Add spherical geometry functions
This commit is contained in:
Tom Payne
189
src/ol/sphere.js
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189
src/ol/sphere.js
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/**
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* @license
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* Latitude/longitude spherical geodesy formulae taken from
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* http://www.movable-type.co.uk/scripts/latlong.html
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* Licenced under CC-BY-3.0.
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*/
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// FIXME add intersection of two paths given start points and bearings
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// FIXME add rhumb lines
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goog.provide('ol.Sphere');
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goog.require('goog.math');
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goog.require('ol.Coordinate');
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/**
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* @constructor
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* @param {number} radius Radius.
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*/
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ol.Sphere = function(radius) {
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/**
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* @type {number}
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*/
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this.radius = radius;
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};
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/**
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* Returns the distance from c1 to c2 using the spherical law of cosines.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {number} Spherical law of cosines distance.
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*/
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ol.Sphere.prototype.cosineDistance = function(c1, c2) {
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var lat1 = goog.math.toRadians(c1.y);
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var lat2 = goog.math.toRadians(c2.y);
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var deltaLon = goog.math.toRadians(c2.x - c1.x);
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return this.radius * Math.acos(
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Math.sin(lat1) * Math.sin(lat2) +
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Math.cos(lat1) * Math.cos(lat2) * Math.cos(deltaLon));
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};
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/**
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* Returns the distance of c3 from the great circle path defined by c1 and c2.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @param {ol.Coordinate} c3 Coordinate 3.
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* @return {number} Cross-track distance.
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*/
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ol.Sphere.prototype.crossTrackDistance = function(c1, c2, c3) {
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var d12 = this.cosineDistance(c1, c2);
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var d13 = this.cosineDistance(c1, c2);
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var theta12 = goog.math.toRadians(this.initialBearing(c1, c2));
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var theta13 = goog.math.toRadians(this.initialBearing(c1, c3));
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return this.radius *
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Math.asin(Math.sin(d13 / this.radius) * Math.sin(theta13 - theta12));
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};
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/**
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* Returns the distance from c1 to c2 using Pythagoras's theorem on an
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* equirectangular projection.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {number} Equirectangular distance.
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*/
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ol.Sphere.prototype.equirectangularDistance = function(c1, c2) {
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var lat1 = goog.math.toRadians(c1.y);
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var lat2 = goog.math.toRadians(c2.y);
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var deltaLon = goog.math.toRadians(c2.x - c1.x);
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var x = deltaLon * Math.cos((lat1 + lat2) / 2);
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var y = lat2 - lat1;
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return this.radius * Math.sqrt(x * x + y * y);
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};
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/**
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* Returns the final bearing from c1 to c2.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {number} Initial bearing.
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*/
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ol.Sphere.prototype.finalBearing = function(c1, c2) {
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return (this.initialBearing(c2, c1) + 180) % 360;
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};
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/**
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* Returns the distance from c1 to c2 using the haversine formula.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {number} Haversine distance.
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*/
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ol.Sphere.prototype.haversineDistance = function(c1, c2) {
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var lat1 = goog.math.toRadians(c1.y);
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var lat2 = goog.math.toRadians(c2.y);
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var deltaLatBy2 = (lat2 - lat1) / 2;
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var deltaLonBy2 = goog.math.toRadians(c2.x - c1.x) / 2;
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var a = Math.sin(deltaLatBy2) * Math.sin(deltaLatBy2) +
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Math.sin(deltaLonBy2) * Math.sin(deltaLonBy2) *
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Math.cos(lat1) * Math.cos(lat2);
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return 2 * this.radius * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
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};
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/**
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* Returns the initial bearing from c1 to c2.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {number} Initial bearing.
