How can I connect points with line segments?

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Robert Enright 2017-8-14

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评论： Robert Enright 2017-8-16

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.

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Image Analyst 2017-8-15

Are you talking about edge linking? Or something different?

Robert Enright 2017-8-15

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

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Answer 1

Guillaume 2017-8-15

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在 MATLAB Online 中打开

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')

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Guillaume 2017-8-15

在 MATLAB Online 中打开

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 2017-8-15

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 2017-8-16

Thank you so much.

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Answer 2

John D'Errico 2017-8-14

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编辑：John D'Errico 2017-8-14

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?

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Robert Enright 2017-8-15

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

Image Analyst 2017-8-15

With the line() function.

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