I was plotting a fractal and wanted a false-perspective view, where the magnification is really high at one point, and decreases in a log-like way further out from there. Like that cartoon map of the U.S. from the point of view of Manhattan. The mapping needs to be like a log until you get close to zero, then flatten out. I don't know whether it was Henry Baker's comment from last August that triggered it, but I thought of the asinh function. Here is the nice result: http://www.tiac.net/~sw/2007/02/asinh_perspective In the process of programming this, I needed an asinh for Postscript. The one I found is in a package called "pst-math.pro". (.pro is apparently a suffix for Postscript libraries.) The definition basically means asinh( x ) = ln( x + sqrt( x^2 + 1 ) ) which is the standard definition, but there is a precision-slash- overflow problem when x < 0 if you actually calculate it that way in floating point. The link above has a trippy graph of the problem. There is Postscript source code there for both pictures. --Steve
From: Henry Baker <hbaker1@pipeline.com> Date: Sun, 06 Aug 2006 21:39:29 -0700
BTW, "asinh" now has a real paying job. I searched using Google and I found that astronomers are now using asinh instead of log to compute brightness of stars in a star catalog.
I have advocated the use of asinh in audio & video processing to do "dynamic range compression" in a way which is somewhat smoother than current ad hoc methods and floating point methods.
Another job is its use in genetic engineering & statistics to smooth data better than log when very small magnitudes are encountered, which would otherwise drive log nuts (i.e., very substantially negative).