Draw ellipses around points

Question

I\'m trying to draw ellipses around points of a group on a graph, with matplotlib. I would like to obtain something like this:

Answer 1

This is a well-studied problem. First take the convex hull of the set of points you wish to enclose. Then perform computations as described in the literature. I provide two sources below.

"Smallest Enclosing Ellipses--An Exact and Generic Implementation in C++" (abstract link).

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Charles F. Van Loan. "Using the Ellipse to Fit and Enclose Data Points." (PDF download).

Answer 2

This has a lot more to do with mathematics than programming ;)

Since you already have the dimensions and only want to find the angle, here is what I would do (based on my instinct):

Try to find the line that best fits the given set of points (trendline), this is also called Linear Regression. There are several methods to do this but the Least Squares method is a relatively easy one (see below).

Once you found the best fitting line, you could use the slope as your angle.

Least Squares Linear Regression

The least squares linear regression method is used to find the slope of the trendline, exactly what we want.

Here is a video explaining how it works

Let's assume you have a data set: data = [(x1, y1), (x2, y2), ...]

Using the least square method, your slope would be:

# I see in your example that you already have x_mean and y_mean
# No need to calculate them again, skip the two following lines
# and use your values in the rest of the example
avg_x = sum(element[0] for element in data)/len(data)
avg_y = sum(element[1] for element in data)/len(data)

x_diff = [element[0] - avg_x for element in data]
y_diff = [element[1] - avg_y for element in data]

x_diff_squared = [element**2 for element in x_diff]

slope = sum(x * y for x,y in zip(x_diff, y_diff)) / sum(x_diff_squared)

Once you have that, you are almost done. The slope is equal to the tangent of the angle slope = tan(angle)

Use python's math module angle = math.atan(slope) this will return the angle in radians. If you want it in degrees you have to convert it using math.degrees(angle)

Combine this with the dimensions and position you already have and you got yourself an ellipse ;)

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This is how I would solve this particular problem, but there are probably a thousand different methods that would have worked too and may eventually be better (and more complex) than what I propose.