问题
I'm trying to produce 2D perlin noise using numpy, but instead of something smooth I get this :
my broken perlin noise, with ugly squares everywhere
For sure, I'm mixing up my dimensions somewhere, probably when I combine the four gradients ... But I can't find it and my brain is melting right now. Anyone can help me pinpoint the problem ?
Anyway, here is the code:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
def perlin(x,y,seed=0):
# permutation table
np.random.seed(seed)
p = np.arange(256,dtype=int)
np.random.shuffle(p)
p = np.stack([p,p]).flatten()
# coordinates of the first corner
xi = x.astype(int)
yi = y.astype(int)
# internal coordinates
xf = x - xi
yf = y - yi
# fade factors
u = fade(xf)
v = fade(yf)
# noise components
n00 = gradient(p[p[xi]+yi],xf,yf)
n01 = gradient(p[p[xi]+yi+1],xf,yf-1)
n11 = gradient(p[p[xi+1]+yi+1],xf-1,yf-1)
n10 = gradient(p[p[xi+1]+yi],xf-1,yf)
# combine noises
x1 = lerp(n00,n10,u)
x2 = lerp(n10,n11,u)
return lerp(x2,x1,v)
def lerp(a,b,x):
"linear interpolation"
return a + x * (b-a)
def fade(t):
"6t^5 - 15t^4 + 10t^3"
return 6 * t**5 - 15 * t**4 + 10 * t**3
def gradient(h,x,y):
"grad converts h to the right gradient vector and return the dot product with (x,y)"
vectors = np.array([[0,1],[0,-1],[1,0],[-1,0]])
g = vectors[h%4]
return g[:,:,0] * x + g[:,:,1] * y
lin = np.linspace(0,5,100,endpoint=False)
y,x = np.meshgrid(lin,lin)
plt.imshow(perlin(x,y,seed=0))
回答1:
Thanks to Paul Panzer and a good night of sleep it works now ...
def perlin(x,y,seed=0):
# permutation table
np.random.seed(seed)
p = np.arange(256,dtype=int)
np.random.shuffle(p)
p = np.stack([p,p]).flatten()
# coordinates of the top-left
xi = x.astype(int)
yi = y.astype(int)
# internal coordinates
xf = x - xi
yf = y - yi
# fade factors
u = fade(xf)
v = fade(yf)
# noise components
n00 = gradient(p[p[xi]+yi],xf,yf)
n01 = gradient(p[p[xi]+yi+1],xf,yf-1)
n11 = gradient(p[p[xi+1]+yi+1],xf-1,yf-1)
n10 = gradient(p[p[xi+1]+yi],xf-1,yf)
# combine noises
x1 = lerp(n00,n10,u)
x2 = lerp(n01,n11,u) # FIX1: I was using n10 instead of n01
return lerp(x1,x2,v) # FIX2: I also had to reverse x1 and x2 here
def lerp(a,b,x):
"linear interpolation"
return a + x * (b-a)
def fade(t):
"6t^5 - 15t^4 + 10t^3"
return 6 * t**5 - 15 * t**4 + 10 * t**3
def gradient(h,x,y):
"grad converts h to the right gradient vector and return the dot product with (x,y)"
vectors = np.array([[0,1],[0,-1],[1,0],[-1,0]])
g = vectors[h%4]
return g[:,:,0] * x + g[:,:,1] * y
lin = np.linspace(0,5,100,endpoint=False)
x,y = np.meshgrid(lin,lin) # FIX3: I thought I had to invert x and y here but it was a mistake
plt.imshow(perlin(x,y,seed=2),origin='upper')
来源:https://stackoverflow.com/questions/42147776/producing-2d-perlin-noise-with-numpy