Matlab 3D极坐标图

Question

I am struggling with the concepts behind plotting a surface polar plot.

I am trying to plot the values measured by a sensor at a combination of different angles over a hemisphere.

I have an array containing the following information:

A(:,1) = azimuth values from 0 to 360º

A(:,2) = zenith values from 0 to 90º

A(:,3) = values measured at the combination of angles of A(:,1) and A(:,2)

For example, here is a snippet:

0   15  0.489502132167206
0   30  0.452957556748497
0   45  0.468147850273115
0   60  0.471115818950192
0   65  0.352532182508945
30  15  0.424997863795610
30  30  0.477814980942155
30  45  0.383999653859467
30  60  0.509625464595446
30  75  0.440940431784788
60  15  0.445028058361392
60  30  0.522388502880219
60  45  0.428092266657885
60  60  0.429315072676194
60  75  0.358172892912138
90  15  0.493704001125912
90  30  0.508762762699997
90  45  0.450598496609200
90  58  0.468523071441297
120 15  0.501619699042408
120 30  0.561755273071577
120 45  0.489660355057938
120 60  0.475478615354648
120 75  0.482572226928475
150 15  0.423716506205776
150 30  0.426735372570756
150 45  0.448548968227972
150 60  0.478055144126694
150 75  0.437389584937356

To clarify, here is a piece of code that shows the measurement points on a polar plot.

th = A(:,1)*pi/180

polar(th,A(:,2))
view([180 90])

This gives me the following plot:

I would like now to plot the same thing, but instead of the points, use the values of these points stored in A(:,3). Then, I would like to interpolate the data to get a colored surface.

After some research, I found that I need to interpolate my values over a grid, then translate to Cartesian coordinates. From there I do not know how to proceed. Could someone point me in the right direction?

I have trouble getting the concept of the interpolation, but this is what I have attempted:

x1 = linspace(0,2*pi,100)

x2 = linspace(0,90,100)

[XX,YY] = meshgrid(x1,x2) 

[x,y] = pol2cart(th,A(:,2)) 

gr=griddata(x,y,A(:,3),XX,YY,'linear') 

Answer 1

With this piece of code, your example data points are converted into cartesian coords, and then plotted as "lines". The two tips of a line are one data point and the origin.

az = bsxfun(@times, A(:,1), pi/180);
el = bsxfun(@times, A(:,2), pi/180);
r = A(:,3);

[x,y,z] = sph2cart(az,el,r);
cx = 0; % center of the sphere
cy = 0;
cz = 0;
X = [repmat(cx,1,length(x));x'];
Y = [repmat(cy,1,length(y));y'];
Z = [repmat(cz,1,length(z));z'];

Still thinking how to interpolate the data so you can draw a sphere. See my comments to your question.