Xref: utzoo comp.graphics:14208 sci.math:13229
Path: utzoo!utgpu!watserv1!watmath!att!att!linac!pacific.mps.ohio-state.edu!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!cica!iuvax!shirley
From: shirley@iuvax.cs.indiana.edu (peter shirley)
Newsgroups: comp.graphics,sci.math
Subject: Re: question regarding random numbers
Message-ID: <69636@iuvax.cs.indiana.edu>
Date: 2 Nov 90 21:56:18 GMT
References: <29358@pasteur.Berkeley.EDU>
Organization: Indiana University, Bloomington
Lines: 2386

ph@miro.Berkeley.EDU (Paul Heckbert) writes:

>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


Here is an appendix (in postscript) from my thesis that may or may not
be useful.  It is on Monte Carlo methods, And the last section addresses
Paul's question.  If you can't print it, I can send you a dvi file.

pete shirley
shirley@cs.indiana.edu

Save file in file "whatever" and then, after leaving the news reader, type
"uudecode whatever" and a file called "mc.ps" should appear.

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end