diff --git a/src/ol/PluggableMap.js b/src/ol/PluggableMap.js
index 689c8d0dd5..17394eec2b 100644
--- a/src/ol/PluggableMap.js
+++ b/src/ol/PluggableMap.js
@@ -28,7 +28,7 @@ import {getMapRendererPlugins} from './plugins.js';
 import RendererType from './renderer/Type.js';
 import {hasArea} from './size.js';
 import PriorityQueue from './structs/PriorityQueue.js';
-import _ol_transform_ from './transform.js';
+import {create as createTransform, apply as applyTransform} from './transform.js';
 
 
 /**
@@ -164,13 +164,13 @@ const PluggableMap = function(options) {
    * @private
    * @type {ol.Transform}
    */
-  this.coordinateToPixelTransform_ = _ol_transform_.create();
+  this.coordinateToPixelTransform_ = createTransform();
 
   /**
    * @private
    * @type {ol.Transform}
    */
-  this.pixelToCoordinateTransform_ = _ol_transform_.create();
+  this.pixelToCoordinateTransform_ = createTransform();
 
   /**
    * @private
@@ -707,7 +707,7 @@ PluggableMap.prototype.getCoordinateFromPixel = function(pixel) {
   if (!frameState) {
     return null;
   } else {
-    return _ol_transform_.apply(frameState.pixelToCoordinateTransform, pixel.slice());
+    return applyTransform(frameState.pixelToCoordinateTransform, pixel.slice());
   }
 };
 
@@ -795,7 +795,7 @@ PluggableMap.prototype.getPixelFromCoordinate = function(coordinate) {
   if (!frameState) {
     return null;
   } else {
-    return _ol_transform_.apply(frameState.coordinateToPixelTransform,
+    return applyTransform(frameState.coordinateToPixelTransform,
       coordinate.slice(0, 2));
   }
 };
diff --git a/src/ol/geom/Geometry.js b/src/ol/geom/Geometry.js
index ac37cda3f6..7dcec4dcd4 100644
--- a/src/ol/geom/Geometry.js
+++ b/src/ol/geom/Geometry.js
@@ -8,7 +8,7 @@ import {FALSE} from '../functions.js';
 import {transform2D} from '../geom/flat/transform.js';
 import {get as getProjection, getTransform} from '../proj.js';
 import Units from '../proj/Units.js';
-import _ol_transform_ from '../transform.js';
+import {create as createTransform, compose as composeTransform} from '../transform.js';
 
 /**
  * @classdesc
@@ -62,7 +62,7 @@ const Geometry = function() {
    * @private
    * @type {ol.Transform}
    */
-  this.tmpTransform_ = _ol_transform_.create();
+  this.tmpTransform_ = createTransform();
 
 };
 
@@ -261,7 +261,7 @@ Geometry.prototype.transform = function(source, destination) {
       const pixelExtent = source.getExtent();
       const projectedExtent = source.getWorldExtent();
       const scale = getHeight(projectedExtent) / getHeight(pixelExtent);
-      _ol_transform_.compose(tmpTransform,
+      composeTransform(tmpTransform,
         projectedExtent[0], projectedExtent[3],
         scale, -scale, 0,
         0, 0);
diff --git a/src/ol/render.js b/src/ol/render.js
index 4e07812871..3445606d26 100644
--- a/src/ol/render.js
+++ b/src/ol/render.js
@@ -2,7 +2,7 @@
  * @module ol/render
  */
 import {DEVICE_PIXEL_RATIO} from './has.js';
-import _ol_transform_ from './transform.js';
+import {create as createTransform, scale as scaleTransform} from './transform.js';
 import CanvasImmediateRenderer from './render/canvas/Immediate.js';
 
 
@@ -38,6 +38,6 @@ export function toContext(context, opt_options) {
     canvas.style.height = size[1] + 'px';
   }
   const extent = [0, 0, canvas.width, canvas.height];
-  const transform = _ol_transform_.scale(_ol_transform_.create(), pixelRatio, pixelRatio);
+  const transform = scaleTransform(createTransform(), pixelRatio, pixelRatio);
   return new CanvasImmediateRenderer(context, pixelRatio, extent, transform, 0);
 }
diff --git a/src/ol/render/Feature.js b/src/ol/render/Feature.js
index 1d8cad934a..765ccd84eb 100644
--- a/src/ol/render/Feature.js
+++ b/src/ol/render/Feature.js
@@ -9,7 +9,7 @@ import {linearRingss as linearRingssCenter} from '../geom/flat/center.js';
 import {getInteriorPointOfArray, getInteriorPointsOfMultiArray} from '../geom/flat/interiorpoint.js';
 import {interpolatePoint} from '../geom/flat/interpolate.js';
 import {transform2D} from '../geom/flat/transform.js';
-import _ol_transform_ from '../transform.js';
+import {create as createTransform, compose as composeTransform} from '../transform.js';
 
