Fast Geometric Fit Algorithm for Sphere Using Exact Solution
This is an incremental improvement for researchers and engineers needing efficient sphere fitting in science and engineering applications.
The paper tackles the problem of sphere fitting by extending a 2D circle fitting method to provide an exact, non-iterative solution for center and radius, enabling hard-coded equations for high performance, with comparisons to other methods.
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.