Rayne

<?php

define('BOT_TOKEN', 'XXXXXXXX:XXXXXXXXXXXXXXXXXXXXXXXX'); // place bot token of your bot here

function checkTelegramAuthorization($auth_data) {
  $check_hash = $auth_data['hash'];
  unset($auth_data['hash']);
  $data_check_arr = [];
  foreach ($auth_data as $key => $value) {
    $data_check_arr[] = $key . '=' . $value;

Rayne

Conventions

• A = [xA, yA] is a point on the 2D plane. Same for B, C, ...
• lengths are in any unit (ex: pixels)
• code snippets are in JavaScript

Degrees to radians

angleRad = angleDeg * Math.PI / 180;