 /**
  * Lightweight, read-only, {@link ol.Feature} and {@link ol.geom.Geometry} like
@@ -78,7 +78,7 @@ const RenderFeature = function(type, flatCoordinates, ends, properties, id) {
    * @private
    * @type {ol.Transform}
    */
-  this.tmpTransform_ = _ol_transform_.create();
+  this.tmpTransform_ = createTransform();
 };
 
 
@@ -268,7 +268,7 @@ RenderFeature.prototype.transform = function(source, destination) {
   const projectedExtent = source.getWorldExtent();
   const scale = getHeight(projectedExtent) / getHeight(pixelExtent);
   const transform = this.tmpTransform_;
-  _ol_transform_.compose(transform,
+  composeTransform(transform,
     projectedExtent[0], projectedExtent[3],
     scale, -scale, 0,
     0, 0);
diff --git a/src/ol/render/canvas.js b/src/ol/render/canvas.js
index 8553bb3744..66f2323e1a 100644
--- a/src/ol/render/canvas.js
+++ b/src/ol/render/canvas.js
@@ -5,7 +5,7 @@ import {getFontFamilies} from '../css.js';
 import {createCanvasContext2D} from '../dom.js';
 import {clear} from '../obj.js';
 import LRUCache from '../structs/LRUCache.js';
-import _ol_transform_ from '../transform.js';
+import {create as createTransform} from '../transform.js';
 
 
 /**
@@ -257,7 +257,7 @@ export function rotateAtOffset(context, rotation, offsetX, offsetY) {
 }
 
 
-export const resetTransform = _ol_transform_.create();
+export const resetTransform = createTransform();
 
 
 /**
diff --git a/src/ol/render/canvas/Immediate.js b/src/ol/render/canvas/Immediate.js
index 1fce058810..b31eb31e54 100644
--- a/src/ol/render/canvas/Immediate.js
+++ b/src/ol/render/canvas/Immediate.js
@@ -15,7 +15,7 @@ import {transform2D} from '../../geom/flat/transform.js';
 import {CANVAS_LINE_DASH} from '../../has.js';
 import VectorContext from '../VectorContext.js';
 import {defaultTextAlign, defaultFillStyle, defaultLineCap, defaultLineDash, defaultLineDashOffset, defaultLineJoin, defaultLineWidth, defaultMiterLimit, defaultStrokeStyle, defaultTextBaseline, defaultFont} from '../canvas.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, compose as composeTransform} from '../../transform.js';
 
 /**
  * @classdesc
@@ -234,7 +234,7 @@ const CanvasImmediateRenderer = function(context, pixelRatio, extent, transform,
    * @private
    * @type {ol.Transform}
    */
-  this.tmpLocalTransform_ = _ol_transform_.create();
+  this.tmpLocalTransform_ = createTransform();
 
 };
 
@@ -275,7 +275,7 @@ CanvasImmediateRenderer.prototype.drawImages_ = function(flatCoordinates, offset
     if (rotation !== 0 || this.imageScale_ != 1) {
       const centerX = x + this.imageAnchorX_;
       const centerY = y + this.imageAnchorY_;
-      _ol_transform_.compose(localTransform,
+      composeTransform(localTransform,
         centerX, centerY,
         this.imageScale_, this.imageScale_,
         rotation,
@@ -325,7 +325,7 @@ CanvasImmediateRenderer.prototype.drawText_ = function(flatCoordinates, offset,
     const x = pixelCoordinates[offset] + this.textOffsetX_;
     const y = pixelCoordinates[offset + 1] + this.textOffsetY_;
     if (rotation !== 0 || this.textScale_ != 1) {
-      const localTransform = _ol_transform_.compose(this.tmpLocalTransform_,
+      const localTransform = composeTransform(this.tmpLocalTransform_,
         x, y,
         this.textScale_, this.textScale_,
         rotation,
diff --git a/src/ol/render/canvas/Replay.js b/src/ol/render/canvas/Replay.js
index b96545dcaa..7a7a5a205a 100644
--- a/src/ol/render/canvas/Replay.js
+++ b/src/ol/render/canvas/Replay.js
@@ -18,7 +18,12 @@ import VectorContext from '../VectorContext.js';
 import {drawImage, resetTransform, defaultPadding, defaultFillStyle, defaultStrokeStyle, defaultMiterLimit, defaultLineWidth, defaultLineJoin, defaultLineDashOffset, defaultLineDash, defaultLineCap} from '../canvas.js';
 import CanvasInstruction from '../canvas/Instruction.js';
 import _ol_render_replay_ from '../replay.js';
-import _ol_transform_ from '../../transform.js';
+import {
+  create as createTransform,
+  compose as composeTransform,
+  apply as applyTransform,
+  setFromArray as transformSetFromArray
+} from '../../transform.js';
 
