How can you make a loop with perlin3d?

[ouhenio]

Hi!

I'd like to make something like the example gif of perlin3d, but I can't get how to get a loop on noise with perlin3d.

[pvigier]

Hi!

I have already answer to a similar request in issue #1. To have loopable noise you have to constrain the first layer of gradients to be equal to the last:

def generate_perlin_noise_3d(shape, res):
    def f(t):
        return 6*t**5 - 15*t**4 + 10*t**3

    delta = (res[0] / shape[0], res[1] / shape[1], res[2] / shape[2])
    d = (shape[0] // res[0], shape[1] // res[1], shape[2] // res[2])
    grid = np.mgrid[0:res[0]:delta[0],0:res[1]:delta[1],0:res[2]:delta[2]]
    grid = grid.transpose(1, 2, 3, 0) % 1
    # Gradients
    theta = 2*np.pi*np.random.rand(res[0]+1, res[1]+1, res[2]+1)
    phi = 2*np.pi*np.random.rand(res[0]+1, res[1]+1, res[2]+1)
    gradients = np.stack((np.sin(phi)*np.cos(theta), np.sin(phi)*np.sin(theta), np.cos(phi)), axis=3)
    # Make the noise loopable
    gradients[-1] = gradients[0]
   # Same as before
    g000 = gradients[0:-1,0:-1,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g100 = gradients[1:  ,0:-1,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g010 = gradients[0:-1,1:  ,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g110 = gradients[1:  ,1:  ,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g001 = gradients[0:-1,0:-1,1:  ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g101 = gradients[1:  ,0:-1,1:  ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g011 = gradients[0:-1,1:  ,1:  ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    g111 = gradients[1:  ,1:  ,1:  ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
    # Ramps
    n000 = np.sum(np.stack((grid[:,:,:,0]  , grid[:,:,:,1]  , grid[:,:,:,2]  ), axis=3) * g000, 3)
    n100 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]  , grid[:,:,:,2]  ), axis=3) * g100, 3)
    n010 = np.sum(np.stack((grid[:,:,:,0]  , grid[:,:,:,1]-1, grid[:,:,:,2]  ), axis=3) * g010, 3)
    n110 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]-1, grid[:,:,:,2]  ), axis=3) * g110, 3)
    n001 = np.sum(np.stack((grid[:,:,:,0]  , grid[:,:,:,1]  , grid[:,:,:,2]-1), axis=3) * g001, 3)
    n101 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]  , grid[:,:,:,2]-1), axis=3) * g101, 3)
    n011 = np.sum(np.stack((grid[:,:,:,0]  , grid[:,:,:,1]-1, grid[:,:,:,2]-1), axis=3) * g011, 3)
    n111 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]-1, grid[:,:,:,2]-1), axis=3) * g111, 3)
    # Interpolation
    t = f(grid)
    n00 = n000*(1-t[:,:,:,0]) + t[:,:,:,0]*n100
    n10 = n010*(1-t[:,:,:,0]) + t[:,:,:,0]*n110
    n01 = n001*(1-t[:,:,:,0]) + t[:,:,:,0]*n101
    n11 = n011*(1-t[:,:,:,0]) + t[:,:,:,0]*n111
    n0 = (1-t[:,:,:,1])*n00 + t[:,:,:,1]*n10
    n1 = (1-t[:,:,:,1])*n01 + t[:,:,:,1]*n11
    return ((1-t[:,:,:,2])*n0 + t[:,:,:,2]*n1)

Let me know if you have any problem.

Best

[ouhenio]

It works! Awesome, thanks!

[pvigier]

You're welcome!