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*/
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ol.Sphere.prototype.initialBearing = function(c1, c2) {
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var lat1 = goog.math.toRadians(c1.y);
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var lat2 = goog.math.toRadians(c2.y);
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var deltaLon = goog.math.toRadians(c2.x - c1.x);
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var y = Math.sin(deltaLon) * Math.cos(lat2);
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var x = Math.cos(lat1) * Math.sin(lat2) -
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Math.sin(lat1) * Math.cos(lat2) * Math.cos(deltaLon);
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return goog.math.toDegrees(Math.atan2(y, x));
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};
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/**
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* Returns the maximum latitude of the great circle defined by bearing and
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* latitude.
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*
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* @param {number} bearing Bearing.
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* @param {number} latitude Latitude.
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* @return {number} Maximum latitude.
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*/
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ol.Sphere.prototype.maximumLatitude = function(bearing, latitude) {
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return Math.cos(Math.abs(Math.sin(goog.math.toRadians(bearing)) *
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Math.cos(goog.math.toRadians(latitude))));
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};
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/**
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* Returns the midpoint between c1 and c2.
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*
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* @param {ol.Coordinate} c1 Coordinate 1.
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* @param {ol.Coordinate} c2 Coordinate 2.
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* @return {ol.Coordinate} Midpoint.
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*/
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ol.Sphere.prototype.midpoint = function(c1, c2) {
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var lat1 = goog.math.toRadians(c1.y);
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var lat2 = goog.math.toRadians(c2.y);
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var lon1 = goog.math.toRadians(c1.x);
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var deltaLon = goog.math.toRadians(c2.x - c1.x);
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var Bx = Math.cos(lat2) * Math.cos(deltaLon);
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var By = Math.cos(lat2) * Math.sin(deltaLon);
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var cosLat1PlusBx = Math.cos(lat1) + Bx;
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var lat = Math.atan2(Math.sin(lat1) + Math.sin(lat2),
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Math.sqrt(cosLat1PlusBx * cosLat1PlusBx + By * By));
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var lon = lon1 + Math.atan2(By, cosLat1PlusBx);
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return new ol.Coordinate(goog.math.toDegrees(lon), goog.math.toDegrees(lat));
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};
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/**
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* Returns the coordinate at the given distance and bearing from c.
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*
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* @param {ol.Coordinate} c1 Coordinate.
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* @param {number} distance Distance.
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* @param {number} bearing Bearing.
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* @return {ol.Coordinate} Coordinate.
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*/
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ol.Sphere.prototype.offset = function(c1, distance, bearing) {
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var lat1 = goog.math.toRadians(c1.y);
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var lon1 = goog.math.toRadians(c1.x);
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var dByR = distance / this.radius;
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var lat = Math.asin(
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Math.sin(lat1) * Math.cos(dByR) +
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Math.cos(lat1) * Math.sin(dByR) * Math.cos(bearing));
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var lon = lon1 + Math.atan2(
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Math.sin(bearing) * Math.sin(dByR) * Math.cos(lat1),
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Math.cos(dByR) - Math.sin(lat1) * Math.sin(lat));
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return new ol.Coordinate(goog.math.toDegrees(lon), goog.math.toDegrees(lat));
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};
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551
test/spec/ol/sphere.test.js
Normal file
551
test/spec/ol/sphere.test.js
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@@ -0,0 +1,551 @@
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// See http://www.movable-type.co.uk/scripts/latlong.html
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// FIXME add tests for crossTrackDistance
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// FIXME add tests for maximumLatitude
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// FIXME add tests for offset
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goog.provide('ol.test.Sphere');
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describe('ol.Sphere', function() {
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var sphere = new ol.Sphere(6371);
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var expected = [
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(0, 0),
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cosineDistance: 0,
