Here is a scheme that is vastly simpler than any so far.
Divide the surface of the blob into triangular facets.
To compute the potential at point X divide the blob into units composed of the convex hulls of a facet and X.
This is a <i>sliver</i>.
The contributed potential of each sliver is easy to compute:
<br>(∫[0:1]x<sup>2</sup>/x)/(∫[0:1]x<sup>2</sup>) = (½)/(⅓) = 3/2
<br>P = (3/2)∫(x/|x|)∙da where da is the vector area of an element of the surface and x is the vector from X to the area centroid.
<br>The potential is 3/2 times what it would be if the same total mass were concentrated all at the centroid of the facet.
<p>Some dot products will be negative.
Still (∫x∙da)/3 is the volume of the blob and ∫da = 0.
da is the vector normal to the facet whose length is proportional to the area.
We also compute <a href=moment.html>moments</a> 0, 1 and 2 of the blob, m0, m1 &amp; m2.

<p><a href=ccode.html>Some code</a>
<br><a href=High.html>Ideas</a>
<hr>(2017 Feb 1)
<br>Moving the vertices around is like herding cats.
They find too many interesting directions to go.
There are just now two problems to solve:<ul>
<li>Keep the triangles nearly the same size.
<li>Avoid negative volumes—points with negative winding numbers.</ul>