Dr. @LeoDorst’s paper on the fitting of k-spheres in n-dimensional space is a prototype example for Conformal Geometric Algebra. It presents an elegant decomposition of random points in orthogonal best matching spheres, the intersections of which represent best matching elements of all grades.
I mentioned this in another post and thought I’d add an example. In its most simple incarnation, it allows one to find the best fitting circle given a set of random points. Drag the points below to see the fit adjust in real time.
I will shortly add this to the ganja.js coffeeshop.