import matplotlib.pyplot as plt
from scipy.linalg import solve
import numpy as np
from matplotlib.patches import Circle

'''
求三角形外接圓和內(nèi)切圓
'''
# 畫個三角形
def plot_triangle(A, B, C):
  x = [A[0], B[0], C[0], A[0]]
  y = [A[1], B[1], C[1], A[1]]

  ax = plt.gca()
  ax.plot(x, y, linewidth=2)

# 畫個圓
def draw_circle(x, y, r):
  ax = plt.gca()
  cir = Circle(xy=(x, y), radius=r, alpha=0.5)
  ax.add_patch(cir)
  ax.plot()

# 外接圓
def get_outer_circle(A, B, C):
  xa, ya = A[0], A[1]
  xb, yb = B[0], B[1]
  xc, yc = C[0], C[1]

  # 兩條邊的中點
  x1, y1 = (xa + xb) / 2.0, (ya + yb) / 2.0
  x2, y2 = (xb + xc) / 2.0, (yb + yc) / 2.0

  # 兩條線的斜率
  ka = (yb - ya) / (xb - xa) if xb != xa else None
  kb = (yc - yb) / (xc - xb) if xc != xb else None

  alpha = np.arctan(ka) if ka != None else np.pi / 2
  beta = np.arctan(kb) if kb != None else np.pi / 2

  # 兩條垂直平分線的斜率
  k1 = np.tan(alpha + np.pi / 2)
  k2 = np.tan(beta + np.pi / 2)

  # 圓心
  y, x = solve([[1.0, -k1], [1.0, -k2]], [y1 - k1 * x1, y2 - k2 * x2])
  # 半徑
  r1 = np.sqrt((x - xa)**2 + (y - ya)**2)

  return(x, y, r1)

# 內(nèi)切圓
def get_inner_circle(A, B, C):
  xa, ya = A[0], A[1]
  xb, yb = B[0], B[1]
  xc, yc = C[0], C[1]

  ka = (yb - ya) / (xb - xa) if xb != xa else None
  kb = (yc - yb) / (xc - xb) if xc != xb else None

  alpha = np.arctan(ka) if ka != None else np.pi / 2
  beta = np.arctan(kb) if kb != None else np.pi / 2

  a = np.sqrt((xb - xc)**2 + (yb - yc)**2)
  b = np.sqrt((xa - xc)**2 + (ya - yc)**2)
  c = np.sqrt((xa - xb)**2 + (ya - yb)**2)

  ang_a = np.arccos((b**2 + c**2 - a**2) / (2 * b * c))
  ang_b = np.arccos((a**2 + c**2 - b**2) / (2 * a * c))

  # 兩條角平分線的斜率
  k1 = np.tan(alpha + ang_a / 2)
  k2 = np.tan(beta + ang_b / 2)
  kv = np.tan(alpha + np.pi / 2)

  # 求圓心
  y, x = solve([[1.0, -k1], [1.0, -k2]], [ya - k1 * xa, yb - k2 * xb])
  ym, xm = solve([[1.0, -ka], [1.0, -kv]], [ya - ka * xa, y - kv * x])
  r1 = np.sqrt((x - xm)**2 + (y - ym)**2)

  return(x, y, r1)

if __name__ == '__main__':
  A = (1., 1.)
  B = (5., 2.)
  C = (5., 5.)

  plt.axis('equal')
  plt.axis('off')
  plot_triangle(A, B, C)

  x, y, r1 = get_outer_circle(A, B, C)
  plt.plot(x, y, 'ro')
  draw_circle(x, y, r1)

  x_inner, y_inner, r_inner = get_inner_circle(A, B, C)
  plt.plot(x_inner, y_inner, 'ro')
  draw_circle(x_inner, y_inner, r_inner)

  plt.show()