diff --git a/src/ol/geom/MultiPolygon.js b/src/ol/geom/MultiPolygon.js
index 60bc7fe335..d2e47f058b 100644
--- a/src/ol/geom/MultiPolygon.js
+++ b/src/ol/geom/MultiPolygon.js
@@ -12,7 +12,7 @@ import SimpleGeometry from '../geom/SimpleGeometry.js';
 import {linearRingss as linearRingssArea} from '../geom/flat/area.js';
 import _ol_geom_flat_center_ from '../geom/flat/center.js';
 import _ol_geom_flat_closest_ from '../geom/flat/closest.js';
-import _ol_geom_flat_contains_ from '../geom/flat/contains.js';
+import {linearRingssContainsXY} from '../geom/flat/contains.js';
 import _ol_geom_flat_deflate_ from '../geom/flat/deflate.js';
 import _ol_geom_flat_inflate_ from '../geom/flat/inflate.js';
 import _ol_geom_flat_interiorpoint_ from '../geom/flat/interiorpoint.js';
@@ -151,8 +151,7 @@ MultiPolygon.prototype.closestPointXY = function(x, y, closestPoint, minSquaredD
  * @inheritDoc
  */
 MultiPolygon.prototype.containsXY = function(x, y) {
-  return _ol_geom_flat_contains_.linearRingssContainsXY(
-    this.getOrientedFlatCoordinates(), 0, this.endss_, this.stride, x, y);
+  return linearRingssContainsXY(this.getOrientedFlatCoordinates(), 0, this.endss_, this.stride, x, y);
 };
 
 
diff --git a/src/ol/geom/Polygon.js b/src/ol/geom/Polygon.js
index b85d4637c4..388b5ec39b 100644
--- a/src/ol/geom/Polygon.js
+++ b/src/ol/geom/Polygon.js
@@ -12,7 +12,7 @@ import SimpleGeometry from '../geom/SimpleGeometry.js';
 import {offset as sphereOffset} from '../sphere.js';
 import {linearRings as linearRingsArea} from '../geom/flat/area.js';
 import _ol_geom_flat_closest_ from '../geom/flat/closest.js';
-import _ol_geom_flat_contains_ from '../geom/flat/contains.js';
+import {linearRingsContainsXY} from '../geom/flat/contains.js';
 import _ol_geom_flat_deflate_ from '../geom/flat/deflate.js';
 import _ol_geom_flat_inflate_ from '../geom/flat/inflate.js';
 import _ol_geom_flat_interiorpoint_ from '../geom/flat/interiorpoint.js';
@@ -141,8 +141,7 @@ Polygon.prototype.closestPointXY = function(x, y, closestPoint, minSquaredDistan
  * @inheritDoc
  */
 Polygon.prototype.containsXY = function(x, y) {
-  return _ol_geom_flat_contains_.linearRingsContainsXY(
-    this.getOrientedFlatCoordinates(), 0, this.ends_, this.stride, x, y);
+  return linearRingsContainsXY(this.getOrientedFlatCoordinates(), 0, this.ends_, this.stride, x, y);
 };
 
 
diff --git a/src/ol/geom/flat/contains.js b/src/ol/geom/flat/contains.js
index cd4c54bf8b..acc843e992 100644
--- a/src/ol/geom/flat/contains.js
+++ b/src/ol/geom/flat/contains.js
@@ -2,7 +2,6 @@
  * @module ol/geom/flat/contains
  */
 import {forEachCorner} from '../../extent.js';
-const _ol_geom_flat_contains_ = {};
 
