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Improving Pixel Shader Ridged Multifractal Function


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#1 multifractal   Members   -  Reputation: 229

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Posted 16 September 2013 - 08:21 PM

Hello,

I recently decided to switch from creating heightmaps in openCL to a pixel shader. While this makes things easier to work with I have one major issue. For terrain I am relying primarily on this ridged multifractal function:

float RMF(in vec3 v)  {

		 float result, frequency, signal, weight;
		 float H = 1.0;
		 float lacunarity = 2.143212;
		 int octaves = 12;
		 float offset = 1.0;
		 float gain = 2.1;
         int i;
         bool first = true;
		float exponentArray[12];
             frequency =.6;
             if(first){     	 
             for (i=0; i<octaves; i++) {
                   exponentArray[i] =  pow(frequency, -H); 
                   frequency *= lacunarity;
                     
             }
             first = false;
             }

       
         signal = inoise(v);
         
         if (signal < 0.0) signal = -signal;
             

         signal = offset - signal;
         
         signal *=signal;
        
         result = signal;
         weight = 1.0;

         for (i = 1; i < octaves; i++) {
    
             v*=lacunarity;

          
             weight = signal * gain;

             if ( weight > 1.0 ) weight = 1.0;
                 
             if ( weight < 0.0 ) weight = 0.0;
                 

            signal = (inoise(v));

             if ( signal < 0.0 ) signal = -signal;
                 

             signal = offset - signal;
             signal *= signal;
       
             signal *= weight;
             result += signal * exponentArray[i];
         }
         return (result - 1.0) / 2.0;        
     }

Using openCl I could produce heightmap such as the following:

img.png

 

This resulted in "strong" terrain features and rough mountains yet smooth valleys. 

Using a pixel shader I cannot reproduce such quality. 

At best I can create something like below: 

image.png

 

Which is far too rough and lacks the height features of the other implementation. 

I can think of no other cause of these disparities than the actual perlin noise function being used. 

For the pixel shader I am using the noise described here: http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter26.html

while in openCL I was using the following function:

float sgnoise2d(float2 position)
{
	float2 p = position;
	float2 pf = floor(p);
	int2 ip = (int2)((int)pf.x, (int)pf.y);
	float2 fp = p - pf;        
    ip &= P_MASK;
	
	const int2 I00 = (int2)(0, 0);
	const int2 I01 = (int2)(0, 1);
	const int2 I10 = (int2)(1, 0);
	const int2 I11 = (int2)(1, 1);
	
	const float2 F00 = (float2)(0.0f, 0.0f);
	const float2 F01 = (float2)(0.0f, 1.0f);
	const float2 F10 = (float2)(1.0f, 0.0f);
	const float2 F11 = (float2)(1.0f, 1.0f);

	float n00 = gradient2d(ip + I00, fp - F00);
	float n10 = gradient2d(ip + I10, fp - F10);
	float n01 = gradient2d(ip + I01, fp - F01);
	float n11 = gradient2d(ip + I11, fp - F11);

	const float2 n0001 = (float2)(n00, n01);
	const float2 n1011 = (float2)(n10, n11);

	float2 n2 = mix2d(n0001, n1011, smooth(fp.x));
	float n = mix1d(n2.x, n2.y, smooth(fp.y));
	return n * (1.0f / 0.7f);
}

float ugnoise2d(float2 position)
{
    return (0.5f - 0.5f * sgnoise2d(position));
}

I would like to keep using the improved glsl noise that I am using but I was wondering if anyone had any experience with good ridged multifractal functions to use in a pixel shader. Thanks for any help whatsoever. 



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#2 unbird   Crossbones+   -  Reputation: 6012

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Posted 16 September 2013 - 08:53 PM

If you used that implementation I'm pretty sure you're fine. Looking at those pictures I guess you have no more than a different scaling issue. Looking at the Level stats in Paint.NET it's quote obvious actually: The second one doesn't go over 0.5. Try scaling it by 2.



#3 multifractal   Members   -  Reputation: 229

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Posted 17 September 2013 - 03:07 PM

If you used that implementation I'm pretty sure you're fine. Looking at those pictures I guess you have no more than a different scaling issue. Looking at the Level stats in Paint.NET it's quote obvious actually: The second one doesn't go over 0.5. Try scaling it by 2.

Yea that was stupid of me:

 

image.png

 

Although that still doesn't look great, I could probably just fiddle with the variables more.

Thanks.



#4 unbird   Crossbones+   -  Reputation: 6012

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Posted 17 September 2013 - 03:44 PM

Yea that was stupid of me

 
No, I could have been wrong as well wink.png
 
Unless you have some automatic normalization you can get pretty far off results, especially when using low res color formats (your latest screenshot still does not use the full range). So yeah, play around and get familiar with it. GPU-noise is nice in this regard since you can get results interactively.




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