获取离散点的拟合平面，并以离散点中心（位于拟合平面上）为中心，绘制正三角形，中心到各顶点距离为1

gistfile1.txt

import numpy as np

# 参考 https://blog.csdn.net/qq_45427038/article/details/100139330

# 获取离散点的拟合平面，并以离散点中心（位于拟合平面上）为中心，绘制正三角形，中心到各顶点距离为1

# 最少需要3个顶点
size = 10 

# 创建函数，用于生成不同属于一个平面的10个离散点
def not_all_in_plane(a, b, c):
    x = np.random.uniform(-10, 10, size=size)
    y = np.random.uniform(-10, 10, size=size)
    z = (a * x + b * y + c) + np.random.normal(-1, 1, size=size)
    return x, y, z
 
# 调用函数，生成离散点
x, y, z = not_all_in_plane(2, 5, 6)

a = np.ones((size, 3))
for i in range(0, size):
    a[i, 0] = x[i]
    a[i, 1] = y[i]
b = np.zeros((size, 1))
for i in range(0, size):
    b[i, 0] = z[i]
A_T = a.T
A1 = np.dot(A_T, a)
A2 = np.linalg.inv(A1)
A3 = np.dot(A2, A_T)
X = np.dot(A3, b)
print('平面拟合结果为：z = %.3f * x + %.3f * y + %.3f'%(X[0,0],X[1,0],X[2,0]))

matrix = np.mat([(x[i], y[i], z[i]) for i in range(0, size)])
co = np.mean(matrix, 0)
# 获取离散点的中心点
c = (co[0,0], co[0,1], X[0,0] * co[0,0] + X[1,0] * co[0,1] + X[2,0])

# 拟合平面的法向量
n = np.array([X[0,0], X[1,0], -1])    

a = np.cross(n, np.array([1,0,0]))
b = np.cross(n, a)
a = a / np.linalg.norm(a)
b = b / np.linalg.norm(b)

# 圆半径
r = 1
angle = np.array([0, 240, 120]) * np.pi/180
x = c[0] + r * a[0] * np.cos(angle) + r * b[0] * np.sin(angle)
y = c[1] + r * a[1] * np.cos(angle) + r * b[1] * np.sin(angle)
z = c[2] + r * a[2] * np.cos(angle) + r * b[2] * np.sin(angle)

print([(x[i], y[i], z[i]) for i in range(0, np.size(angle))])