利用Python求阴影部分的面积实例代码

import matplotlib.pyplot as plt
import numpy as np


def init():
 plt.xlabel('X')
 plt.ylabel('Y')

 fig = plt.gcf()
 fig.set_facecolor('lightyellow')
 fig.set_edgecolor("black")

 ax = plt.gca()
 ax.patch.set_facecolor("lightgray") # 设置ax区域背景颜色    
 ax.patch.set_alpha(0.1) # 设置ax区域背景颜色透明度 
 ax.spines['right'].set_color('none')
 ax.spines['top'].set_color('none')
 ax.xaxis.set_ticks_position('bottom')
 ax.yaxis.set_ticks_position('left')
 ax.spines['bottom'].set_position(('data', 0))
 ax.spines['left'].set_position(('data', 0))


# 原下半函数
def f1(px, r, a, b):
 return b - np.sqrt(r**2 - (px - a)**2)


# 斜线函数
def f2(px, m, n):
 return px*n/m


# 斜线函数2
def f3(px, m, n):
 return n-1*px*n/m


if __name__ == '__main__':
 r = 4 # 圆半径
 m = 8 # 宽
 n = 4 # 高
 a, b = (4, 4) # 圆心坐标
 init()

 x = np.linspace(0, m, 100*m)
 y = np.linspace(0, n, 100*n)

 # 半圆形
 y1 = f1(x, r, a, b)
 plt.plot(x, y1)
 # 矩形横线
 plt.plot((x.min(), x.max()), (y.min(), y.min()), 'g')
 plt.plot((x.min(), x.max()), (y.max(), y.max()), 'g')
 plt.plot((x.max(), x.max()), (y.max()+2, y.max()+2), 'g') # 画点（8,6）避免图形变形
 # 矩形纵向
 plt.plot((x.min(), x.min()), (y.min(), y.max()), 'g')
 plt.plot((x.max(), x.max()), (y.min(), y.max()), 'g')
 # 斜线方法
 y2 = f2(x, m, n)
 plt.plot(x, y2, 'purple')

 # 阴影部分填充
 xf = x[np.where(x <= 0.5*x.max())]
 plt.fill_between(xf, y.min(), f1(xf, r, a, b), where=f1(xf, r, a, b) <= f2(xf, m, n),
      facecolor='y', interpolate=True)
 plt.fill_between(xf, y.min(), f2(xf, m, n), where=f1(xf, r, a, b) > f2(xf, m, n),
      facecolor='y', interpolate=True)
 # 半圆填充
 plt.fill_between(x, y1, y.max(), facecolor='r', alpha=0.25)
 plt.show()

Draw.py

import numpy as np


def f1(px, r, a, b):
 return b - np.sqrt(r**2 - (px - a)**2)


def f2(px, m, n):
 return px*n/m


if __name__ == '__main__':
 r = 4 # 圆半径
 m = 8 # 宽
 n = 4 # 高
 a, b = (4, 4) # 圆心坐标
 t = 100 # 精度

 xs = np.linspace(0, m, 2*t*m)
 ys = np.linspace(0, n, t*n)

 # 半圆形
 y1 = f1(xs, r, a, b)
 # 斜线
 y2 = f2(xs, m, n)

 numin = 0
 numtotel = 0
 side = True # 是否计算边框
 for x in xs:
  for y in ys:
   if not side:
    if (x <= 0) | (x >= 8) | (y <= 0) | (y >= 4):
     continue
   numtotel += 1
   if x >= 4:
    continue
   y1 = f1(x, r, a, b)
   y2 = f2(x, m, n)
   if y1 - y2 >= 0:
    if y2 - y > 0:
     numin += 1
    if (y2 - y == 0) and side:
     numin += 1
   elif y2 - y1 > 0:
    if y1 - y > 0:
     numin += 1
    if (y2 - y == 0) and side:
     numin += 1

 print(32*numin/numtotel)

calc.py