How to get random points from upper semisphere

Hello eveyone,

I use this code to get random points from a sphere with radius 5:

clear all

clc

fullFileName = fullfile(pwd, 'DataPoints.txt')

% Open a text file.

fileHandle = fopen(fullFileName, 'wt');

% Write out the things we want to write out.

rng(0,'twister')

rvals = pi*rand(100,1)+pi/2;

azimuth = 2*pi*rand(100,1);

[x,y,z] = sph2cart(azimuth,rvals,5);

figure

plot3(x,y,z,'.')

axis equal

fprintf(fileHandle, '{%f, %f ,%f},',[x,y,z]');

fprintf(fileHandle, '[%f, %f ,%f],',[x,y,z]');

fprintf(fileHandle, '%f, %f , %f;',[x,y,z]');

% Close the file.

fclose(fileHandle);

% Open it in notepad (Windows OS only)

winopen(fullFileName);

, but I want to have random points from upper semisphere with this radius.

Thanks in advance.

Answer 1

[Bruno Luong]

Put

...
[x,y,z] = sph2cart(azimuth,rvals,5);
z = abs(z)
...

[Mojtaba Mohareri]

Thank you very very much.

Answer 2

[Bruno Luong]

Your code won't generate uniform point on half sphere, there is a bigger density on the north pole (try to generate with 10000 points you'll see).

A better approach would be

radius = 5;
xyz = randn(3,100);
xyz = xyz .* (radius ./ sqrt(sum(xyz.^2,1)));
x = xyz(1,:);
y = xyz(2,:);
z = abs(xyz(3,:));

[Mojtaba Mohareri]

I didn't know that. I've tried it. You're right. But when I run your code, there is this error

Error using .*

Matrix dimensions must agree.

Error in Untitled4 (line 5)

xyz = xyz .* (radius ./ sqrt(sum(xyz.^2,1)));

[Bruno Luong]

You have very old matlab version, replace with

xyz = bsxfun(@times, xyz, radius ./ sqrt(sum(xyz.^2,1)));

[Mojtaba Mohareri]

Yes, unfortunately it's MATLAB R2015a. It's works properly. Thank you very very much.