Generate procedural\perlin noise in matlab

Question

I am looking for a simple way to generate something similar to procedural\perlin noise in matlab.

It just needs to have the general perlin noise traits, not to replicate ken perlin's method exactly.

Answer 1

An easy way to do it in in Matlab, as shown in Octave by the Nullprogramm blog is:

n = 64;
m = 64;
im = zeros(n, m);
im = perlin_noise(im);

figure; imagesc(im); colormap gray;

function im = perlin_noise(im)

    [n, m] = size(im);
    i = 0;
    w = sqrt(n*m);

    while w > 3
        i = i + 1;
        d = interp2(randn(n, m), i-1, 'spline');
        im = im + i * d(1:n, 1:m);
        w = w - ceil(w/2 - 1);
    end

Answer 2

perlin noise implementation already exists in several programming languages and is freely available on the internet. For instance, there is a java class on Ken Perlin's homepage (3D version / 4D version) that could be used with Matlab.

However, if you absolutely want to use Matlab language, I guess it is just a matter of "translating" which should be pretty straightforward. Here is a try for dimensions 1 to 3 which should work. It is not optimized nor thoroughly tested (seem to have some border problems). Hope it helps you.

function noise=perlin(values,x,y,z)
if(numel(values)~=512)
    values=randperm(256)-1;
    values=[values values];
end
x=abs(x);
X=bitand(floor(x),255);
x=x-floor(x);
u=fade(x);
A=values(1+X);
noise=linterp(u,grad1d(values(1+X),x),grad1d(values(1+X+1),x-1));
if(nargin>2)
    y=abs(y);
    Y=bitand(floor(y),255);
    y=y-floor(y);
    v=fade(y);
    A=A+Y;
    B=values(1+X+1)+Y;
    noise=linterp(u,linterp(u,grad2d(values(1+A),x,y),grad2d(values(1+B),x-1,y)),linterp(u,grad2d(values(1+A+1),x,y-1),grad2d(values(1+B+1),x-1,y-1)));
end
if(nargin>3)
    z=abs(z);
    Z=bitand(floor(z),255);
    z=z-floor(z);
    w=fade(z);
    AA=values(1+A)+Z;
    AB=values(1+A+1)+Z;
    BA=values(1+B)+Z;
    BB=values(1+B+1)+Z;
    noise=linterp(  w, ... 
                    linterp(v, ... 
                            linterp(u, ... 
                                    grad3d(values(1+AA),x,y,z), ... 
                                    grad3d(values(1+BA),x-1,y,z)), ...
                            linterp(u, ...
                                    grad3d(values(1+AB),x,y-1,z), ...
                                    grad3d(values(1+BB),x-1,y-1,z))), ...
                    linterp(v, ...
                            linterp(u, ... 
                                    grad3d(values(1+AA+1),x,y,z-1), ... 
                                    grad3d(values(1+BA+1),x-1,y,z-1)), ...
                            linterp(u, ...
                                    grad3d(values(1+AB+1),x,y-1,z-1), ...
                                    grad3d(values(1+BB+1),x-1,y-1,z-1))));
end
end

function l=linterp(t,a,b)
l=a+t*(b-a);
end

function t=fade(t)
t=6*t^5-15*t^4+10*t^3;
end

function g=grad1d(hash,x)
if(bitand(hash,1))
    g=-x;
else
    g=x;
end
end

function g=grad2d(hash,x,y)
h=bitand(hash,3);
if(bitand(h,2))
    u=-x;
else
    u=x;
end
if(bitand(h,1))
    v=-y;
else
    v=y;
end
g=u+v;
end

function g=grad3d(hash,x,y,z)
h=bitand(hash,15);
if(h<8)
    u=x;
else
    u=y;
end
if(h<4)
    v=y;
elseif(h==12 || h==14)
    v=x;
else
    v=z;
end
if(bitand(h,1))
    if(bitand(h,2))
        g=-u-v;
    else
        g=-u+v;
    end
else
    if(bitand(h,2))
        g=u-v;
    else
        g=u+v;
    end
end
end

Answer 3

I have recently tried to translate Ken Perlin's "Improved Noise". The results are at the end of this post. Note that it takes 10 seconds to make a 256 by 256 matrix. Visualize with imagesc.

Not that I have found that gradient(rand(w, h)) seems to give decent results. I don't know much about noise, so I don't know if this is the "same thing", but it sure seems to work. For larger grids, all you need is to interpolate points in a smaller rand.

function n = noise(x, y, z)
% noise(x, y, z) generates (I believe) 3 dimensional noise. To use, iterate
% through your array and generate each value with a call this function.
% Note that it is very slow.
% 
% Based Ken Perlin's "Improved Noise" in 2001, or 2002, or something.

% The unit cube which contains this point
uX = mod(floor(x), 256);
uY = mod(floor(y), 256);
uZ = mod(floor(z), 256);

% Find relative x, y, z of point in cube
x =x- floor(x);
y =y- floor(y);
z =z- floor(z);

% The mysterious "fade" function
fade = @(t) t * t * t * (t * (t * 6 - 15) + 10);

% Compute fade curved for each of x, y, z
u = fade(x);
v = fade(y);
w = fade(z);

% Hash coordinates of the 8 cube corners
p_half = randi(256, 256, 1) - 1;
p = [p_half, p_half];

a = p(1+uX) + uY;
aa = p(1+a) + uZ;
ab = p(1+a + 1) + uZ;

b = p(1+uX + 1) + uY;
ba = p(1+b) + uZ;
bb = p(1+b + 1) + uZ;

% "Lerp" is a shorter, more confusing name for "linear interpolation"
lerp = @(t, a, b) a + t * (b - a);

% This is how he gets the gradient
    function g = grad(hash, x, y, z)
        %Convert the low 4 bits of hash code into 12 gradient directions
        h = mod(hash, 16);

        % 50% chance for u to be on x or y
        if h < 8
            u_comp = x;
        else
            u_comp = y;
        end

        % 50% chance to reverse either component
        if mod(h, 2) == 0
            u_comp = -u_comp;
        end

        % 12.5% chance for v to be on x, 25% chance to be on y, 62.5% chance for z
        if (h == 12 || h == 14)
            v_comp = x;
        elseif (h < 4)
            v_comp = y;
        else
            v_comp = z;
        end

        % 50% chance to reverse either component
        if mod(h/2, 2) == 0
            v_comp = -v_comp;
        end

        g = u_comp + v_comp;
    end

% And add blended results from 8 corners of cube
n = lerp(w, lerp(v, lerp(u, grad(p(1+aa), x, y, z), ...
    grad(p(1+ba), x - 1, y, z)), ...
    lerp(u, grad(p(1+ab), x, y - 1, z), ...
    grad(p(1+bb), x - 1, y - 1, z))), ...
    lerp(v, lerp(u, grad(p(1+aa + 1), x, y, z - 1), ...
    grad(p(1+ba + 1), x - 1, y, z - 1)), ...
    lerp(u, grad(p(1+ab + 1), x, y - 1, z - 1), ...
    grad(p(1+bb + 1), x - 1, y - 1, z - 1))));
end