Perlin Noise and GLSL

June 21st, 2012

After reading this post on Creative Applications and then going to Inigo Quilez’s website and reading his post about warping, I decided to have some fun with GLSL, Perlin Noise and Openframeworks. The results are just beautiful:

I am just posting a small code example I did, if somebody wants to take things further or just play around.

Openframeworks Draw Code:

    ofBackground(0, 0, 0);
    shader.begin();
    shader.setUniform1f("time", ofGetFrameNum() * 0.001);
    ofRect(0,0,1024,768);
    shader.end();

Vertex Shader:

uniform float time;

void main() {
     gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
}

Fragment Shader:

uniform float time;

vec4 mod289(vec4 x)
{
    return x - floor(x * (1.0 / 289.0)) * 289.0;
}

vec4 permute(vec4 x)
{
    return mod289(((x*34.0)+1.0)*x);
}

vec4 taylorInvSqrt(vec4 r)
{
    return 1.79284291400159 - 0.85373472095314 * r;
}

vec2 fade(vec2 t) {
    return t*t*t*(t*(t*6.0-15.0)+10.0);
}

// Classic Perlin noise
float cnoise(vec2 P)
{
    vec4 Pi = floor(P.xyxy) + vec4(0.0, 0.0, 1.0, 1.0);
    vec4 Pf = fract(P.xyxy) - vec4(0.0, 0.0, 1.0, 1.0);
    Pi = mod289(Pi); // To avoid truncation effects in permutation
    vec4 ix = Pi.xzxz;
    vec4 iy = Pi.yyww;
    vec4 fx = Pf.xzxz;
    vec4 fy = Pf.yyww;
    
    vec4 i = permute(permute(ix) + iy);
    
    vec4 gx = fract(i * (1.0 / 41.0)) * 2.0 - 1.0 ;
    vec4 gy = abs(gx) - 0.5 ;
    vec4 tx = floor(gx + 0.5);
    gx = gx - tx;
    
    vec2 g00 = vec2(gx.x,gy.x);
    vec2 g10 = vec2(gx.y,gy.y);
    vec2 g01 = vec2(gx.z,gy.z);
    vec2 g11 = vec2(gx.w,gy.w);
    
    vec4 norm = taylorInvSqrt(vec4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
    g00 *= norm.x;  
    g01 *= norm.y;  
    g10 *= norm.z;  
    g11 *= norm.w;  
    
    float n00 = dot(g00, vec2(fx.x, fy.x));
    float n10 = dot(g10, vec2(fx.y, fy.y));
    float n01 = dot(g01, vec2(fx.z, fy.z));
    float n11 = dot(g11, vec2(fx.w, fy.w));
    
    vec2 fade_xy = fade(Pf.xy);
    vec2 n_x = mix(vec2(n00, n01), vec2(n10, n11), fade_xy.x);
    float n_xy = mix(n_x.x, n_x.y, fade_xy.y);
    return 2.3 * n_xy;
}

// Classic Perlin noise, periodic variant
float pnoise(vec2 P, vec2 rep)
{
    vec4 Pi = floor(P.xyxy) + vec4(0.0, 0.0, 1.0, 1.0);
    vec4 Pf = fract(P.xyxy) - vec4(0.0, 0.0, 1.0, 1.0);
    Pi = mod(Pi, rep.xyxy); // To create noise with explicit period
    Pi = mod289(Pi);        // To avoid truncation effects in permutation
    vec4 ix = Pi.xzxz;
    vec4 iy = Pi.yyww;
    vec4 fx = Pf.xzxz;
    vec4 fy = Pf.yyww;
    
    vec4 i = permute(permute(ix) + iy);
    
    vec4 gx = fract(i * (1.0 / 41.0)) * 2.0 - 1.0 ;
    vec4 gy = abs(gx) - 0.5 ;
    vec4 tx = floor(gx + 0.5);
    gx = gx - tx;
    
    vec2 g00 = vec2(gx.x,gy.x);
    vec2 g10 = vec2(gx.y,gy.y);
    vec2 g01 = vec2(gx.z,gy.z);
    vec2 g11 = vec2(gx.w,gy.w);
    
    vec4 norm = taylorInvSqrt(vec4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
    g00 *= norm.x;  
    g01 *= norm.y;  
    g10 *= norm.z;  
    g11 *= norm.w;  
    
    float n00 = dot(g00, vec2(fx.x, fy.x));
    float n10 = dot(g10, vec2(fx.y, fy.y));
    float n01 = dot(g01, vec2(fx.z, fy.z));
    float n11 = dot(g11, vec2(fx.w, fy.w));
    
    vec2 fade_xy = fade(Pf.xy);
    vec2 n_x = mix(vec2(n00, n01), vec2(n10, n11), fade_xy.x);
    float n_xy = mix(n_x.x, n_x.y, fade_xy.y);
    return 2.3 * n_xy;
}

float fbm(vec2 P, int octaves, float lacunarity, float gain)
{
	float sum = 0.0;
	float amp = 1.0;
    vec2 pp = P;
    
	int i;
	
	for(i = 0; i < octaves; i+=1)
	{
        amp *= gain; 
		sum += amp * cnoise(pp);
        pp *= lacunarity;
    }
	return sum;

}


float pattern(in vec2 p) {
    float l = 2.5;
    float g = 0.4;
    int oc = 10;
    
    vec2 q = vec2( fbm( p + vec2(0.0,0.0),oc,l,g),fbm( p + vec2(5.2,1.3),oc,l,g));
    vec2 r = vec2( fbm( p + 4.0*q + vec2(1.7,9.2),oc,l,g ), fbm( p + 4.0*q + vec2(8.3,2.8) ,oc,l,g));
    return fbm( p + 4.0*r ,oc,l,g);    
}

float pattern2( in vec2 p, out vec2 q, out vec2 r , in float time)
{
    float l = 2.3;
    float g = 0.4;
    int oc = 10; 
    
    q.x = fbm( p + vec2(time,time),oc,l,g);
    q.y = fbm( p + vec2(5.2*time,1.3*time) ,oc,l,g);
    
    r.x = fbm( p + 4.0*q + vec2(1.7,9.2),oc,l,g );
    r.y = fbm( p + 4.0*q + vec2(8.3,2.8) ,oc,l,g);
    
    return fbm( p + 4.0*r ,oc,l,g);
}

void main() {
    
    vec2 q = gl_FragCoord.xy / vec2(640.0,480.0);
    vec2 p = -1.0 + 2.0 * q;
    vec2 qq;
    vec2 r;
    float color = pattern2(p,qq,r,time);
    
    vec4 c = vec4(color,color,color,color);
    c *= 3.5;
    
    gl_FragColor = c;
}

Comments:

PAEz says:
2012-10-28 12:22:01
Here's your sample code on GLSL Sandbox... http://glsl.heroku.com/e#4555.0 The only bit I really had to change was in fbm() where you compare i against octaves in the for loop....seems you have to compare against a constant in webgl....what a pain ;) Thanks for this, was looking for a simple example. Have a good one

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