 
 /**
@@ -13,18 +12,17 @@ const _ol_geom_flat_contains_ = {};
  * @param {ol.Extent} extent Extent.
  * @return {boolean} Contains extent.
  */
-_ol_geom_flat_contains_.linearRingContainsExtent = function(flatCoordinates, offset, end, stride, extent) {
+export function linearRingContainsExtent(flatCoordinates, offset, end, stride, extent) {
   const outside = forEachCorner(extent,
     /**
-       * @param {ol.Coordinate} coordinate Coordinate.
-       * @return {boolean} Contains (x, y).
-       */
+     * @param {ol.Coordinate} coordinate Coordinate.
+     * @return {boolean} Contains (x, y).
+     */
     function(coordinate) {
-      return !_ol_geom_flat_contains_.linearRingContainsXY(flatCoordinates,
-        offset, end, stride, coordinate[0], coordinate[1]);
+      return !linearRingContainsXY(flatCoordinates, offset, end, stride, coordinate[0], coordinate[1]);
     });
   return !outside;
-};
+}
 
 
 /**
@@ -36,7 +34,7 @@ _ol_geom_flat_contains_.linearRingContainsExtent = function(flatCoordinates, off
  * @param {number} y Y.
  * @return {boolean} Contains (x, y).
  */
-_ol_geom_flat_contains_.linearRingContainsXY = function(flatCoordinates, offset, end, stride, x, y) {
+export function linearRingContainsXY(flatCoordinates, offset, end, stride, x, y) {
   // http://geomalgorithms.com/a03-_inclusion.html
   // Copyright 2000 softSurfer, 2012 Dan Sunday
   // This code may be freely used and modified for any purpose
@@ -61,7 +59,7 @@ _ol_geom_flat_contains_.linearRingContainsXY = function(flatCoordinates, offset,
     y1 = y2;
   }
   return wn !== 0;
-};
+}
 
 
 /**
@@ -73,22 +71,20 @@ _ol_geom_flat_contains_.linearRingContainsXY = function(flatCoordinates, offset,
  * @param {number} y Y.
  * @return {boolean} Contains (x, y).
  */
-_ol_geom_flat_contains_.linearRingsContainsXY = function(flatCoordinates, offset, ends, stride, x, y) {
+export function linearRingsContainsXY(flatCoordinates, offset, ends, stride, x, y) {
   if (ends.length === 0) {
     return false;
   }
-  if (!_ol_geom_flat_contains_.linearRingContainsXY(
-    flatCoordinates, offset, ends[0], stride, x, y)) {
+  if (!linearRingContainsXY(flatCoordinates, offset, ends[0], stride, x, y)) {
     return false;
   }
   for (let i = 1, ii = ends.length; i < ii; ++i) {
-    if (_ol_geom_flat_contains_.linearRingContainsXY(
-      flatCoordinates, ends[i - 1], ends[i], stride, x, y)) {
+    if (linearRingContainsXY(flatCoordinates, ends[i - 1], ends[i], stride, x, y)) {
       return false;
     }
   }
   return true;
-};
+}
 
 
 /**
@@ -100,18 +96,16 @@ _ol_geom_flat_contains_.linearRingsContainsXY = function(flatCoordinates, offset
  * @param {number} y Y.
  * @return {boolean} Contains (x, y).
  */
-_ol_geom_flat_contains_.linearRingssContainsXY = function(flatCoordinates, offset, endss, stride, x, y) {
+export function linearRingssContainsXY(flatCoordinates, offset, endss, stride, x, y) {
   if (endss.length === 0) {
     return false;
   }
   for (let i = 0, ii = endss.length; i < ii; ++i) {
     const ends = endss[i];
-    if (_ol_geom_flat_contains_.linearRingsContainsXY(
-      flatCoordinates, offset, ends, stride, x, y)) {
+    if (linearRingsContainsXY(flatCoordinates, offset, ends, stride, x, y)) {
       return true;
     }
     offset = ends[ends.length - 1];
   }
   return false;
-};
-export default _ol_geom_flat_contains_;
+}
diff --git a/src/ol/geom/flat/interiorpoint.js b/src/ol/geom/flat/interiorpoint.js
index 1c189648f9..8045d4980a 100644
--- a/src/ol/geom/flat/interiorpoint.js
+++ b/src/ol/geom/flat/interiorpoint.js
@@ -2,7 +2,7 @@
  * @module ol/geom/flat/interiorpoint
  */
 import {numberSafeCompareFunction} from '../../array.js';
-import _ol_geom_flat_contains_ from '../flat/contains.js';
+import {linearRingsContainsXY} from '../flat/contains.js';
 const _ol_geom_flat_interiorpoint_ = {};
 
