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From: ph@miro.Berkeley.EDU (Paul Heckbert)
Newsgroups: comp.graphics,sci.math
Subject: question regarding random numbers
Message-ID: <29358@pasteur.Berkeley.EDU>
Date: 30 Oct 90 04:42:35 GMT
Sender: news@pasteur.Berkeley.EDU
Reply-To: ph@miro.Berkeley.EDU (Paul Heckbert)
Organization: University of California at Berkeley
Lines: 23

I'm looking for good references on techniques for generating random numbers
with arbitrary density functions.  For example, to generate a gaussian
random number from uniform random numbers:

	r = sqrt(-2*log(U));
	t = 2*pi*U;
	x = r*sin(t);
	y = r*cos(t);
	where U is a random number between 0 and 1, different every time

x and y will then be gaussian-distributed between -inf and inf.

Similarly, you can generate a point uniformly distributed inside a circle with:

	r = radius*sqrt(U);
	theta = 2*pi*U;

I assume the method is well known in probability and statistics.
What are good references for such techniques of distribution shaping?

Paul Heckbert, Computer Science Dept.
570 Evans Hall, UC Berkeley		INTERNET: ph@miro.berkeley.edu
Berkeley, CA 94720			UUCP: ucbvax!miro.berkeley.edu!ph