randsphere.m

% randsphere
% from https://www.mathworks.com/matlabcentral/fileexchange/9443-random-points-in-an-n-dimensional-hypersphere

function X = randsphere(m,n,r)
 
    % This function returns an m by n array, X, in which 
    % each of the m rows has the n Cartesian coordinates 
    % of a random point uniformly-distributed over the 
    % interior of an n-dimensional hypersphere with 
    % radius r and center at the origin.  The function 
    % 'randn' is initially used to generate m sets of n 
    % random variables with independent multivariate 
    % normal distribution, with mean 0 and variance 1.
    % Then the incomplete gamma function, 'gammainc', 
    % is used to map these points radially to fit in the 
    % hypersphere of finite radius r with a uniform % spatial distribution.
    % Roger Stafford - 12/23/05
 
    X = randn(m,n);
    s2 = sum(X.^2,2);
    X = X.*repmat(r*(gammainc(s2/2,n/2).^(1/n))./sqrt(s2),1,n);
end