496 lines
17 KiB
JavaScript
496 lines
17 KiB
JavaScript
"use strict";
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// This file is part of Leaflet.Geodesic.
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// Copyright (C) 2017 Henry Thasler
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// based on code by Chris Veness Copyright (C) 2014 https://github.com/chrisveness/geodesy
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//
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// Leaflet.Geodesic is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// Leaflet.Geodesic is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with Leaflet.Geodesic. If not, see <http://www.gnu.org/licenses/>.
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/** Extend Number object with method to convert numeric degrees to radians */
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if (typeof Number.prototype.toRadians === "undefined") {
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Number.prototype.toRadians = function() {
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return this * Math.PI / 180;
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};
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}
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/** Extend Number object with method to convert radians to numeric (signed) degrees */
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if (typeof Number.prototype.toDegrees === "undefined") {
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Number.prototype.toDegrees = function() {
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return this * 180 / Math.PI;
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};
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}
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var INTERSECT_LNG = 179.999; // Lng used for intersection and wrap around on map edges
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L.Geodesic = L.Polyline.extend({
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options: {
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color: "blue",
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steps: 10,
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dash: 1,
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wrap: true
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},
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initialize: function(latlngs, options) {
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this.options = this._merge_options(this.options, options);
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this.options.dash = Math.max(1e-3, Math.min(1, parseFloat(this.options.dash) || 1));
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this.datum = {};
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this.datum.ellipsoid = {
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a: 6378137,
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b: 6356752.3142,
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f: 1 / 298.257223563
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}; // WGS-84
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this._latlngs = this._generate_Geodesic(latlngs);
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L.Polyline.prototype.initialize.call(this, this._latlngs, this.options);
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},
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setLatLngs: function(latlngs) {
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this._latlngs = this._generate_Geodesic(latlngs);
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L.Polyline.prototype.setLatLngs.call(this, this._latlngs);
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},
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/**
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* Calculates some statistic values of current geodesic multipolyline
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* @returns (Object} Object with several properties (e.g. overall distance)
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*/
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getStats: function() {
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let obj = {
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distance: 0,
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points: 0,
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polygons: this._latlngs.length
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}, poly, points;
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for (poly = 0; poly < this._latlngs.length; poly++) {
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obj.points += this._latlngs[poly].length;
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for (points = 0; points < (this._latlngs[poly].length - 1); points++) {
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obj.distance += this._vincenty_inverse(this._latlngs[poly][points],
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this._latlngs[poly][points + 1]).distance;
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}
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}
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return obj;
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},
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/**
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* Creates geodesic lines from geoJson. Replaces all current features of this instance.
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* Supports LineString, MultiLineString and Polygon
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* @param {Object} geojson - geosjon as object.
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*/
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geoJson: function(geojson) {
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let normalized = L.GeoJSON.asFeature(geojson);
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let features = normalized.type === "FeatureCollection" ? normalized.features : [
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normalized
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];
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this._latlngs = [];
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for (let feature of features) {
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let geometry = feature.type === "Feature" ? feature.geometry :
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feature,
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coords = geometry.coordinates;
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switch (geometry.type) {
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case "LineString":
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this._latlngs.push(this._generate_Geodesic([L.GeoJSON.coordsToLatLngs(
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coords, 0)]));
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break;
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case "MultiLineString":
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case "Polygon":
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this._latlngs.push(this._generate_Geodesic(L.GeoJSON.coordsToLatLngs(
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coords, 1)));
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break;
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case "Point":
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case "MultiPoint":
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console.log("Dude, points can't be drawn as geodesic lines...");
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break;
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default:
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console.log("Drawing " + geometry.type +
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" as a geodesic is not supported. Skipping...");
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}
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}
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L.Polyline.prototype.setLatLngs.call(this, this._latlngs);
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},
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/**
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* Creates a great circle. Replaces all current lines.
