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OK ... I finished one of these 0PPS-pictures, and went on to my next POV-project ...
I'm working on something like the clutter-macro, we've already seen here ...
At least, I want to place a lot objects (currently spheres) in the scene (currently
on a surface, so its 2D) without intersection ...
currently I use the simple, dumb, standard algorithm, that checks for every new
sphere, if theres another one already placed, which would intersect. If so, then
I calculate another position, until I find a free place ...
The thing is, that this algorithm works in O(n^2) which means it can get quite slow
in POV-SDL (of course, not only SDL). Currently for an instance of n=10,000 I have
a parse-time of ~40mins, and I want to go even higher for n.
So I wonder, if there are other, more advanced algorithms out there, which are
faster ...
I thought about doing something like putting the spheres in boxes and only test
for the spheres, that are in the current and the adjacent boxes. This would save
the time to test EVERY other sphere, but would add some overhead for small number
of objects ...
So, has anyone done something like that already, or is there interest in such a
macro or at least testresults ?
If you are interested, I could do some tests when I have some time, but don't
count on this beeing soon ...
-- Jan
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If the spheres are very tight to each other then jittering is the keyword: instead of
true pseudo-casual (forgive the oxymoron) positions you put your spheres through a
loop, then translate each position by a little random amount.
Otherwise dividing your Universe into boxes and checking the adjacent boxes only
should speed things of course. Try also this: if a position fail don't trash it but
try and translate that by a little amount (for example the diameter of the sphere) in
the four directions. You could use the number of spheres already in the box as
indicator of the probability (so the feasibility) of success of these translations.
--
Jonathan.
Home: http://digilander.iol.it/jrgpov
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But also small translation (or jittering) of the sphere would involve
a complete check of all other spheres if I don't do anything else...
Maybe I could (after I detected some collisions) save the nearest ones
and only check these ones ...
But I found a problem in my other approach. Does POV-Ray support some-
thing like chained-lists efficiently ? I don't know, how to find out,
if I have a given box, which of my thousands spheres are in that very
one box.
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"Jan Walzer" wrote:
> But also small translation (or jittering) of the sphere would involve
> a complete check of all other spheres if I don't do anything else...
> Maybe I could (after I detected some collisions) save the nearest ones
> and only check these ones ...
Usually jittering is done in such way to make it impossible to have intersections.
That would make it a O(0)... ;-)
If R is the radius of the sphere you're placing and 1/L^2 is the density you want to
get (x_step=L, z_step=L) then you can translate your sphere by L/2-R maximum in any
direction. That should prevent any intersection, and yet make it possible to have
spheres touching each other.
Of course L>=2*max(Ri)i=1,2,...n.
> But I found a problem in my other approach. Does POV-Ray support some-
> thing like chained-lists efficiently ? I don't know, how to find out,
> if I have a given box, which of my thousands spheres are in that very
> one box.
I did it once. IIRC it was a real puzzle, I began to meet arrays in my not so quiet
dreams... :-|
--
Jonathan.
Home: http://digilander.iol.it/jrgpov
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"JRG" <jrg### [at] hotmail com> schrieb im Newsbeitrag news:3cbc95a6@news.povray.org...
> "Jan Walzer" wrote:
> > But also small translation (or jittering) of the sphere would involve
> > a complete check of all other spheres if I don't do anything else...
> > Maybe I could (after I detected some collisions) save the nearest ones
> > and only check these ones ...
>
> Usually jittering is done in such way to make it impossible to have intersections.
> That would make it a O(0)... ;-)
> If R is the radius of the sphere you're placing and 1/L^2 is the density you want to
> get (x_step=L, z_step=L) then you can translate your sphere by L/2-R maximum in any
> direction. That should prevent any intersection, and yet make it possible to have
> spheres touching each other.
> Of course L>=2*max(Ri)i=1,2,...n.
lets see, if I understood this correct ...
You say, that I should first place all the spheres in a grid, and then jitter this
to make a random distribution ? ... sounds interesting ...
My current approach is, that I select a random point in the area, and compute
the size of the sphere (currently the size of the sphere depends from a function, so
I have a bit control about the size)...
Then I look through an array of the already positioned spheres and if there's
another sphere intersecting, then I look for another place ...
> > But I found a problem in my other approach. Does POV-Ray support some-
> > thing like chained-lists efficiently ? I don't know, how to find out,
> > if I have a given box, which of my thousands spheres are in that very
> > one box.
