diff --git a/src/ol/geom/polygon.js b/src/ol/geom/polygon.js
index 1a4f7ff944..2db8dced32 100644
--- a/src/ol/geom/polygon.js
+++ b/src/ol/geom/polygon.js
@@ -3,6 +3,7 @@ goog.provide('ol.geom.Polygon');
 goog.require('ol.geom.Geometry');
 goog.require('ol.geom.LinearRing');
 goog.require('ol.geom.flat');
+goog.require('ol.geom.simplify');
 
 
 
@@ -104,6 +105,23 @@ ol.geom.Polygon.prototype.getLinearRings = function() {
 };
 
 
+/**
+ * @inheritDoc
+ */
+ol.geom.Polygon.prototype.getSimplifiedGeometryInternal =
+    function(squaredTolerance) {
+  var simplifiedFlatCoordinates = [];
+  var simplifiedEnds = [];
+  simplifiedFlatCoordinates.length = ol.geom.simplify.douglasPeuckers(
+      this.flatCoordinates, 0, this.ends_, this.stride, squaredTolerance,
+      simplifiedFlatCoordinates, 0, simplifiedEnds);
+  var simplifiedPolygon = new ol.geom.Polygon(null);
+  simplifiedPolygon.setFlatCoordinates(
+      ol.geom.GeometryLayout.XY, simplifiedFlatCoordinates, simplifiedEnds);
+  return simplifiedPolygon;
+};
+
+
 /**
  * @inheritDoc
  */
diff --git a/test/spec/ol/geom/polygon.test.js b/test/spec/ol/geom/polygon.test.js
index 632888fe63..a4410ff881 100644
--- a/test/spec/ol/geom/polygon.test.js
+++ b/test/spec/ol/geom/polygon.test.js
@@ -310,6 +310,35 @@ describe('ol.geom.Polygon', function() {
 
   });
 
+  describe('with a simple polygon', function() {
+
+    var polygon;
+    beforeEach(function() {
+      polygon = new ol.geom.Polygon(
+          [[[3, 0], [1, 3], [0, 6], [2, 6], [3, 7], [4, 6], [6, 6], [4, 3]]]);
+    });
+
+    describe('#getSimplifiedGeometry', function() {
+
+      it('returns the expected result', function() {
+        var simplifiedGeometry = polygon.getSimplifiedGeometry(1);
+        expect(simplifiedGeometry).to.be.an(ol.geom.Polygon);
+        expect(simplifiedGeometry.getCoordinates()).to.eql(
+            [[[3, 0], [0, 6], [6, 6], [4, 3]]]);
+      });
+
+      it('caches multiple simplified geometries', function() {
+        var simplifiedGeometry1 = polygon.getSimplifiedGeometry(1);
+        var simplifiedGeometry2 = polygon.getSimplifiedGeometry(2);
+        var simplifiedGeometry3 = polygon.getSimplifiedGeometry(1);
+        var simplifiedGeometry4 = polygon.getSimplifiedGeometry(2);
+        expect(simplifiedGeometry1).to.be(simplifiedGeometry3);
+        expect(simplifiedGeometry2).to.be(simplifiedGeometry4);
+      });
+
+    });
+  });
+
 });