Mon Apr 23 20:10:02 PDT 2012 Kevin Karplus

The three files
	svd_FitHypersphere.py
	numpy_FitHypersphere.py
	scipy_FitHypersphere.py
all provide the same function: fit_hypersphere(data,method)

The svd version is the slowest, but is the only one that is capable of
    handling the singular values that arise when the noise level is very
    low (when the data falls precisely on a hypersphere).
    It uses only routines from the numpy package.
    On my laptop it take 18.1 seconds to solve 200 circles for 1000 points
    using both Pratt and Hyper methods.
    It implements Hyper, Taubin, and Pratt methods

The numpy version is a faster version, taking only 3.9 seconds to
    solve 200 circles for 1000 points using both Pratt and Hyper
    methods.  It crashes when the error is very low, as it tries to
    get the eigenvalues of singular matrix.
    It implements Hyper and Pratt methods

The scipy version takes 3.9 seconds to solve 200 circles for 1000
    points using both Pratt and Hyper methods.  It crashes when the
    error is very low, as it tries to get the eigenvalues of singular
    matrix.  It requires installing scipy, which is much more trouble
    than installing numpy, as scipy requires a working fortarn
    compiler.
    It implements Hyper, Taubin, Pratt and Kasa methods.


Bottom-line: the numpy version is fast and easy to install, the svd
version is most robust, and the scipy version is fast and has the most
variants.

If you need speed, use the numpy version with Hyper.
If you need robustness, use the svd version with Hyper.
If you need the Kasa algorithm, use the scipy version.



Creative Commons Attribution-ShareAlike 3.0 Unported License.
http://creativecommons.org/licenses/by-sa/3.0/