> Very nice! How does it compare to CubicCurve.solveCubic() (which I > know > has issues with the 2 root case, but I got it from a "reliable source" > - > some textbook on Numerical Recipes)?
I wrote a tests that generated 2559960 polynomials, and in 2493075 of those, the computed roots were identical to within 1e-9. They were different in the remaining 66885 cases, so that's 97.4% agreement. I've looked through some of the differences, and in every case the function from graphics gems is better in one of two ways: 1. the gg version will report more roots than the cc2d version, in which case the polynomial has a double root and the cc2d version completely misses it (example poly: a=19.000000, b=-20.000000, c=-17.000000, d=18.000000, where cc2d misses the root at 1). 2. the gg version will report fewer roots than the cc2d version, in which case there was a 0 root and the cc2d version incorrectly split it into -1e-163 and 1e-163. So, the graphics gems version seems to be much more stable. It does have a problem where it can return NaN sometimes, because it assumes that the polynomial is not a quadratic one, but that can easily be fixed. So, should I put this new cubic root finder in CubicCurve.solveCubic and use that in pisces? Regards, Denis.
