Add latitude, longitude to Berlin-Center network

[michael-markl]

Hi there.

This adds (actual) coordinates in the form of latitude, longitude to the Berlin-Center network.

Method

We (@philippwarode and me), annotated some coordinates manually to map from the existing X and Y coordinates to latitude and longitude.

The following script does the conversion (using a "least squared" projection):

import pandas as pd
import numpy as np

file_path = "berlin-center_node.tntp"
df = pd.read_csv(file_path, sep='\\s+', names=["Node", "X", "Y"], header=0, index_col=False)


point_pairs = [
    (
        (30.3472, 15.5548),
        (52.48451118111, 13.4795021186)
    ),
    (
        (15.0876, 23.8881),
        (52.6089911679386, 13.12120813435784)
    ),
    (
        (21.9021, 5.9863),
        (52.3486098110478, 13.27550789714637)
    ),
    (
        (22.5198, 16.915),
        (52.5064096135837, 13.294727326071)
    ),
    (
        (29.1741, 20.9011),
        (52.56221199420036, 13.45425618012204)
    )
]

def compute_transformation_matrix():
    # Calculate the coefficients for the affine transformation
    A = np.array([(x,y,1) for ((x,y), _) in point_pairs])
    B = np.array([latlon for (_, latlon) in point_pairs])

    # Solve for the transformation matrix
    solution, residuals, rank, singular_values = np.linalg.lstsq(A, B, rcond=None)
    return solution

transformation_matrix = compute_transformation_matrix()
print("Transformation Matrix:\n", transformation_matrix)

def transform_xy_to_lat_lon(point):
    # Apply the transformation
    x, y = point
    lat = transformation_matrix[0, 0] * x + transformation_matrix[1, 0] * y + transformation_matrix[2, 0]
    lon = transformation_matrix[0, 1] * x + transformation_matrix[1, 1] * y + transformation_matrix[2, 1]

    # We round the numbers to avoid bloating the file.
    # We round to 7 decimals since the input has 6 significant digits, and the whole number part and the first 
    # decimal of both latitude and longitude are mostly constant.
    lat = round(lat, 7)
    lon = round(lon, 7)

    return lat, lon

# Apply the transformation to the x, y coordinates in the DataFrame
df["Lat"], df["Lon"] = zip(*df[["X", "Y"]].apply(transform_xy_to_lat_lon, axis=1))

# Append a column with header ";" and fill it with ";" for the TNTP format
df.insert(5, ";", ";")

df.to_csv("berlin-center_node_fixed.tntp", sep='\t', index=False)

This is the printed transformation matrix:

 [[-2.64907129e-04  2.37143766e-02]
 [ 1.44469375e-02  4.14005018e-04]
 [ 5.22679252e+01  1.27535993e+01]]

Result

Here's an image that shows the mapped coordinates on top of the OSM map.

And here a cropped image, with a smaller region.