Newsgroups: comp.graphics
Path: utzoo!utgpu!watserv1!watcgl!jdchrist
From: jdchrist@watcgl.waterloo.edu (Dan Christensen)
Subject: Re: Random points on a sphere
Message-ID: <1990May4.150632.27212@watcgl.waterloo.edu>
Keywords: random points sphere
Organization: Computer Graphics Lab, University of Waterloo
References: <434@ticipa.ti.com> <1990Apr26.151056.25145@laguna.ccsf.caltech.edu> <1990Apr27.201704.16711@cs.UAlberta.CA>
Distribution: na
Date: Fri, 4 May 90 15:06:32 GMT
Lines: 12

In article <1990Apr27.201704.16711@cs.UAlberta.CA> cdshaw@cs.UAlberta.CA (Chris Shaw) writes:
>How about using 4 random numbers in the range from [0.0, 1.0]
>to generate a quaternion [w,x,y,z]? Normalize the quaternion so that
>(w*w + x*x + y*y + z*z) = 1.0 , and use this as a rotation of a unit vector
>[ 1, 0, 0 ].

I think this presents the same problem as just choosing random x, y and
z from [0.0, 1.0] and normalizing without rejection, namely that the
resulting distribution is not uniform.  The quaternions that your method
generates will more dense near the corner's of the hypercube in 4-space.

Dan Christensen