Finding an equally spread subselection of XY-points

I have a big list of 2D points with XY-coordinates. I want to find a subselection of those which are equally spread.

One of the methods I used for this is the follwing: First I make a grid with dx and dy as the desired distance between the points of the subselection. Then for every square of the grid, find the point closest to the center. This way I get a subselection.

You can see the result in attached graphs. The unfilled scatter plot are the input points and the filled scatter plot are the remaining output points of the sub selection.

As you can see in the second picture. This doesn't give a nice distribution in certain cases. Does any of you have an idea how to improve this? I don't really know any terms to google on to find algorithms.

Thanks in advance!

Answer 1

[Image Analyst]

Try this:

% Make 100 randomly located points between 0 and 100
x = 100 * rand(1, 100);
y = ones(1, length(x));
subplot(2, 1, 1);
plot(x, y, 'bs');
grid on;
% Make linearly spaced "desired" locations
% from 10 to 90 spaced every 10.
desiredx = 10:10:90;
% Find which of the actual data is closest to the desired data.
for k = 1 : length(desiredx)
  [minDistance, index(k)] = min(abs(x - desiredx(k)));
end
% Extract the closest points.
closestx = x(index);
y = ones(1, length(closestx));
% Plot them
subplot(2, 1, 2);
plot(closestx, y, 'rs');
grid on;

[Image Analyst]

Another option is to use John D'Errico's interparc, depending on what you mean: https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc

[Jordy W]

Thanks for your reply. I think the script that you posted does exactly the same as what I explained. It works in one dimension, but wouldn't work for the twodimensional dataset in my post. It would give the same undesired output as in the picture.

Btw, I think the same issue could also arise in the onedimensional case for certain inputs. I will now look into the link you posted.

[Image Analyst]

Why wouldn't it work in 2-D? I didn't have your y values so I just used 1 but I don't see why it wouldn't work with any y values. Attach your data if you want.

Be aware that the interparc goes for uniform distances along the arc, not just uniform in the x or y direction. This is a different concept. You have to decide which way you want it.

[Jordy W]

For example, if you take the following (not so random) input for the script you posted:

a= 39.5;
b= 40.7;
c= 39 * rand(1, 40);
d= 60 + 40 * rand(1, 40);
x=[a,b,c,d];

In that case it will find close points at around 40. I think this has something to do with the fact that I have a sparse input. This behavior is more apparent with the large 2D datasets I have.

Additionally, I'm not really sure about how to implement the interparc you posted to my scenario. In the screenshot I posted all input points are along a line, but they may be branching out, crossing, randomly stopping, etc.