In the end I got really annoyed, and here is a a solution to calculate the positions (mathemetica, matlab did not help much so I did it by hand) and you can find here the algo for this particular problem: <a href="http://www.schwietering.com/jayduino/#newtonmethod">http://www.schwietering.com/jayduino/#newtonmethod</a> (in 4 iterations you get a 1E-09 result). robtillaart