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