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* @param {Object} center - geographic position
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* @param {number} radius - radius of the circle in metres
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*/
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createCircle: function(center, radius) {
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let polylineIndex = 0;
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let prev = {
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lat: 0,
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lng: 0,
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brg: 0
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};
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let step;
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this._latlngs = [];
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this._latlngs[polylineIndex] = [];
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let direct = this._vincenty_direct(L.latLng(center), 0, radius, this.options
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.wrap);
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prev = L.latLng(direct.lat, direct.lng);
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this._latlngs[polylineIndex].push(prev);
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for (step = 1; step <= this.options.steps;) {
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direct = this._vincenty_direct(L.latLng(center), 360 / this.options
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.steps * step, radius, this.options.wrap);
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let gp = L.latLng(direct.lat, direct.lng);
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if (Math.abs(gp.lng - prev.lng) > 180) {
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let inverse = this._vincenty_inverse(prev, gp);
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let sec = this._intersection(prev, inverse.initialBearing, {
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lat: -89,
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lng: ((gp.lng - prev.lng) > 0) ? -INTERSECT_LNG : INTERSECT_LNG
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}, 0);
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if (sec) {
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this._latlngs[polylineIndex].push(L.latLng(sec.lat, sec.lng));
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polylineIndex++;
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this._latlngs[polylineIndex] = [];
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prev = L.latLng(sec.lat, -sec.lng);
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this._latlngs[polylineIndex].push(prev);
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} else {
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polylineIndex++;
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this._latlngs[polylineIndex] = [];
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this._latlngs[polylineIndex].push(gp);
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prev = gp;
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step++;
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}
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} else {
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this._latlngs[polylineIndex].push(gp);
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prev = gp;
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step++;
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}
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}
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L.Polyline.prototype.setLatLngs.call(this, this._latlngs);
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},
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/**
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* Creates a geodesic Polyline from given coordinates
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* Note: dashed lines are under work
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* @param {Object} latlngs - One or more polylines as an array. See Leaflet doc about Polyline
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* @returns (Object} An array of arrays of geographical points.
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*/
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_generate_Geodesic: function(latlngs) {
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let _geo = [], _geocnt = 0;
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for (let poly = 0; poly < latlngs.length; poly++) {
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_geo[_geocnt] = [];
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let prev = L.latLng(latlngs[poly][0]);
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for (let points = 0; points < (latlngs[poly].length - 1); points++) {
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// use prev, so that wrapping behaves correctly
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let pointA = prev;
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let pointB = L.latLng(latlngs[poly][points + 1]);
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if (pointA.equals(pointB)) {
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continue;
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}
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let inverse = this._vincenty_inverse(pointA, pointB);
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_geo[_geocnt].push(prev);
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for (let s = 1; s <= this.options.steps;) {
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let distance = inverse.distance / this.options.steps;
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// dashed lines don't go the full distance between the points
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let dist_mult = s - 1 + this.options.dash;
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let direct = this._vincenty_direct(pointA, inverse.initialBearing, distance*dist_mult, this.options.wrap);
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let gp = L.latLng(direct.lat, direct.lng);
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if (Math.abs(gp.lng - prev.lng) > 180) {
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let sec = this._intersection(pointA, inverse.initialBearing, {
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lat: -89,
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lng: ((gp.lng - prev.lng) > 0) ? -INTERSECT_LNG : INTERSECT_LNG
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}, 0);
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if (sec) {
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_geo[_geocnt].push(L.latLng(sec.lat, sec.lng));
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_geocnt++;
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_geo[_geocnt] = [];
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prev = L.latLng(sec.lat, -sec.lng);
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_geo[_geocnt].push(prev);
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} else {
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_geocnt++;
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_geo[_geocnt] = [];
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_geo[_geocnt].push(gp);
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prev = gp;
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s++;
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}
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} else {
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_geo[_geocnt].push(gp);
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// Dashed lines start a new line
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if (this.options.dash < 1){
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_geocnt++;
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// go full distance this time, to get starting point for next line
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let direct_full = this._vincenty_direct(pointA, inverse.initialBearing, distance*s, this.options.wrap);
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_geo[_geocnt] = [];
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prev = L.latLng(direct_full.lat, direct_full.lng);
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_geo[_geocnt].push(prev);
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}
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else prev = gp;
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s++;
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}
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}
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}
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_geocnt++;
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}
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return _geo;
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},
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/**
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* Vincenty direct calculation.
