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From: cca@newton.physics.purdue.edu (Charles C. Allen)
Newsgroups: comp.graphics
Subject: Re: random points on surface of sphere
Summary: communication is easier if people use standard notation...
Keywords: uniform spherical distribution, random walk
Message-ID: <3675@newton.physics.purdue.edu>
Date: 9 May 90 04:39:12 GMT
References: <1523@ryn.esg.dec.com+ <40768@apple.Apple.COM> <1220@med.Stanford.EDU> <13955@cgl.ucsf.EDU>
Organization: Purdue Univ. Physics Dept, W.Lafayette, IN
Lines: 20

> 1) pick theta randomly between -pi and pi
> 2) pick z randomly between -R and R

The above method (azimuthal angle between -pi and pi, z between -R and
R) works fine, but it does not save you a trig function call unless
that's all you need.  You have one arccos call if you want the polar
angle, and at least one more plus some square roots if you want the
(x,y,z) triple.  Which method is "fastest" depends not only on what
hardware you have, but also what you want for a final result.

[Minor personal note - every single math & physics text I have uses
theta for the polar angle and phi for the azimuthal angle when
discussing spherical coordinates.  Perhaps my brain has calcified, but
it *is* a little disconcerting to realize that a posting isn't making
sense because someone is using a different notation.]

Charles Allen			Internet: cca@newton.physics.purdue.edu
Department of Physics		HEPnet:   purdnu::allen, fnal::cca
Purdue University		talknet:  317/494-9776
West Lafayette, IN  47907