project 3D point to certain plane with parameter A, B, C (w.r.t. Ax+By+Cz=1)

project_points

def project_points(x, y, z, a, b, c):
    """
    Projects the points with coordinates x, y, z onto the plane
    defined by a*x + b*y + c*z = 1
    """
    vector_norm = a * a + b * b + c * c
    normal_vector = np.array([a, b, c]) / np.sqrt(vector_norm)
    point_in_plane = np.array([a, b, c]) / vector_norm

    points = np.column_stack((x, y, z))
    points_from_point_in_plane = points - point_in_plane
    proj_onto_normal_vector = np.dot(points_from_point_in_plane,
                                     normal_vector)
    proj_onto_plane = (points_from_point_in_plane -
                       proj_onto_normal_vector[:, None] * normal_vector)

    return point_in_plane + proj_onto_plane