 /**
  * @constructor
@@ -129,7 +134,7 @@ const CanvasReplay = function(tolerance, maxExtent, resolution, pixelRatio, over
    * @private
    * @type {!ol.Transform}
    */
-  this.renderedTransform_ = _ol_transform_.create();
+  this.renderedTransform_ = createTransform();
 
   /**
    * @protected
@@ -159,13 +164,13 @@ const CanvasReplay = function(tolerance, maxExtent, resolution, pixelRatio, over
    * @private
    * @type {!ol.Transform}
    */
-  this.tmpLocalTransform_ = _ol_transform_.create();
+  this.tmpLocalTransform_ = createTransform();
 
   /**
    * @private
    * @type {!ol.Transform}
    */
-  this.resetTransform = _ol_transform_.create();
+  this.resetTransform = createTransform();
 };
 
 inherits(CanvasReplay, VectorContext);
@@ -256,14 +261,14 @@ CanvasReplay.prototype.replayImage_ = function(context, x, y, image,
   if (rotation !== 0) {
     const centerX = x + anchorX;
     const centerY = y + anchorY;
-    transform = _ol_transform_.compose(localTransform,
+    transform = composeTransform(localTransform,
       centerX, centerY, 1, 1, rotation, -centerX, -centerY);
 
     createOrUpdateEmpty(box);
-    extendCoordinate(box, _ol_transform_.apply(localTransform, p1));
-    extendCoordinate(box, _ol_transform_.apply(localTransform, p2));
-    extendCoordinate(box, _ol_transform_.apply(localTransform, p3));
-    extendCoordinate(box, _ol_transform_.apply(localTransform, p4));
+    extendCoordinate(box, applyTransform(localTransform, p1));
+    extendCoordinate(box, applyTransform(localTransform, p2));
+    extendCoordinate(box, applyTransform(localTransform, p3));
+    extendCoordinate(box, applyTransform(localTransform, p4));
   } else {
     createOrUpdate(boxX, boxY, boxX + boxW, boxY + boxH, box);
   }
@@ -457,7 +462,7 @@ CanvasReplay.prototype.beginGeometry = function(geometry, feature) {
  */
 CanvasReplay.prototype.fill_ = function(context) {
   if (this.fillOrigin_) {
-    const origin = _ol_transform_.apply(this.renderedTransform_, this.fillOrigin_.slice());
+    const origin = applyTransform(this.renderedTransform_, this.fillOrigin_.slice());
     context.translate(origin[0], origin[1]);
     context.rotate(this.viewRotation_);
   }
@@ -551,7 +556,7 @@ CanvasReplay.prototype.replay_ = function(
     pixelCoordinates = transform2D(
       this.coordinates, 0, this.coordinates.length, 2,
       transform, this.pixelCoordinates_);
-    _ol_transform_.setFromArray(this.renderedTransform_, transform);
+    transformSetFromArray(this.renderedTransform_, transform);
   }
   const skipFeatures = !isEmpty(skippedFeaturesHash);
   let i = 0; // instruction index
diff --git a/src/ol/render/canvas/ReplayGroup.js b/src/ol/render/canvas/ReplayGroup.js
index 4a3c2da437..436349b897 100644
--- a/src/ol/render/canvas/ReplayGroup.js
+++ b/src/ol/render/canvas/ReplayGroup.js
@@ -15,7 +15,7 @@ import CanvasLineStringReplay from '../canvas/LineStringReplay.js';
 import CanvasPolygonReplay from '../canvas/PolygonReplay.js';
 import CanvasTextReplay from '../canvas/TextReplay.js';
 import _ol_render_replay_ from '../replay.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, compose as composeTransform} from '../../transform.js';
 
