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Enable arbitrary resolution in 2D noise #14

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a29c29e
Enable arbitrary resolution in 2D noise
dli7319 Apr 21, 2023
dafecb3
Same fix for 3d
dli7319 Jul 23, 2023
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33 changes: 17 additions & 16 deletions perlin_numpy/perlin2d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -14,8 +14,7 @@ def generate_perlin_noise_2d(
shape: The shape of the generated array (tuple of two ints).
This must be a multple of res.
res: The number of periods of noise to generate along each
axis (tuple of two ints). Note shape must be a multiple of
res.
axis (tuple of two ints).
tileable: If the noise should be tileable along each axis
(tuple of two bools). Defaults to (False, False).
interpolant: The interpolation function, defaults to
Expand All @@ -27,29 +26,31 @@ def generate_perlin_noise_2d(
Raises:
ValueError: If shape is not a multiple of res.
"""
delta = (res[0] / shape[0], res[1] / shape[1])
d = (shape[0] // res[0], shape[1] // res[1])
grid = np.mgrid[0:res[0]:delta[0], 0:res[1]:delta[1]]\
.transpose(1, 2, 0) % 1
# Gradients
angles = 2*np.pi*np.random.rand(res[0]+1, res[1]+1)
gradients = np.dstack((np.cos(angles), np.sin(angles)))
if tileable[0]:
gradients[-1,:] = gradients[0,:]
if tileable[1]:
gradients[:,-1] = gradients[:,0]
gradients = gradients.repeat(d[0], 0).repeat(d[1], 1)
g00 = gradients[ :-d[0], :-d[1]]
g10 = gradients[d[0]: , :-d[1]]
g01 = gradients[ :-d[0],d[1]: ]
g11 = gradients[d[0]: ,d[1]: ]
grid = np.stack(np.meshgrid(
np.arange(0, shape[1]) * res[1] / shape[1],
np.arange(0, shape[0]) * res[0] / shape[0],
)[::-1], axis=-1)
grid_floor = np.floor(grid).astype(int)
grid_ceil = np.ceil(grid).astype(int)
g00 = gradients[grid_floor[:,:,0], grid_floor[:,:,1]]
g10 = gradients[grid_ceil[:,:,0], grid_floor[:,:,1]]
g01 = gradients[grid_floor[:,:,0], grid_ceil[:,:,1]]
g11 = gradients[grid_ceil[:,:,0], grid_ceil[:,:,1]]
grid_frac = grid - grid_floor
# Ramps
n00 = np.sum(np.dstack((grid[:,:,0] , grid[:,:,1] )) * g00, 2)
n10 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1] )) * g10, 2)
n01 = np.sum(np.dstack((grid[:,:,0] , grid[:,:,1]-1)) * g01, 2)
n11 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1]-1)) * g11, 2)
n00 = np.sum(np.dstack((grid_frac[:,:,0] , grid_frac[:,:,1] )) * g00, 2)
n10 = np.sum(np.dstack((grid_frac[:,:,0]-1, grid_frac[:,:,1] )) * g10, 2)
n01 = np.sum(np.dstack((grid_frac[:,:,0] , grid_frac[:,:,1]-1)) * g01, 2)
n11 = np.sum(np.dstack((grid_frac[:,:,0]-1, grid_frac[:,:,1]-1)) * g11, 2)
# Interpolation
t = interpolant(grid)
t = interpolant(grid_frac)
n0 = n00*(1-t[:,:,0]) + t[:,:,0]*n10
n1 = n01*(1-t[:,:,0]) + t[:,:,0]*n11
return np.sqrt(2)*((1-t[:,:,1])*n0 + t[:,:,1]*n1)
Expand Down
48 changes: 25 additions & 23 deletions perlin_numpy/perlin3d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -26,11 +26,6 @@ def generate_perlin_noise_3d(
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)
Expand All @@ -44,26 +39,33 @@ def generate_perlin_noise_3d(
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]: ]
grid = np.stack(np.meshgrid(
np.arange(0, shape[1]) * res[1] / shape[1],
np.arange(0, shape[0]) * res[0] / shape[0],
np.arange(0, shape[2]) * res[2] / shape[2],
), axis=-1)[...,[1,0,2]]
grid_floor = np.floor(grid).astype(int)
grid_ceil = np.ceil(grid).astype(int)
g000 = gradients[grid_floor[...,0], grid_floor[...,1], grid_floor[...,2]]
g100 = gradients[ grid_ceil[...,0], grid_floor[...,1], grid_floor[...,2]]
g010 = gradients[grid_floor[...,0], grid_ceil[...,1], grid_floor[...,2]]
g110 = gradients[ grid_ceil[...,0], grid_ceil[...,1], grid_floor[...,2]]
g001 = gradients[grid_floor[...,0], grid_floor[...,1], grid_ceil[...,2]]
g101 = gradients[ grid_ceil[...,0], grid_floor[...,1], grid_ceil[...,2]]
g011 = gradients[grid_floor[...,0], grid_ceil[...,1], grid_ceil[...,2]]
g111 = gradients[ grid_ceil[...,0], grid_ceil[...,1], grid_ceil[...,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)
grid_frac = grid - np.floor(grid)
n000 = np.sum(np.stack((grid_frac[:,:,:,0] , grid_frac[:,:,:,1] , grid_frac[:,:,:,2] ), axis=3) * g000, 3)
n100 = np.sum(np.stack((grid_frac[:,:,:,0]-1, grid_frac[:,:,:,1] , grid_frac[:,:,:,2] ), axis=3) * g100, 3)
n010 = np.sum(np.stack((grid_frac[:,:,:,0] , grid_frac[:,:,:,1]-1, grid_frac[:,:,:,2] ), axis=3) * g010, 3)
n110 = np.sum(np.stack((grid_frac[:,:,:,0]-1, grid_frac[:,:,:,1]-1, grid_frac[:,:,:,2] ), axis=3) * g110, 3)
n001 = np.sum(np.stack((grid_frac[:,:,:,0] , grid_frac[:,:,:,1] , grid_frac[:,:,:,2]-1), axis=3) * g001, 3)
n101 = np.sum(np.stack((grid_frac[:,:,:,0]-1, grid_frac[:,:,:,1] , grid_frac[:,:,:,2]-1), axis=3) * g101, 3)
n011 = np.sum(np.stack((grid_frac[:,:,:,0] , grid_frac[:,:,:,1]-1, grid_frac[:,:,:,2]-1), axis=3) * g011, 3)
n111 = np.sum(np.stack((grid_frac[:,:,:,0]-1, grid_frac[:,:,:,1]-1, grid_frac[:,:,:,2]-1), axis=3) * g111, 3)
# Interpolation
t = interpolant(grid)
t = interpolant(grid_frac)
n00 = n000*(1-t[:,:,:,0]) + t[:,:,:,0]*n100
n10 = n010*(1-t[:,:,:,0]) + t[:,:,:,0]*n110
n01 = n001*(1-t[:,:,:,0]) + t[:,:,:,0]*n101
Expand Down