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* based on the work of Chris Veness (https://github.com/chrisveness/geodesy)
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*
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* @private
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* @param {number} initialBearing - Initial bearing in degrees from north.
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* @param {number} distance - Distance along bearing in metres.
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* @returns (Object} Object including point (destination point), finalBearing.
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*/
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_vincenty_direct: function(p1, initialBearing, distance, wrap) {
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var φ1 = p1.lat.toRadians(),
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λ1 = p1.lng.toRadians();
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var α1 = initialBearing.toRadians();
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var s = distance;
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var a = this.datum.ellipsoid.a,
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b = this.datum.ellipsoid.b,
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f = this.datum.ellipsoid.f;
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var sinα1 = Math.sin(α1);
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var cosα1 = Math.cos(α1);
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var tanU1 = (1 - f) * Math.tan(φ1),
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cosU1 = 1 / Math.sqrt((1 + tanU1 * tanU1)),
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sinU1 = tanU1 * cosU1;
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var σ1 = Math.atan2(tanU1, cosα1);
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var sinα = cosU1 * sinα1;
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var cosSqα = 1 - sinα * sinα;
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var uSq = cosSqα * (a * a - b * b) / (b * b);
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var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 *
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uSq)));
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var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
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var σ = s / (b * A),
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σʹ, iterations = 0;
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var sinσ, cosσ;
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var cos2σM;
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do {
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cos2σM = Math.cos(2 * σ1 + σ);
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sinσ = Math.sin(σ);
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cosσ = Math.cos(σ);
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var Δσ = B * sinσ * (cos2σM + B / 4 * (cosσ * (-1 + 2 * cos2σM *
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cos2σM) -
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B / 6 * cos2σM * (-3 + 4 * sinσ * sinσ) * (-3 + 4 * cos2σM *
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cos2σM)));
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σʹ = σ;
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σ = s / (b * A) + Δσ;
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} while (Math.abs(σ - σʹ) > 1e-12 && ++iterations);
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var x = sinU1 * sinσ - cosU1 * cosσ * cosα1;
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var φ2 = Math.atan2(sinU1 * cosσ + cosU1 * sinσ * cosα1, (1 - f) *
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Math.sqrt(sinα * sinα + x * x));
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var λ = Math.atan2(sinσ * sinα1, cosU1 * cosσ - sinU1 * sinσ * cosα1);
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var C = f / 16 * cosSqα * (4 + f * (4 - 3 * cosSqα));
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var L = λ - (1 - C) * f * sinα *
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(σ + C * sinσ * (cos2σM + C * cosσ * (-1 + 2 * cos2σM * cos2σM)));
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var λ2;
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if (wrap) {
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λ2 = (λ1 + L + 3 * Math.PI) % (2 * Math.PI) - Math.PI; // normalise to -180...+180
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} else {
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λ2 = (λ1 + L); // do not normalize
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}
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var revAz = Math.atan2(sinα, -x);
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return {
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lat: φ2.toDegrees(),
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lng: λ2.toDegrees(),
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finalBearing: revAz.toDegrees()
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};
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},
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/**
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* Vincenty inverse calculation.
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* based on the work of Chris Veness (https://github.com/chrisveness/geodesy)
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*
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* @private
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* @param {LatLng} p1 - Latitude/longitude of start point.
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* @param {LatLng} p2 - Latitude/longitude of destination point.
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* @returns {Object} Object including distance, initialBearing, finalBearing.
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* @throws {Error} If formula failed to converge.
