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I still don't see the normal distribution's connection to filling the sphere's volume...

TheUsualAlex?, Jason? ... I'm in need of enlightment.

Oh sorry, if you provide a different seeds to this function for all three axes, you'll get a cloud of points distributed in a sphere volume. Nothing fancy...

So:

Add SOP : create a point

|

Copy SOP: create 1000's of copies

|

Point SOP: Translate [ gaussrand($PT) ] [ gaussrand($PT*1029) ] [ gaussrand($PT*6464) ]

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your method also depends on choosing a uniform distribution of points on the sphere

The radius of the sphere is also changing randomly, isn't it? So maybe the function for the radius should be gaussian distributed?

Does the PDFCFGInvCF Stuff work for non spherical Volumes?

If the method uses 'rejection' wich I interpret currently as deleting non valid points, we would have to iterate until a given number of points is reached?

If it comes to non spherical volumes I think rejection is the only way to get a volume filled, unless we 'voxel' the volume into spheres.

How does the popnetwork handle such stuff? Wouldn't this be the fastest way to fill volumes apart from the value of really understanding how to fill volumes?

Georg

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Jason,

cloud of points distributed in a sphere volume.

this flocks in the center - as gaussian always does?

gauss.jpg

Georg

Edited by rdg

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I read that page differently. I think the second paragaph refers to a completely separate method?

Ooops. Yup, I mixed those two up, you're right.

So if rvSpherical() was replaced with Muller 1959, then we have a way of doing it with using the gaussian distribution? (inefficiently :) ).

Hehe. Right again. Inefficiently. :)

Oh sorry, if you provide a different seeds to this function for all three axes, you'll get a cloud of points distributed in a sphere volume.

Thanks for the clarification, Jason.

Here I was, trying to think how the heck the gaussian could be used to make the distribution uniform (by volume) -- something that maybe you could hint at but not say out loud as it were ;)

This does give us a spherical distribution, and it's totally valid in and of itself, but if the goal is to cover the volume as uniformly as possible, then it's got some undesirable properties:

1. Points are not guaranteed to lie in the unit sphere, or any other specific radius for that matter (the gaussian never decays to zero -- that's a feature of the distribution).

2. Points are concentrated toward the center, and their population decays normally (in the statistical sense) as you move away from {0,0,0} -- again, a feature of a normal distribution, but it also means that the points are not uniformly distributed by volume.

3. If applied as an hscript function like that, it's very expensive to compute. But that could be remedied with maybe a combination of HDK and a faster algorith (there's one out there that I use, but now I can't find the web page). No matter what you do though, you have to use some numerical approximation.

Here's what it looks like (scaled by 1/3):

post-148-1175184493_thumb.jpg

The radius of the sphere is also changing randomly, isn't it? So maybe the function for the radius should be gaussian distributed?

Well yes, it's changing randomly in the "Uniform Solid Angle" case. In the "Uniform Volume" case, it is still random, but with a specific distribution. If you swap that distribution for a standard normal distribution (what Jason is using), it will just bunch up points near the center even more (for the reasons you already noted yourself). Jason was using the gaussian for the initial distribution itself, not for warping an already existing one.

Does the PDFCFGInvCF Stuff work for non spherical Volumes?

Only if you know the distribution you're after beforehand, which is true for a sphere, but not necessarily true in the general case. And even when you do know what you're after, many times the inversion won't have a closed solution and you have to use some numerical approximation (like in the gaussian case that jason posted).

So yeah, rejection would be the safest/easiest method for an arbitrary volume: fill the bounding box and reject points outside the volume. Repeat until the requested number of points is reached.

Cheers!

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Hi

this is becoming quite a thread

i see I poked into a beehive again :blink:

great stuff and lots to learn

z

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But that could be remedied with maybe a combination of HDK and a faster algorith (there's one out there that I use, but now I can't find the web page)

AHA! Found it!

Here's that algorithm I mentioned that I couldn't find. This also computes a random number with a standard normal distribution (like Jason's) but is quite a bit faster. Have a look.

