# AUTOGENERATED FILE! PLEASE DON'T EDIT
import numpy as np, matplotlib.pyplot as plt, matplotlib as mpl
from typing import Any, List, Union, Tuple
__all__ = ["perlin3d"]
def interpolant(t):
return t*t*t*(t*(t*6 - 15) + 10)
[docs]def perlin3d(shape=(100, 100, 100), res=(2, 2, 2), tileable=(False, False, False), interpolant=interpolant):
"""Generate a 3D numpy array of perlin noise. Not my code! All credits go
to the author of this library: https://github.com/pvigier/perlin-numpy
:param shape: The shape of the generated array (tuple of three ints).
This must be a multiple of res.
:param res: The number of periods of noise to generate along each
axis (tuple of three ints). Note shape must be a multiple
of res.
:param tileable: If the noise should be tileable along each axis
(tuple of three bools). Defaults to (False, False, False).
:param interpolant: The interpolation function, defaults to
t*t*t*(t*(t*6 - 15) + 10).
:return: A numpy array of shape shape with the generated noise.
:raises ValueError: If shape is not a multiple of res."""
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 = 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
)
if tileable[0]:
gradients[-1,:,:] = gradients[0,:,:]
if tileable[1]:
gradients[:,-1,:] = gradients[:,0,:]
if tileable[2]:
gradients[:,:,-1] = gradients[:,:,0]
gradients = gradients.repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
g000 = gradients[ :-d[0], :-d[1], :-d[2]]
g100 = gradients[d[0]: , :-d[1], :-d[2]]
g010 = gradients[ :-d[0],d[1]: , :-d[2]]
g110 = gradients[d[0]: ,d[1]: , :-d[2]]
g001 = gradients[ :-d[0], :-d[1],d[2]: ]
g101 = gradients[d[0]: , :-d[1],d[2]: ]
g011 = gradients[ :-d[0],d[1]: ,d[2]: ]
g111 = gradients[d[0]: ,d[1]: ,d[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 = interpolant(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)