function [swarming_ind] = fuzzySwarm2d(M,S);
% COMPSWARM(M,S) ----  This is a computational version of the Swarming Index 
% presented in Watt et al. (1997), calculated for the array 'M', if M is in the 
% standard format.  This is essentially the mean of the ratios for each group of
% the number in the group to the perimeter of the group.  
%
% The actual index used a grid of 4 squares by 6; perimeter was estimated by the 
% number of sides necessary to enclose the group.  This function uses convhull to 
% find peripheral points, then the distances between each set to generate an actual 
% measure of the perimeter of the polygon enclosing the group.  Number per group 
% is found by the findgroups2d function, from which the input 'S' to this function
% is the output.  

% First, a matrix to hold to groups' swarming values is initialized.
SWARM = [];

% Now, one loop will consider the groups, one at a time.  First the rows from the 
% original array, M, for the group of interest are removed and recombined with each 
% other.  The count and perimeter can then be found.
for i = 1:size(S,2)                 % Loop over each group.
    
    GI = S(i).members;              % Find the indices into M for the group members' 
                                    %  rows.
    
    G = M(GI',:);                   % The group matrix, G, is built from these rows. 
    
    g_size = size(G,1);             % The number in the group, g_size, is simply the
                                    %  number of rows in G.
    
    % The original index only considers groups larger than 3; so, a check is now 
    % performed to see that the group meets this criterion, and completes the
    % calculations only if it does.  Otherwise, matrix SWARM is left empty.
    if g_size > 3                       % Checks for group of more than 3.
        
        K = convhull(G(:,2),G(:,3));    % The convhull function is used to find the
                                        %  perimeter individuals.
        
        circ = 0;                       % Initialize CIRCumference measure.
        for j = 1:(size(K,1)-1)         % This will loop over all perimeter segments.
            
            P = G(K(j,1),:);            % P is the first endpoint of the segment
            P2 = G(K(j+1,1),:);         % P2 is the other endpoint.
            
            d = dist2d(P(1,2),P(1,3),P2(1,2),P2(1,3));  % And the distance between, d.
            
            circ = circ + d;            % Then these d's are added up one by one 
                                        %  to the circumference of the group.
        end
        
        % Now, the swarming index for this group is calculated, gswarm.  It is put 
        % in a matrix SWARM.
        gswarm = g_size / circ;
        
        SWARM = [SWARM; gswarm];
        
        
    end                         % Ends the size check loop.
end                        % Ends the group loop.


% Since groups of 3 or less will have been ignored, a final check must be performed.
% If there were any 'legal' groups at all, SWARM will have been filled with their 
% values.  So, if SWARM is not empty at this point, the mean of it is taken (i.e. the
% average index for the array is found).  If there were no legal groups, i.e. only 
% stragglers/pairs/triplets, then -999 is entered for the index (which can easily be 
% weeded out later).  
if size(SWARM) ~= [0 0];
    
    swarming_ind = mean(SWARM);
    
else
    swarming_ind = -999;
end