diff --git a/examples/sphere-mollweide.js b/examples/sphere-mollweide.js
index 7540cd095b..83fc6adcc4 100644
--- a/examples/sphere-mollweide.js
+++ b/examples/sphere-mollweide.js
@@ -17,8 +17,8 @@ register(proj4);
 // and a world extent. These are required for the Graticule.
 const sphereMollweideProjection = new Projection({
   code: 'ESRI:53009',
-  extent: [-9009954.605703328, -9009954.605703328,
-    9009954.605703328, 9009954.605703328],
+  extent: [-18019909.21177587, -9009954.605703328,
+    18019909.21177587, 9009954.605703328],
   worldExtent: [-179, -89.99, 179, 89.99]
 });
 
@@ -37,6 +37,6 @@ const map = new Map({
   view: new View({
     center: [0, 0],
     projection: sphereMollweideProjection,
-    zoom: 0
+    zoom: 1
   })
 });
diff --git a/src/ol/extent.js b/src/ol/extent.js
index cc74b803fb..94eb9cb249 100644
--- a/src/ol/extent.js
+++ b/src/ol/extent.js
@@ -778,18 +778,38 @@ export function intersectsSegment(extent, start, end) {
  * @param {import("./proj.js").TransformFunction} transformFn Transform function.
  * Called with `[minX, minY, maxX, maxY]` extent coordinates.
  * @param {Extent=} opt_extent Destination extent.
+ * @param {number=} opt_stops Number of stops per side used for the transform.
+ * By default only the corners are used.
  * @return {Extent} Extent.
  * @api
  */
-export function applyTransform(extent, transformFn, opt_extent) {
-  const coordinates = [
-    extent[0], extent[1],
-    extent[0], extent[3],
-    extent[2], extent[1],
-    extent[2], extent[3]
-  ];
+export function applyTransform(extent, transformFn, opt_extent, opt_stops) {
+  let coordinates = [];
+  if (opt_stops > 1) {
+    const width = extent[2] - extent[0];
+    const height = extent[3] - extent[1];
+    for (let i = 0; i < opt_stops; ++i) {
+      coordinates.push(
+        extent[0] + width * i / opt_stops, extent[1],
+        extent[2], extent[1] + height * i / opt_stops,
+        extent[2] - width * i / opt_stops, extent[3],
+        extent[0], extent[3] - height * i / opt_stops
+      );
+    }
+  } else {
+    coordinates = [
+      extent[0], extent[1],
+      extent[2], extent[1],
+      extent[2], extent[3],
+      extent[0], extent[3]
+    ];
+  }
   transformFn(coordinates, coordinates, 2);
-  const xs = [coordinates[0], coordinates[2], coordinates[4], coordinates[6]];
-  const ys = [coordinates[1], coordinates[3], coordinates[5], coordinates[7]];
+  const xs = [];
+  const ys = [];
+  for (let i = 0, l = coordinates.length; i < l; i += 2) {
+    xs.push(coordinates[i]);
+    ys.push(coordinates[i + 1]);
+  }
   return _boundingExtentXYs(xs, ys, opt_extent);
 }
diff --git a/src/ol/layer/Graticule.js b/src/ol/layer/Graticule.js
index f1480dddc9..31e0f5aaee 100644
--- a/src/ol/layer/Graticule.js
+++ b/src/ol/layer/Graticule.js
@@ -144,7 +144,8 @@ const INTERVALS = [
 
 /**
  * @classdesc
- * Layer that renders a grid for a coordinate system.
+ * Layer that renders a grid for a coordinate system (currently only EPSG:4326 is supported).
+ * Note that the view projection must define both extent and worldExtent.
  *
  * @fires import("../render/Event.js").RenderEvent
  * @api
@@ -677,7 +678,7 @@ class Graticule extends VectorLayer {
       Math.min(extent[3], this.maxLatP_)
     ];
 
-    validExtent = transformExtent(validExtent, this.projection_, 'EPSG:4326');
+    validExtent = transformExtent(validExtent, this.projection_, 'EPSG:4326', 8);
     const maxLat = validExtent[3];
     const maxLon = validExtent[2];
     const minLat = validExtent[1];
@@ -896,7 +897,7 @@ class Graticule extends VectorLayer {
     const epsg4326Projection = getProjection('EPSG:4326');
 
     const worldExtent = projection.getWorldExtent();
-    const worldExtentP = transformExtent(worldExtent, epsg4326Projection, projection);
+    const worldExtentP = transformExtent(worldExtent, epsg4326Projection, projection, 8);
 
     this.maxLat_ = worldExtent[3];
     this.maxLon_ = worldExtent[2];
diff --git a/src/ol/proj.js b/src/ol/proj.js
index f64cc05a85..d2be0feb3f 100644
--- a/src/ol/proj.js
+++ b/src/ol/proj.js
@@ -476,12 +476,14 @@ export function transform(coordinate, source, destination) {
  * @param {import("./extent.js").Extent} extent The extent to transform.
  * @param {ProjectionLike} source Source projection-like.
  * @param {ProjectionLike} destination Destination projection-like.
+ * @param {number=} opt_stops Number of stops per side used for the transform.
+ * By default only the corners are used.
  * @return {import("./extent.js").Extent} The transformed extent.
  * @api
  */
-export function transformExtent(extent, source, destination) {
+export function transformExtent(extent, source, destination, opt_stops) {
   const transformFunc = getTransform(source, destination);
-  return applyTransform(extent, transformFunc);
+  return applyTransform(extent, transformFunc, undefined, opt_stops);
 }