>
> I did it once. IIRC it was a real puzzle, I began to meet arrays in my not so quiet
> dreams... :-|
that doesn't sound nice ... you mean I should leave this to an external program ?
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"Jan Walzer" wrote:
>
> lets see, if I understood this correct ...
>
> You say, that I should first place all the spheres in a grid, and then jitter this
> to make a random distribution ? ... sounds interesting ...
Ideally. In fact you jitter the spheres as you place them. You should come up with
something like:
#declare N = 400;
#declare L = 0.3+1; //max_radius + epsilon
#declare RS = seed (123);
union {
#local i=0;
#while (i<sqrt(N))
#local j=0;
#while (j<sqrt(N))
#declare RADIUS = 0.1+0.2*rand(RS); // your function here
sphere {
0,RADIUS
translate <i*L -(L/2-RADIUS)+2*(L/2-RADIUS)*rand(RS), RADIUS, j*L -
(L/2-RADIUS)+2*(L/2-RADIUS)*rand(RS)>
pigment {rgb 1}
}
#local j=j+1;
#end
#local i=i+1;
#end
}
The pitfall of this approach is that not always it's that easy to get a reasonably
random look (you can try increasing the maximum translation amount till you can
observe clear intersections).
There's almost no parsing time...
> > I did it once. IIRC it was a real puzzle, I began to meet arrays in my not so
quiet
> > dreams... :-|
>
> that doesn't sound nice ... you mean I should leave this to an external program ?
You mean an external language (like C)? That would make it faster and simpler, but
you would lose flexibility.
--
Jonathan.
Home: http://digilander.iol.it/jrgpov
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"JRG" wrote:
> #declare N = 400;
> #declare L = 0.3+1; //max_radius + epsilon
Oops, as I said that should be:
#declare L = 2*max_radius+ delta;
No real harm done here. It's like:
#declare L = 2*0.3 + 0.7;// 2*max_radius + epsilon.
--
Jonathan.
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On Tue, 16 Apr 2002 19:26:01 +0200, "Jan Walzer" <jan### [at] lzernet>
wrote:
>So I wonder, if there are other, more advanced algorithms out there, which are
>faster ...
Use an oct-tree like POV does for bounding slabs.
Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG e-mail : pet### [at] tagpovrayorg
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"Jan Walzer" <jan### [at] lzernet> schrieb im Newsbeitrag
news:3cbc990e@news.povray.org...
> You say, that I should first place all the spheres in a grid, and then
jitter this
> to make a random distribution ? ... sounds interesting ...
And it works very well. Look in p.b.i for my test render of 50.000 spheres.
I made a array of 500x500 squares. In every square there can only be 1
sphere. After detecting a free square I translated the sphere randomly
within the square and marked the square as loaded. That's it. Here is some
code:
// Initialising the array
#declare gitter = array[501][501];
#declare array_help_x = 0;
#declare array_help_z = 0;
#while (array_help_x < 501)
#while (array_help_z < 501)
#declare gitter[array_help_x][array_help_z] = 0;
#declare array_help_z = array_help_z + 1;
#end
#declare array_help_x = array_help_x + 1;
#declare array_help_z = 0;
#end
#declare i = 1;
#declare zufall = seed(123456);
#while (i < 50000)
// Find a square to start
#declare neu_x = floor(500*rand(zufall)+0.5);
#declare neu_z = floor(500*rand(zufall)+0.5);
// If the square is loaded, find another one
#while (gitter[neu_x][neu_z] = 1)
#declare neu_x = floor(500*rand(zufall)+0.5);
#declare neu_z = floor(500*rand(zufall)+0.5);
#end
// Mark the square as loaded
#declare gitter[neu_x][neu_z] = 1;
// Random radius
#declare neu_radius = 0.5*rand(zufall);
// Creating the sphere
sphere
{
<neu_x+2*(0.5-neu_radius)*rand(zufall)-(0.5-neu_radius),
neu_radius, neu_z+2*(0.5-neu_radius)*rand(zufall)-(0.5-neu_radius)>,
neu_radius
texture
{
pigment
{
color rgb <1, 1, 0>
}
}
}
#declare i = i + 1;
#end
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yeah ... interesting technique ...
how well will this work with
different sized spheres ?
would this mean that I have to
mark some adjacent boxes as
loaded ?
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