From 544f399e04d1716e95210240ade2d06d7bbd8eb2 Mon Sep 17 00:00:00 2001 From: Tom Payne Date: Fri, 15 Feb 2013 17:55:29 +0100 Subject: [PATCH] Add spherical geometry functions --- src/ol/sphere.js | 189 +++++++++++++ test/spec/ol/sphere.test.js | 551 ++++++++++++++++++++++++++++++++++++ 2 files changed, 740 insertions(+) create mode 100644 src/ol/sphere.js create mode 100644 test/spec/ol/sphere.test.js diff --git a/src/ol/sphere.js b/src/ol/sphere.js new file mode 100644 index 0000000000..70c154ca64 --- /dev/null +++ b/src/ol/sphere.js @@ -0,0 +1,189 @@ +/** + * @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'); +goog.require('ol.Coordinate'); + + + +/** + * @constructor + * @param {number} radius Radius. + */ +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.y); + var lat2 = goog.math.toRadians(c2.y); + var deltaLon = goog.math.toRadians(c2.x - c1.x); + 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 d12 = this.cosineDistance(c1, c2); + 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.y); + var lat2 = goog.math.toRadians(c2.y); + var deltaLon = goog.math.toRadians(c2.x - c1.x); + 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.y); + var lat2 = goog.math.toRadians(c2.y); + var deltaLatBy2 = (lat2 - lat1) / 2; + var deltaLonBy2 = goog.math.toRadians(c2.x - c1.x) / 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 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.y); + var lat2 = goog.math.toRadians(c2.y); + var deltaLon = goog.math.toRadians(c2.x - c1.x); + 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.y); + var lat2 = goog.math.toRadians(c2.y); + var lon1 = goog.math.toRadians(c1.x); + var deltaLon = goog.math.toRadians(c2.x - c1.x); + 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 new ol.Coordinate(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.y); + var lon1 = goog.math.toRadians(c1.x); + 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 new ol.Coordinate(goog.math.toDegrees(lon), goog.math.toDegrees(lat)); +}; diff --git a/test/spec/ol/sphere.test.js b/test/spec/ol/sphere.test.js new file mode 100644 index 0000000000..ee5b9b6dd5 --- /dev/null +++ b/test/spec/ol/sphere.test.js @@ -0,0 +1,551 @@ +// See http://www.movable-type.co.uk/scripts/latlong.html +// FIXME add tests for crossTrackDistance +// FIXME add tests for maximumLatitude +// FIXME add tests for offset + +goog.provide('ol.test.Sphere'); + + +describe('ol.Sphere', function() { + + var sphere = new ol.Sphere(6371); + var expected = [ + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(0, 0), + cosineDistance: 0, + equirectangularDistance: 0, + finalBearing: 180, + haversineDistance: 0, + initialBearing: 0, + midpoint: new ol.Coordinate(0, 0) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(45, 45), + cosineDistance: 6671.695598673524, + equirectangularDistance: 6812.398372654371, + finalBearing: 54.735610317245346, + haversineDistance: 6671.695598673525, + initialBearing: 35.264389682754654, + midpoint: new ol.Coordinate(18.434948822922006, 24.0948425521107) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(-45, 45), + cosineDistance: 6671.695598673524, + equirectangularDistance: 6812.398372654371, + finalBearing: 305.26438968275465, + haversineDistance: 6671.695598673525, + initialBearing: -35.264389682754654, + midpoint: new ol.Coordinate(-18.434948822922006, 24.0948425521107) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(-45, -45), + cosineDistance: 6671.695598673524, + equirectangularDistance: 6812.398372654371, + finalBearing: 234.73561031724535, + haversineDistance: 6671.695598673525, + initialBearing: -144.73561031724535, + midpoint: new ol.Coordinate(-18.434948822922006, -24.0948425521107) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(45, -45), + cosineDistance: 6671.695598673524, + equirectangularDistance: 6812.398372654371, + finalBearing: 125.26438968275465, + haversineDistance: 6671.695598673525, + initialBearing: 144.73561031724535, + midpoint: new ol.Coordinate(18.434948822922006, -24.0948425521107) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(90, 180), + cosineDistance: 10007.543398010286, + equirectangularDistance: 20015.086796020572, + finalBearing: 90, + haversineDistance: 10007.543398010288, + initialBearing: -90, + midpoint: new ol.Coordinate(-45.00000000000005, 4.961398865471767e-15) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(-90, 180), + cosineDistance: 10007.543398010286, + equirectangularDistance: 20015.086796020572, + finalBearing: 270, + haversineDistance: 10007.543398010288, + initialBearing: 90, + midpoint: new ol.Coordinate(45.00000000000005, 4.961398865471767e-15) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(90, -180), + cosineDistance: 10007.543398010286, + equirectangularDistance: 20015.086796020572, + finalBearing: 90, + haversineDistance: 10007.543398010288, + initialBearing: -90.00000000000001, + midpoint: new ol.Coordinate(-45.00000000000005, -4.961398865471767e-15) + }, + { + c1: new ol.Coordinate(0, 0), + c2: new ol.Coordinate(90, -180), + cosineDistance: 10007.543398010286, + equirectangularDistance: 20015.086796020572, + finalBearing: 90, + haversineDistance: 10007.543398010288, + initialBearing: -90.00000000000001, + midpoint: new ol.Coordinate(-45.00000000000005, -4.961398865471767e-15) + }, + { + 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: 234.73561031724535, + haversineDistance: 6671.695598673525, + initialBearing: -54.73561031724535, + midpoint: new ol.Coordinate(0, 54.735610317245346) + }, + { + c1: new ol.Coordinate(45, 45), + c2: new ol.Coordinate(-45, -45), + cosineDistance: 13343.391197347048, + equirectangularDistance: 14152.803599503475, + finalBearing: 234.73561031724535, + haversineDistance: 13343.391197347048, + initialBearing: -125.26438968275465, + midpoint: new ol.Coordinate(0, 0) + }, + { + 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(90, 180), + cosineDistance: 13343.39119734705, + equirectangularDistance: 15132.953174634127, + finalBearing: 35.264389682754654, + 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: 6671.695598673524, + equirectangularDistance: 16072.9523901477, + finalBearing: 324.73561031724535, + 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: 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), + 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');