From: Michael Gross (adv) <adv@md...>  20070114 01:38:39

Erik Krause wrote: > I'm pretty sure you and Michael know this already  just in case...: > http://www.helpfeeds.com/showthread.php?p=1489664 I read this before. As far as I understand Abramowitz/Stegun 17.3.24 does not apply here because we have an incomplete elliptic integral and the 17.3. chapter is about complete elliptic integrals. However the inverse of the elliptic integral is no problem, as this is the Jacobi Function and can be easily calculated with the help of Numerical Recipes (sncndn). The problems start later when inverting all those equations full of sin and cos functions. Maple can invert it but the results are full of square roots so you have multiple results (as far as I understand these are the quadrants). In my first trials I did try to use the equations I get from Maple but I introduced some bugs I couldn't find and I gave up with this approach. After reading your mail I decided to give it another chance and now it works: Because I don't understand what Maple does when solving the equations, I can't tell which signs are right. So I have to try all combinations of signs  for each sqrt on time +1.0*sqrt and one time 1.0*sqrt. As there are 12 sqrts there are 2^12 = 4096 combinations. After I get a lambda/phi of one combination I put the result into the forward function and compare the resulting x and y. This solution is of course much better than the interpolation/minimization approach I did before. It is also a lot faster: http://mdgrosse.net/pano/peircequincuncial.c Michael 