Spherical geometry utility class for WME scripts
此脚本不应直接安装。它是供其他脚本使用的外部库，要使用该库请加入元指令 // @require https://update.greasyfork.org/scripts/571719/1793257/GeoUtils.js
// ==UserScript==
// @name GeoUtils
// @description Spherical geometry utility class for WME scripts
// @author Anton Shevchuk
// @license MIT License
// @version 0.0.1
// @match *://*/*
// @grant none
// @namespace https://greasyfork.org/users/227648
// ==/UserScript==
(function () {
'use strict';
/**
* A utility class for spherical geometry (geodesy).
*
* All coordinates use [longitude, latitude] order in degrees.
* Distances are in meters unless noted otherwise.
* Bearings are in degrees (0-360, clockwise from north).
* Angular distances are in radians.
*
* @example
* // Distance between Kyiv and London
* GeoUtils.getDistance([30.52, 50.45], [-0.13, 51.51]) // ~2131 km
*
* // Bearing from Kyiv to London
* GeoUtils.getBearing([30.52, 50.45], [-0.13, 51.51]) // ~289°
*/
class GeoUtils {
/**
* Convert degrees to radians.
* @param degrees - Angle in degrees
* @returns Angle in radians
*/
static _toRadians(degrees) {
return degrees * (Math.PI / 180);
}
/**
* Convert radians to degrees.
* @param radians - Angle in radians
* @returns Angle in degrees
*/
static _toDegrees(radians) {
return radians * (180 / Math.PI);
}
/**
* Normalize an angle to the range [-180, 180] degrees.
* @param degrees - Angle in degrees (any range)
* @returns Normalized angle in degrees
*/
static _normalizeAngle(degrees) {
return (degrees + 540) % 360 - 180;
}
/**
* Calculate the initial bearing (forward azimuth) from point A to point B.
*
* @param pA - Start point [lon, lat]
* @param pB - End point [lon, lat]
* @returns Bearing in degrees (0-360, clockwise from north)
*
* @example
* GeoUtils.getBearing([0, 0], [0, 1]) // 0 (due north)
* GeoUtils.getBearing([0, 0], [1, 0]) // 90 (due east)
*/
static getBearing(pA, pB) {
const latA = GeoUtils._toRadians(pA[1]);
const lonA = GeoUtils._toRadians(pA[0]);
const latB = GeoUtils._toRadians(pB[1]);
const lonB = GeoUtils._toRadians(pB[0]);
const deltaLon = lonB - lonA;
const y = Math.sin(deltaLon) * Math.cos(latB);
const x = Math.cos(latA) * Math.sin(latB) -
Math.sin(latA) * Math.cos(latB) * Math.cos(deltaLon);
const bearingRad = Math.atan2(y, x);
return (GeoUtils._toDegrees(bearingRad) + 360) % 360;
}
/**
* Calculate the interior angle at vertex p2 formed by points p1-p2-p3.
*
* @param p1 - First point [lon, lat]
* @param p2 - Vertex point [lon, lat]
* @param p3 - Third point [lon, lat]
* @returns Angle in degrees (0-180)
*
* @example
* // Right angle
* GeoUtils.findAngle([0, 0], [0, 1], [1, 1]) // ~90°
*
* // Straight line
* GeoUtils.findAngle([0, 0], [0, 1], [0, 2]) // ~180°
*/
static findAngle(p1, p2, p3) {
const bearing21 = GeoUtils.getBearing(p2, p1);
const bearing23 = GeoUtils.getBearing(p2, p3);
let angle = Math.abs(bearing21 - bearing23);
if (angle > 180) {
angle = 360 - angle;
}
return angle;
}
/**
* Calculate the distance between two points using the Haversine formula.
*
* @param pA - First point [lon, lat]
* @param pB - Second point [lon, lat]
* @returns Distance in meters
*
* @example
* GeoUtils.getDistance([30.52, 50.45], [-0.13, 51.51]) // ~2131000 m
*/
static getDistance(pA, pB) {
return GeoUtils.getAngularDistance(pA, pB) * 6371000;
}
/**
* Calculate the angular distance between two points using the Haversine formula.
*
* @param pA - First point [lon, lat]
* @param pB - Second point [lon, lat]
* @returns Angular distance in radians
*/
static getAngularDistance(pA, pB) {
const latA = GeoUtils._toRadians(pA[1]);
const lonA = GeoUtils._toRadians(pA[0]);
const latB = GeoUtils._toRadians(pB[1]);
const lonB = GeoUtils._toRadians(pB[0]);
const deltaLat = latB - latA;
const deltaLon = lonB - lonA;
const a = Math.sin(deltaLat / 2) * Math.sin(deltaLat / 2) +
Math.cos(latA) * Math.cos(latB) *
Math.sin(deltaLon / 2) * Math.sin(deltaLon / 2);
return 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
}
/**
* Calculate the destination point given a start point, bearing, and angular distance.
