diff --git a/lib/OpenLayers/Geometry/LineString.js b/lib/OpenLayers/Geometry/LineString.js
index 72ecbb2549..28fc9ab2ed 100644
--- a/lib/OpenLayers/Geometry/LineString.js
+++ b/lib/OpenLayers/Geometry/LineString.js
@@ -640,3 +640,139 @@ OpenLayers.Geometry.LineString = OpenLayers.Class(OpenLayers.Geometry.Curve, {
 
     CLASS_NAME: "OpenLayers.Geometry.LineString"
 });
+
+
+/**
+ * Function: OpenLayers.Geometry.LineString.geodesic
+ *
+ * Parameters:
+ * interpolate - {function(number): OpenLayers.Geometry.Point} Interpolate
+ *     function.
+ * transform - {function(OpenLayers.Geometry.Point): OpenLayers.Geometry.Point}
+ *     Transform from longitude/latitude to projected coordinates.
+ * squaredTolerance - {number} Squared tolerance.
+ *
+ * Returns:
+ * {OpenLayers.Geometry.LineString}
+ */
+OpenLayers.Geometry.LineString.geodesic =
+        function(interpolate, transform, squaredTolerance) {
+    // FIXME reduce garbage generation
+    // FIXME optimize stack operations
+
+    var components = [];
+
+    var geoA = interpolate(0);
+    var geoB = interpolate(1);
+
+    var a = transform(geoA);
+    var b = transform(geoB);
+
+    var geoStack = [geoB, geoA];
+    var stack = [b, a];
+    var fractionStack = [1, 0];
+
+    var fractions = {};
+
+    var maxIterations = 1e5;
+    var geoM, m, fracA, fracB, fracM, key;
+
+    while (--maxIterations > 0 && fractionStack.length > 0) {
+        // Pop the a coordinate off the stack
+        fracA = fractionStack.pop();
+        geoA = geoStack.pop();
+        a = stack.pop();
+        // Add the a coordinate if it has not been added yet
+        key = fracA.toString();
+        if (!(key in fractions)) {
+            components.push(a);
+            fractions[key] = true;
+        }
+        // Pop the b coordinate off the stack
+        fracB = fractionStack.pop();
+        geoB = geoStack.pop();
+        b = stack.pop();
+        // Find the m point between the a and b coordinates
+        fracM = (fracA + fracB) / 2;
+        geoM = interpolate(fracM);
+        m = transform(geoM);
+        if (OpenLayers.Geometry.distanceSquaredToSegment(m, {x1: a.x, y1: a.y,
+                x2: b.x, y2: b.y}).distance < squaredTolerance) {
+            // If the m point is sufficiently close to the straight line, then
+            // we discard it. Just use the b coordinate and move on to the next
+            // line segment.
+            components.push(b);
+            key = fracB.toString();
+            fractions[key] = true;
+        } else {
+            // Otherwise, we need to subdivide the current line segment.
+            // Split it into two and push the two line segments onto the stack.
+            fractionStack.push(fracB, fracM, fracM, fracA);
+            stack.push(b, m, m, a);
+            geoStack.push(geoB, geoM, geoM, geoA);
+        }
+    }
+
+    return new OpenLayers.Geometry.LineString(components);
+};
+
+
+/**
+ * Function: OpenLayers.Geometry.LineString.geodesicMeridian
+ * Generate a meridian (line at constant longitude).
+ *
+ * Parameters:
+ * lon - {number} Longitude.
+ * lat1 - {number} Latitude 1.
+ * lat2 - {number} Latitude 2.
+ * projection - {OpenLayers.Projection} Projection.
+ * squaredTolerance - {number} Squared tolerance.
+ *
+ * Returns:
+ * {OpenLayers.Geometry.LineString} Line geometry for the meridian at <lon>.
+ */
+OpenLayers.Geometry.LineString.geodesicMeridian =
+        function(lon, lat1, lat2, projection, squaredTolerance) {
+    var epsg4326Projection = new OpenLayers.Projection('EPSG:4326');
+    return OpenLayers.Geometry.LineString.geodesic(
+        function(frac) {
+            return new OpenLayers.Geometry.Point(
+                    lon, lat1 + ((lat2 - lat1) * frac));
+        },
+        function(point) {
+            return point.transform(epsg4326Projection, projection);
+        },
+        squaredTolerance
+  );
+};
+
+
+/**
+ * Function: OpenLayers.Geometry.LineString.geodesicParallel
+ * Generate a parallel (line at constant latitude).
+ *
+ * Parameters:
+ * lat - {number} Latitude.
+ * lon1 - {number} Longitude 1.
+ * lon2 - {number} Longitude 2.
+ * projection {OpenLayers.Projection} Projection.
+ * squaredTolerance - {number} Squared tolerance.
+ *
+ * Returns:
+ * {OpenLayers.Geometry.LineString} Line geometry for the parallel at <lat>.
+ */
+OpenLayers.Geometry.LineString.geodesicParallel =
+        function(lat, lon1, lon2, projection, squaredTolerance) {
+    var epsg4326Projection = new OpenLayers.Projection('EPSG:4326');
+    return OpenLayers.Geometry.LineString.geodesic(
+        function(frac) {
+            return new OpenLayers.Geometry.Point(
+                    lon1 + ((lon2 - lon1) * frac), lat);
+        },
+        function(point) {
+            return point.transform(epsg4326Projection, projection);
+        },
+        squaredTolerance
+    );
+};
+