 
 /**
@@ -115,7 +115,7 @@ const CanvasReplayGroup = function(
    * @private
    * @type {ol.Transform}
    */
-  this.hitDetectionTransform_ = _ol_transform_.create();
+  this.hitDetectionTransform_ = createTransform();
 };
 
 inherits(CanvasReplayGroup, ReplayGroup);
@@ -301,7 +301,7 @@ CanvasReplayGroup.prototype.forEachFeatureAtCoordinate = function(
 
   hitTolerance = Math.round(hitTolerance);
   const contextSize = hitTolerance * 2 + 1;
-  const transform = _ol_transform_.compose(this.hitDetectionTransform_,
+  const transform = composeTransform(this.hitDetectionTransform_,
     hitTolerance + 0.5, hitTolerance + 0.5,
     1 / resolution, -1 / resolution,
     -rotation,
diff --git a/src/ol/render/webgl/Replay.js b/src/ol/render/webgl/Replay.js
index 9163dc0f33..6b0961415f 100644
--- a/src/ol/render/webgl/Replay.js
+++ b/src/ol/render/webgl/Replay.js
@@ -4,7 +4,13 @@
 import {inherits} from '../../index.js';
 import {getCenter} from '../../extent.js';
 import VectorContext from '../VectorContext.js';
-import _ol_transform_ from '../../transform.js';
+import {
+  create as createTransform,
+  reset as resetTransform,
+  rotate as rotateTransform,
+  scale as scaleTransform,
+  translate as translateTransform
+} from '../../transform.js';
 import {create, fromTransform} from '../../vec/mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 
@@ -46,19 +52,19 @@ const WebGLReplay = function(tolerance, maxExtent) {
    * @private
    * @type {ol.Transform}
    */
-  this.projectionMatrix_ = _ol_transform_.create();
+  this.projectionMatrix_ = createTransform();
 
   /**
    * @private
    * @type {ol.Transform}
    */
-  this.offsetRotateMatrix_ = _ol_transform_.create();
+  this.offsetRotateMatrix_ = createTransform();
 
   /**
    * @private
    * @type {ol.Transform}
    */
-  this.offsetScaleMatrix_ = _ol_transform_.create();
+  this.offsetScaleMatrix_ = createTransform();
 
   /**
    * @private
@@ -294,17 +300,17 @@ WebGLReplay.prototype.replay = function(context,
   const locations = this.setUpProgram(gl, context, size, pixelRatio);
 
   // set the "uniform" values
-  const projectionMatrix = _ol_transform_.reset(this.projectionMatrix_);
-  _ol_transform_.scale(projectionMatrix, 2 / (resolution * size[0]), 2 / (resolution * size[1]));
-  _ol_transform_.rotate(projectionMatrix, -rotation);
-  _ol_transform_.translate(projectionMatrix, -(center[0] - this.origin[0]), -(center[1] - this.origin[1]));
+  const projectionMatrix = resetTransform(this.projectionMatrix_);
+  scaleTransform(projectionMatrix, 2 / (resolution * size[0]), 2 / (resolution * size[1]));
+  rotateTransform(projectionMatrix, -rotation);
+  translateTransform(projectionMatrix, -(center[0] - this.origin[0]), -(center[1] - this.origin[1]));
 
-  const offsetScaleMatrix = _ol_transform_.reset(this.offsetScaleMatrix_);
-  _ol_transform_.scale(offsetScaleMatrix, 2 / size[0], 2 / size[1]);
+  const offsetScaleMatrix = resetTransform(this.offsetScaleMatrix_);
+  scaleTransform(offsetScaleMatrix, 2 / size[0], 2 / size[1]);
 
-  const offsetRotateMatrix = _ol_transform_.reset(this.offsetRotateMatrix_);
+  const offsetRotateMatrix = resetTransform(this.offsetRotateMatrix_);
   if (rotation !== 0) {
-    _ol_transform_.rotate(offsetRotateMatrix, -rotation);
+    rotateTransform(offsetRotateMatrix, -rotation);
   }
 
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
diff --git a/src/ol/renderer/Map.js b/src/ol/renderer/Map.js
index b35fd3d667..e4aaf05695 100644
--- a/src/ol/renderer/Map.js
+++ b/src/ol/renderer/Map.js
@@ -10,7 +10,7 @@ import {TRUE} from '../functions.js';
 import {visibleAtResolution} from '../layer/Layer.js';
 import {getLayerRendererPlugins} from '../plugins.js';
 import {iconImageCache} from '../style.js';
-import _ol_transform_ from '../transform.js';
+import {compose as composeTransform, invert as invertTransform, setFromArray as transformSetFromArray} from '../transform.js';
 
