%% Group Scattered Data Using a Tolerance
% This example shows how to group scattered data points based on their proximity to points of interest.
% Create a set of random 2-D points. Then create and plot a grid of equally spaced points on top of the random data.

x = rand(10000,2);
[a,b] = meshgrid(0:0.1:1);
gridPoints = [a(:), b(:)];
plot(x(:,1), x(:,2), '.')
hold on
plot(gridPoints(:,1), gridPoints(:,2), 'xr', 'Markersize', 6)

%
% Use ismembertol to locate the data points in x that are within tolerance of the grid points in gridPoints. Use these options with ismembertol:
% Specify ByRows as true, since the point coordinates are in the rows of x.
% Specify OutputAllIndices as true to return all of the indices for rows in x that are within tolerance of the corresponding row in gridPoints.

[LIA,LocB] = ismembertol(gridPoints, x, 0.05, ...
    'ByRows', true, 'OutputAllIndices', true);

%
% For each grid point, plot the points in x that are within tolerance of that grid point.

figure
hold on
for k = 1:length(LocB)
    plot(x(LocB{k},1), x(LocB{k},2), '.')
end
plot(gridPoints(:,1), gridPoints(:,2), 'xr', 'Markersize', 6)

% Copyright 2015 The MathWorks, Inc.