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equirectangularDistance: 0,
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finalBearing: 180,
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haversineDistance: 0,
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initialBearing: 0,
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midpoint: new ol.Coordinate(0, 0)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(45, 45),
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cosineDistance: 6671.695598673524,
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equirectangularDistance: 6812.398372654371,
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finalBearing: 54.735610317245346,
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haversineDistance: 6671.695598673525,
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initialBearing: 35.264389682754654,
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midpoint: new ol.Coordinate(18.434948822922006, 24.0948425521107)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(-45, 45),
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cosineDistance: 6671.695598673524,
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equirectangularDistance: 6812.398372654371,
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finalBearing: 305.26438968275465,
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haversineDistance: 6671.695598673525,
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initialBearing: -35.264389682754654,
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midpoint: new ol.Coordinate(-18.434948822922006, 24.0948425521107)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(-45, -45),
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cosineDistance: 6671.695598673524,
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equirectangularDistance: 6812.398372654371,
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finalBearing: 234.73561031724535,
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haversineDistance: 6671.695598673525,
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initialBearing: -144.73561031724535,
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midpoint: new ol.Coordinate(-18.434948822922006, -24.0948425521107)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(45, -45),
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cosineDistance: 6671.695598673524,
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equirectangularDistance: 6812.398372654371,
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finalBearing: 125.26438968275465,
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haversineDistance: 6671.695598673525,
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initialBearing: 144.73561031724535,
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midpoint: new ol.Coordinate(18.434948822922006, -24.0948425521107)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(90, 180),
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cosineDistance: 10007.543398010286,
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equirectangularDistance: 20015.086796020572,
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finalBearing: 90,
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haversineDistance: 10007.543398010288,
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initialBearing: -90,
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midpoint: new ol.Coordinate(-45.00000000000005, 4.961398865471767e-15)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(-90, 180),
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cosineDistance: 10007.543398010286,
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equirectangularDistance: 20015.086796020572,
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finalBearing: 270,
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haversineDistance: 10007.543398010288,
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initialBearing: 90,
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midpoint: new ol.Coordinate(45.00000000000005, 4.961398865471767e-15)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(90, -180),
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cosineDistance: 10007.543398010286,
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equirectangularDistance: 20015.086796020572,
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finalBearing: 90,
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haversineDistance: 10007.543398010288,
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initialBearing: -90.00000000000001,
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midpoint: new ol.Coordinate(-45.00000000000005, -4.961398865471767e-15)
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},
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{
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c1: new ol.Coordinate(0, 0),
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c2: new ol.Coordinate(90, -180),
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cosineDistance: 10007.543398010286,
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equirectangularDistance: 20015.086796020572,
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finalBearing: 90,
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haversineDistance: 10007.543398010288,
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initialBearing: -90.00000000000001,
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midpoint: new ol.Coordinate(-45.00000000000005, -4.961398865471767e-15)
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},
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{
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c1: new ol.Coordinate(45, 45),
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c2: new ol.Coordinate(45, 45),
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cosineDistance: 0,
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equirectangularDistance: 0,
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finalBearing: 180,
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haversineDistance: 0,
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initialBearing: 0,
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midpoint: new ol.Coordinate(45.00000000000005, 45)
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},
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{
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c1: new ol.Coordinate(45, 45),
