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Re: quick & easy random dir vector, how?

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From Tim Rentsch <tr.17687@z991.linuxsc.com>
Newsgroups comp.lang.c
Subject Re: quick & easy random dir vector, how?
Date Wed, 05 Jun 2019 08:05:49 -0700
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richard@cogsci.ed.ac.uk (Richard Tobin) writes:

> In article <87r2891i5d.fsf@bsb.me.uk>,
> Ben Bacarisse  <ben.usenet@bsb.me.uk> wrote:
>
>>> I will say this with regard to my solution... as I see it, I'm
>>> trying to get random values on the surface of a sphere.
>>
>> That's easy.  Pick x, y and z in [-1, 1] and normalise.  You don't get a
>> uniform distribution though.
>
> Pick x, y and z in [-1, 1].  If they're outside the unit sphere, try
> again until they are inside - this will take 2 x 3 / pi attempts
> average.  You now have a point with uniform distribution within the
> unit sphere.  Normalize to get a point on the surface.

Slight refinement, assuming a 64-bit integer RNG is used:  generate
one 64-bit random number, divide into three 21-bit values mapped to
the range [-1048575,1048575] (discarding samples that would produce
the value -1048576), testing x*x + y*y + z*z <= 1048575*1048575.
When the test passes normalize appropriately.

> Apologies if this has already been suggested - I haven't read the
> whole thread.  And it's not particularly efficient.

But probably more efficient than a "more direct" method using trig
functions, especially since the rejection tests can be done using
integer-only calculations.

