Add ol.Sphere#interpolate

src/ol/sphere/sphere.js

@@ -139,6 +139,42 @@ ol.Sphere.prototype.haversineDistance = function(c1, c2) {
 };
 
 
+/**
+ * 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.
  *

test/spec/ol/sphere/sphere.test.js

@@ -227,6 +227,26 @@ describe('ol.Sphere', function() {
 
   });
 
+  describe('interpolate', function() {
+
+    it('results match at the start, midpoint, and end', function() {
+      var e, i;
+      for (i = 0; i < expected.length; ++i) {
+        e = expected[i];
+        var c1 = sphere.interpolate(e.c1, e.c2, 0);
+        expect(c1[0]).to.roughlyEqual(e.c1[0], 1e-9);
+        expect(c1[1]).to.roughlyEqual(e.c1[1], 1e-9);
+        var midpoint = sphere.interpolate(e.c1, e.c2, 0.5);
+        expect(midpoint[0]).to.roughlyEqual(e.midpoint[0], 1e-9);
+        expect(midpoint[1]).to.roughlyEqual(e.midpoint[1], 1e-9);
+        var c2 = sphere.interpolate(e.c1, e.c2, 1);
+        expect(c2[0]).to.roughlyEqual(e.c2[0], 1e-9);
+        expect(c2[1]).to.roughlyEqual(e.c2[1], 1e-9);
+      }
+    });
+
+  });
+
   describe('midpoint', function() {
 
     it('results match Chris Veness\'s reference implementation', function() {