 /**
  * @constructor
@@ -56,14 +56,14 @@ MapRenderer.prototype.calculateMatrices2D = function(frameState) {
   const coordinateToPixelTransform = frameState.coordinateToPixelTransform;
   const pixelToCoordinateTransform = frameState.pixelToCoordinateTransform;
 
-  _ol_transform_.compose(coordinateToPixelTransform,
+  composeTransform(coordinateToPixelTransform,
     frameState.size[0] / 2, frameState.size[1] / 2,
     1 / viewState.resolution, -1 / viewState.resolution,
     -viewState.rotation,
     -viewState.center[0], -viewState.center[1]);
 
-  _ol_transform_.invert(
-    _ol_transform_.setFromArray(pixelToCoordinateTransform, coordinateToPixelTransform));
+  invertTransform(
+    transformSetFromArray(pixelToCoordinateTransform, coordinateToPixelTransform));
 };
 
 
diff --git a/src/ol/renderer/canvas/ImageLayer.js b/src/ol/renderer/canvas/ImageLayer.js
index 8d6aea62a3..9549626b86 100644
--- a/src/ol/renderer/canvas/ImageLayer.js
+++ b/src/ol/renderer/canvas/ImageLayer.js
@@ -13,7 +13,7 @@ import {assign} from '../../obj.js';
 import {getLayerRendererPlugins} from '../../plugins.js';
 import RendererType from '../Type.js';
 import IntermediateCanvasRenderer from '../canvas/IntermediateCanvas.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, compose as composeTransform} from '../../transform.js';
 
 /**
  * @constructor
@@ -35,7 +35,7 @@ const CanvasImageLayerRenderer = function(imageLayer) {
    * @private
    * @type {ol.Transform}
    */
-  this.imageTransform_ = _ol_transform_.create();
+  this.imageTransform_ = createTransform();
 
   /**
    * @type {!Array.<string>}
@@ -175,13 +175,13 @@ CanvasImageLayerRenderer.prototype.prepareFrame = function(frameState, layerStat
     const imagePixelRatio = image.getPixelRatio();
     const scale = pixelRatio * imageResolution /
         (viewResolution * imagePixelRatio);
-    const transform = _ol_transform_.compose(this.imageTransform_,
+    const transform = composeTransform(this.imageTransform_,
       pixelRatio * size[0] / 2, pixelRatio * size[1] / 2,
       scale, scale,
       0,
       imagePixelRatio * (imageExtent[0] - viewCenter[0]) / imageResolution,
       imagePixelRatio * (viewCenter[1] - imageExtent[3]) / imageResolution);
-    _ol_transform_.compose(this.coordinateToCanvasPixelTransform,
+    composeTransform(this.coordinateToCanvasPixelTransform,
       pixelRatio * size[0] / 2 - transform[4], pixelRatio * size[1] / 2 - transform[5],
       pixelRatio / viewResolution, -pixelRatio / viewResolution,
       0,
diff --git a/src/ol/renderer/canvas/IntermediateCanvas.js b/src/ol/renderer/canvas/IntermediateCanvas.js
index e8d6dc4568..f2ff25a5a4 100644
--- a/src/ol/renderer/canvas/IntermediateCanvas.js
+++ b/src/ol/renderer/canvas/IntermediateCanvas.js
@@ -6,7 +6,7 @@ import {scale as scaleCoordinate} from '../../coordinate.js';
 import {createCanvasContext2D} from '../../dom.js';
 import {containsExtent, intersects} from '../../extent.js';
 import CanvasLayerRenderer from '../canvas/Layer.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, apply as applyTransform} from '../../transform.js';
 
 /**
  * @constructor
@@ -22,7 +22,7 @@ const IntermediateCanvasRenderer = function(layer) {
    * @protected
    * @type {ol.Transform}
    */
-  this.coordinateToCanvasPixelTransform = _ol_transform_.create();
+  this.coordinateToCanvasPixelTransform = createTransform();
 
