openlayers
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Build tools and sources for developing OpenLayers based mapping applications
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JavaScript
/**
* @license
* Latitude/longitude spherical geodesy formulae taken from
* http://www.movable-type.co.uk/scripts/latlong.html
* Licensed under CC-BY-3.0.
*/
goog.provide('ol.Sphere');
goog.require('ol.math');
/**
* @classdesc
* Class to create objects that can be used with {@link
* ol.geom.Polygon.circular}.
*
* For example to create a sphere whose radius is equal to the semi-major
* axis of the WGS84 ellipsoid:
*
* ```js
* var wgs84Sphere= new ol.Sphere(6378137);
* ```
*
* @constructor
* @param {number} radius Radius.
* @api
*/
ol.Sphere = function(radius) {
/**
* @type {number}
*/
this.radius = radius;
};
/**
* Returns the geodesic area for a list of coordinates.
*
* [Reference](http://trs-new.jpl.nasa.gov/dspace/handle/2014/40409)
* Robert. G. Chamberlain and William H. Duquette, "Some Algorithms for
* Polygons on a Sphere", JPL Publication 07-03, Jet Propulsion
* Laboratory, Pasadena, CA, June 2007
*
* @param {Array.<ol.Coordinate>} coordinates List of coordinates of a linear
* ring. If the ring is oriented clockwise, the area will be positive,
* otherwise it will be negative.
* @return {number} Area.
* @api
*/
ol.Sphere.prototype.geodesicArea = function(coordinates) {
var area = 0, len = coordinates.length;
var x1 = coordinates[len - 1][0];
var y1 = coordinates[len - 1][1];
for (var i = 0; i < len; i++) {
var x2 = coordinates[i][0], y2 = coordinates[i][1];
area += ol.math.toRadians(x2 - x1) *
(2 + Math.sin(ol.math.toRadians(y1)) +
Math.sin(ol.math.toRadians(y2)));
x1 = x2;
y1 = y2;
}
return area * this.radius * this.radius / 2.0;
};
/**
* Returns the distance from c1 to c2 using the haversine formula.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {number} Haversine distance.
* @api
*/
ol.Sphere.prototype.haversineDistance = function(c1, c2) {
var lat1 = ol.math.toRadians(c1[1]);
var lat2 = ol.math.toRadians(c2[1]);
var deltaLatBy2 = (lat2 - lat1) / 2;
var deltaLonBy2 = ol.math.toRadians(c2[0] - c1[0]) / 2;
var a = Math.sin(deltaLatBy2) * Math.sin(deltaLatBy2) +
Math.sin(deltaLonBy2) * Math.sin(deltaLonBy2) *
Math.cos(lat1) * Math.cos(lat2);
return 2 * this.radius * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
};
/**
* Returns the coordinate at the given distance and bearing from `c1`.
*
* @param {ol.Coordinate} c1 The origin point (`[lon, lat]` in degrees).
* @param {number} distance The great-circle distance between the origin
* point and the target point.
* @param {number} bearing The bearing (in radians).
* @return {ol.Coordinate} The target point.
*/
ol.Sphere.prototype.offset = function(c1, distance, bearing) {
var lat1 = ol.math.toRadians(c1[1]);
var lon1 = ol.math.toRadians(c1[0]);
var dByR = distance / this.radius;
var lat = Math.asin(
Math.sin(lat1) * Math.cos(dByR) +
Math.cos(lat1) * Math.sin(dByR) * Math.cos(bearing));
var lon = lon1 + Math.atan2(
Math.sin(bearing) * Math.sin(dByR) * Math.cos(lat1),
Math.cos(dByR) - Math.sin(lat1) * Math.sin(lat));
return [ol.math.toDegrees(lon), ol.math.toDegrees(lat)];
};