Shade a subset of a sphere's surface in MATLAB - matlab

Question

I'm attempting to generate a plot of a hemisphere with a shaded area on the surface bound by max/min values of elevation and azimuth. Essentially I'm trying to reproduce this:
Generating the hemisphere is easy enough, but past that I'm stumped. Any ideas?
Here's the code I used to generate this sphere:
[x,y,z] = sphere;
x = x(11:end,:);
y = y(11:end,:);
z = z(11:end,:);
r = 90;
surf(r.*x,r.*y,r.*z,'FaceColor','yellow','FaceAlpha',0.5);
axis equal;

Answer 1

If you want to highlight a certain area of your hemisphere, first you decide the minimum and maximum azimuth (horizontal sweep) and elevation (vertical sweep) angles. Once you do this, take your x,y,z co-ordinates and convert them into their corresponding angles in spherical co-ordinates. Once you do that, you can then subset your x,y,z co-ordinates based on these angles. To convert from Cartesian to spherical, you would thus do:
Source: Wikipedia
theta is your elevation while phi is your azimuth. r would be the radius of the sphere. Because sphere generates co-ordinates for a unit sphere, r = 1. Therefore, to calculate the angles, we simply need to do:
theta = acosd(z);
phi = atan2d(y, x);
Take note that the elevation / theta is restricted 0 to 180 degrees, while the azimuth / phi is restricted between -180 to 180 degrees. Because you're only creating half of a sphere, the elevation should simply vary from 0 to 90 degrees. Also note that acosd and atan2d return the result in degrees. Now that we're here, you just have to subset what part of the sphere you want to draw. For example, let's say we wanted to restrict the sphere such that the min. and max. azimuth span from -90 to 90 degrees while the elevation only spans from 0 to 45 degrees. As such, let's find those x,y,z co-ordinates that satisfy these constraints, and ensure that anything outside of this range is set to NaN so that these points aren't drawn on the sphere. As such:
%// Change your ranges here
minAzimuth = -90;
maxAzimuth = 90;
minElevation = 0;
maxElevation = 45;
%// Compute angles - assuming that you have already run the code for sphere
%// [x,y,z] = sphere;
%// x = x(11:end,:);
%// y = y(11:end,:);
%// z = z(11:end,:);
theta = acosd(z);
phi = atan2d(y, x);
%%%%%// Begin highlighting logic
ind = (phi >= minAzimuth & phi <= maxAzimuth) & ...
(theta >= minElevation & theta <= maxElevation); % // Find those indices
x2 = x; y2 = y; z2 = z; %// Make a copy of the sphere co-ordinates
x2(~ind) = NaN; y2(~ind) = NaN; z2(~ind) = NaN; %// Set those out of bounds to NaN
%%%%%// Draw our original sphere and then the region we want on top
r = 90;
surf(r.*x,r.*y,r.*z,'FaceColor','white','FaceAlpha',0.5); %// Base sphere
hold on;
surf(r.*x2,r.*y2,r.*z2,'FaceColor','red'); %// Highlighted portion
axis equal;
view(40,40); %// Adjust viewing angle for better view
... and this is what I get:
I've made the code modular so that all you have to do is change the four variables that are defined at the beginning of the code, and the output will highlight that desired part of the hemisphere that are bounded by those min and max ranges.
Hope this helps!

Answer 2

One option is to create an array with the corresponding color you want to attribute to each point.
A minimal example (use trigonometry to convert your azimuth and elevation to logical conditions on x, y, and z):
c=(y>0).*(x>0).*(z>0.1).*(z<0.5);
c(c==0)=NaN;
surf(r.*x,r.*y,r.*z,c ,'FaceAlpha',0.5); axis equal;
yields this:
Note: this only works with the resolution of the grid. (i.e each 'patch' of the surface can have a different color). To exactly reproduce your plot, you might want to superpose the grid sphere with another one that has a much larger number of grid points on which you apply the above code.