GSP_CUBE - Create a graph corresponding to the sampling of an hyper-cube

function [ G ] = gsp_cube( param )
%GSP_CUBE Create a graph corresponding to the sampling of an hyper-cube
%   Usage :  G = gsp_cube();
%            G = gsp_cube( param );
%
%   Input parameters:
%       param       : Structure of optional parameters
%
%   Output parameters:
%       G           : Resulting graph
%
%   'gsp_cube( param )' creates a graph from points sampled on a
%   hyper-cube. The dimension of the cube can be passed as a parameter.
%   It can be sampled in a uniform voxel grid or randomly.  
%
%   Additional parameters
%   ---------------------
%
%    param.radius    : float                 the edge length
%    param.nb_pts    : int                   the number of vertices
%    param.nb_dim    : int                   the dimension
%    param.sampling  : ['random']            the variance of the distance kernel
%
%   Example:
%
%          G = gsp_cube();
%          gsp_plot_graph(G);
%          axis square
%
%   See also: gsp_sphere
%
%
%   Url: https://epfl-lts2.github.io/gspbox-html/doc/graphs/gsp_cube.html

% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.5
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program.  If not, see <http://www.gnu.org/licenses/>.

% If you use this toolbox please kindly cite
%     N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
%     and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
%     ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781

% Author : Johan Paratte
     if nargin < 1
       param = {};
    end
    
    %Parameters
    if ~isfield(param, 'radius'), param.radius = 1; end
    if ~isfield(param, 'nb_pts'), param.nb_pts = 300; end
    if ~isfield(param, 'nb_dim'), param.nb_dim = 3; end
    if ~isfield(param, 'sampling'), param.sampling = 'random'; end
    
    N = param.nb_pts;
    K = param.nb_dim;
    
    if (K > 3) 
       error('Dimension > 3 not supported yet !'); 
    end
    
    switch param.sampling
        %case 'uniform'
            %Define iteration of each dimension
            
        case 'random'
            % Draw angles randomly
            if (K == 2)
               pts = rand(N, N);
               G = pts;
            end
            
            if (K == 3)
               
               n = floor(N/6);
               
               pts = zeros(n*6, 3);
               pts(1:n, :) = [zeros(n,1), rand(n, 2)];
               pts(n+1:2*n, :) = [ones(n,1), rand(n, 2)];
               
               pts(2*n+1:3*n, :) = [rand(n, 1), zeros(n,1), rand(n, 1)];
               pts(3*n+1:4*n, :) = [rand(n, 1), ones(n,1), rand(n, 1)];
               
               pts(4*n+1:5*n, :) = [rand(n, 2), zeros(n,1)];
               pts(5*n+1:6*n, :) = [rand(n, 2), ones(n,1)];
               
            end

            %TODO Implement http://en.wikipedia.org/wiki/Hypersphere#CITEREFMarsaglia1972
            
        otherwise
            error('Unknown sampling !');
    end
    
    param.type = 'knn';
    param.k = 10;
    G = gsp_nn_graph(pts, param);
    
end