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*/
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_vincenty_inverse: function(p1, p2) {
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var φ1 = p1.lat.toRadians(),
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λ1 = p1.lng.toRadians();
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var φ2 = p2.lat.toRadians(),
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λ2 = p2.lng.toRadians();
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var a = this.datum.ellipsoid.a,
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b = this.datum.ellipsoid.b,
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f = this.datum.ellipsoid.f;
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var L = λ2 - λ1;
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var tanU1 = (1 - f) * Math.tan(φ1),
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cosU1 = 1 / Math.sqrt((1 + tanU1 * tanU1)),
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sinU1 = tanU1 * cosU1;
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var tanU2 = (1 - f) * Math.tan(φ2),
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cosU2 = 1 / Math.sqrt((1 + tanU2 * tanU2)),
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sinU2 = tanU2 * cosU2;
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var λ = L,
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λʹ, iterations = 0;
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var cosSqα, sinσ, cos2σM, cosσ, σ, sinλ, cosλ;
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do {
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sinλ = Math.sin(λ);
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cosλ = Math.cos(λ);
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var sinSqσ = (cosU2 * sinλ) * (cosU2 * sinλ) + (cosU1 * sinU2 -
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sinU1 * cosU2 * cosλ) * (cosU1 * sinU2 - sinU1 * cosU2 * cosλ);
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sinσ = Math.sqrt(sinSqσ);
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if (sinσ == 0) return 0; // co-incident points
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cosσ = sinU1 * sinU2 + cosU1 * cosU2 * cosλ;
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σ = Math.atan2(sinσ, cosσ);
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var sinα = cosU1 * cosU2 * sinλ / sinσ;
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cosSqα = 1 - sinα * sinα;
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cos2σM = cosσ - 2 * sinU1 * sinU2 / cosSqα;
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if (isNaN(cos2σM)) cos2σM = 0; // equatorial line: cosSqα=0 (§6)
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var C = f / 16 * cosSqα * (4 + f * (4 - 3 * cosSqα));
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λʹ = λ;
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λ = L + (1 - C) * f * sinα * (σ + C * sinσ * (cos2σM + C * cosσ * (-
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1 + 2 * cos2σM * cos2σM)));
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} while (Math.abs(λ - λʹ) > 1e-12 && ++iterations < 100);
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if (iterations >= 100) {
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console.log("Formula failed to converge. Altering target position.");
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return this._vincenty_inverse(p1, {
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lat: p2.lat,
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lng: p2.lng - 0.01
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});
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// throw new Error('Formula failed to converge');
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}
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var uSq = cosSqα * (a * a - b * b) / (b * b);
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var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 *
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uSq)));
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var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
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var Δσ = B * sinσ * (cos2σM + B / 4 * (cosσ * (-1 + 2 * cos2σM *
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cos2σM) -
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B / 6 * cos2σM * (-3 + 4 * sinσ * sinσ) * (-3 + 4 * cos2σM *
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cos2σM)));
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var s = b * A * (σ - Δσ);
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var fwdAz = Math.atan2(cosU2 * sinλ, cosU1 * sinU2 - sinU1 * cosU2 *
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cosλ);
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var revAz = Math.atan2(cosU1 * sinλ, -sinU1 * cosU2 + cosU1 * sinU2 *
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cosλ);
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s = Number(s.toFixed(3)); // round to 1mm precision
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return {
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distance: s,
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initialBearing: fwdAz.toDegrees(),
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finalBearing: revAz.toDegrees()
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};
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},
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/**
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* Returns the point of intersection of two paths defined by point and bearing.
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* based on the work of Chris Veness (https://github.com/chrisveness/geodesy)
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*
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* @param {LatLon} p1 - First point.
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* @param {number} brng1 - Initial bearing from first point.
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* @param {LatLon} p2 - Second point.
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* @param {number} brng2 - Initial bearing from second point.
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* @returns {Object} containing lat/lng information of intersection.