 
@@ -52,8 +52,7 @@ _ol_geom_flat_interiorpoint_.linearRings = function(flatCoordinates, offset,
     const segmentLength = Math.abs(x2 - x1);
     if (segmentLength > maxSegmentLength) {
       x = (x1 + x2) / 2;
-      if (_ol_geom_flat_contains_.linearRingsContainsXY(
-        flatCoordinates, offset, ends, stride, x, y)) {
+      if (linearRingsContainsXY(flatCoordinates, offset, ends, stride, x, y)) {
         pointX = x;
         maxSegmentLength = segmentLength;
       }
diff --git a/src/ol/geom/flat/intersectsextent.js b/src/ol/geom/flat/intersectsextent.js
index 911743f282..c12cc82eb7 100644
--- a/src/ol/geom/flat/intersectsextent.js
+++ b/src/ol/geom/flat/intersectsextent.js
@@ -2,7 +2,7 @@
  * @module ol/geom/flat/intersectsextent
  */
 import {containsExtent, createEmpty, extendFlatCoordinates, intersects, intersectsSegment} from '../../extent.js';
-import _ol_geom_flat_contains_ from '../flat/contains.js';
+import {linearRingContainsXY, linearRingContainsExtent} from '../flat/contains.js';
 import _ol_geom_flat_segments_ from '../flat/segments.js';
 const _ol_geom_flat_intersectsextent_ = {};
 
@@ -78,20 +78,16 @@ _ol_geom_flat_intersectsextent_.linearRing = function(flatCoordinates, offset, e
     flatCoordinates, offset, end, stride, extent)) {
     return true;
   }
-  if (_ol_geom_flat_contains_.linearRingContainsXY(
-    flatCoordinates, offset, end, stride, extent[0], extent[1])) {
+  if (linearRingContainsXY(flatCoordinates, offset, end, stride, extent[0], extent[1])) {
     return true;
   }
-  if (_ol_geom_flat_contains_.linearRingContainsXY(
-    flatCoordinates, offset, end, stride, extent[0], extent[3])) {
+  if (linearRingContainsXY(flatCoordinates, offset, end, stride, extent[0], extent[3])) {
     return true;
   }
-  if (_ol_geom_flat_contains_.linearRingContainsXY(
-    flatCoordinates, offset, end, stride, extent[2], extent[1])) {
+  if (linearRingContainsXY(flatCoordinates, offset, end, stride, extent[2], extent[1])) {
     return true;
   }
-  if (_ol_geom_flat_contains_.linearRingContainsXY(
-    flatCoordinates, offset, end, stride, extent[2], extent[3])) {
+  if (linearRingContainsXY(flatCoordinates, offset, end, stride, extent[2], extent[3])) {
     return true;
   }
   return false;
@@ -115,8 +111,7 @@ _ol_geom_flat_intersectsextent_.linearRings = function(flatCoordinates, offset,
     return true;
   }
   for (let i = 1, ii = ends.length; i < ii; ++i) {
-    if (_ol_geom_flat_contains_.linearRingContainsExtent(
-      flatCoordinates, ends[i - 1], ends[i], stride, extent)) {
+    if (linearRingContainsExtent(flatCoordinates, ends[i - 1], ends[i], stride, extent)) {
       return false;
     }
   }
diff --git a/src/ol/render/webgl/PolygonReplay.js b/src/ol/render/webgl/PolygonReplay.js
index dabce0cb48..433ae5634c 100644
--- a/src/ol/render/webgl/PolygonReplay.js
+++ b/src/ol/render/webgl/PolygonReplay.js
@@ -6,7 +6,7 @@ import {equals} from '../../array.js';
 import {asArray} from '../../color.js';
 import {intersects} from '../../extent.js';
 import {isEmpty} from '../../obj.js';
-import _ol_geom_flat_contains_ from '../../geom/flat/contains.js';
+import {linearRingContainsXY} from '../../geom/flat/contains.js';
 import _ol_geom_flat_orient_ from '../../geom/flat/orient.js';
 import _ol_geom_flat_transform_ from '../../geom/flat/transform.js';
 import _ol_render_webgl_polygonreplay_defaultshader_ from '../webgl/polygonreplay/defaultshader.js';
@@ -663,8 +663,7 @@ WebGLPolygonReplay.prototype.getPointsInTriangle_ = function(p0, p1, p2, rtree,
       if (typeof p === 'object' && (!opt_reflex || p.reflex)) {
         if ((p.x !== p0.x || p.y !== p0.y) && (p.x !== p1.x || p.y !== p1.y) &&
             (p.x !== p2.x || p.y !== p2.y) && result.indexOf(p) === -1 &&
-            _ol_geom_flat_contains_.linearRingContainsXY([p0.x, p0.y, p1.x, p1.y,
-              p2.x, p2.y], 0, 6, 2, p.x, p.y)) {
+            linearRingContainsXY([p0.x, p0.y, p1.x, p1.y, p2.x, p2.y], 0, 6, 2, p.x, p.y)) {
           result.push(p);
         }
       }
diff --git a/test/spec/ol/geom/flat/contains.test.js b/test/spec/ol/geom/flat/contains.test.js
index 3853f230b5..ae7411834e 100644
--- a/test/spec/ol/geom/flat/contains.test.js
+++ b/test/spec/ol/geom/flat/contains.test.js
@@ -1,4 +1,4 @@
-import _ol_geom_flat_contains_ from '../../../../../src/ol/geom/flat/contains.js';
+import {linearRingContainsXY} from '../../../../../src/ol/geom/flat/contains.js';
 
