How to get random points from upper semisphere

Question

Mojtaba Mohareri 2020-8-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/581486-how-to-get-random-points-from-upper-semisphere

评论： Mojtaba Mohareri 2020-8-19

采纳的回答： Bruno Luong

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.

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Answer 1

Bruno Luong 2020-8-19

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https://ww2.mathworks.cn/matlabcentral/answers/581486-how-to-get-random-points-from-upper-semisphere#answer_481964

在 MATLAB Online 中打开

Put

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

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Mojtaba Mohareri 2020-8-19

Thank you very very much.

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Answer 2

Bruno Luong 2020-8-19

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/581486-how-to-get-random-points-from-upper-semisphere#answer_481973

编辑：Bruno Luong 2020-8-19

在 MATLAB Online 中打开

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,:));

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Bruno Luong 2020-8-19

在 MATLAB Online 中打开

You have very old matlab version, replace with

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

Mojtaba Mohareri 2020-8-19

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

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