Am 25.07.2018 um 16:38 schrieb [email protected]:
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.
And how would this affect the image? For no correction at all the
function is linear with a slope of 45°. If there are a, b and c
parameters the d parameter is adjusted such that the curve always goes
through (1,1). For some parameter values it is not 45° at (0,0), but
this results in a different magnification in the center, like to be
expected if you want to correct pincushion or barrel distortion.
My math is too rusty to argue with you, but I would be interested
whether you can estimate how large the error would be? Will it be as
large or larger than the error f.e. introduced by parallax due to
entrance pupil shift (which is pronounced for fisheye lenses but also
present for rectilinear wide angles).
--
Erik Krause
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