# OpenGL Fast computed noise

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In this thread I'm going to speak of some experiments I've been making on 3D noise generated on the GPU. Reference test The reference 3D noise implementation is from Stefan Gustavson in GLSL. Here is the thread about it with a link to the full GLSL code: GLSL 3D Noise by Stefan Gustavson I'm generating, combining and rendering 32 octaves of his noise per pixel into a 513x513 fp32 texture. I'm getting 20 fps on an ATI Radeon X1950 XT. Computed noise The idea with the computed noise basis is to generate some kind of coherent noise (like Perlin noise), but avoiding the permutation/lookup tables and integer/bit-shifting arithmetics. Originally, it was developped for the CPU, to be easily optimized in SSE2. Here's the port to GLSL:
float randomizer(const float x)
{
float z = mod(x, 5612.0);
z = mod(z, 3.1415927 * 2.0);
return(fract(cos(z) * 56812.5453));
}

const float A = 1.0;
const float B = 57.0;
const float C = 113.0;
const vec3 ABC = vec3(A, B, C);

float cnoise(const in vec3 xx)
{
vec3 x = mod(xx + 32768.0, 65536.0);
vec3 ix = floor(x);
vec3 fx = fract(x);
vec3 wx = fx*fx*(3.0-2.0*fx);
float nn = dot(ix, ABC);

float re = mix(mix(mix(randomizer(nn),
randomizer(nn + A),wx.x),
mix(randomizer(nn + B),
randomizer(nn + A + B),wx.x),wx.y),
mix(mix(randomizer(nn + C),
randomizer(nn + C + A),wx.x),
mix(randomizer(nn + C + B),
randomizer(nn + C + B + A),wx.x),wx.y),wx.z);

return 1.0 - 2.0 * re;
}

This version runs at 50 fps in 82 asm instructions. Fast computed noise I then optimized it a bit further by working on 4 values at a time instead of a scalar:
vec4 randomizer4(const vec4 x)
{
vec4 z = mod(x, vec4(5612.0));
z = mod(z, vec4(3.1415927 * 2.0));
return(fract(cos(z) * vec4(56812.5453)));
}

const float A = 1.0;
const float B = 57.0;
const float C = 113.0;
const vec3 ABC = vec3(A, B, C);
const vec4 A3 = vec4(0, B, C, C+B);
const vec4 A4 = vec4(A, A+B, C+A, C+A+B);

float cnoise4(const in vec3 xx)
{
vec3 x = mod(xx + 32768.0, 65536.0);
vec3 ix = floor(x);
vec3 fx = fract(x);
vec3 wx = fx*fx*(3.0-2.0*fx);
float nn = dot(ix, ABC);

vec4 N1 = nn + A3;
vec4 N2 = nn + A4;
vec4 R1 = randomizerSin4(N1);
vec4 R2 = randomizerSin4(N2);
vec4 R = mix(R1, R2, wx.x);
float re = mix(mix(R.x, R.y, wx.y), mix(R.z, R.w, wx.y), wx.z);

return 1.0 - 2.0 * re;
}

This version is considerably shorter and a bit faster: 62 fps in 47 asm instructions. This is 3 times faster than the reference noise, and it's pure arithmetic (no texture lookups or anything). It's also suitable for shader model 2.0 cards. Quality Of course, you don't get a noise that is 3 times faster without paying a price. Here are the drawbacks of this version as far as I know: 1. There's a seam in the noise around coordinates +-32768 (tiling). Originally it was around 0, due to the mod() operations in the randomizer function, but I moved this seam to +-32768 with the first line: vec3 x = mod(xx + 32768.0, 65536.0); 2. Like my "fast noise" implementation on the cpu (cf. my journal), the features aren't distributed as well as the original noise. Quality might be okay or not, depending on your use. See comparison screenshots below.. Reference noise Fast computed noise 3. And my main problem: the results are different on NVidia and ATI cards. I believe this is due to internal precision in the registers. It decreases when the big constants (65536, 56812.5453, etc.. ) are reduced, but the noise begins to have pretty ugly repeating patterns. 4. It needs a better randomizer function: all the constants and formulas are arbitrary and found by trial & error. I would be glad if somebody found a better randomizer function that behaves the same on NV / ATI cards and that doesn't have horrible/repeating patterns. Basically, I'm posting it here in the hope that it'll be useful to somebody in its current state, or that somebody could experiment with it and improve its quality (I'm currently lacking time to continue on it). Y.

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Hmm, is it just me who can't see the decreased quality in the fast version?
Sure, it looks different, but not particularly badly distributed or anything imo.

And yeah, when I looked at Gustavson's implementation I wondered why it worked on scalars too, but didn't get around to implementing a proper vectorized version. Nice job. :)

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The difference of quality won't become apparent until you take the first derivative of the image (the normal map or bump map) which is typically used for coming up with local slope and for lighting.

The idea of Perlin's fast gradient noise was not to improve the quality of several octaves of fBm noise... that looks just fine without interpolating gradients. The entire point was to improve the visual quality of the BUMP map or normal map of fBm for real-time lighting and such, this is where the axis-aligned nature of non-gradient interpolation shows its ugly face.

If we really want to compare quality, we should be posting images of the resulting bump map, not of the raw fBm output.

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