Cut off scatterplot markers in matplotlib after autoscale

I'm generating a simple image with a scatter and two dots and I want the dots to be fully visible, but ax.autoscale_view() seems not to work properly.

fig, ax = plt.subplots(figsize=(3, 3), dpi=150)
ax.scatter([0, 1], [0, 1], s=2000)
ax.autoscale_view()

Am I doing something wrong? How can I get the dots to be fully visible no matter the marker size s?

To adjust the axis so that the perimeter of points is inside of the plotting area, we need to:

• Find the x and y extend of the perimeter of the dots in data-coordinate-space.
• Adjust the margins accordingly to fit size of the points.

The size parameter s in ax.scatter sets the area of the bounding box (a square) of the marker (the dot) in units of points^2. The marker also has a line drawn around it, controlled by the parameter linewidth. The default is 1.0. To get the radius in points and the linewidth in points:

fig, ax = plt.subplots(figsize=(3,3), dpi=150)
c = ax.scatter([0, 1], [0, 1], s=2000)

r_face = sqrt(2000) / 2     # = 22.36 points
lw = c.get_linewidth()[0]   # = 1.0 points
r_points = r_face + lw      # = 23.36 points

To convert to pixel-coordinate-space, we need to convert from points to inches (72 points per inch), and then multiply by the DPI.

r_pixel = r_points / 72 * 150  # = 48.67 pixels

You can get the center of a point (we will use the point at 1, 1) and the boundary extent in pixel-coordinate-space using:

x_pixel, y_pixel = ax.transData.transform((1, 1))
bx_pixel = x_pixel + r_pixel
by_pixel = y_pixel + r_pixel

Because the dot radius is fixed in pixel-coordinate-space, it does not scale 1-to-1 with the data coordinates. This makes a direct calculation difficult (I believe it is possible, I just don't know how). We can iteratively adjust the margins and calculate whether the boundary is within the bounds of the data-coordinates.

bx_data, by_data = ax.transData.inverted().transform((bx_pixel, by_pixel))
xmin, xmax = ax.get_xlim()
ymin, ymax = ax.get_ylim()
while (bx_data > xmax) or (by_data > ymax):
    margin_x, margin_y = ax.margins()
    margin_x += 0.05
    margin_y += 0.05
    ax.margins(margin_x, margin_y)
    x_pixel, y_pixel = ax.transData.transform((1, 1))
    bx_pixel = x_pixel + r_pixel
    by_pixel = y_pixel + r_pixel
    bx_data, by_data = ax.transData.inverted().transform((bx_pixel, by_pixel))
    xmin, xmax = ax.get_xlim()
    ymin, ymax = ax.get_ylim()
ax.autoscale()