Fast Geometric Fit Algorithm for Sphere Using Exact Solution

Abstract

Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we extend the methods of Thomas Chan and Landau who fitted the 2D data using circle. This work closely resemble their work in redefining the error estimate and solving the sphere fitting problem exactly. The solutions for center and radius of the sphere can be found exactly and the equations can be hard coded for high performance. We have also shown some comparison with other popular methods and how this method behaves.