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Groups > comp.lang.c > #144530
| From | James Kuyper <jameskuyper@alumni.caltech.edu> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: quick & easy random dir vector, how? |
| Date | 2019-06-06 09:14 -0400 |
| Organization | A noiseless patient Spider |
| Message-ID | <qdb3j3$7f9$1@dont-email.me> (permalink) |
| References | (7 earlier) <6a84cb4a-d629-41a8-9f5e-dcdeb82bddd9@googlegroups.com> <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> |
On 6/3/19 6:40 PM, James Kuyper wrote:
> On Monday, June 3, 2019 at 10:32:32 AM UTC-4, Rick C. Hodgin wrote:
>> On Monday, June 3, 2019 at 10:17:59 AM UTC-4, Ben Bacarisse wrote:
> ...
>>> I don't think so. What is the actual method you are suggesting (best in
>>> C given the group)? Your words are not entirely clear.
>>
>> Code (off the top of my head, untested):
>>
>> const double _2PI = 6.28318530718...;
>>
>> // Assuming a random function that returns 0..MAX_UNSIGNED_INT
>> double get_random_value(void)
>> {
>> double theta = _2PI * ((double)rand() /
>> (double)MAX_UNSIGNED_INT);
>> return sin(theta);
>> }
>>
>> 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;
> the same is true for either of the other two axes. However,
> setting all three direction cosines independently won't satisfy
> the constraints. Following up by rescaling them to a unit vector
> solves that problem, but then they won't have the right
> distribution.
>
> What you need to do is to keep that constraint in mind while
> generating those values. The following modifications to your
> routine will do the job:
>
> double x = get_random_value();
> double y = sqrt(1-x*x)*get_random_value();
> double z = sqrt(1-x*x-y*y)*(get_random_value() > 0.0 ? 1.0 :-1.0);
>
> The sqrt() calls are what enforce the constraints, and they do so
> in a way that produces the desired exactly spherically symmetric
> distribution.
>
> However, this is mathematically equivalent to the more
> conventional approach described in the stackexchange answer
> cited by Eli, which is simpler.
I've been very busy lately, with few opportunities for recreational use
of usenet. As a result, I snatched one such opportunity despite the fact
that I was apparently suffering more from lack of sleep than I thought.
Most of the above is nonsense. The main exception is the constraint x^2
+ y^2 + z^2 == 1.0
The x, y, and z values should be calculated from the appropriate angle
by taking the cosine of that angle, not the sine, as is indicated by the
name "direction cosine". As far as the distribution of values is
concerned, that doesn't matter - since you generate angles uniformly
covering a full circle, the distribution of values is the same whether
you use sine or cosine.
The key fact is that the portion of the surface of a sphere of radius R
that lies between the latitudes lat_lo and lat_hi is
2*pi*R*R*(sin(lat_hi)-sin(lat_lo))
Therefore, in order to generate latitudes randomly that are evenly
distributed over the surface of the sphere, what you need to do is
generate a random value z, uniformly distributed over the range from
-1.0 to 1.0, and then calculate latitude = asin(z).
What you did is equivalent to randomly generating latitudes evenly
distributed from -pi/2 to pi/2, and then calculating z = sin(latitude).
The latitudes should not be evenly distributed - there should be a lot
more directions generated with latitudes near the equator than near the
poles, because a much larger portion of the surface of the sphere is
near the equator than to the poles.
The problem with your original suggestion was that it calculated
positions uniformly distributed over the volume of a cube centered at
the center of the sphere. Such a method will produce a
disproportionately large number of directions close to the corners of
the cube, because those corners are farthest from the center of the
sphere. It will produce a disproportionately small number of directions
close to the centers of each face of the cube, because those centers are
closest to the center of the sphere.
Changing from a uniform distribution for each coordinate, to calculating
the coordinate by using the sine of a uniformly distributed angle, makes
the problem much worse. That method increases the RMS value of the
distribution, biasing it toward large values, increasing the likelihood
of generating directions pointing near the corners of the cube, and
reducing the likelihood of generating ones that point near the centers
of the faces of the cube.
I don't have a plot ready to be displayed, but when I made my first stab
at such a plot, I found that the bias was much stronger than I expected,
which was what led me to realize how badly I was mistaken in what I
wrote earlier.
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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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