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c2: new ol.Coordinate(-45, 45),
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cosineDistance: 6671.695598673525,
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equirectangularDistance: 7076.401799751738,
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finalBearing: 234.73561031724535,
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haversineDistance: 6671.695598673525,
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initialBearing: -54.73561031724535,
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midpoint: new ol.Coordinate(0, 54.735610317245346)
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},
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{
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c1: new ol.Coordinate(45, 45),
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c2: new ol.Coordinate(-45, -45),
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cosineDistance: 13343.391197347048,
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equirectangularDistance: 14152.803599503475,
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finalBearing: 234.73561031724535,
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haversineDistance: 13343.391197347048,
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initialBearing: -125.26438968275465,
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midpoint: new ol.Coordinate(0, 0)
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},
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{
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c1: new ol.Coordinate(45, 45),
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c2: new ol.Coordinate(45, -45),
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cosineDistance: 10007.543398010284,
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equirectangularDistance: 10007.543398010286,
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finalBearing: 180,
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haversineDistance: 10007.543398010286,
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initialBearing: 180,
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midpoint: new ol.Coordinate(45.00000000000005, 0)
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},
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{
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c1: new ol.Coordinate(45, 45),
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c2: new ol.Coordinate(90, 180),
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cosineDistance: 13343.39119734705,
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equirectangularDistance: 15132.953174634127,
|
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finalBearing: 35.264389682754654,
|
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haversineDistance: 13343.391197347048,
|
||||
initialBearing: -54.735610317245346,
|
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midpoint: new ol.Coordinate(-45.00000000000005, 45.00000000000001)
|
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},
|
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{
|
||||
c1: new ol.Coordinate(45, 45),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 6671.695598673524,
|
||||
equirectangularDistance: 16072.9523901477,
|
||||
finalBearing: 324.73561031724535,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: 125.26438968275465,
|
||||
midpoint: new ol.Coordinate(71.56505117707799, 24.094842552110702)
|
||||
},
|
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{
|
||||
c1: new ol.Coordinate(45, 45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 25092.03003421417,
|
||||
finalBearing: 35.264389682754654,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: -54.735610317245346,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, 45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, 45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 25092.03003421417,
|
||||
finalBearing: 35.264389682754654,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: -54.735610317245346,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, 45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(-45, 45),
|
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cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, 45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(-45, -45),
|
||||
cosineDistance: 10007.543398010284,
|
||||
equirectangularDistance: 10007.543398010286,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 10007.543398010286,
|
||||
initialBearing: 180,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(45, -45),
|
||||
cosineDistance: 13343.391197347048,
|
||||
equirectangularDistance: 14152.803599503475,
|
||||
finalBearing: 125.26438968275465,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: 125.26438968275465,
|
||||
midpoint: new ol.Coordinate(0, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(90, 180),
|
||||
cosineDistance: 6671.695598673524,
|
||||
equirectangularDistance: 16072.9523901477,
|
||||
finalBearing: 35.264389682754654,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, 24.094842552110702)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 15132.953174634127,
|
||||
finalBearing: 324.73561031724535,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: 54.735610317245346,
|
||||
midpoint: new ol.Coordinate(45.00000000000005, 45.00000000000001)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 6671.695598673525,
|
||||
equirectangularDistance: 25669.894779453065,
|
||||
finalBearing: 35.264389682754654,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, 24.0948425521107)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, 45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 6671.695598673525,
|
||||
equirectangularDistance: 25669.894779453065,
|
||||
finalBearing: 35.264389682754654,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, 24.0948425521107)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(-45, -45),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, -45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(45, -45),
|
||||
cosineDistance: 6671.695598673525,
|
||||
equirectangularDistance: 7076.401799751738,
|
||||
finalBearing: 54.735610317245346,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: 125.26438968275465,
|
||||
midpoint: new ol.Coordinate(0, -54.735610317245346)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(90, 180),
|
||||
cosineDistance: 6671.695598673525,
|
||||
