Hallöchen! [email protected] writes:
> [...] > > But polar corrdinates are slightly peculiar at vector-r=0, and to > have them differentiable there the function in r must be odd. > (More general, odd f(r) for f(r)*sin(2n*phi+phi0) and even f(r) > for f(r)*sin((2n+1)*phi+phi0) I agree that infinite differentiability has strong implications, and vanishing even exponents in an approximation may be one of them. Complex differentiability is even stronger. However I wonder: What is the physical reason for these hefty requirements? I can understand continuous, but why must the mapping of rays of light be holomorphic? Let me play the devil's advocate. Let sgn(r)*r**2 be the mapping function of a lens. Granted, it is not infinitely differentiable at r=0. But it is continuous, and odd. What hinders the production of such a lens? That said, we do observe in the Lensfun lens database that a and c are strongly damped. b (the only odd coefficient) mostly has the biggest absolute value. Tschö, Torsten. -- Torsten Bronger -- A list of frequently asked questions is available at: http://wiki.panotools.org/Hugin_FAQ --- You received this message because you are subscribed to the Google Groups "hugin and other free panoramic software" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/hugin-ptx/878t5zz4jg.fsf%40wilson.bronger.org. For more options, visit https://groups.google.com/d/optout.
