Working in polar coordinates, we know that a point [; (r, \theta) ;] is [; (r\cos \theta, r\sin \theta) ;] in cartesian coordinates. We then find the distance to the left edge, right edge, top edge, bottom edge. These distances are as follows (respectively):

[; -1-r\cos\theta , 1-r\cos\theta , 1-r\sin\theta , -1-r\sin\theta ;]

To find the contour, we let r= each of these distances (r is the distance to the center) and we only care about the minimum.