CoveringRadiusΒΆ

% Calculate the covering radius of the given samples.
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% USAGE:
%    radius = CoveringRadius(grad)
%    radius = CoveringRadius(grad, ind)
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% INPUT
%    grad     :  Nx3 matrix, each row is a point in sphere.
%    ind      :  If it is given, calculate the minimal distance between
%                the ind-th sample and the other samples in grad.
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%
% OUTPUT
%    radius   :  covering radius, i.e., the minimal spherical distance between any two samples.
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%
% References:
%   1.  http://mathworld.wolfram.com/SphericalCode.html
%   2. "Designing Single- and Multiple-Shell Sampling Schemes for Diffusion MRI Using Spherical Code",
%       Jian Cheng, Dinggang Shen, Pew-Thian Yap, MICCAI 2014.
%   3. "Novel single and multiple shell uniform sampling schemes for diffusion MRI using spherical codes",
%       Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser, MICCAI 2015.
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% Copyright (c) 2014, Jian Cheng <jian.cheng.1983@gmail.com>
%