True 3D Julia

[Buddhi]

Hi
I stay with my render method. It needs lots of memory and it's very slow but I can generate accurate shadows, transparent fog, environment mapping (based on normal vectors). Now I'm working to prepare full raytracing (with reflections). I agree with you that distance estimation method will be helpfull for rendering because this distance information we can use to calculate step distance in for example raytracing algorithm.  Rendering will be much more faster. But now I know how to calculate distance only using quaternions. Quaternions fractals has unfortunately few interesting details.
Below there is new rendering of Julia fractal.

[Buddhi]

Last times I have rendered two new Julia 3D Fractals using Twinbee formula. For shading I used global illumination and hard shadows algorithms.

Julia constant  = -0.78 + 0.15i + 0.07j

http://www.fractalforums.com/gallery/?sa=view;id=1000

Julia constant  = -0.4360393 + 0.0147539i + 0j

http://www.fractalforums.com/gallery/?sa=view;id=1017

[David Makin]

Awesome renders !

[cKleinhuis]

indeed
 

[lycium]

global illumination and hard shadows algorithms

even if that's a contradiction, i must also agree: very fine renders!

[cKleinhuis]

as i said in the gallery, the first of the last 2 really looks like a coral water plant ... actually REALLY IN the water! 

[JColyer]

@buddhi - i've been working on a similar rendering technique to yours for about the past week or so, biggest difference is that I'm storing my pre-render data in a DB instead of JPEG files.  I've gotten quite far in the ray-tracing process but i'm having a devil of a time trying to figure out how to come up with the normals?  any suggestions or guidance you can offer?

thanks!

JC

[Buddhi]

@JColyer - bellow is some fragment of code from my program where is procedure for calculation normal vector. This algorithm calculates average gradient for some small area near calculated point.

Code:

for(int k=-smooth; k<=smooth; k++)
{
	for(int j=-smooth; j<=smooth; j++)
	{
		for(int i=-smooth; i<=smooth; i++)
		{
			double delta2X = Interpol3D(x+0.5+i,y+0.5+j,z+0.5+k,fractal3D)
			            	-Interpol3D(x-0.5+i,y-0.5+j,z-0.5+k,fractal3D);
			double delta2Y = Interpol3D(x+0.5+i,y+0.5+j,z+0.5+k,fractal3D)
			            	-Interpol3D(x-0.5+i,y-0.5+j,z-0.5+k,fractal3D);
			double delta2Z = Interpol3D(x+0.5+i,y+0.5+j,z+0.5+k,fractal3D)
			           	-Interpol3D(x-0.5+i,y-0.5+j,z-0.5+k,fractal3D);
			deltaX+=delta2X;
			deltaY+=delta2Y;
			deltaZ+=delta2Z;
       		}
       	}
}
       			            
//length of vector (normalization factor)
double modul = sqrt(deltaX*deltaX + deltaY*deltaY + deltaZ*deltaZ);
			            
if(modul>0.001)
{
     	//normalization of normal vector
       	normalX = deltaX/modul;
       	normalY = deltaY/modul;
       	normalZ = deltaZ/modul;
}

Interpol3D function calculates linear interpolation between adjacent points of 3D array which consist fractal slices. It is for more smooth results.

I know that it is not optimal algorithm but this is only one I know. Maybe it helps you.

I resigned from pre-calculating slices into array, because it is not effective (program have to calculate points also inside Mandelbulb) and needs lots of memory. Maximum array size which I achieved was 1500x1500x1500 (3,2GiB of RAM). Unfortunately it is not enough for any perspective views. Now I'm calculating fractal iterations directly in 3D view and it is about 10 times faster than with calculated fractal slices. It is faster because program have to calculate only visible points.

[JColyer]

@buddhi - ah thank you, i had read about using a linear gradient function but hand't quite been able to get my brain wrapped around it.  as of last night I built a very crude fractal ray tracer and it works ok, but needs a load of work.  I'm working with dataset driven rendering as I'm rendering the interior structures of julia sets and the method I use requires post-generation data mapping to get full quality and detail from the data.  I'll get some pics posted asap!

thanks for pointing me in the right direction!

JC