PM 2Ring wrote:
> Tor Olav Kristensen <tor### [at] TOBEREMOVEDgmailcom> wrote:
>> PM 2Ring wrote:
>> ...
>>> That sounds great, Warp. But after over an hour of searching for Marching
>>> Triangles code, I haven't located anything yet, not even pseudocode. :( Do you
>>> have any suggestions for where I should look?
>> ...
>>
>> You can find some code in this thread:
> 
> Thanks, Tor Olav. I'll have a look at it when I wake up. :)

I see from your answer to Fredrik that it is not Marching Tetrahedrons you're after,
so what I linked to is probably not relevant for you.

-- 
Tor Olav
http://subcube.com

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Tor Olav Kristensen <tor### [at] TOBEREMOVEDgmailcom> wrote:
> PM 2Ring wrote:
> > Tor Olav Kristensen <tor### [at] TOBEREMOVEDgmailcom> wrote:
> >> PM 2Ring wrote:
> >> ...
> >>> That sounds great, Warp. But after over an hour of searching for Marching
> >>> Triangles code, I haven't located anything yet, not even pseudocode. :( Do you
> >>> have any suggestions for where I should look?
> >> ...
> >>
> >> You can find some code in this thread:
> >
> > Thanks, Tor Olav. I'll have a look at it when I wake up. :)
>
> I see from your answer to Fredrik that it is not Marching Tetrahedrons you're after,
> so what I linked to is probably not relevant for you.
>
> --
> Tor Olav
> http://subcube.com

That's OK. Once I had a look at the code, I realized it wasn't Marching
Triangles, but decided to try it out anyway. The meshes it produces do look
better than Marching Cubes, but of course it is very slow on large data sets,
being in POV SDL rather than C. Especially with recursion depth of 3 or more.

FWIW, in one of my tests I got an error message from POV saying that a normal
vector can't be <0,0,0>.

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Here's my latest Mandelbulb, rendered using the isosurface / df3 method.

but no radiosity: it was just too slow. This render took over 7 days on my
480MHz machine. I was hoping for a more impressive looking result, after all
that render time. Oh well.

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Attachments:
Download 'mandelbulbja0s90.jpg' (124 KB)

Preview of image 'mandelbulbja0s90.jpg'

"PM 2Ring" <nomail@nomail> schreef in bericht 
news:web.4b247f29ce81d185f4c648ed0@news.povray.org...
> Here's my latest Mandelbulb, rendered using the isosurface / df3 method.

> sources,
> but no radiosity: it was just too slow. This render took over 7 days on my
> 480MHz machine. I was hoping for a more impressive looking result, after 
> all
> that render time. Oh well.

I do find it pretty impressive. Reminds me of some kind of delicate 
porcelaine vase. The absence of shadows increases that feeling. I am 
impressed by your patience too ;)

Thomas

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"Thomas de Groot" <tDOTdegroot@interDOTnlANOTHERDOTnet> wrote:

> I do find it pretty impressive. Reminds me of some kind of delicate
> porcelaine vase. The absence of shadows increases that feeling. I am
> impressed by your patience too ;)

Thanks, Thomas. I think my next Mandelbulb renders will be close-ups rather than
trying to do the whole thing. And I might compromise & use a mesh instead of the
isosurface. These complex objects take up so much memory, I couldn't really do
much else while rendering, or the machine would start using virtual memory. That
would've taken months!

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PM 2Ring wrote:
> Here's my latest Mandelbulb, rendered using the isosurface / df3 method.

> but no radiosity: it was just too slow. This render took over 7 days on my
> 480MHz machine. I was hoping for a more impressive looking result, after all
> that render time. Oh well.
> 
> 
> 
> 
> ------------------------------------------------------------------------
> 
Nice.

Here's a 800^3 isosurface/df3, with radiosity and real HDRI, but I can't 
figure out what's wrong with my code, since the shape isn't right. It 
was supposed to be the n=8 shape from <-1.2,-1.2,-1.2> to <1.2,1.2,1.2>.

Time: 26 minutes with max_gradient 200 on a 2.6 GHz quad-core (AMD 
Phenom 9950) for the render, and somewhere around there for the 
generation on an older dual-core linux box.

Here's my c++ code for the iterations if anyone can figure out what is 
wrong, I've gone through it many times and can't figure out what's not 
right...

Chris

--------------------------------------------------------------------------
/* Iterates the formula at a given x,y,z and returns the smoothed number 
of iterations used */
float IteratePoint(double cx, double cy, double cz, double n, double 
bailout, int maxiter){
	double x=0.0,y=0.0,z=0.0;
	double r=0.0,rn=0.0,phin,thetan,sinthetan;
	for(int i=0;i<maxiter;i++){
		r=sqrt(pow(x,2)+pow(y,2)+pow(z,2));
		if(r>bailout){
			rn=pow(r,n);
			thetan=atan2(sqrt(pow(x,2)+pow(y,2)),z)*n;
			phin=atan2(y,z)*n;
			x=rn*sin(thetan)*cos(phin)+cx;
			y=rn*sin(thetan)*sin(phin)+cy;
			z=rn*cos(thetan)+cz;
			r=sqrt(pow(x,2)+pow(y,2)+pow(z,2));
			return (float)i + 1 - (log(log(r)/log(bailout)))/log(n);
		}
		rn=pow(r,n);
		thetan=atan2(sqrt(pow(x,2)+pow(y,2)),z)*n;
		phin=atan2(y,z)*n;
		x=rn*sin(thetan)*cos(phin)+cx;
		y=rn*sin(thetan)*sin(phin)+cy;
		z=rn*cos(thetan)+cz;
	}
	return (float)maxiter;
}

