refactor dLat/dLon <-> meters calcs and use slightly better WGS84 constants

js/id/geo.js

@@ -21,11 +21,38 @@ iD.geo.euclideanDistance = function(a, b) {
     var x = a[0] - b[0], y = a[1] - b[1];
     return Math.sqrt((x * x) + (y * y));
 };
+
+// using WGS84 polar radius (6356752.314245179 m)
+// const = 2 * PI * r / 360
+iD.geo.latToMeters = function(dLat) {
+    return dLat * 110946.257617;
+};
+
+// using WGS84 equatorial radius (6378137.0 m)
+// const = 2 * PI * r / 360
+iD.geo.lonToMeters = function(dLon, atLat) {
+    return Math.abs(atLat) >= 90 ? 0 :
+        dLon * 111319.490793 * Math.abs(Math.cos(atLat * (Math.PI/180)));
+};
+
+// using WGS84 polar radius (6356752.314245179 m)
+// const = 2 * PI * r / 360
+iD.geo.metersToLat = function(m) {
+    return m / 110946.257617;
+};
+
+// using WGS84 equatorial radius (6378137.0 m)
+// const = 2 * PI * r / 360
+iD.geo.metersToLon = function(m, atLat) {
+    return Math.abs(atLat) >= 90 ? 0 :
+        m / 111319.490793 / Math.abs(Math.cos(atLat * (Math.PI/180)));
+};
+
 // Equirectangular approximation of spherical distances on Earth
 iD.geo.sphericalDistance = function(a, b) {
-    var x = Math.cos(a[1]*Math.PI/180) * (a[0] - b[0]),
-        y = a[1] - b[1];
-    return 6.3710E6 * Math.sqrt((x * x) + (y * y)) * Math.PI/180;
+    var x = iD.geo.lonToMeters(a[0] - b[0], (a[1] + b[1]) / 2),
+        y = iD.geo.latToMeters(a[1] - b[1]);
+    return Math.sqrt((x * x) + (y * y));
 };
 
 iD.geo.edgeEqual = function(a, b) {

js/id/geo/extent.js

@@ -58,8 +58,8 @@ _.extend(iD.geo.Extent.prototype, {
     },
 
     padByMeters: function(meters) {
-        var dLat = meters / 111132.954,
-            dLon = meters / 111132.954 / Math.abs(Math.cos(this.center()[1] * (Math.PI / 180)));
+        var dLat = iD.geo.metersToLat(meters),
+            dLon = iD.geo.metersToLon(meters, this.center()[1]);
         return iD.geo.Extent(
                 [this[0][0] - dLon, this[0][1] - dLat],
                 [this[1][0] + dLon, this[1][1] + dLat]);

js/id/ui/scale.js

@@ -4,25 +4,10 @@ iD.ui.Scale = function(context) {
         maxLength = 180,
         tickHeight = 8;
 
-    // http://stackoverflow.com/a/27943/7620
-    // Haversine distance formula
-    function distance(loc1, loc2) {
-        var R = 6371009;  // Mean radius of the earth in m
-        var dLat = (loc2[1] - loc1[1]) * (Math.PI / 180);
-        var dLon = (loc2[0] - loc1[0]) * (Math.PI / 180);
-        var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
-            Math.cos(loc1[1] * (Math.PI / 180)) *
-            Math.cos(loc2[1] * (Math.PI / 180)) *
-            Math.sin(dLon / 2) * Math.sin(dLon / 2);
-        var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
-        var d = R * c;  // Distance in m
-        return d;
-    }
-
     function scaleDefs(loc1, loc2) {
         var lat = (loc2[1] + loc1[1]) / 2,
             conversion = (imperial ? 3.28084 : 1),
-            dist = distance(loc1, loc2) * conversion,
+            dist = iD.geo.lonToMeters(loc2[0] - loc1[0], lat) * conversion,
             scale = { dist: 0, px: 0, text: '' },
             buckets, i, val, dLon;
 
@@ -41,7 +26,7 @@ iD.ui.Scale = function(context) {
             }
         }
 
-        dLon = scale.dist / (111132.954 * conversion) / Math.abs(Math.cos( lat * (Math.PI / 180)));
+        dLon = iD.geo.metersToLon(scale.dist / conversion, lat);
         scale.px = Math.round(projection([loc1[0] + dLon, loc1[1]])[0]);
 
         if (imperial) {