/**
* @license
* Latitude/longitude spherical geodesy formulae taken from
* http://www.movable-type.co.uk/scripts/latlong.html
* Licenced under CC-BY-3.0.
*/
// FIXME add intersection of two paths given start points and bearings
// FIXME add rhumb lines
goog.provide('ol.Sphere');
goog.require('goog.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 distance from c1 to c2 using the spherical law of cosines.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {number} Spherical law of cosines distance.
*/
ol.Sphere.prototype.cosineDistance = function(c1, c2) {
var lat1 = goog.math.toRadians(c1[1]);
var lat2 = goog.math.toRadians(c2[1]);
var deltaLon = goog.math.toRadians(c2[0] - c1[0]);
return this.radius * Math.acos(
Math.sin(lat1) * Math.sin(lat2) +
Math.cos(lat1) * Math.cos(lat2) * Math.cos(deltaLon));
};
/**
* Returns the distance of c3 from the great circle path defined by c1 and c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @param {ol.Coordinate} c3 Coordinate 3.
* @return {number} Cross-track distance.
*/
ol.Sphere.prototype.crossTrackDistance = function(c1, c2, c3) {
var d13 = this.cosineDistance(c1, c2);
var theta12 = goog.math.toRadians(this.initialBearing(c1, c2));
var theta13 = goog.math.toRadians(this.initialBearing(c1, c3));
return this.radius *
Math.asin(Math.sin(d13 / this.radius) * Math.sin(theta13 - theta12));
};
/**
* Returns the distance from c1 to c2 using Pythagoras's theorem on an
* equirectangular projection.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {number} Equirectangular distance.
*/
ol.Sphere.prototype.equirectangularDistance = function(c1, c2) {
var lat1 = goog.math.toRadians(c1[1]);
var lat2 = goog.math.toRadians(c2[1]);
var deltaLon = goog.math.toRadians(c2[0] - c1[0]);
var x = deltaLon * Math.cos((lat1 + lat2) / 2);
var y = lat2 - lat1;
return this.radius * Math.sqrt(x * x + y * y);
};
/**
* Returns the final bearing from c1 to c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {number} Initial bearing.
*/
ol.Sphere.prototype.finalBearing = function(c1, c2) {
return (this.initialBearing(c2, c1) + 180) % 360;
};
/**
* 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.
*/
ol.Sphere.prototype.haversineDistance = function(c1, c2) {
var lat1 = goog.math.toRadians(c1[1]);
var lat2 = goog.math.toRadians(c2[1]);
var deltaLatBy2 = (lat2 - lat1) / 2;
var deltaLonBy2 = goog.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 point at `fraction` along the segment of the great circle passing
* through c1 and c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @param {number} fraction Fraction.
* @return {ol.Coordinate} Coordinate between c1 and c2.
*/
ol.Sphere.prototype.interpolate = function(c1, c2, fraction) {
var lat1 = goog.math.toRadians(c1[1]);
var lon1 = goog.math.toRadians(c1[0]);
var lat2 = goog.math.toRadians(c2[1]);
var lon2 = goog.math.toRadians(c2[0]);
var cosLat1 = Math.cos(lat1);
var sinLat1 = Math.sin(lat1);
var cosLat2 = Math.cos(lat2);
var sinLat2 = Math.sin(lat2);
var cosDeltaLon = Math.cos(lon2 - lon1);
var d = sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosDeltaLon;
if (1 <= d) {
return c2.slice();
}
d = fraction * Math.acos(d);
var cosD = Math.cos(d);
var sinD = Math.sin(d);
var y = Math.sin(lon2 - lon1) * cosLat2;
var x = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosDeltaLon;
var theta = Math.atan2(y, x);
var lat = Math.asin(sinLat1 * cosD + cosLat1 * sinD * Math.cos(theta));
var lon = lon1 + Math.atan2(Math.sin(theta) * sinD * cosLat1,
cosD - sinLat1 * Math.sin(lat));
return [goog.math.toDegrees(lon), goog.math.toDegrees(lat)];
};
/**
* Returns the initial bearing from c1 to c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {number} Initial bearing.
*/
ol.Sphere.prototype.initialBearing = function(c1, c2) {
var lat1 = goog.math.toRadians(c1[1]);
var lat2 = goog.math.toRadians(c2[1]);
var deltaLon = goog.math.toRadians(c2[0] - c1[0]);
var y = Math.sin(deltaLon) * Math.cos(lat2);
var x = Math.cos(lat1) * Math.sin(lat2) -
Math.sin(lat1) * Math.cos(lat2) * Math.cos(deltaLon);
return goog.math.toDegrees(Math.atan2(y, x));
};
/**
* Returns the maximum latitude of the great circle defined by bearing and
* latitude.
*
* @param {number} bearing Bearing.
* @param {number} latitude Latitude.
* @return {number} Maximum latitude.
*/
ol.Sphere.prototype.maximumLatitude = function(bearing, latitude) {
return Math.cos(Math.abs(Math.sin(goog.math.toRadians(bearing)) *
Math.cos(goog.math.toRadians(latitude))));
};
/**
* Returns the midpoint between c1 and c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @return {ol.Coordinate} Midpoint.
*/
ol.Sphere.prototype.midpoint = function(c1, c2) {
var lat1 = goog.math.toRadians(c1[1]);
var lat2 = goog.math.toRadians(c2[1]);
var lon1 = goog.math.toRadians(c1[0]);
var deltaLon = goog.math.toRadians(c2[0] - c1[0]);
var Bx = Math.cos(lat2) * Math.cos(deltaLon);
var By = Math.cos(lat2) * Math.sin(deltaLon);
var cosLat1PlusBx = Math.cos(lat1) + Bx;
var lat = Math.atan2(Math.sin(lat1) + Math.sin(lat2),
Math.sqrt(cosLat1PlusBx * cosLat1PlusBx + By * By));
var lon = lon1 + Math.atan2(By, cosLat1PlusBx);
return [goog.math.toDegrees(lon), goog.math.toDegrees(lat)];
};
/**
* Returns the coordinate at the given distance and bearing from c.
*
* @param {ol.Coordinate} c1 Coordinate.
* @param {number} distance Distance.
* @param {number} bearing Bearing.
* @return {ol.Coordinate} Coordinate.
*/
ol.Sphere.prototype.offset = function(c1, distance, bearing) {
var lat1 = goog.math.toRadians(c1[1]);
var lon1 = goog.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 [goog.math.toDegrees(lon), goog.math.toDegrees(lat)];
};
OpenLayers 3