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    %% Average Similar Data Points Using a Tolerance
% This example shows how to use |uniquetol| to find the average
% |z|-coordinate of 3-D points that have similar (within tolerance) |x| and
% |y| coordinates. 
%
% Use random points picked from the |peaks| function in the domain $[-3,3]
% \times [-3,3]$ as the data set. Add a small amount of noise to the data.

% Copyright 2015 The MathWorks, Inc.

xy = rand(10000,2)*6-3; 
z = peaks(xy(:,1),xy(:,2)) + 0.5-rand(10000,1);
A = [xy z];
plot3(A(:,1), A(:,2), A(:,3), '.')
view(-28,32)

%%
% Find points that have similar |x| and |y| coordinates using |uniquetol|
% with these options:
%
% * Specify |ByRows| as |true|, since the rows of |A| contain the point
% coordinates. 
% * Specify |OutputAllIndices| as |true| to return the indices for all
% points that are within tolerance of each other.
% * Specify |DataScale| as |[1 1 Inf]| to use an absolute tolerance for the
% |x| and |y| coordinates, while ignoring the |z|-coordinate.
DS = [1 1 Inf];
[C,ia] = uniquetol(A, 0.3, 'ByRows', true, ...
    'OutputAllIndices', true, 'DataScale', DS);

%% 
% Average each group of points that are within tolerance (including the
% |z|-coordinates), producing a reduced data set that still holds the
% general shape of the original data.
for k = 1:length(ia)
    aveA(k,:) = mean(A(ia{k},:),1); 
end

%%
% Plot the resulting averaged-out points on top of the original data.
hold on
plot3(aveA(:,1), aveA(:,2), aveA(:,3), '.r', 'MarkerSize', 15)