There&#x27;s an neat technique for fitting RBF representations to dense point clouds. Instead of the impractical matrix inversion, the trick is to solve the linear system with a fast multipole method, similar to the Barnes-Hut algorithm for the n-body problem.<p>Carr, J.C. et al, &quot;Reconstruction and Representation of 3D Objects with Radial Basis  Functions&quot;, Siggraph 2001<p><a href="http:&#x2F;&#x2F;dl.acm.org&#x2F;citation.cfm?id=383266" rel="nofollow">http:&#x2F;&#x2F;dl.acm.org&#x2F;citation.cfm?id=383266</a>