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| import numpy as np from scipy.linalg import solve import matplotlib.pyplot as plt from matplotlib.patches import Circle
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)
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()
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]
x1, y1 = (xa + xb) / 2.0, (ya + yb) / 2.0 x2, y2 = (xb + xc) / 2.0, (yb + yc) / 2.0
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
k1 = np.tan(alpha + np.pi / 2) k2 = np.tan(beta + np.pi / 2)
y, x = solve([[1.0, -k1], [1.0, -k2]], [y1 - k1 * x1, y2 - k2 * x2]) r1 = np.sqrt((x - xa)**2 + (y - ya)**2)
return(x, y, r1)
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))
k1 = np.tan(alpha + ang_a / 2) k2 = np.tan(beta + ang_b / 2) kv = np.tan(alpha + np.pi / 2)
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()
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