diff --git a/src/ol/proj/epsg3857.js b/src/ol/proj/epsg3857.js
index 16dfe11d98..09864be283 100644
--- a/src/ol/proj/epsg3857.js
+++ b/src/ol/proj/epsg3857.js
@@ -116,10 +116,17 @@ ol.proj.EPSG3857.fromEPSG4326 = function(input, opt_output, opt_dimension) {
   }
   ol.DEBUG && console.assert(output.length % dimension === 0,
       'modulus of output.length with dimension should be 0');
+  var halfSize = ol.proj.EPSG3857.HALF_SIZE;
   for (var i = 0; i < length; i += dimension) {
-    output[i] = ol.proj.EPSG3857.RADIUS * Math.PI * input[i] / 180;
-    output[i + 1] = ol.proj.EPSG3857.RADIUS *
+    output[i] = halfSize * input[i] / 180;
+    var y = ol.proj.EPSG3857.RADIUS *
         Math.log(Math.tan(Math.PI * (input[i + 1] + 90) / 360));
+    if (y > halfSize) {
+      y = halfSize;
+    } else if (y < -halfSize) {
+      y = -halfSize;
+    }
+    output[i + 1] = y;
   }
   return output;
 };
@@ -148,7 +155,7 @@ ol.proj.EPSG3857.toEPSG4326 = function(input, opt_output, opt_dimension) {
   ol.DEBUG && console.assert(output.length % dimension === 0,
       'modulus of output.length with dimension should be 0');
   for (var i = 0; i < length; i += dimension) {
-    output[i] = 180 * input[i] / (ol.proj.EPSG3857.RADIUS * Math.PI);
+    output[i] = 180 * input[i] / ol.proj.EPSG3857.HALF_SIZE;
     output[i + 1] = 360 * Math.atan(
         Math.exp(input[i + 1] / ol.proj.EPSG3857.RADIUS)) / Math.PI - 90;
   }
diff --git a/test/spec/ol/proj/epsg3857.test.js b/test/spec/ol/proj/epsg3857.test.js
index 9854d96c20..2402b2854e 100644
--- a/test/spec/ol/proj/epsg3857.test.js
+++ b/test/spec/ol/proj/epsg3857.test.js
@@ -2,6 +2,7 @@ goog.provide('ol.test.proj.EPSG3857');
 
 goog.require('ol.proj');
 goog.require('ol.proj.common');
+
 describe('ol.proj.EPSG3857', function() {
 
   afterEach(function() {
@@ -9,6 +10,38 @@ describe('ol.proj.EPSG3857', function() {
     ol.proj.common.add();
   });
 
+  describe('fromEPSG4326()', function() {
+
+    it('transforms from geographic to Web Mercator', function() {
+      var forward = ol.proj.EPSG3857.fromEPSG4326;
+      var edge = ol.proj.EPSG3857.HALF_SIZE;
+
+      var tolerance = 1e-5;
+
+      var cases = [{
+        g: [0, 0],
+        m: [0, 0]
+      }, {
+        g: [-180, -90],
+        m: [-edge, -edge]
+      }, {
+        g: [180, 90],
+        m: [edge, edge]
+      }, {
+        g: [-111.0429, 45.6770],
+        m: [-12361239.084208, 5728738.469095]
+      }];
+
+      for (var i = 0, ii = cases.length; i < ii; ++i) {
+        var point = cases[i].g;
+        var transformed = forward(point);
+        expect(transformed[0]).to.roughlyEqual(cases[i].m[0], tolerance);
+        expect(transformed[1]).to.roughlyEqual(cases[i].m[1], tolerance);
+      }
+    });
+
+  });
+
   describe('getPointResolution', function() {
 
     it('returns the correct point scale at the equator', function() {
@@ -37,7 +70,7 @@ describe('ol.proj.EPSG3857', function() {
       var epsg4326 = ol.proj.get('EPSG:4326');
       var resolution = 19.11;
       var latitude;
-      for (latitude = 0; latitude < 90; ++latitude) {
+      for (latitude = 0; latitude <= 85; ++latitude) {
         var point = ol.proj.transform([0, latitude], epsg4326, epsg3857);
         expect(epsg3857.getPointResolution(resolution, point)).
             to.roughlyEqual(19.11 * Math.cos(Math.PI * latitude / 180), 1e-9);
diff --git a/test_rendering/spec/ol/layer/expected/inverted-star.png b/test_rendering/spec/ol/layer/expected/inverted-star.png
new file mode 100644
index 0000000000..07399ffcb4
Binary files /dev/null and b/test_rendering/spec/ol/layer/expected/inverted-star.png differ
diff --git a/test_rendering/spec/ol/layer/vector.test.js b/test_rendering/spec/ol/layer/vector.test.js
index 563d231fb4..3bdaeea688 100644
--- a/test_rendering/spec/ol/layer/vector.test.js
+++ b/test_rendering/spec/ol/layer/vector.test.js
@@ -3,6 +3,7 @@ goog.provide('ol.test.rendering.layer.Vector');
 goog.require('ol.Feature');
 goog.require('ol.Map');
 goog.require('ol.View');
+goog.require('ol.format.GeoJSON');
 goog.require('ol.geom.Circle');
 goog.require('ol.geom.LineString');
 goog.require('ol.geom.Polygon');
@@ -271,6 +272,64 @@ describe('ol.rendering.layer.Vector', function() {
     });
   });
 
+  describe.only('polygon rendering', function() {
+
+    var map;
+    beforeEach(function() {
+      map = new ol.Map({
+        target: createMapDiv(128, 128),
+        view: new ol.View({
+          center: [0, 0],
+          zoom: 0
+        })
+      });
+    });
+
+    afterEach(function() {
+      disposeMap(map);
+    });
+
+    it('renders a feature that spans the world', function(done) {
+      var json = {
+        type: 'Feature',
+        geometry: {
+          type: 'Polygon',
+          coordinates: [
+            [
+              [-180, -90], [180, -90], [180, 90], [-180, 90], [-180, -90]
+            ],
+            [
+              [0, 60], [-17.6336, 24.2705], [-57.0634, 18.5410], [-28.5317, -9.2705], [-35.2671, -48.5410], [0, -30], [35.2671, -48.5410], [28.5317, -9.2705], [57.0634, 18.5410], [17.6336, 24.2705], [0, 60]
+            ]
+          ]
+        },
+        properties: {}
+      };
+
+      var format = new ol.format.GeoJSON({featureProjection: 'EPSG:3857'});
+      var feature = format.readFeature(json);
+
+      var layer = new ol.layer.Vector({
+        source: new ol.source.Vector({
+          features: [feature]
+        }),
+        style: new ol.style.Style({
+          fill: new ol.style.Fill({
+            color: 'blue'
+          })
+        })
+      });
+
+      map.addLayer(layer);
+
+      map.once('postrender', function() {
+        expectResemble(map, 'spec/ol/layer/expected/inverted-star.png', 1, done);
+      });
+
+    });
+
+  });
+
   describe('Polygon simplification', function() {
 
     var layer, map;