connecting adjacents points in a scatter plot with a line

Hi, I have a set of unorganized points that I plot with scatter. The result is a slightly sigmoidal shape. I would like to plot a line through these points.

The problem is that simply plotting a line results in the points being connected by their current order, not whether or not they are adjacent in the scatter plot. It's possible I need some kind of curvefit, but I am thinking I am just missing a simple solution somehow.

Here's what the data looks like plotted with just scatter.

Even when I sort the data, plot(X,Y) results in the following:

What I want is just the adjacent points connected so my line essentially outlines the data and makes the same sigmoidal shape.

I have attached a .mat file with the scatter plot values. The third column is all "1" and just refers to the contour value I exported. It can be ignored.

Thank you for the help. I'm running Matlab 2015a if that makes a difference for various functions that may handle this.

[Walter Roberson]

The file did not get attached

[Monica W]

Oh, sorry about that. brittle.mat should now be there

Answer 1

[Walter Roberson]

Sort the data, take every second point in the forward direction, then take the other half in the reverse direction?

[Monica W]

So for this particular dataset, it looks like that would work, but points are still out of order.

I tried splitting the dataset into two separate matrices by taking every other point:

a = testbrittle(1:2:end,:) and b = testbrittle(2:2:end,:)

Then I sorted one forwards and one backwards.

asort = sortrows(a,-1) bsort = sortrows(b,1)

That did not work. I also tried sorting by column 1, then by column 2:

example: asort = sortrows(a,[-1 2])

Then I put the datasets back together:

new = ones(197,3) new(1:2:end,:) = asort; new(2:2:end,:) = bsort;

plot(new(:,1),new(:,2))

No matter how I seem to sort the split datasets, I cannot get the data to plot correctly. Some data points are still flipped.

I was hoping there was a function to just connect points that plot adjacently, essentially a "connect the dots" function.

[Walter Roberson]

Your data doubles back on itself at the outside corners, so you are going to run into problems.

[Walter Roberson]

If you do

A = brittle2000m;
D = sqrt(bsxfun(@minus, A(:,1), A(:,1).').^2 + bsxfun(@minus, A(:,2), A(:,2).').^2);

Then D is the distance matrix from each point to each other point. Once you have that, you could use any of the Traveling Salesman Problem (TSP) solvers, such as http://www.mathworks.com/help/optim/ug/travelling-salesman-problem.html

For the most part the algorithm would be "go to the next closest point", but those left and right corners of your data are messy, the left more so.

The "every second point" strategy will not work.

Possibly for your purposes it would be enough to do envelope detection; see http://www.mathworks.com/help/signal/ug/envelope-extraction-using-the-analytic-signal.html and http://www.mathworks.com/help/signal/ref/envelope.html

[Monica W]

Great, I will try those the second I have time. In the meantime I will mark this the answer.

I know the data is messy, so it could be there is no automatic way to do it. My current plan is to just convert points to a line in Illustrator for the purposes of creating the figure I need.

Thank you so much for the detailed suggestions. I'd never heard of TSP solvers.

[Walter Roberson]

Everywhere except the corners, the proper next connection is easy to find -- but at the corners it is not easy.

Ah, I just had a thought. Since you are using R2014b or later, you could possibly use the new boundary() call, which will use alpha shapes to use found the "outside" of your set of points. Potentially right at the corners that might leave some points unconnected as they might be determined to be "inside" with the default alpha shape parameters; in that case you could work more directly with the new alphashape() to "shrink" more tightly around your data.