   /**
    * @private
@@ -128,7 +128,7 @@ IntermediateCanvasRenderer.prototype.forEachLayerAtCoordinate = function(coordin
     // so that for example also transparent polygons are detected
     return CanvasLayerRenderer.prototype.forEachLayerAtCoordinate.apply(this, arguments);
   } else {
-    const pixel = _ol_transform_.apply(this.coordinateToCanvasPixelTransform, coordinate.slice());
+    const pixel = applyTransform(this.coordinateToCanvasPixelTransform, coordinate.slice());
     scaleCoordinate(pixel, frameState.viewState.resolution / this.renderedResolution);
 
     if (!this.hitCanvasContext_) {
diff --git a/src/ol/renderer/canvas/Layer.js b/src/ol/renderer/canvas/Layer.js
index 44558c5dd7..aa400f1ee1 100644
--- a/src/ol/renderer/canvas/Layer.js
+++ b/src/ol/renderer/canvas/Layer.js
@@ -9,7 +9,7 @@ import RenderEventType from '../../render/EventType.js';
 import {rotateAtOffset} from '../../render/canvas.js';
 import CanvasImmediateRenderer from '../../render/canvas/Immediate.js';
 import LayerRenderer from '../Layer.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, apply as applyTransform, compose as composeTransform} from '../../transform.js';
 
 /**
  * @constructor
@@ -31,7 +31,7 @@ const CanvasLayerRenderer = function(layer) {
    * @private
    * @type {ol.Transform}
    */
-  this.transform_ = _ol_transform_.create();
+  this.transform_ = createTransform();
 
 };
 
@@ -54,10 +54,10 @@ CanvasLayerRenderer.prototype.clip = function(context, frameState, extent) {
   const bottomRight = getBottomRight(/** @type {ol.Extent} */ (extent));
   const bottomLeft = getBottomLeft(/** @type {ol.Extent} */ (extent));
 
-  _ol_transform_.apply(frameState.coordinateToPixelTransform, topLeft);
-  _ol_transform_.apply(frameState.coordinateToPixelTransform, topRight);
-  _ol_transform_.apply(frameState.coordinateToPixelTransform, bottomRight);
-  _ol_transform_.apply(frameState.coordinateToPixelTransform, bottomLeft);
+  applyTransform(frameState.coordinateToPixelTransform, topLeft);
+  applyTransform(frameState.coordinateToPixelTransform, topRight);
+  applyTransform(frameState.coordinateToPixelTransform, bottomRight);
+  applyTransform(frameState.coordinateToPixelTransform, bottomLeft);
 
   context.save();
   rotateAtOffset(context, -rotation, width / 2, height / 2);
@@ -168,7 +168,7 @@ CanvasLayerRenderer.prototype.getTransform = function(frameState, offsetX) {
   const angle = -viewState.rotation;
   const dx2 = -viewState.center[0] + offsetX;
   const dy2 = -viewState.center[1];
-  return _ol_transform_.compose(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
+  return composeTransform(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
 };
 
 
diff --git a/src/ol/renderer/canvas/Map.js b/src/ol/renderer/canvas/Map.js
index c58eb92388..b76abb83a3 100644
--- a/src/ol/renderer/canvas/Map.js
+++ b/src/ol/renderer/canvas/Map.js
@@ -3,7 +3,7 @@
  */
 // FIXME offset panning
 
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, apply as applyTransform, compose as composeTransform} from '../../transform.js';
 import {inherits} from '../../index.js';
 import {stableSort} from '../../array.js';
 import {CLASS_UNSELECTABLE} from '../../css.js';
@@ -56,7 +56,7 @@ const CanvasMapRenderer = function(container, map) {
    * @private
    * @type {ol.Transform}
    */
-  this.transform_ = _ol_transform_.create();
+  this.transform_ = createTransform();
 
 };
 
@@ -123,7 +123,7 @@ CanvasMapRenderer.prototype.getTransform = function(frameState) {
   const angle = -viewState.rotation;
   const dx2 = -viewState.center[0];
   const dy2 = -viewState.center[1];
-  return _ol_transform_.compose(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
+  return composeTransform(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
 };
 
 
@@ -216,7 +216,7 @@ CanvasMapRenderer.prototype.forEachLayerAtPixel = function(pixel, frameState, ca
   const layerStates = frameState.layerStatesArray;
   const numLayers = layerStates.length;
 
-  const coordinate = _ol_transform_.apply(
+  const coordinate = applyTransform(
     frameState.pixelToCoordinateTransform, pixel.slice());
 
   let i;
diff --git a/src/ol/renderer/canvas/TileLayer.js b/src/ol/renderer/canvas/TileLayer.js
index d845ed31d1..5227dde96b 100644
--- a/src/ol/renderer/canvas/TileLayer.js
+++ b/src/ol/renderer/canvas/TileLayer.js
@@ -10,7 +10,7 @@ import {createCanvasContext2D} from '../../dom.js';
 import {containsExtent, createEmpty, equals, getIntersection, isEmpty} from '../../extent.js';
 import RendererType from '../Type.js';
 import IntermediateCanvasRenderer from '../canvas/IntermediateCanvas.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform, compose as composeTransform} from '../../transform.js';
 
