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	2019-05-31 22:49 +0100
Organization	A noiseless patient Spider
Message-ID	<87pnnyguqd.fsf@bsb.me.uk> (permalink)
References	(3 earlier) <e3bf2bf2-1919-4fdd-b442-daa834bdc62a@googlegroups.com> <678a85fc-ee82-4a00-af6e-739b0432d7e4@googlegroups.com> <e0f63976-6c03-4ca0-bd75-18228329f655@googlegroups.com> <87ef4eit16.fsf@bsb.me.uk> <f454d0d5-0763-4b48-b3f4-f189207b5e5b@googlegroups.com>

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

> On Friday, May 31, 2019 at 10:43:29 AM UTC-4, Ben Bacarisse wrote:
>> "Rick C. Hodgin" <rick.c.hodgin@gmail.com> writes:
>> 
>> > On Friday, May 31, 2019 at 8:55:04 AM UTC-4, Malcolm McLean wrote:
>> >> On Friday, 31 May 2019 13:20:21 UTC+1, Rick C. Hodgin  wrote:
>> >> > On Thursday, May 30, 2019 at 9:08:57 PM UTC-4, Ben Bacarisse wrote:
>> >> > > "Rick C. Hodgin" <rick.c.hodgin@gmail.com> writes:
>> >> > > > The discussion of good random algorithms came up a few months ago.
>> >> > > > Chris Thomasson posted a great algorithm:
>> >> > > >
>> >> > > >     https://groups.google.com/d/msg/comp.lang.c/RI0rdENv59s/BVUWgMBFDQAJ
>> >> > > >
>> >> > > > Use multi-channels, one for each [axis], with different seeds, and
>> >> > > > then perform the math to determine your values between 0.0 and 1.0.
>> >> > > 
>> >> > > I think it's unlikely that that is the problematic part.  Once you have
>> >> > > a source of uniformly distributed floating-point numbers, the question
>> >> > > remains of how to pick a point on the unit sphere so that every point
>> >> > > (AKA direction) is equally likely.
>> >> > 
>> >> > If he's looking for random vectors, you would not seek to move on
>> >> > the unit sphere, but in whatever directions there are on each axis.
>> >> > 
>> >> > One could calculate the distance from your starting point to the
>> >> > ending point so that you move one logical unit.  An arbitrary velo-
>> >> > city on each axis (within reason), and an arbitrary direction on
>> >> > each axis, and you can move 1 unit at a time using completely ran-
>> >> > dom values without worrying anything about the unit sphere.  You
>> >> > could calculate them as random values 0..2pi and then resolve their
>> >> > (axis-relative) cos,sin coordinates to get real vector values, but
>> >> > that's just one way to do it.
>> >> > 
>> >> > Is mine a correct thinking?
>> >> > 
>> >> No, you want each point on the sphere surrounding your origin to have
>> >> an equal chance of being hit.
>> >> So if you take a random point of longitude, you get a random point on
>> >> the equator, which is a good start. But if you then take a random point
>> >> of latitude, the points cluster up near the poles - not so good.
>> >> 
>> >> Another approach might be to take random x, y, z on a uniform box.
>> >> However then you get more random points towards the corners of the box.
>> >> You can get round this be excluding all points that don't lie within
>> >> the unit sphere. That's a bit icky, but it will work and is your first
>> >> method.
>> >
>> > If you're using vectors, you have an arbitrary X, arbitrary Y, and
>> > arbitrary Z direction you're moving.  It should not bunch up on any
>> > axis, and should be linear across the spectrum of random values.
>> >
>> > A random value for each axis computed between 0.0 and 2.0, then sub-
>> > tract 1.0 to make it -1.0 to 1.0, and then scale by your velocity
>> > vector whatever that is (a random value, or a known variable).
>> 
>> The question was rather specific -- to pick a random direction.
>
> That's what my solution does.

Yes, but I thought you were aiming for what the OP wanted.  You can pick
a random direction with one bit 0=left, 1=right.  As I said right at the
start: "the question remains of how to pick a point on the unit sphere
so that every point (AKA direction) is equally likely".

> You have random movement on the X axis, the Y axis, the Z axis.
> Each one is independent.  Each one is linear.

Did you mean uniform?

>> The
>> solution in 2D is to pick a random point on the unit circle --
>> essentially just scaling [0, 1) to the range [0, 2pi).  Try picking an x
>> and y value and using the resulting direction.  You will find they are
>> not uniformly distributed.
>
> For that reason, it's not a good solution.

That's one way to look at it!

> You need linear
> values, which can be accomplished with vectors and not sin/cos
> values relative to a rotational theta.

I don't understand this.  Are you suggesting an algorithm?

The task is to pick random points uniformly distributed over the
surface of the unit sphere.

-- 
Ben.

Thread

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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