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# source_grid

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

### Function Synopsis

    [L1,L2,L3,L4,L5,L6,L7,L8,L9] = ...

### Help Text

    SOURCE_GRID - generate variable grid of possible source locations
     function [L1,L2,L3,L4,L5,L6,L7,L8,L9] = ...
         source_grid(sensor_r,source_maxr,source_minr,Factor,STATS,VERBOSE);
     Given the scalar radius to the sensors sensor_r,
      the maximum scalar radius to the sources source_rmax,
      the minimum scalar radius to the sources source_rmin,
      then generate possible dipole source locations L in the upper hemisphere.

     Optional Factor is the fraction considered significant, default 0.1;
     Optional STATS flag means prepend stats onto the first rows of L
     Optional VERBOSE flag means describe the results.
     Optional [L1,L2,L3,...,L9] = source_grid(...
      generate higher order expansion points.

     If(STATS), then in each location matrix,
      L(1) give the number of surfaces used,
      L(2,:) to L(L(1)+1,:) are statistics.  The first column of the statistics
      rows gives the radial distance of the surface, the second column gives
      the spacing used on that surface, and the third gives the number of
      source points assigned on that surface.  Thus delete L(1:(L(1)+1),:)
      after viewing or extracting the statistics.

### Cross-Reference Information

This function calls

    sensor_ring                        C:\BrainStorm_2001\Toolbox\sensor_ring.m

This function is called by

    overlapping_sphere                 C:\BrainStorm_2001\Toolbox\overlapping_sphere.m

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

    function [L1,L2,L3,L4,L5,L6,L7,L8,L9] = ...
        source_grid(sensor_r,source_maxr,source_minr,Factor,STATS,VERBOSE);
    %SOURCE_GRID - generate variable grid of possible source locations
    % function [L1,L2,L3,L4,L5,L6,L7,L8,L9] = ...
    %     source_grid(sensor_r,source_maxr,source_minr,Factor,STATS,VERBOSE);
    % Given the scalar radius to the sensors sensor_r,
    %  the maximum scalar radius to the sources source_rmax,
    %  the minimum scalar radius to the sources source_rmin,
    %  then generate possible dipole source locations L in the upper hemisphere.
    %
    % Optional Factor is the fraction considered significant, default 0.1;
    % Optional STATS flag means prepend stats onto the first rows of L
    % Optional VERBOSE flag means describe the results.
    % Optional [L1,L2,L3,...,L9] = source_grid(...
    %  generate higher order expansion points.
    %
    % If(STATS), then in each location matrix,
    %  L(1) give the number of surfaces used,
    %  L(2,:) to L(L(1)+1,:) are statistics.  The first column of the statistics
    %  rows gives the radial distance of the surface, the second column gives
    %  the spacing used on that surface, and the third gives the number of
    %  source points assigned on that surface.  Thus delete L(1:(L(1)+1),:)
    %  after viewing or extracting the statistics.

    %<autobegin> ---------------------- 26-May-2004 11:34:30 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Forward Modeling
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\sensor_ring.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 11:34:30 -----------------------

    % John C. Mosher, Ph.D.
    % See Copyright.m file for information
    % $Date: 5/26/04 10:02a $ $Revision: 12 $
    %
    % February 8, 1995 author
    % JCM 2/27/95 cleanup from test version to production
    % JCM 7/26/95 move first gridding surface down somewhat below the source_maxr

    % uses: sensor_ring

    if(exist('Factor') ~= 1),    % user gave no Factor
      Factor = 0.1;         % what Factor is considered insignificant
    end
    if(exist('STATS') ~= 1),    % user did not give
      STATS = 0;             % do not prepend statistics
    end
    if(exist('VERBOSE') ~= 1),    % user did not give
      VERBOSE = 0;             % silent running
    end

    for order = 1:nargout,        % foreach requested expansion order

      % Theory is that an uncovered source is min_d from the nearest sensor.  We
      % want to be b_offset below this source, such that b_offset + min_d provide
      % sufficient coverage.  The radius of coverage is such that two
      % intersecting circles intersect such that the radius by distance is still
      % equivalent to the Factor.  So radius of coverage = Factor *
      % (min_d+offset). Spacing = sqrt(2)*radius of coverage. Interlace
      % sensor_ring routine by 1/2 the spacing on every other surface.

      next_source_r = source_maxr; % initialize first source surface
      Rdip = [];            % source locations
      Rstat = [];            % statistics
      isurfaces = 0;        % number of surfaces used

      while(next_source_r > source_minr),     % for appropriate spherical surfaces
        % minimum distance between source and sensor
        min_d = sensor_r - next_source_r;
        % calculate radius of coverage of these expansions
        if(isurfaces == 0),        % first surface only
          b_offset = min_d/((1/Factor)*sqrt(2)-1);
        else
          b_offset = min_d/((1/Factor)-1);
        end
        radius_of_coverage = Factor*(min_d+b_offset);
        % set our expansion surface
        next_expan_r = next_source_r - b_offset;
        % keep sensible
        next_expan_r = max(next_expan_r,0);

        % create equally spaced expansion points on this surface,
        %  spaced sqrt(2)*radius_of_coverage apart
        isurfaces = isurfaces + 1;
        % spacing between sensors on this expansion surface
        spacing = sqrt(2)*radius_of_coverage; % (equal to the b_offset*2)
        if(spacing > (2*next_expan_r)),    % spacing is bigger than radius
          Rn = [0 0 next_expan_r];    % single sensor point
        else            % radius bigger than spacing
          theta_inc = acos(1 - 0.5*(spacing/next_expan_r)^2); % sensor increment

          if(rem(isurfaces,2)),     % if an odd numbered surface
        Rn = sensor_ring(next_expan_r,theta_inc,'half');
        theta_inc_old = theta_inc; % drop into old bucke
          else            % interleave from previous theta_inc
        Rn = sensor_ring(next_expan_r,[theta_inc_old/2 theta_inc],'half');
          end

        end                % generate spacing on surface
        Rdip = [Rdip;Rn];         % add these source locations
        % what was the radius and spacing and how many
        Rstat = [Rstat; [next_expan_r spacing size(Rn,1)]]; % statistics

        % next surface of uncovered sources is at least b_offset below this
        %   surface.
        next_source_r = next_expan_r - b_offset;
        % then repeat for this source radius
      end

      if(STATS),            % user wants statistics as well
        eval(sprintf('L%.0f = [isurfaces 0 0;Rstat;Rdip];',order));
      else                % use doesn't want stats
        eval(sprintf('L%.0f = [Rdip];',order));
      end

      if(VERBOSE),
        disp(' ')
        disp(sprintf('Order %.0f, %.0f surfaces, %.0f sources.',...
        order,isurfaces,size(Rdip,1)));
        disp(['Surface distances' sprintf(' %.1f',Rstat(:,1)*1000) ' (mm)'])
        disp(['Surface spacings ' sprintf(' %.1f',Rstat(:,2)*1000) ' (mm)'])
      end

    end

    if(STATS & VERBOSE),        % wanted statistics and verbosity
      disp(' ')
      disp(...
       'Remember to delete the first "surfaces + 1" statistical rows of each L')
    end

    return

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