matplotlib - radius in polygon edges - is it possible?

You can use arcs by making the polygons from paths.

A normal square:

import matplotlib.path as mpath
import matplotlib.patches as patches

verts = [(0,0),
         (1,0),
         (1,1),
         (0,1),
         (0,0)]

codes = [mpath.Path.MOVETO] + (len(verts)-1)*[mpath.Path.LINETO]
square_verts = mpath.Path(verts, codes)

fig, ax = plt.subplots(subplot_kw={'aspect': 1.0, 'xlim': [-0.2,1.2], 'ylim': [-0.2,1.2]})

square = patches.PathPatch(square_verts, facecolor='orange', lw=2)
ax.add_patch(square)

A rounded square can be made with:

verts = [(0.2, 0.0),
         (0.8, 0.0), # start of the lower right corner
         (1.0, 0.0), # intermediate point (as if it wasn't rounded)
         (1.0, 0.2), # end point of the lower right corner
         (1.0, 0.8), # move to the next point etc.
         (1.0, 1.0),
         (0.8, 1.0),
         (0.2, 1.0),
         (0.0, 1.0),
         (0.0, 0.8),
         (0.0, 0.2),
         (0.0, 0.0),
         (0.2, 0.0)]

codes = [mpath.Path.MOVETO,
         mpath.Path.LINETO,
         mpath.Path.CURVE3,
         mpath.Path.CURVE3,
         mpath.Path.LINETO,
         mpath.Path.CURVE3,
         mpath.Path.CURVE3,
         mpath.Path.LINETO,
         mpath.Path.CURVE3,
         mpath.Path.CURVE3,
         mpath.Path.LINETO,
         mpath.Path.CURVE3,
         mpath.Path.CURVE3]


rounded_verts = mpath.Path(verts, codes)

fig, ax = plt.subplots(subplot_kw={'aspect': 1.0, 'xlim': [-0.2,1.2], 'ylim': [-0.2,1.2]})

rounded_verts = patches.PathPatch(rounded_verts, facecolor='orange', lw=2)
ax.add_patch(rounded_verts)

For your example, you would need to specify an intermediate point which uses the x-coordinate from Point1 and the y-coordinate from Point2.

The matplotlib path tutorial provides a detailed description of how paths can be made: http://matplotlib.org/users/path_tutorial.html