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# shepards

## (Toolbox/shepards.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    varargout = shepards(X,x,v,n);

### Help Text

    SHEPARDS - (X,x,v,n); 3D nearest-neighbor interpolation using Shepard's weighting
     function varargout = shepards(X,x,v,n);

     Inputs
     v : Nxt array of data to be interpolated
     x : Nx3 array of original locations
     X : NN x 3 array of locations onto v will be interpolated
     n : Number of nearest neighbors to be considered in the interpolation (default is 8)

     Outputs
     V : NN x t array of interpolated measures

### Cross-Reference Information

This function calls

    norlig                             C:\BrainStorm_2001\Toolbox\norlig.m

This function is called by

    carto_sph                          C:\BrainStorm_2001\Toolbox\carto_sph.m
    interp_mail                        C:\BrainStorm_2001\Toolbox\interp_mail.m

### Listing of function C:\BrainStorm_2001\Toolbox\shepards.m

    function varargout = shepards(X,x,v,n);
    %SHEPARDS - (X,x,v,n); 3D nearest-neighbor interpolation using Shepard's weighting
    % function varargout = shepards(X,x,v,n);
    %
    % Inputs
    % v : Nxt array of data to be interpolated
    % x : Nx3 array of original locations
    % X : NN x 3 array of locations onto v will be interpolated
    % n : Number of nearest neighbors to be considered in the interpolation (default is 8)
    %
    % Outputs
    % V : NN x t array of interpolated measures

    %<autobegin> ---------------------- 26-May-2004 11:34:22 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Utility - Numeric
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\norlig.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 12 $  $Date: 5/26/04 10:02a $
    %
    % This software is part of BrainStorm Toolbox Version 2.0 (Alpha) 24-May-2004
    %
    % Principal Investigators and Developers:
    % ** Richard M. Leahy, PhD, Signal & Image Processing Institute,
    %    University of Southern California, Los Angeles, CA
    % ** John C. Mosher, PhD, Biophysics Group,
    %    Los Alamos National Laboratory, Los Alamos, NM
    % ** Sylvain Baillet, PhD, Cognitive Neuroscience & Brain Imaging Laboratory,
    %    CNRS, Hopital de la Salpetriere, Paris, France
    %
    % See BrainStorm website at http://neuroimage.usc.edu for further information.
    %
    % Copyright (c) 2004 BrainStorm by the University of Southern California
    % This software distributed  under the terms of the GNU General Public License
    % as published by the Free Software Foundation. Further details on the GPL
    % license can be found at http://www.gnu.org/copyleft/gpl.html .
    %
    % FOR RESEARCH PURPOSES ONLY. THE SOFTWARE IS PROVIDED "AS IS," AND THE
    % UNIVERSITY OF SOUTHERN CALIFORNIA AND ITS COLLABORATORS DO NOT MAKE ANY
    % WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF
    % MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, NOR DO THEY ASSUME ANY
    % LIABILITY OR RESPONSIBILITY FOR THE USE OF THIS SOFTWARE.
    %<autoend> ------------------------ 26-May-2004 11:34:22 -----------------------

    if nargin == 3
        n = 8; % Default number of neighbors for interpolation
    end

    varargout{1} = zeros(size(X,1),size(v,2));

    %Wmat = sparse(size(X,1),size(v,1));
    Wmat = spalloc(size(X,1),size(v,1),n*size(X,1));

    for node = 1:size(X,1)

        dist2grid = norlig(x - ones(size(x,1),1)*X(node,:));
        [dist2grid isort] = sort(dist2grid);
        icube = isort(1:n);
        dist2cube = dist2grid(1:n);
        clear dist2grid isort

        R = max(dist2cube);
        W = power((R - dist2cube)./ (R*dist2cube),2); % Interpolation weights from Shepards method
        W = W/sum(W);

        Wmat(node,icube) = W;

    end

    varargout{1} = Wmat * v;

    if nargout > 1
        varargout{2} = Wmat;
    end

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