equirectangularDistance: 25669.894779453065,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -54.735610317245346,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, -24.0948425521107)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 25092.03003421417,
|
||||
finalBearing: 215.26438968275465,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: 125.26438968275465,
|
||||
midpoint: new ol.Coordinate(45.00000000000005, -45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 6671.695598673524,
|
||||
equirectangularDistance: 16072.9523901477,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -54.73561031724536,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, -24.094842552110702)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-45, -45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 6671.695598673524,
|
||||
equirectangularDistance: 16072.9523901477,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: -54.73561031724536,
|
||||
midpoint: new ol.Coordinate(-71.56505117707799, -24.094842552110702)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, -45),
|
||||
c2: new ol.Coordinate(45, -45),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(45.00000000000005, -45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, -45),
|
||||
c2: new ol.Coordinate(90, 180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 25092.03003421417,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, -45)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, -45),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 6671.695598673525,
|
||||
equirectangularDistance: 25669.894779453065,
|
||||
finalBearing: 215.26438968275465,
|
||||
haversineDistance: 6671.695598673525,
|
||||
initialBearing: 54.735610317245346,
|
||||
midpoint: new ol.Coordinate(71.56505117707799, -24.0948425521107)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, -45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 15132.953174634127,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, -45.00000000000001)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(45, -45),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 13343.39119734705,
|
||||
equirectangularDistance: 15132.953174634127,
|
||||
finalBearing: 144.73561031724535,
|
||||
haversineDistance: 13343.391197347048,
|
||||
initialBearing: -125.26438968275465,
|
||||
midpoint: new ol.Coordinate(-45.00000000000005, -45.00000000000001)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, 180),
|
||||
c2: new ol.Coordinate(90, 180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, 7.0164775638926606e-15)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, 180),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 20015.086796020572,
|
||||
equirectangularDistance: 20015.086796020572,
|
||||
finalBearing: 26.565051177077976,
|
||||
haversineDistance: 20015.086796020572,
|
||||
initialBearing: 153.43494882292202,
|
||||
midpoint: new ol.Coordinate(-180, 63.43494882292201)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, 180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 40030.173592041145,
|
||||
finalBearing: 0,
|
||||
haversineDistance: 1.5603934160404731e-12,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, 180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 40030.173592041145,
|
||||
finalBearing: 0,
|
||||
haversineDistance: 1.5603934160404731e-12,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-90, 180),
|
||||
c2: new ol.Coordinate(-90, 180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(90, 7.0164775638926606e-15)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-90, 180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 20015.086796020572,
|
||||
equirectangularDistance: 44755.09465146047,
|
||||
finalBearing: 270,
|
||||
haversineDistance: 20015.086796020572,
|
||||
initialBearing: -90,
|
||||
midpoint: new ol.Coordinate(-180, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(-90, 180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 20015.086796020572,
|
||||
equirectangularDistance: 44755.09465146047,
|
||||
finalBearing: 270,
|
||||
haversineDistance: 20015.086796020572,
|
||||
initialBearing: -90,
|
||||
midpoint: new ol.Coordinate(-180, 0)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, -180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, -7.0164775638926606e-15)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, -180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, -7.0164775638926606e-15)
|
||||
},
|
||||
{
|
||||
c1: new ol.Coordinate(90, -180),
|
||||
c2: new ol.Coordinate(90, -180),
|
||||
cosineDistance: 0,
|
||||
equirectangularDistance: 0,
|
||||
finalBearing: 180,
|
||||
haversineDistance: 0,
|
||||
initialBearing: 0,
|
||||
midpoint: new ol.Coordinate(-90, -7.0164775638926606e-15)
|
||||
}
|
||||
];
|
||||
|
||||
describe('cosineDistance', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
expect(sphere.cosineDistance(e.c1, e.c2)).toRoughlyEqual(
|
||||
e.cosineDistance, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('equirectangularDistance', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
expect(sphere.equirectangularDistance(e.c1, e.c2)).toRoughlyEqual(
|
||||
e.equirectangularDistance, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('finalBearing', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
expect(sphere.finalBearing(e.c1, e.c2)).toRoughlyEqual(
|
||||
e.finalBearing, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('haversineDistance', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
expect(sphere.haversineDistance(e.c1, e.c2)).toRoughlyEqual(
|
||||
e.haversineDistance, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('initialBearing', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
expect(sphere.initialBearing(e.c1, e.c2)).toRoughlyEqual(
|
||||
e.initialBearing, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
describe('midpoint', function() {
|
||||
|
||||
it('results match Chris Veness\'s reference implementation', function() {
|
||||
var e, i;
|
||||
for (i = 0; i < expected.length; ++i) {
|
||||
e = expected[i];
|
||||
midpoint = sphere.midpoint(e.c1, e.c2);
|
||||
// Test modulo 360 to avoid unnecessary expensive modulo operations
|
||||
// in our implementation.
|
||||
expect(goog.math.modulo(midpoint.x, 360)).toRoughlyEqual(
|
||||
goog.math.modulo(e.midpoint.x, 360), 1e-9);
|
||||
expect(midpoint.y).toRoughlyEqual(e.midpoint.y, 1e-9);
|
||||
}
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
|
||||
goog.require('ol.Coordinate');
|
||||
goog.require('ol.Sphere');
|
||||
Reference in New Issue
Block a user