GSP_SWISS_ROLL - Initialize a swiss roll graph

function [G, tt]=gsp_swiss_roll(N,rand_state,param)
%GSP_SWISS_ROLL Initialize a swiss roll graph
%   Usage:  G = gsp_swiss_roll(N,rand_state,param);
%
%   Input parameters:
%         N          : Number of vertices.
%         s          : sigma ( default: sqrt(2/N))
%         thresh     : threshold (default: 1e-6)
%         rand_state : rand seed (default: 0)
%   Output parameters:
%         G     : Graph structure.
%
%   'gsp_create_swiss_roll(N,s,thresh,rand_state)' initializes a graph
%   structure containing the swiss roll graph
%
%   Example:
%
%          G = gsp_swiss_roll(200);
%          gsp_plot_graph(G);
%
%
%   Url: https://epfl-lts2.github.io/gspbox-html/doc/graphs/gsp_swiss_roll.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 : David I Shuman, Nathanael Perraudin
% Test: test_graphs

if nargin<1
    N = 200;
end

if nargin<2
   rand_state = 0; 
end

gsp_reset_seed(rand_state);



a = 1;   % swiss roll goes from a*pi to b*pi
b = 4;   
y = rand(2,N);
% uniform distribution along the manifold (in data space)
tt = sqrt((b*b-a*a)*y(1,:)+a*a);
tt = pi*tt;
% now tt should go from a*pi to b*pi
height = y(2,:);
x = [tt.*cos(tt)/b^2; height; tt.*sin(tt)/b^2];

if nargin<3
    param = struct;
end

if ~isfield(param,'k'), param.k = 6; end
G = gsp_nn_graph(x',param);
G.map_coord = y';
G.type = 'Swiss Roll';

end