Point to plane projection

Algorithm principle ：

1. Find the direction vector from the point on the plane to the point outside the plane ：

v = point-orig（ In each dimension ）;

2. Compare the point of the vector with the unit normal vector n Obtain the projection distance by dot multiplication ：

dist = vx*nx + vy*ny + vz*nz;dist # The distance from the point to the plane 

3. Multiply the unit normal vector by the distance , Then subtract the vector from the point outside the plane to obtain the projection point .

projected_point = point -dist*normal;

Above picture ： Red as v;dist It's blue and green in length , be equal to v Point multiplication normal. Blue is normal*dist. Green is the same as blue , They are just drawn in different places . To find the Planar_xyz, Please start at , Then subtract the green vector .

Code implementation ：

import numpy as np

point_in_plane = np.array([0, 0, 0])
normal_in_plane = np.array([0, 13, 1])
points = np.array([1, 1, 1])


def ProjectPointsToPlane(point_in_plane, normal_in_plane, points):
    v = points - point_in_plane
    normalized_normal_in_plane = normal_in_plane / np.linalg.norm(normal_in_plane)
    dist = v.dot(normalized_normal_in_plane)
    projected_points = (points - dist * normalized_normal_in_plane)

    return projected_points


ProjectPointsToPlane(point_in_plane, normal_in_plane, points)