python實作點到平面的距離
目錄
python實作點到平面的距離
1.三點定面
2.點到面的距離
3.python實作點到面的距離
關于點線面之間關系可以參考:平面方程與點到平面的距離_西檬飯_點到平面距離
1.三點定面
空間上任意三個不共線的點,可以确定一個平面,三點定面的例子:
2.點到面的距離
3.python實作點到面的距離
import numpy as np
def define_area(point1, point2, point3):
"""
法向量 :n={A,B,C}
空間上某點:p={x0,y0,z0}
點法式方程:A(x-x0)+B(y-y0)+C(z-z0)=Ax+By+Cz-(Ax0+By0+Cz0)
https://wenku.baidu.com/view/12b44129af45b307e87197e1.html
:param point1:
:param point2:
:param point3:
:param point4:
:return:(Ax, By, Cz, D)代表:Ax + By + Cz + D = 0
"""
point1 = np.asarray(point1)
point2 = np.asarray(point2)
point3 = np.asarray(point3)
AB = np.asmatrix(point2 - point1)
AC = np.asmatrix(point3 - point1)
N = np.cross(AB, AC) # 向量叉乘,求法向量
# Ax+By+Cz
Ax = N[0, 0]
By = N[0, 1]
Cz = N[0, 2]
D = -(Ax * point1[0] + By * point1[1] + Cz * point1[2])
return Ax, By, Cz, D
def point2area_distance(point1, point2, point3, point4):
"""
:param point1:資料框的行切片,三維
:param point2:
:param point3:
:param point4:
:return:點到面的距離
"""
Ax, By, Cz, D = define_area(point1, point2, point3)
mod_d = Ax * point4[0] + By * point4[1] + Cz * point4[2] + D
mod_area = np.sqrt(np.sum(np.square([Ax, By, Cz])))
d = abs(mod_d) / mod_area
return d
if __name__ == '__main__':
# 初始化資料
point1 = [2, 3, 1]
point2 = [4, 1, 2]
point3 = [6, 3, 7]
point4 = [-5, -4, 8]
# 計算點到面的距離
d1 = point2area_distance(point1, point2, point3, point4) # s=8.647058823529413
print("點到面的距離s: " + str(d1))