 /**
  * @constructor
@@ -68,7 +68,7 @@ const CanvasTileLayerRenderer = function(tileLayer) {
    * @private
    * @type {ol.Transform}
    */
-  this.imageTransform_ = _ol_transform_.create();
+  this.imageTransform_ = createTransform();
 
   /**
    * @protected
@@ -275,13 +275,13 @@ CanvasTileLayerRenderer.prototype.prepareFrame = function(frameState, layerState
   }
 
   const scale = this.renderedResolution / viewResolution;
-  const transform = _ol_transform_.compose(this.imageTransform_,
+  const transform = composeTransform(this.imageTransform_,
     pixelRatio * size[0] / 2, pixelRatio * size[1] / 2,
     scale, scale,
     0,
     (this.renderedExtent_[0] - viewCenter[0]) / this.renderedResolution * pixelRatio,
     (viewCenter[1] - this.renderedExtent_[3]) / this.renderedResolution * pixelRatio);
-  _ol_transform_.compose(this.coordinateToCanvasPixelTransform,
+  composeTransform(this.coordinateToCanvasPixelTransform,
     pixelRatio * size[0] / 2 - transform[4], pixelRatio * size[1] / 2 - transform[5],
     pixelRatio / viewResolution, -pixelRatio / viewResolution,
     0,
diff --git a/src/ol/renderer/canvas/VectorTileLayer.js b/src/ol/renderer/canvas/VectorTileLayer.js
index bd2b2f6788..eb7139a7cf 100644
--- a/src/ol/renderer/canvas/VectorTileLayer.js
+++ b/src/ol/renderer/canvas/VectorTileLayer.js
@@ -19,7 +19,13 @@ import _ol_render_replay_ from '../../render/replay.js';
 import RendererType from '../Type.js';
 import CanvasTileLayerRenderer from '../canvas/TileLayer.js';
 import {getSquaredTolerance as getSquaredRenderTolerance, renderFeature} from '../vector.js';
-import _ol_transform_ from '../../transform.js';
+import {
+  create as createTransform,
+  compose as composeTransform,
+  reset as resetTransform,
+  scale as scaleTransform,
+  translate as translateTransform
+} from '../../transform.js';
 
 
 /**
@@ -79,7 +85,7 @@ const CanvasVectorTileLayerRenderer = function(layer) {
    * @private
    * @type {ol.Transform}
    */
-  this.tmpTransform_ = _ol_transform_.create();
+  this.tmpTransform_ = createTransform();
 
   // Use lower resolution for pure vector rendering. Closest resolution otherwise.
   this.zDirection = layer.getRenderMode() == VectorTileRenderType.VECTOR ? 1 : 0;
@@ -327,7 +333,7 @@ CanvasVectorTileLayerRenderer.prototype.getReplayTransform_ = function(tile, fra
   const size = frameState.size;
   const offsetX = Math.round(pixelRatio * size[0] / 2);
   const offsetY = Math.round(pixelRatio * size[1] / 2);
-  return _ol_transform_.compose(this.tmpTransform_,
+  return composeTransform(this.tmpTransform_,
     offsetX, offsetY,
     tileResolution / renderResolution, tileResolution / renderResolution,
     viewState.rotation,
@@ -502,9 +508,9 @@ CanvasVectorTileLayerRenderer.prototype.renderTileImage_ = function(
         continue;
       }
       const pixelScale = pixelRatio / resolution;
-      const transform = _ol_transform_.reset(this.tmpTransform_);
-      _ol_transform_.scale(transform, pixelScale, -pixelScale);
-      _ol_transform_.translate(transform, -tileExtent[0], -tileExtent[3]);
+      const transform = resetTransform(this.tmpTransform_);
+      scaleTransform(transform, pixelScale, -pixelScale);
+      translateTransform(transform, -tileExtent[0], -tileExtent[3]);
       const replayGroup = sourceTile.getReplayGroup(layer, tile.tileCoord.toString());
       replayGroup.replay(context, transform, 0, {}, replays);
     }
diff --git a/src/ol/renderer/webgl/ImageLayer.js b/src/ol/renderer/webgl/ImageLayer.js
index ad7c40df41..0211f6092f 100644
--- a/src/ol/renderer/webgl/ImageLayer.js
+++ b/src/ol/renderer/webgl/ImageLayer.js
@@ -10,7 +10,16 @@ import {getIntersection, isEmpty} from '../../extent.js';
 import {TRUE} from '../../functions.js';
 import RendererType from '../Type.js';
 import WebGLLayerRenderer from '../webgl/Layer.js';
-import _ol_transform_ from '../../transform.js';
+import {
+  create as createTransform,
+  rotate as rotateTransform,
+  translate as translateTransform,
+  scale as scaleTransform,
+  reset as resetTransform,
+  apply as applyTransform,
+  invert as invertTransform,
+  multiply as multiplyTransform
+} from '../../transform.js';
 import _ol_webgl_ from '../../webgl.js';
 import {createTexture} from '../../webgl/Context.js';
 
