On Thursday, January 6, 2011 5:09:06 AM UTC+1, Tom Sharpless wrote: > > > It has been pointed out that the polynomial should only consist of > > even numbered powers, both for speed and for mathematical soundness. > > > I'm not convinced there is anything wrong with odd powers in a radial > correction function; since R is always >= 0 the odd symmetry is never > manifested. >
Isn't there? There is a sharp discontinuity in (the derivative of) any odd-powered polynomial, when mirrored around the Y-axis. Since R can only have positive values, this discontinuity will happen at the image "center" which is used to compute R from. Therefore, it makes sense to avoid odd powers. In fact, instead of a polynomial, any continuous mathematical function which returns 0 when R==0 and mirrors nicely around the Y-axis could be used as a component of the radial correction function. E.g., 1-cos(x), 1-(exp(-x^2/2)). I'm not saying that any lens will fit with such a function, but mathematically it's correct. By the way: nice way to fiddle around with functions online can be found at http://numcalc.com. Just enter 'plot("x", "1-cos(x)", -1, 1)' to evaluate the given function in the range from -1 to 1. -- Bart -- You received this message because you are subscribed to the Google Groups "Hugin and other free panoramic software" group. A list of frequently asked questions is available at: http://wiki.panotools.org/Hugin_FAQ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/hugin-ptx