 
 describe('ol.geom.flat.contains', function() {
@@ -11,27 +11,27 @@ describe('ol.geom.flat.contains', function() {
     describe('ol.geom.flat.contains.linearRingContainsXY', function() {
 
       it('returns true for point inside a simple polygon', function() {
-        expect(_ol_geom_flat_contains_.linearRingContainsXY(
+        expect(linearRingContainsXY(
           flatCoordinatesSimple, 0, flatCoordinatesSimple.length, 2, 0.5, 0.5)).to.be(true);
       });
 
       it('returns false for point outside a simple polygon', function() {
-        expect(_ol_geom_flat_contains_.linearRingContainsXY(
+        expect(linearRingContainsXY(
           flatCoordinatesSimple, 0, flatCoordinatesSimple.length, 2, 1.5, 1.5)).to.be(false);
       });
 
       it('returns true for point inside a non-simple polygon', function() {
-        expect(_ol_geom_flat_contains_.linearRingContainsXY(
+        expect(linearRingContainsXY(
           flatCoordinatesNonSimple, 0, flatCoordinatesNonSimple.length, 2, 1, 1)).to.be(true);
       });
 
       it('returns true for point inside an overlap of a non-simple polygon', function() {
-        expect(_ol_geom_flat_contains_.linearRingContainsXY(
+        expect(linearRingContainsXY(
           flatCoordinatesNonSimple, 0, flatCoordinatesNonSimple.length, 2, 1.5, 2.5)).to.be(true);
       });
 
       it('returns false for a point inside a hole of a non-simple polygon', function() {
-        expect(_ol_geom_flat_contains_.linearRingContainsXY(
+        expect(linearRingContainsXY(
           flatCoordinatesNonSimple, 0, flatCoordinatesNonSimple.length, 2, 2.5, 1.5)).to.be(false);
       });