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Re: quick & easy random dir vector, how?

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups comp.lang.c
Subject Re: quick & easy random dir vector, how?
Date 2019-06-04 16:31 +0100
Organization A noiseless patient Spider
Message-ID <87r2891i5d.fsf@bsb.me.uk> (permalink)
References (8 earlier) <9a4ef818-9470-436a-9829-c94e2f0a785d@googlegroups.com> <87lfyi4usz.fsf@bsb.me.uk> <1ac4b5ea-fb71-4691-8dad-fca9cc976dd3@googlegroups.com> <e736450f-cb1e-4061-ae3c-091808102aff@googlegroups.com> <24945ada-c036-4b67-91a3-714f0ff5e5ef@googlegroups.com>

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"Rick C. Hodgin" <rick.c.hodgin@gmail.com> writes:

> On Monday, June 3, 2019 at 6:40:46 PM UTC-4, James Kuyper wrote:
>> On Monday, June 3, 2019 at 10:32:32 AM UTC-4, Rick C. Hodgin wrote:
>> > Use that function for each angle.  You have three angles to work
>> > with on a sphere, one on the XY plane, one on the XZ plane, and
>> > one on the YZ plane:
>> > 
>> >     double x = get_random_value();
>> >     double y = get_random_value();
>> >     double z = get_random_value();
>> > 
>> > These all exist somewhere between -1.0 and 1.0, and were projected
>> > evenly by choosing an angle around the circle to obtain the coord-
>> > inate to use for each axes.
>> 
>> What you're referring to are not angles - they are conventionally
>> called direction cosines, being equal to the cosine of the
>> corresponding angle. You're onto something by considering them,
>> but the direction cosines are not independent of each other: they
>> have a constraint that x^2+y^2+z^2 == 1.0. For a spherically
>> symmetric distribution of directions, the direction cosine for
>> the x axis, considered on it's own, would have a distribution
>> proportional to sqrt(1-x^2), which x = sin(theta) will produce;
>
> This is where you lose me.  I don't know enough about what you're
> saying to know what questions to ask here.  Is there a video or
> animated GIF example or something you can point me to so I can
> see what you're talking about?
>
> [I'll snip the rest of your reply for now and come back to it]
>
> 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.

> That means
> I need an X,Y,Z coordinate to achieve a point, and the surface is
> the set of points that are valid.

Yup.

> By choosing a random point around the unit circle on the ZX, XY,
> YZ planes I obtain three angles which give me three points.  Each
> of those points is at a random location around the unit circle in
> its plane.  It would address all of the points in the set of points
> that are the unit sphere's surface.

The points your posted code picks are not all on the sphere.  You need
to normalise these vectors too, and the result is very much not a
uniform distribution.  You are correct that every point on the sphere
(AKA direction) has non-zero probability (i.e. could be picked) but
there are much simpler ways to do that (and with less bias).

An another problem crops up which is that your code does appear to
correspond to the description you give here.

In spherical polar coordinates, only two angles are needed to specify a
point on the unit sphere, so the third one is odd.  Taking the sin of
each is even odder.  What method are you thinking of to combine the
three uniformly chosen angle into a point on the sphere?

> I'd have to see how it would be skewed visually to wrap my mind
> around it.

You have a method in mind, but I don't know what it is.  I can show you
the distribution you get taking the sin of the three angles, but I don't
think that's really what you mean.  If you post an actual algorithm, I
can show the distribution.

-- 
Ben.

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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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