How can I connect points with line segments?

I have a list of x and y values. I want to connect all points within a set distance of one another.

In other words, I would like to draw polygons from the vertices. I want to set a threshold above which the points will not be connected.

Next, when I have drawn the polygons, I would like to measure the angles formed between line segments.

Is this possible? Thank you so much.

[Rik]

What have you tried?

You can check distances quite easily with a combination of meshgrid and the Pythagorean theorem.

[Robert Enright]

I have tried using alphaShape, but it seems to draw as many triangles as possible, and I can't get it to use a threshold for maximum distance between points. I don't think alphaShape is the best route for this case, but I don't know of any other way to draw shapes.

[Robert Enright]

Also,I know the distance threshold I want, and I don't need to precisely measure distances.

[Image Analyst]

Are you talking about edge linking? Or something different?

[Robert Enright]

No, I'm not talking about edge linking. I'm not doing image analysis.

Answer 1

[Guillaume]

As John said, what's the problem? Get the pairwise distance between all points, find the index of the pairs below your threshold, then plot:

x = randi([0 100], 100, 1);  %random demo data
y = randi([0 100], 100, 1);  
plot(x, y, '.');  %plot all points
distancethreshold = 5;

pairwisedist = hypot(x - x', y - y');  %or use pdist
[p1, p2] = find(tril(pairwisedist <= distancethreshold & pairwisedist > 0))
hold on;
indexpairs = [p1, p2]';
plot(x(indexpairs), y(indexpairs), '-r')

[Robert Enright]

Thank you! That worked for the first part of what I wanted to do. Now that I have connected each pair, can I find the angle between each line segment at a certain point?

[Image Analyst]

With atan2d().

[Robert Enright]

I used atan2d(p1,p2). p1 and p2 are from the code provided in the above answer. I think the output is the angle between each line segment and the horizontal axis.

I suppose these angles can be subtracted from one another to find the angles I am looking for, but how can I make matlab selectively subtract to find angles on only line segments that share an endpoint.

Is atan2d() the best command to use to generate a list of angle measures for line segments that share an endpoint?

Thanks

[Guillaume]

The main difficulty will be to identify all point triplets that form connected segments. One way:

[p1, p2] = find(pairwisedist <= distancethreshold & pairwisedist > 0);  %want the full symmetric matrix this time so don't use tril
[commonpoints, ~, subs] = unique(p1);
endpoints = accumarray(subs, p2, [], @(v) {v});  %get a cell array of all points connected to the same point
numconnected = cellfun(@numel, endpoints);
commonpoints(numconnected < 2) = [];  %remove points that have only one connection
endpoints(numconnected < 2) = [];
endpairs = cellfun(@(v) nchoosek(v, 2), endpoints, 'UniformOutput', false);  %generate all combinations of end points
pointtriplets = [repelem(commonpoints, cellfun(@(m) size(m, 1), endpairs)), cell2mat(endpairs)]

Then, as suggested by IA you can use atan2 or atan2d to get the angle between each triplet

angles = atan2d(y(pointtriplets(:, 2)) - y(pointtriplets(:, 1)), x(pointtriplets(:, 2)) - x(pointtriplets(:, 1))) - ...
         atan2d(y(pointtriplets(:, 3)) - y(pointtriplets(:, 1)), x(pointtriplets(:, 3)) - x(pointtriplets(:, 1)))

[Image Analyst]

If you use just x and y, then yes, you will get the angles from the axes. However I meant that you'd use delta x and delta y. See Guillaume's code. With that, you get the angle between points, not the angle from the x axis.

[Robert Enright]

Thank you so much.

Answer 2

[John D'Errico]

An alpha shape or delaunay triangulation are both wrong, because you are asking to draw lines between ALL pairs of points that are less than the threshhold apart.

So just ue a tool like pdist (stats toolbox). Take all pairs of points with an inter-point distance less than your threshold, and draw the lines. WTP?

[Robert Enright]

How would I draw the lines after measuring all of the distances with pdist?

[Image Analyst]

With the line() function.