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*
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* @example
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* var p1 = LatLon(51.8853, 0.2545), brng1 = 108.55;
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* var p2 = LatLon(49.0034, 2.5735), brng2 = 32.44;
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* var pInt = LatLon.intersection(p1, brng1, p2, brng2); // pInt.toString(): 50.9078°N, 4.5084°E
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*/
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_intersection: function(p1, brng1, p2, brng2) {
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// see http://williams.best.vwh.net/avform.htm#Intersection
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var φ1 = p1.lat.toRadians(),
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λ1 = p1.lng.toRadians();
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var φ2 = p2.lat.toRadians(),
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λ2 = p2.lng.toRadians();
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var θ13 = Number(brng1).toRadians(),
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θ23 = Number(brng2).toRadians();
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var Δφ = φ2 - φ1,
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Δλ = λ2 - λ1;
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var δ12 = 2 * Math.asin(Math.sqrt(Math.sin(Δφ / 2) * Math.sin(Δφ / 2) +
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Math.cos(φ1) * Math.cos(φ2) * Math.sin(Δλ / 2) * Math.sin(Δλ /
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2)));
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if (δ12 == 0) return null;
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// initial/final bearings between points
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var θ1 = Math.acos((Math.sin(φ2) - Math.sin(φ1) * Math.cos(δ12)) /
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(Math.sin(δ12) * Math.cos(φ1)));
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if (isNaN(θ1)) θ1 = 0; // protect against rounding
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var θ2 = Math.acos((Math.sin(φ1) - Math.sin(φ2) * Math.cos(δ12)) /
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(Math.sin(δ12) * Math.cos(φ2)));
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var θ12, θ21;
|
||
if (Math.sin(λ2 - λ1) > 0) {
|
||
θ12 = θ1;
|
||
θ21 = 2 * Math.PI - θ2;
|
||
} else {
|
||
θ12 = 2 * Math.PI - θ1;
|
||
θ21 = θ2;
|
||
}
|
||
|
||
var α1 = (θ13 - θ12 + Math.PI) % (2 * Math.PI) - Math.PI; // angle 2-1-3
|
||
var α2 = (θ21 - θ23 + Math.PI) % (2 * Math.PI) - Math.PI; // angle 1-2-3
|
||
|
||
if (Math.sin(α1) == 0 && Math.sin(α2) == 0) return null; // infinite intersections
|
||
if (Math.sin(α1) * Math.sin(α2) < 0) return null; // ambiguous intersection
|
||
|
||
//α1 = Math.abs(α1);
|
||
//α2 = Math.abs(α2);
|
||
// ... Ed Williams takes abs of α1/α2, but seems to break calculation?
|
||
|
||
var α3 = Math.acos(-Math.cos(α1) * Math.cos(α2) +
|
||
Math.sin(α1) * Math.sin(α2) * Math.cos(δ12));
|
||
var δ13 = Math.atan2(Math.sin(δ12) * Math.sin(α1) * Math.sin(α2),
|
||
Math.cos(α2) + Math.cos(α1) * Math.cos(α3));
|
||
var φ3 = Math.asin(Math.sin(φ1) * Math.cos(δ13) +
|
||
Math.cos(φ1) * Math.sin(δ13) * Math.cos(θ13));
|
||
var Δλ13 = Math.atan2(Math.sin(θ13) * Math.sin(δ13) * Math.cos(φ1),
|
||
Math.cos(δ13) - Math.sin(φ1) * Math.sin(φ3));
|
||
var λ3 = λ1 + Δλ13;
|
||
λ3 = (λ3 + 3 * Math.PI) % (2 * Math.PI) - Math.PI; // normalise to -180..+180º
|
||
|
||
return {
|
||
lat: φ3.toDegrees(),
|
||
lng: λ3.toDegrees()
|
||
};
|
||
},
|
||
|
||
/**
|
||
* Overwrites obj1's values with obj2's and adds obj2's if non existent in obj1
|
||
* @param obj1
|
||
* @param obj2
|
||
* @returns obj3 a new object based on obj1 and obj2
|
||
*/
|
||
_merge_options: function(obj1, obj2) {
|
||
let obj3 = {};
|
||
for (let attrname in obj1) {
|
||
obj3[attrname] = obj1[attrname];
|
||
}
|
||
for (let attrname in obj2) {
|
||
obj3[attrname] = obj2[attrname];
|
||
}
|
||
return obj3;
|
||
}
|
||
});
|
||
|
||
L.geodesic = function(latlngs, options) {
|
||
return new L.Geodesic(latlngs, options);
|
||
};
|