import numpy as np

plt.rcParams['font.sans-serif'] = ['FangSong'] # 指定默认字体
plt.rcParams['axes.unicode_minus'] = False #解决中文显示为方块的问题

def rotate(p, d):
  """返回点p绕原点逆时针旋转d度的坐标"""
  
  a = np.radians(d)
  m = np.array([[np.cos(a), np.sin(a)],[-np.sin(a), np.cos(a)]])
  return np.dot(p, m)

def koch_curve(p, q):
  """将线段pq生成科赫曲线，返回uvw三个点"""
  
  p, q = np.array(p), np.array(q)
  u = p + (q-p)/3 # 三等分点u的坐标
  v = q - (q-p)/3 # 三等分点V的坐标
  w = rotate(v-u, 60) + u # 线段uv绕u点逆时针旋转60°得到点w的坐标
  
  return u.tolist(), v.tolist(), w.tolist()
  
def snow(triangle, k):
  """给定三角形，生成封闭的科赫雪花"""
  
  for i in range(k):
    result = list()
    t_len = len(triangle)
    for j in range(t_len):
      p = triangle[j]
      q = triangle[(j+1)%t_len]
      u, v, w = koch_curve(p, q)
      result.extend([p, u, w, v])
    triangle = result.copy()
  
  triangle.append(triangle[0])
  return triangle

import numpy as np
import matplotlib.pyplot as plt

def plot_snow(snow_list):
  """绘制雪花"""
  
  for triangle, k in snow_list:
    data = np.array(snow(triangle, k))
    x, y = np.split(data, 2, axis=1)
    plt.plot(x, y)
  
  plt.axis('equal') 
  plt.show()

snow_list = [
  ([(0,0), (0.5,0.8660254), (1,0)], 5),
  ([(1.1,0.4), (1.35,0.8330127), (1.6,0.4)], 4),
  ([(1.1,-0.1), (1.25,0.15980761), (1.4,-0.1)], 3)
]
plot_snow(snow_list)

import numpy as np
import matplotlib.pyplot as plt
from PIL import Image

def draw_scenery():
  """绘制雪景图"""
  
  im = Image.open('brage.png')
  bg = np.array(im)
  plt.imshow(bg) # 绘制背景图
  
  for i in range(80):
    x = np.random.randint(80, im.size[0]-80)
    y = np.random.randint(30, im.size[1]-30)
    r = np.random.randint(5, 20)
    a = np.random.random()*0.6 + 0.2
    v = np.array((x-r/2, y))
    u = np.array((x+r/2, y))
    w = rotate(v-u, 60) + u
    
    data = np.array(snow([(u[0],u[1]),(w[0],w[1]),(v[0],v[1])], 5))
    x, y = np.split(data, 2, axis=1)
    plt.plot(x, y, c='#AABBCC', lw=1, ls='-', alpha=a)
  
  plt.axis('equal') 
  plt.show()

draw_scenery()