libnoise.glsl

// Classic Perlin Noise by Stefan Gustavson
vec2 fade(vec2 t) {return t*t*t*(t*(t*6.0-15.0)+10.0);}
vec3 fade(vec3 t) {return t*t*t*(t*(t*6.0-15.0)+10.0);}
vec4 permute(vec4 x){return mod(((x*34.0)+1.0)*x, 289.0);}
vec4 taylorInvSqrt(vec4 r){return 1.79284291400159 - 0.85373472095314 * r;}

float perlin_noise(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 = mod(Pi, 289.0); // 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 = 2.0 * fract(i * 0.0243902439) - 1.0; // 1/41 = 0.024...
	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 = 1.79284291400159 - 0.85373472095314 * 
		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 perlin_noise(vec3 P) {
	vec3 Pi0 = floor(P); // Integer part for indexing
	vec3 Pi1 = Pi0 + vec3(1.0); // Integer part + 1
	Pi0 = mod(Pi0, 289.0);
	Pi1 = mod(Pi1, 289.0);
	vec3 Pf0 = fract(P); // Fractional part for interpolation
	vec3 Pf1 = Pf0 - vec3(1.0); // Fractional part - 1.0
	vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
	vec4 iy = vec4(Pi0.yy, Pi1.yy);
	vec4 iz0 = Pi0.zzzz;
	vec4 iz1 = Pi1.zzzz;

	vec4 ixy = permute(permute(ix) + iy);
	vec4 ixy0 = permute(ixy + iz0);
	vec4 ixy1 = permute(ixy + iz1);

	vec4 gx0 = ixy0 / 7.0;
	vec4 gy0 = fract(floor(gx0) / 7.0) - 0.5;
	gx0 = fract(gx0);
	vec4 gz0 = vec4(0.5) - abs(gx0) - abs(gy0);
	vec4 sz0 = step(gz0, vec4(0.0));
	gx0 -= sz0 * (step(0.0, gx0) - 0.5);
	gy0 -= sz0 * (step(0.0, gy0) - 0.5);

	vec4 gx1 = ixy1 / 7.0;
	vec4 gy1 = fract(floor(gx1) / 7.0) - 0.5;
	gx1 = fract(gx1);
	vec4 gz1 = vec4(0.5) - abs(gx1) - abs(gy1);
	vec4 sz1 = step(gz1, vec4(0.0));
	gx1 -= sz1 * (step(0.0, gx1) - 0.5);
	gy1 -= sz1 * (step(0.0, gy1) - 0.5);

	vec3 g000 = vec3(gx0.x,gy0.x,gz0.x);
	vec3 g100 = vec3(gx0.y,gy0.y,gz0.y);
	vec3 g010 = vec3(gx0.z,gy0.z,gz0.z);
	vec3 g110 = vec3(gx0.w,gy0.w,gz0.w);
	vec3 g001 = vec3(gx1.x,gy1.x,gz1.x);
	vec3 g101 = vec3(gx1.y,gy1.y,gz1.y);
	vec3 g011 = vec3(gx1.z,gy1.z,gz1.z);
	vec3 g111 = vec3(gx1.w,gy1.w,gz1.w);

	vec4 norm0 = taylorInvSqrt(vec4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
	g000 *= norm0.x;
	g010 *= norm0.y;
	g100 *= norm0.z;
	g110 *= norm0.w;
	vec4 norm1 = taylorInvSqrt(vec4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
	g001 *= norm1.x;
	g011 *= norm1.y;
	g101 *= norm1.z;
	g111 *= norm1.w;

	float n000 = dot(g000, Pf0);
	float n100 = dot(g100, vec3(Pf1.x, Pf0.yz));
	float n010 = dot(g010, vec3(Pf0.x, Pf1.y, Pf0.z));
	float n110 = dot(g110, vec3(Pf1.xy, Pf0.z));
	float n001 = dot(g001, vec3(Pf0.xy, Pf1.z));
	float n101 = dot(g101, vec3(Pf1.x, Pf0.y, Pf1.z));
	float n011 = dot(g011, vec3(Pf0.x, Pf1.yz));
	float n111 = dot(g111, Pf1);

	vec3 fade_xyz = fade(Pf0);
	vec4 n_z = mix(vec4(n000, n100, n010, n110), vec4(n001, n101, n011, n111), fade_xyz.z);
	vec2 n_yz = mix(n_z.xy, n_z.zw, fade_xyz.y);
	float n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 
	return 2.2 * n_xyz;
}