function varargout = normnd(data,varargin)
% NORMND computes the vector normal to points in an N-D point cloud
%
% NORMND(DATA) computes the vector normal to the N-dimensional sample
% point locations in DATA. DATA is defined as an MxN matrix where M is
% the number of samples. Each column contains the sample locations in
% each of the orthogonal dimensions in N-dimensional space
%
% Example:
% % Compute the normal vector to 3-D sample points
% data = randn(20,3);
% % Bias the normal vector toward the Z-axis
% data(:,3) = data(:,3)./10;
% v = normnd(data);
% % Plot
% figure; scatter3(data(:,1),data(:,2),data(:,3));
% hold on; quiver3(mean(data(:,1)),mean(data(:,2)),mean(data(:,3)),v(1),v(2),v(3))
%
% See also: cov, eig.
%
%
%
% Jered R Wells
% 2013/05/02
% jered [dot] wells [at] gmail [dot] com
%
% v1.0
%
% UPDATES
% YYYY/MM/DD - jrw - v1.1
%
%
%% INPUT CHECK
narginchk(1,1);
nargoutchk(0,1);
fname = 'norm3d';
% Checked required inputs
validateattributes(data,{'single','double'},{},fname,'DATA',1);
%% PROCESS
% Center the input indicies (center of mass computation)
data = data - repmat(mean(data,1),size(data,1),1);
% Compute the MxM covariance matrix A
A = cov(data);
% Compute the eigenvector of A
[V, LAMBDA] = eig(A);
% Find the eigenvector corresponding to the minimum eigenvalue in A
% This should always be the first column, but check just in case
[~,idx] = min(diag(LAMBDA));
% Normalize
V = V(:,idx)./norm(V(:,idx));
% Assemble the VARARGOUT cell array
varargout = {V};
end % MAIN
