How can I convert from scatter size to data coordinates in matplotlib?

Question

I would like to programmatically test whether two scatterplot glyphs will overlap in matplotlib. So given a pair of (x, y) coordinates and a size (which as i understand is the area of the circle, in points), I would like to plot

plt.scatter(x, y, s=s)

and then have a function called points_overlap that takes these parameters and returns True if the points will overlap and False otherwise.

def points_overlap(x, y, s):
    if ...
        return True
    else:
        return False

I know there are transformation matrices to take me between the different matplotlib coordinate systems, but I can't figure out the right steps for writing this function.

Answer 1

This needs some testing, but it might work? These should all be in Display space

def overlap(x, y, sx, sy):
    return np.linalg.norm(x - y) < np.linalg.norm(sx + sy)

test:

In [227]: X = np.array([[1, 1], [2, 1], [2.5, 1]])
In [228]: s = np.array([20, 10000, 10000])

In [229]: fig, ax = plt.subplots()

In [230]: ax.scatter(X[:, 0], X[:, 1], s=s)
Out[230]: <matplotlib.collections.PathCollection at 0x10c32f28>

In [231]: plt.draw()

Test every pair:

Xt = ax.transData.transform(X)
st = np.sqrt(s)

pairs = product(Xt, Xt)
sizes = product(st, st)

for i, ((x, y), (sx, sy)) in enumerate(zip(pairs, sizes)):
    h = i % 3
    j = i // 3
    if h != j and overlap(x, y, sx, sy):
        print((i, h, j))

There's lots of room for improvement. It's probably easier to transform all your data and pass that into the points_overlap function instead of doing the transform inside. That'd be much better actually.