from math import pi
import numpy as np
from PIL import Image as Img, ImageDraw as ID
import matplotlib.pyplot as plt

R = 64 # 圓的半徑r為1，放大為R
W = H = 2 * R + 16 # 圖片比圓大一圈以免有些線畫不全
N = 1_00_00 # 這么多次

# 圓心為原點，左上(-1, -1)，右下(1, 1)
# 輸入為原始坐標, N * [x0, y0, x1, y1]
# 畫圖時左上(0, 0)，右下(W, H)
def line (draw, a) :
  a = R - a * R + 8 # a = W - (a + 1) * R - 8
  for i in range(N):
    draw.line( ((a[i,0],a[i,1]), (a[i,2],a[i,3])), fill=255 )

def do_it (i) :
  img = Img.new('L', (W, H)) # 單色'1'比灰度'L'慢
  draw = ID.Draw(img)

  # AI說連續多次rand是均勻分布
  y = np.random.uniform(low=-1.0, high=1.0, size=N)
  x = np.sqrt(1 - y ** 2)
  if i == 0: a = np.column_stack((-x, y, x, y))
  else: # signs別用兩次！
    x *= np.random.choice([-1, 1], size=N)
    if i == 1:
      # (x,y)到(0,-1)
      a = np.column_stack((np.full_like(x, 0), np.full_like(y, -1),  x, y))
    else:
      y2 = np.random.uniform(low=-1.0, high=1.0, size=N)
      x2 = np.sqrt(1 - y2 ** 2) * np.random.choice([-1, 1], size=N)
      a = np.column_stack((x2, y2, x, y))

  line(draw, a); img.save(f'/t/{i}.png')

  # hypotenuse: 斜邊
  a = np.hypot(a[:,2] - a[:,0], a[:,3] - a[:,1])
  prob = np.sum(a > 3 ** 0.5) / N # 概率
  # 弦覆蓋圓嗎？
  print(prob, (img.histogram()[255] / R ** 2) / pi)

  return a, str(prob)

for i in range(3):
  a,p = do_it(i); plt.hist(a, bins=50, alpha=0.5, label=p)

plt.xlabel('Chord Length', fontsize=12)
plt.ylabel('Frequency', fontsize=12)
plt.xticks(rotation=45, fontsize=9)
plt.grid(axis='y', alpha=0.5) # 顯示網格
plt.tight_layout()
plt.legend()
plt.show()