使用 numpy 生成 2D perlin 噪声

Question

我正在尝试使用 numpy 生成 2D perlin 噪声，但我得到的不是平滑的东西：

可以肯定的是，我在某个地方混淆了我的尺寸，可能是当我结合四个梯度时......但我找不到它而且我的大脑现在正在融化。谁能帮我找出问题所在？

无论如何，这是代码：

%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))

Answer 1

感谢 Paul Panzer 和一夜安眠，它现在可以工作了......

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 top-left
    xi, yi = x.astype(int), y.astype(int)
    # internal coordinates
    xf, yf = x - xi, y - yi
    # fade factors
    u, v = fade(xf), 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

# EDIT : generating noise at multiple frequencies and adding them up
p = np.zeros((100,100))
for i in range(4):
    freq = 2**i
    lin = np.linspace(0, freq, 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
    p = perlin(x, y, seed=87) / freq + p

plt.imshow(p, origin='upper')

EDIT(2023)：这篇文章似乎很受欢迎，所以我重新审视了一下。之前，代码使用给定的种子以一个频率产生噪声。

在这个新版本中，我添加了不同频率和振幅的噪音。在这里，我使用的是频率

[1,2,4,8]

，振幅是频率的倒数。这样，低频定义了整体形状，而高频则增加了细节。