python实现点到平面的距离

太过爱你忘了你带给我的痛 2023-06-06 12:01 28阅读 0赞

# python实现点到平面的距离 #

--------------------

**目录**

python实现点到平面的距离

1.三点定面

2.点到面的距离

3.python实现点到面的距离

--------------------

关于点线面之间关系可以参考:[https://blog.csdn.net/qq\_23869697/article/details/82688277][https_blog.csdn.net_qq_23869697_article_details_82688277]

### 1.三点定面 ###

空间上任意三个不共线的点，可以确定一个平面，三点定面的例子：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9wYW5qaW5xdWFuLmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70][]

### 2.点到面的距离 ###

点到面的距离，可参考这个例子

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9wYW5qaW5xdWFuLmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70 1][]

### 3.python实现点到面的距离 ###

空间上不共线的三个点P1，P2，P3确定一个平面，计算空间上某个点P4到\{P1，P2，P3\}组成的平面的距离，可如下计算

import numpy as np
    
    def define_area(point1, point2, point3):
        """
        法向量    ：n={A,B,C}
        空间上某点：p={x0,y0,z0}
        点法式方程：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:数据框的行切片，三维
        :param point2:
        :param point3:
        :param point4:
        :return:点到面的距离
        """
        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__':
        # 初始化数据
        point1 = [2, 3, 1]
        point2 = [4, 1, 2]
        point3 = [6, 3, 7]
        point4 = [-5, -4, 8]
        # 计算点到面的距离
        d1 = point2area_distance(point1, point2, point3, point4)  # s=8.647058823529413
        print("点到面的距离s: " + str(d1))

[https_blog.csdn.net_qq_23869697_article_details_82688277]: https://blog.csdn.net/qq_23869697/article/details/82688277
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9wYW5qaW5xdWFuLmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70]: /images/20230601/5a4bd7b7d4ea4c93a76c2dc6370f59aa.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9wYW5qaW5xdWFuLmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70 1]: /images/20230601/01954be071e14099a01f2463c6db8ae9.png