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this is becoming quite a thread

Cheers to that! thanks for all the great info guys this has been quite educational on the nature of randomness, whether it be Cartesian or Spherical. Alot of good stuff here and I think everyone is a little more random because of it! B) (or at least more evenly distributed random)

-3db

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Isn't evenly distributed randomness like saying Uniform Chaos

And isn't Uniform Chaos an oxymoron?

hmmm The Dichotomatic Theory (di

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Im half kidding Mario.. But I really think theres an answeer to the universe in all this discourse :shocking:

Whereas I understand the need and desire for Uniform Chaos (or Uniformly Distributed Chaos), It still begs the quiestion, is it true Chaos. You're saying...

Given: We don't know what the next value will be.

Given: The value has equal probability to be anywhere in the domain at any given interval.

Therefore: This is Uniformly Distributed Chaos.

(sounds a little like quantum physics though, and sub-atomic particle definitions)

I just can't stop thinking, this all this tells me that true chaos, or true random is a pharce.

CHAOS:

1. a state of utter confusion or disorder; a total lack of organization or order.

As soon as it is uniform, there is a sense of orginization.

RANDOM:

6. without definite aim, purpose, method, or adherence to a prior arrangement; in a haphazard way

The very definition of random defies the possibility of using an algorithim to define it.

So my answer to the question posed at the begining of this thread "How Random is Random?"... it's not. At least not in the strictist definition of the word. True random does not exist, not in a computer and not in nature.

I realize in our computer science world we always want discreet control over everything, and Uniformly Distributed Chaos is desireable, Im just looking at what this all says about nature.

The Dichotomatic Theory - Any move twords chaos, is a move twords order. There is no chance occurance. There is no coincedence, all moments in time have discreet and designed purpose.

Edited by 3dbeing

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Im half kidding Mario.. But I really think theres an answeer to the universe in all this discourse :shocking:

<initiating metaphysical mode> :)

Whereas I understand the need and desire for Uniform Chaos (or Uniformly Distributed Chaos), It still begs the quiestion, is it true Chaos. You're saying...

Well, no. Of course not. None of the stuff mentioned in this thread is "truly random" or chaotic, that's why the generators we use are called "pseudo-random" -- even the non-deterministic generators (like the Mersenne Twister) are still "repeatable". Otherwise we'd be calling them "interesting but useless (for graphics)". :)

I just can't stop thinking, this all this tells me that true chaos, or true random is a pharce.

Not a pharce, sir, merely a phigment! [sic] :P

But seriously... both those definitions basically boil down to "lacking a pattern" (either directed or natural). But a pattern only exists if you're able to see it. If the observer was confined to the unit cube/sphere/R then, from their POV, the appearance of those points would be "truly chaotic" -- i.e: totally unpredictable and lacking a pattern.

So maybe we can leave it at "a total lack of organization...as far as we can see".

This all reminds me of those late-into-the-night discussions I used to have in university... during "beer bashes"... usually accompanied by non-trivial amounts of alcohol and other reality-bending/enhancing substances... where the word "Castaneda", and the obligatory reference to "Spacetime Donuts" never failed to pop up :)

It's all good.

Cheers!

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This all reminds me of those late-into-the-night discussions I used to have in university... during "beer bashes"... usually accompanied by non-trivial amounts of alcohol and other reality-bending/enhancing substances... where the word "Castaneda", and the obligatory reference to "Spacetime Donuts" never failed to pop up :)

That reminds me of the time in 6th and 7th grade, when the school counselors went through my locker, and my parents ransaked my room searching for reality bending/enhancing substances...Much to their suprise, turns out Im just wierd by nature/design. :(

-3db

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That reminds me of the time in 6th and 7th grade, when the school counselors went through my locker, and my parents ransaked my room searching for reality bending/enhancing substances...Much to their suprise, turns out Im just wierd by nature/design. :(

-3db

Hahaha... touch

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"True random does not exist, not in a computer and not in nature."

...I think radioactive decay is truly random. It's impossible to predict when an individual atom will disintegrate, and unaffected by environmental conditions, but if you have billions of them, it's statistically predictable. You just need a geiger counter and a stopwatch. (and a lead suit)

edit: ...looks like there's no need for a fashionable lead suit after all:

http://www.fourmilab.ch/hotbits/

http://www.fourmilab.ch/hotbits/how3.html

Edited by stabby

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