I added arrows to the planes to denote tangential orientation. These arrows are oriented
along the eigenvectors of the covariance matrix. Next: how to estimate the width
and length of the plane (to compute an approximate size). Also, planes aligned along "z" have
a centroid not in the center of the plane.  This is due to non-uniform density along the plane.
Thus we'll compute an approximate density (to be done), which is a function of z (with a
logarithmic dependence, which can be found online, or in Nathan Crock's work.