Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!yale!cmcl2!lanl!matthias@mpx1.lampf.lanl.gov
From: matthias@mpx1.lampf.lanl.gov (Matthias, Bjorn E.)
Newsgroups: comp.graphics
Subject: random points on surface of sphere
Keywords: random, sphere
Message-ID: <50234@lanl.gov>
Date: 4 May 90 02:20:51 GMT
Sender: news@lanl.gov
Reply-To: matthias@mpx1.lampf.lanl.gov
Followup-To: comp.graphics
Organization: LAMPF Data Analysis Center, Los Alamos, New Mexico
Lines: 51


In a recent posting of mine, I was too hasty in claiming that random walk
sampling of a distribution in usually slower than a direct inversion when
the latter is possible.  Sorry about that!  A followup posting from
Jim Roth presented what I think is a very elegant random walk of sorts on
the surface of a sphere.  He says:

>In this case, it is considerably faster to do a random walk on the sphere,
.. 
(his code is available in his posting)
.. 
I timed his random walk and checked the first and second moments of the
PHI and THETA distributions and thought I should post the results together
with those of the other two methods:

rejection method cpu =  31620 msec
 failures = 476793 ;  fraction =   47.68 %
 successes = 523207 ;  fraction =   52.32 %
 diagnostics on distribution:
    number of points = 523207
    first moment of phi =   3.1417506
    second moment of phi =  13.1581593
    first moment of theta =   1.5707290
    second moment of theta =   2.9352241

direct method cpu =  26050 msec
 diagnostics on distribution:
    number of points = 523207
    first moment of phi =   3.1412365
    second moment of phi =  13.1574106
    first moment of theta =   1.5701435
    second moment of theta =   2.9331174

random walk method cpu =  17780 msec
 diagnostics on distribution:
    number of points = 523207
    first moment of phi =   3.1411185
    second moment of phi =  13.1555815
    first moment of theta =   1.5704634
    second moment of theta =   2.9331996

Clearly, the random walk is the superior performer here.
Thanks, Jim!

Regards,
Bjorn


---
Bjorn E. Matthias                       MATTHIAS@LAMPF  (BITNET)
    matthias@mpx0.lampf.lanl.gov  or  matthias@mpx1.lampf.lanl.gov (internet)