Naive total perpendicular distance from points to plane

perp_distance.py

import numpy as np
import math


# ############################################################
# unutbu's model() (https://stackoverflow.com/a/35118683/27358)

def model(params, xyz):
    a, b, c, d = params
    x, y, z = xyz
    length = math.sqrt(a ** 2 + b ** 2 + c ** 2)
    return ((np.abs(a * x + b * y + c * z + d)) ** 2).sum() / length


# ############################################################
# naive implementation

def z_from(x, y, abcd):
    """Returns the z coordinate from a pair of (x, y) coordinates
    and a list of coefficients in the form ax + by + cz + d = 0.
    """
    a, b, c, d = abcd
    return (a * x + b * y + d) / -c


# see https://mathinsight.org/distance_point_plane
def unit_normal_vector(abcd):
    a, b, c, d = abcd
    n = np.array([a, b, c])
    len_n = (a ** 2 + b ** 2 + c ** 2) ** .5
    return n / len_n


# see https://mathinsight.org/distance_point_plane
def dist_point_plane(point, abcd):
    x0, y0, z0 = np.array([0, 0, z_from(0, 0, abcd)])
    x1, y1, z1 = point
    n = unit_normal_vector(abcd)
    v = np.array([x1 - x0, y1 - y0, z1 - z0])
    d = np.abs(np.dot(v, n))
    return d


def total_dist_plane_points(abcd, xyz):
    total = 0
    for i, x in enumerate(xyz[0]):
        y, z = xyz[1][i], xyz[2][i]
        point = [x, y, z]
        total = total + dist_point_plane(point, abcd)
    return total


# ############################################################
# Main program

# points (2, 4, 6), (8, 10, 12), (14, 16, 18)
xyz = [
    [2, 8, 14],
    [4, 10, 16],
    [6, 12, 18]
]
# x + 2y + 3z + 4 = 0
abcd = np.array([1, 2, 3, 4])

expected = total_dist_plane_points(abcd, xyz)
actual = model(abcd, xyz)

print(f"Expected: {expected}")
print(f"Actual:   {actual}")

# =>
# Expected: 54.52129335013458
# Actual:   1160.9828348675715