plot_webmerc_to_wgs84.py

import math
import numpy as np
from matplotlib import pyplot as plt


def webMercatorToLngLat(mx: float, my: float) -> tuple[float, float]:
    lng = (mx * 2 - 1) * 180.0
    lat = (my * 2 - 1) * 180.0
    lat = (
        -180
        / np.pi
        * (2 * np.arctan(np.exp(lat * np.pi / 180.0)) - np.pi / 2.0)
    )
    return lng, lat


def make_rect(x1, y1, x2, y2):
    x_top = np.linspace(x1, x2, 20)
    y_top = np.linspace(y1, y1, 20)

    x_right = np.linspace(x2, x2, 20)
    y_right = np.linspace(y1, y2, 20)

    x_bottom = np.linspace(x2, x1, 20)
    y_bottom = np.linspace(y2, y2, 20)

    x_left = np.linspace(x1, x1, 20)
    y_left = np.linspace(y2, y1, 20)

    x_diag = np.linspace(x1, x2, 20)
    y_diag = np.linspace(y1, y2, 20)

    theta = np.linspace(0, 2 * np.pi, 200)
    x_circle = x1 + (x2 - x1) * (np.cos(theta) / 2 + 0.5)
    y_circle = y1 + (x2 - x1) * (np.sin(theta) / 2 + 0.5)

    x = np.concatenate((x_top, x_right, x_bottom, x_left, x_diag))
    y = np.concatenate((y_top, y_right, y_bottom, y_left, y_diag))

    mx, my = webMercatorToLngLat(x, y)
    mx_circle, my_circle = webMercatorToLngLat(x_circle, y_circle)

    fig = plt.figure()

    ax1 = fig.add_subplot(1, 2, 1)
    ax1.plot(x, y, 'b.-')
    ax1.plot(x_circle, y_circle, 'r.-')
    ax1.set_title("Web Mercator")
    ax1.invert_yaxis()

    ax2 = fig.add_subplot(1, 2, 2)
    ax2.plot(mx, my, 'b.-')
    ax2.plot(mx_circle, my_circle, 'r.-')
    ax2.set_title("WGS84")

    fig.tight_layout()
    plt.show()


print(make_rect(0.85, 0.30, 0.87, 0.32))