first of all: Welcome at CelestialMatters (CM)!
next: for the less initiated readers, let me do a little translation listing of the many acronyms in your post
- CS = Cornette & Shanks Physically reasonable analytic expression for the
single-scattering phase function, APPLIED OPTICS / Vol. 31, No. 16 / 1 June 1992. While my lab pays for access to this journal, it is unfortunately not OpenAccess...Hence I am not allowed to quote the link.
- HG = Henyey &Greenstein
- CDF = Cumulative Distribution Function
- PDF = Probability Density Function
see e.g. also here: viewtopic.php?f=11&t=537
I found the writeup on Cornette Shanks vs HG very enlightening, especially the maple program.
It helped fully understand how to treat the g parameter.
I guess you meant this: http://www.celestialmatters.org/users/t ... s2/out.pdf
What I was wondering is how to calculate the CFD for it, so it can be importance sampled
Your suppose to take the integral of the PDF, but I didn't have access to Maple and it looks nasty
For example for HG:
The CDF is Mu = (1/2g)(1+g^2 - (1-g^2 / 1 + 2gP-g)^2 )
Which is derived from P(mu) = 1/2 int -1 to mu ( (1-g^2) dmu / (1+g^2-2g mu)^3/2 )
So I assume to solve this for CS one would have to
P(mu) = 1/2 int -1 to mu ( 1.5 * (1.0 - g2) * (1.0 + mu* mu) /((2.0 + g2) * pow(1.0 + g2 - 2.0 * g * mu, 1.5)) )
Give me a little more time. I'll check it with Maple.
There are also many resources in the net about how to calculate CDF from PDF in general. E.g.http://math.ucsd.edu/~tlaetsch/pdf/10C_CDFtoPDF.pdf
or Google for "relation between pdf and cdf"
Roughly: d/dx CDF(x) = PDF(x)