*
* @param startPoint - Start point [lon, lat]
* @param bearing - Bearing in degrees (0-360)
* @param distanceRad - Angular distance in radians
* @returns Destination point [lon, lat]
*
* @example
* // Move 100km north from equator
* const dist = 100000 / 6371000; // convert meters to radians
* GeoUtils.getDestination([0, 0], 0, dist) // [0, ~0.9]
*/
static getDestination(startPoint, bearing, distanceRad) {
const lat1 = GeoUtils._toRadians(startPoint[1]);
const lon1 = GeoUtils._toRadians(startPoint[0]);
const brng = GeoUtils._toRadians(bearing);
const d = distanceRad;
const lat2 = Math.asin(Math.sin(lat1) * Math.cos(d) +
Math.cos(lat1) * Math.sin(d) * Math.cos(brng));
const lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(d) * Math.cos(lat1), Math.cos(d) - Math.sin(lat1) * Math.sin(lat2));
const lon2Deg = GeoUtils._toDegrees(lon2);
const lat2Deg = GeoUtils._toDegrees(lat2);
return [(lon2Deg + 540) % 360 - 180, lat2Deg];
}
/**
* Find a point D on the great circle path A→B such that
* the angle ADC equals the specified angle.
*
* Uses the Four-Part (Cotangent) Formula for spherical triangles.
*
* @param pA - Start of line [lon, lat]
* @param pB - End of line [lon, lat]
* @param pC - Third point [lon, lat]
* @param angle - Desired angle at D in degrees (e.g., 90 for perpendicular)
* @returns Coordinates of D [lon, lat], or null if no solution exists
*
* @example
* // Find where line AB makes a 90° angle with point C
* GeoUtils.findIntersection(A, B, C, 90)
*/
static findIntersection(pA, pB, pC, angle) {
// Guard: degenerate angle (0° or 180°) makes cot(D) undefined
if (angle % 180 === 0) {
return null;
}
const angleRad = GeoUtils._toRadians(angle);
const bearingAB = GeoUtils.getBearing(pA, pB);
const bearingAC = GeoUtils.getBearing(pA, pC);
const angleA_rad = GeoUtils._toRadians(bearingAC - bearingAB);
const distb_rad = GeoUtils.getAngularDistance(pA, pC);
// Guard: pA and pC are the same point — cot(b) is undefined
if (distb_rad < 1e-12) {
return null;
}
const cot_b = 1.0 / Math.tan(distb_rad);
const cot_D = 1.0 / Math.tan(angleRad);
const X = cot_b;
const Y = Math.cos(angleA_rad);
const Z = Math.sin(angleA_rad) * cot_D;
const R = Math.hypot(X, Y);
const phi = Math.atan2(Y, X);
const sin_c_minus_phi = Z / R;
if (Math.abs(sin_c_minus_phi) > 1) {
return null;
}
const distAD_rad = phi + Math.asin(sin_c_minus_phi);
return GeoUtils.getDestination(pA, bearingAB, distAD_rad);
}
/**
* Find the perpendicular foot from point C onto the great circle
* defined by points A and B. The resulting point D forms a right
* angle (90°) at vertex D in triangle ADC.
*
* Uses Napier's Rules for right spherical triangles.
*
* @param pA - First point of the line [lon, lat]
* @param pB - Second point of the line [lon, lat] (defines angle at A)
* @param pC - Point to project [lon, lat]
* @returns Coordinates of D [lon, lat] — the perpendicular foot
*
* @example
* // Project point C onto line AB
* const foot = GeoUtils.findRightAngleIntersection(A, B, C)
* GeoUtils.findAngle(A, foot, C) // ~90°
*/
static findRightAngleIntersection(pA, pB, pC) {
const angleA_deg = GeoUtils.findAngle(pB, pA, pC);
const angleA_rad = GeoUtils._toRadians(angleA_deg);
const distAC_rad = GeoUtils.getAngularDistance(pA, pC);
const tan_c = Math.cos(angleA_rad) * Math.tan(distAC_rad);
const distAD_rad = Math.abs(Math.atan(tan_c));
const bearingAC_deg = GeoUtils.getBearing(pA, pC);
const bearingAB_deg = GeoUtils.getBearing(pA, pB);
const angleCAB_raw_diff = GeoUtils._normalizeAngle(bearingAC_deg - bearingAB_deg);
let bearingAD_deg;
if (angleCAB_raw_diff >= 0) {
bearingAD_deg = GeoUtils._normalizeAngle(bearingAC_deg - angleA_deg);
}
else {
bearingAD_deg = GeoUtils._normalizeAngle(bearingAC_deg + angleA_deg);
}
return GeoUtils.getDestination(pA, bearingAD_deg, distAD_rad);
}
}
Object.assign(window, { GeoUtils });
})();