-------------------
and the loop part : (xs/xe are x-start, x-end values, same for y and z)
for (i=0;i<nx;i++){
	for (j=0;j<ny;j++){
	#pragma omp parallel 
shared(df3,nx,ny,nz,xs,xe,ys,ye,zs,ze,bailout,maxiter,n,i,j,chunk) 
private(k,cx,cy,cz)
	{
		#pragma omp for schedule(dynamic,chunk) nowait
		for (k=0;k<nz;k++){
			cx = (((double)i+0.5)/(double)nx)*(xe-xs)+xs;
			cy = (((double)j+0.5)/(double)ny)*(ye-ys)+ys;
			cz = (((double)k+0.5)/(double)nz)*(ze-zs)+zs;
			df3[i][j][k]=IteratePoint(cx,cy,cz,n,bailout,maxiter);
		}
	}
	if(j%2==0)
		ShowStatus(i*nx+j,nx*ny,"Iterating Fractal: ");
	}
}

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Attachments:
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Preview of image 'mandel_df3.jpg'

CShake wrote:
[...]
>  return (float)i + 1 - (log(log(r)/log(bailout)))/log(n);
[...]

You're return value may be a bit off.  The function log(r)/log(bailout) is the
base bailout logarithm of r,* which may not be what you intended.  The usual
formulation of this part is the (base n log of the natural log of the bailout)
minus (the base n log of natural log of the radius), where n is the power of the
mandelbulb.  This can then be simplified a little.

  return (float)i + 1 - ( log(log(bailout))-log(log(r)) )/log(n)
//then
  return (float)i + 1 - log(log(bailout)/log(r)) / log(n)

(Somebody check my math, please.  This might be simplified a bit more using the
root/log relationships...)

I don't know if this is the root of your current problem; the formulation you're
using may be just fine.  I would like to test it, since I've been monkeying with
continuous return values for the last couple of weeks, but won't be able to do
much more on this until after finals.

* http://en.wikipedia.org/wiki/Logarithms#Change_of_base

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waggy wrote:
> CShake wrote:
> [...]
>>  return (float)i + 1 - (log(log(r)/log(bailout)))/log(n);
> [...]
> 
> You're return value may be a bit off.  The function log(r)/log(bailout) is the
> base bailout logarithm of r,* which may not be what you intended.  The usual
> formulation of this part is the (base n log of the natural log of the bailout)
> minus (the base n log of natural log of the radius), where n is the power of the
> mandelbulb.  This can then be simplified a little.
> 
>   return (float)i + 1 - ( log(log(bailout))-log(log(r)) )/log(n)
> //then
>   return (float)i + 1 - log(log(bailout)/log(r)) / log(n)

I spent a bit of time on that problem too, and ended up with my equation 
based on the Escape Time Algorithm as presented at: 
http://en.wikipedia.org/wiki/Mandelbrot_set#Continuous_.28smooth.29_coloring

Unless I'm reading it wrong, that formula is effectively ( i - log[base 
N](log[base bailout](r))), which is what I'm using. I assumed that in 
the formula on wiki that the inner log (hardcoded as base 2) is actually 
base 'bailout', where most formulations of the mandelbrot equation use 2 
as the bailout value. The Zn value is stated as the value after n 
iterations, which in this case is r. Either I interpreted that equation 
wrong, or I'm erroneous in applying the '2d' equation in '3d'.

However, I don't think that's the problem in my equations, since I still 
get the same basic shape if I return 'i' instead of the 'smooth' 
coloring. Also, I wouldn't expect it to completely remove some of the 
features if I got this part of it wrong.

Chris

(I'm also between class and finals, this is how I'm procrastinating 
instead of studying and grading a pile of lab reports... )

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CShake wrote:
> I spent a bit of time on that problem too, and ended up with my equation 
> based on the Escape Time Algorithm as presented at: 
> http://en.wikipedia.org/wiki/Mandelbrot_set#Continuous_.28smooth.29_coloring 

I'm an idiot, please note that I mean 'Normalized Iteration Count 
Algorithm' instead of Escape Time in that sentence.

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CShake wrote:
[...]
>    phin=atan2(y,z)*n;
[...]
>   phin=atan2(y,z)*n;
[...]

Hmm.  Perhaps these have a small error?  I think maybe they should be like this.

   phin=atan2(y,x)*n;

http://www.skytopia.com/project/fractal/2mandelbulb.html#formula

Also, I used the same starting point, then grabbed one of the wikipedia
references and read some more.  (I also think I found a small improvement and
plan to write it up over the break.)

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