Man, my math skills are getting kinda dusty. I've got a function of p (written in c) f = pow(p, (log 0.5)/log m) where m is a parametric constant 0<m<1 (not 0 or 1) and p is in 0<=p<=1. It /can be shown/ that f is also in the range [0,1]
What does this function look like? It seems that it _shouldn't_ be that hard, but I find my head won't seem to work. I know what it is for some values of m: for m=approaching 0 f=> p**0 = 1 for m=0.5, f= p**1 = p for m=approaching 1, f= p**-BIG => 0 This is one of the blend functions available in the GIMP gradient editor, and I'd like to understand it better. It helps to consider it always as a gradient from black to white. The variable p being the relative position along the blend-line, and f gives the factor applied in calculating the resulting color. When f=p, the blend is the same as a linear gradient. The parameter m defines the bias of the blend curve toward the beginning(0) or end(1) of the blend-line. - Small m makes f vary rapidly over the short distance [0,m] mapping the output to the range f=[0,.5] (black to mid-gray), and then that is followed by a more gradual blend over the larger range [m,1] mapping to f=[.5,1] (mid-gray-to-white) - Large m makes f vary slowly over the larger distance [0,m] giving output [0,.5] and then rapidly over the shorter [m,1] mapping output to[.5,1] Hmmm, maybe i should just plot it? What's the easiest tool to plot an analytical function? Regards, ..jim -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-list
