Am Dienstag, 24. Juli 2018 22:37:35 UTC+2 schrieb Erik Krause: > > Am 23.07.2018 um 17:26 schrieb [email protected] <javascript:>: > > > Non-zero parameters a and c introduce singularities at r=0, something a > real lens does not have. > > Since the correction function itself doesn't have a singularity at r=0 > I insist to disagree.
You are talking about a polynomial that covers the radial part in polar coordinates description. Polynomials do not have singularities, yes, in that you are right. But we have to consider a two-dimensional mapping function. Using polar coordinates, it factors, this is nice, the phi mapping is identity, even nicer. 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) As the two-dimensional lens function is differentiable in vector-r=0, introducing non-differentiable functions is not a good idea. and all that changes at r=0 is the slope of the curve there is a change > in magnification only in the center. Since a single mathematical point > can't be magnified there is no singularity either. The point in the > center stays in the center. > Please compute, in cartesian coordinates, the partial derivative d^2/dxdx of the 2-dim mapping function with c=1 as parameter. Hint: you'll encounter some x/abs(x) - like terms. > In the wiki discussion you write "sqrt() has a singularity at 0". This > is not true. sqrt(0) is 0 > In simple language: singularities can be present even if the function is continuous. Best regards Klaus -- 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/92806089-2b5f-4cd5-a324-4781ac4b2829%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