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quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-30 13:47 -0700
  Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-30 13:56 -0700
    Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-05-31 02:08 +0100
      Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 00:51 -0700
      Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-05-31 02:12 -0700
        Re: quick & easy random dir vector, how? Eli the Bearded <*@eli.users.panix.com> - 2019-05-31 19:27 +0000
          Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 12:49 -0700
            Re: quick & easy random dir vector, how? Eli the Bearded <*@eli.users.panix.com> - 2019-05-31 20:36 +0000
              Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 14:00 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 14:19 -0700
      Re: quick & easy random dir vector, how? mark.bluemel@gmail.com - 2019-05-31 03:56 -0700
        Re: quick & easy random dir vector, how? queequeg@trust.no1 (Queequeg) - 2019-05-31 11:57 +0000
        Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-05-31 15:22 +0100
          Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 07:42 -0700
            Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 08:25 -0700
      Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-31 05:20 -0700
        Re: quick & easy random dir vector, how? Bart <bc@freeuk.com> - 2019-05-31 13:39 +0100
          Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-05-31 15:51 +0100
          Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-03 08:26 -0400
        Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-05-31 05:54 -0700
          Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-31 06:15 -0700
            Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 06:23 -0700
            Re: quick & easy random dir vector, how? David Brown <david.brown@hesbynett.no> - 2019-05-31 16:12 +0200
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-31 08:14 -0700
                Re: quick & easy random dir vector, how? David Brown <david.brown@hesbynett.no> - 2019-05-31 18:18 +0200
                Rick should killfile everybody. (Was: quick & easy random dir vector, how?) gazelle@shell.xmission.com (Kenny McCormack) - 2019-05-31 17:39 +0000
                Re: Rick should killfile everybody. (Was: quick & easy random dir vector, how?) "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-31 10:55 -0700
                Re: Rick should killfile everybody. (Was: quick & easy random dir vector, how?) Bart <bc@freeuk.com> - 2019-05-31 22:33 +0100
                Re: Rick should killfile everybody. (Was: quick & easy random dir vector, how?) Keith Thompson <kst-u@mib.org> - 2019-05-31 16:26 -0700
                Re: Rick should killfile everybody. (Was: quick & easy random dir vector, how?) gazelle@shell.xmission.com (Kenny McCormack) - 2019-05-31 23:29 +0000
                Re: Rick should killfile everybody. (Was: quick & easy random dir vector, how?) gazelle@shell.xmission.com (Kenny McCormack) - 2019-05-31 23:28 +0000
                Re: quick & easy random dir vector, how? waterwitch86@gmail.com - 2019-06-09 03:47 -0700
            Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-05-31 15:43 +0100
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-05-31 08:13 -0700
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-05-31 22:49 +0100
            Re: quick & easy random dir vector, how? Richard Damon <Richard@Damon-Family.org> - 2019-05-31 23:01 -0400
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-01 04:10 -0700
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-01 13:47 +0100
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 12:04 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 12:35 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 12:53 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 14:52 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 15:04 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-01 15:41 -0700
            Re: quick & easy random dir vector, how? Anton Shepelev <anton.txt@gmail.com> - 2019-06-01 15:30 +0300
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 05:30 -0700
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 05:39 -0700
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-03 15:17 +0100
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 07:32 -0700
                Re: quick & easy random dir vector, how? David Brown <david.brown@hesbynett.no> - 2019-06-03 18:09 +0200
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-03 21:14 +0100
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 13:18 -0700
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-03 22:42 +0100
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 16:21 -0700
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-03 15:40 -0700
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-04 05:19 -0700
                Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-04 16:31 +0100
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-04 11:48 -0400
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-04 21:09 -0700
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-04 21:11 -0700
                Re: quick & easy random dir vector, how? jadill33@gmail.com - 2019-06-05 12:41 -0700
                Re: quick & easy random dir vector, how? jadill33@gmail.com - 2019-06-05 12:46 -0700
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-05 13:53 -0700
                Re: quick & easy random dir vector, how? Eli the Bearded <*@eli.users.panix.com> - 2019-06-05 21:45 +0000
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-05 23:06 -0700
                Re: quick & easy random dir vector, how? Eli the Bearded <*@eli.users.panix.com> - 2019-06-06 06:47 +0000
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-06 18:32 -0700
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-06 18:44 -0700
                Re: quick & easy random dir vector, how? richard@cogsci.ed.ac.uk (Richard Tobin) - 2019-06-05 13:43 +0000
                Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-06-05 07:24 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-05 13:29 -0700
                Re: quick & easy random dir vector, how? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-06-05 08:05 -0700
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-04 19:01 -0700
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-06 22:57 -0400
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-06 09:14 -0400
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-06 08:10 -0700
                Re: quick & easy random dir vector, how? "F. Russell" <fr@random.info> - 2019-06-06 16:17 +0000
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-06 20:18 -0400
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-06 23:22 -0700
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-07 07:15 -0700
                Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-06-07 00:41 -0700
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-09 13:57 -0700
                Re: quick & easy random dir vector, how? Richard Damon <Richard@Damon-Family.org> - 2019-06-10 08:18 -0400
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-10 08:49 -0400
                Re: quick & easy random dir vector, how? Richard Damon <Richard@Damon-Family.org> - 2019-06-10 20:59 -0400
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-10 18:27 -0700
                Rick is a Marine!!! (Was: quick & easy random dir vector, how?) gazelle@shell.xmission.com (Kenny McCormack) - 2019-06-10 13:53 +0000
                Re: Rick is a Marine!!! (Was: quick & easy random dir vector, how?) "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-10 09:14 -0700
                Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-10 07:24 -0700
            Re: quick & easy random dir vector, how? James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-06-03 08:30 -0400
          Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 06:21 -0700
            Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 06:26 -0700
              Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 06:33 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 07:00 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 07:14 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 10:15 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 10:40 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 14:01 -0700
            Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-05-31 07:07 -0700
              Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 07:15 -0700
  Re: quick & easy random dir vector, how? Anton Shepelev <anton.txt@gmail.com> - 2019-06-01 00:40 +0300
    Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-05-31 14:54 -0700
    Re: quick & easy random dir vector, how? Clifford Heath <no.spam@please.net> - 2019-06-02 23:00 +1000
      Re: quick & easy random dir vector, how? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-06-03 00:00 -0700
        Re: quick & easy random dir vector, how? Clifford Heath <no.spam@please.net> - 2019-06-03 17:33 +1000
          Re: quick & easy random dir vector, how? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-06-03 00:55 -0700
          Re: quick & easy random dir vector, how? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-06-04 10:00 -0700
  Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-01 18:34 -0700
    Re: quick & easy random dir vector, how? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-02 03:13 +0100
      Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-01 21:47 -0700
    Re: quick & easy random dir vector, how? Anton Shepelev <anton.txt@gmail.com> - 2019-06-02 13:16 +0300
      Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-02 05:38 -0700
        Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-02 05:54 -0700
          Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-02 06:08 -0700
            Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-02 06:24 -0700
              Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-02 06:34 -0700
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-02 06:43 -0700
                Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-02 07:06 -0700
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-02 13:12 -0700
              Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-02 06:58 -0700
                Re: quick & easy random dir vector, how? gazelle@shell.xmission.com (Kenny McCormack) - 2019-06-02 14:08 +0000
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-02 21:56 -0700
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-02 21:56 -0700
                Re: quick & easy random dir vector, how? "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2019-06-03 02:47 -0700
                Re: quick & easy random dir vector, how? "Chris M. Thomasson" <invalid_chris_thomasson_invalid@invalid.com> - 2019-06-07 01:32 -0700
  Re: quick & easy random dir vector, how? "F. Russell" <frussell@random.info> - 2019-06-03 12:33 +0000
    Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-03 07:36 -0700
      Re: quick & easy random dir vector, how? "F. Russell" <frussell@random.info> - 2019-06-03 14:46 +0000
        Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-03 08:13 -0700
      Re: quick & easy random dir vector, how? fir <profesor.fir@gmail.com> - 2019-06-03 07:51 -0700

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