A question about scales

[lapinot]

Hi all.

I have 2 separate questions regarding 'scale' and what it means.

1) The scale factor : I have heard people talk about 'scale' as of 'a scale xyz power w mandelbulb' etc... I don't know what it is and how to implement it. For example, here is my mandelbulb glsl code :

Code:

float DE (vec3 pos) {

	vec3 z = pos;
	float wr = length(pos);
	float dr = 1.0;

	float escape = FEscape;
	float Power = FPower;
	float Scale = 1.0;
	
	for (int i = 0; i != FMaxIterations && wr < FEscape; i++) {

		float wo = acos(pos.y / wr);
		float wi = atan(pos.x, pos.z);
		dr = pow(wr, Power - 1) * Power * dr + 1;

		wr = pow(wr, Power);
		wo = wo * Power;
		wi = wi * Power;

		pos.x = sin(wo) * sin(wi);
		pos.y = cos(wo);
		pos.z = sin(wo) * cos(wi);
		pos = pos * wr;

		pos = pos + z;
		wr = length(pos) * Scale;
	}
	
	return min(2.0, 0.5 * log(wr) * wr / dr);
}

This code works as it should. How would I 'insert' a scale variable into the formula ?

2) General size of a fractal : the code above gives me a bulb roughly contained in a radius 2 sphere (I guess). How would I have it contained in a radius 2'000'000 sphere (for example) The idea is : glsl float precision is so bad that I can barely go under the 10^-6 barrier. with a 10⁶ scaled bulb, I would have twice as much precision to play with.

Maybe a similar question has been asked already I dunno    thx for any insight 

[eiffie]

Divide pos and dr by scale before they are used elsewhere and you are done.

[lapinot]

Divide pos and dr by scale before they are used elsewhere and you are done.

Okay thx 

What about part #2 ?  Is it possible to embed the fractal in a larger sphere ?

[cKleinhuis]

2) General size of a fractal : the code above gives me a bulb roughly contained in a radius 2 sphere (I guess). How would I have it contained in a radius 2'000'000 sphere (for example) The idea is : glsl float precision is so bad that I can barely go under the 10^-6 barrier. with a 10⁶ scaled bulb, I would have twice as much precision to play with.

Maybe a similar question has been asked already I dunno    thx for any insight  

just scale everything as you wish, but dont confuse number precision with scale, scaling up does not give any bit of precision extra, shifting the decimal point to the left for a fixed amount will not give you precision gain, precision problems occur when the needed diference of 2 numbers can not be expressed by the floating point, no matter if too big or too small ...

[lapinot]

I know I wont technically get 'more precision'. What I meant is : by starting with a fractal with radius i.e. 2'000'000 instead of 2, I can 'zoom in' twice as much.

Because glsl float precision is rougly 10⁶ - 10^-6. So I would definitely get twice the available zooming by 'starting big'. By the way I posted a pic in the B&W art contest session of this year that illustrate just that. At max zooming level my scene looks like it's composed of voxels. So as you said the dimensions become too small for GLSL to see any difference in values, because of float limitations hence the voxelized look.

[eiffie]

Christian is right but you probably have to try it before it sinks in what is going on.
Set the scale to 10^6 so the functions looks like...

float DE(vec3 pos){
  pos=pos/scale;
  dr=1.0/scale;
  ...continue with the normal function without any reference to scale.

Make sure you back the camera up a bit like 2*10^6.

Now zoom in by halving the distance to the surface each frame (it will become pixelated again in as few frames as before!)
But we would love to be proved wrong, who doesn't want double the space.

[mclarekin]

@ eiffie

......, who doesn't want double the space.

Me, I don't want double the space, i'm lost enough as it is! .  In this already infinite fractal universe