.

I have data for the angle of a beam in theta and phi and the intensity of that beam. I want to plot it on a polar plot, so I can see the intensity of beams coming from different directions. I can use polar to plot this once I have a 2D array of intensities. But before that I must convert the data for beam intensities from a random array of [theta,phi,I] where theat, and phi, and I are all one dimensional vectors, onto some regular spaced grid. When I try meshgrid I get the error that theta or phi are not monotonically increasing. What can I do?

Thanks!

Answer 1

[Robert]

To create a mesh from your data, you could use delaunay and trisurf, which don't need the x and y values to be evenly spaced. Below is an example that should help get you started. In the conversion to Cartesian, you can scale by I to map intensity to position, or leave it out and visualize intensity with color only.

I hope I interpreted your question correctly. At the very least this script makes cool looking plots!

n = 1000; % number of samples

% Example data
theta = rand(n,1)*360;
phi = rand(n,1)*180 - 90;
I = rand(n,1)+4+2*sind(theta).^2;

% Convert to Cartesian
X = cosd(theta).*sind(phi);
Y = sind(theta).*sind(phi);
Z = cosd(phi);
% X = I.*cosd(theta).*sind(phi);
% Y = I.*sind(theta).*sind(phi);
% Z = I.*cosd(phi);

% Create and show a triangle mesh from points
tri = delaunay(X,Y);
trisurf(tri,X,Y,Z,I);

axis equal
rotate3d on
view(2) % show the 2D (XY) view