法向量是通过平面上两个向量的叉积计算得出的,因此应该垂直于平面。但是从图中可以看出,用quiver
产生的法向量不垂直。
是平面计算有误,还是我的法向量或绘制法向量的方法有误?
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
points = [[3.2342, 1.8487, -1.8186],
[2.9829, 1.6434, -1.8019],
[3.4247, 1.5550, -1.8093]]
p0, p1, p2 = points
x0, y0, z0 = p0
x1, y1, z1 = p1
x2, y2, z2 = p2
ux, uy, uz = u = [x1-x0, y1-y0, z1-z0] #first vector
vx, vy, vz = v = [x2-x0, y2-y0, z2-z0] #sec vector
u_cross_v = [uy*vz-uz*vy, uz*vx-ux*vz, ux*vy-uy*vx] #cross product
point = np.array(p1)
normal = np.array(u_cross_v)
d = -point.dot(normal)
print('plane equation:\n{:1.4f}x + {:1.4f}y + {:1.4f}z + {:1.4f} = 0'.format(normal[0], normal[1], normal[2], d))
xx, yy = np.meshgrid(range(10), range(10))
z = (-normal[0] * xx - normal[1] * yy - d) * 1. / normal[2]
# plot the surface
plt3d = plt.figure().gca(projection='3d')
plt3d.quiver(x0, y0, z0, normal[0], normal[1], normal[2], color="m")
plt3d.plot_surface(xx, yy, z)
plt3d.set_xlabel("X", color='red', size=18)
plt3d.set_ylabel("Y", color='green', size=18)
plt3d.set_zlabel("Z", color='b', size=18)
plt.show()