@@ -183,9 +192,9 @@ WebGLImageLayerRenderer.prototype.prepareFrame = function(frameState, layerState
 
     // Translate and scale to flip the Y coord.
     const texCoordMatrix = this.texCoordMatrix;
-    _ol_transform_.reset(texCoordMatrix);
-    _ol_transform_.scale(texCoordMatrix, 1, -1);
-    _ol_transform_.translate(texCoordMatrix, 0, -1);
+    resetTransform(texCoordMatrix);
+    scaleTransform(texCoordMatrix, 1, -1);
+    translateTransform(texCoordMatrix, 0, -1);
 
     this.image_ = image;
     this.texture = texture;
@@ -212,18 +221,18 @@ WebGLImageLayerRenderer.prototype.updateProjectionMatrix_ = function(canvasWidth
   const canvasExtentHeight = canvasHeight * viewResolution;
 
   const projectionMatrix = this.projectionMatrix;
-  _ol_transform_.reset(projectionMatrix);
-  _ol_transform_.scale(projectionMatrix,
+  resetTransform(projectionMatrix);
+  scaleTransform(projectionMatrix,
     pixelRatio * 2 / canvasExtentWidth,
     pixelRatio * 2 / canvasExtentHeight);
-  _ol_transform_.rotate(projectionMatrix, -viewRotation);
-  _ol_transform_.translate(projectionMatrix,
+  rotateTransform(projectionMatrix, -viewRotation);
+  translateTransform(projectionMatrix,
     imageExtent[0] - viewCenter[0],
     imageExtent[1] - viewCenter[1]);
-  _ol_transform_.scale(projectionMatrix,
+  scaleTransform(projectionMatrix,
     (imageExtent[2] - imageExtent[0]) / 2,
     (imageExtent[3] - imageExtent[1]) / 2);
-  _ol_transform_.translate(projectionMatrix, 1, 1);
+  translateTransform(projectionMatrix, 1, 1);
 
 };
 
@@ -248,7 +257,7 @@ WebGLImageLayerRenderer.prototype.forEachLayerAtPixel = function(pixel, frameSta
   if (this.getLayer().getSource().forEachFeatureAtCoordinate !== nullFunction) {
     // for ImageCanvas sources use the original hit-detection logic,
     // so that for example also transparent polygons are detected
-    const coordinate = _ol_transform_.apply(
+    const coordinate = applyTransform(
       frameState.pixelToCoordinateTransform, pixel.slice());
     const hasFeature = this.forEachFeatureAtCoordinate(coordinate, frameState, 0, TRUE, this);
 
@@ -266,7 +275,7 @@ WebGLImageLayerRenderer.prototype.forEachLayerAtPixel = function(pixel, frameSta
         frameState.size, imageSize);
     }
 
-    const pixelOnFrameBuffer = _ol_transform_.apply(
+    const pixelOnFrameBuffer = applyTransform(
       this.hitTransformationMatrix_, pixel.slice());
 
     if (pixelOnFrameBuffer[0] < 0 || pixelOnFrameBuffer[0] > imageSize[0] ||
@@ -304,25 +313,25 @@ WebGLImageLayerRenderer.prototype.forEachLayerAtPixel = function(pixel, frameSta
 WebGLImageLayerRenderer.prototype.getHitTransformationMatrix_ = function(mapSize, imageSize) {
   // the first matrix takes a map pixel, flips the y-axis and scales to
   // a range between -1 ... 1
-  const mapCoordTransform = _ol_transform_.create();
-  _ol_transform_.translate(mapCoordTransform, -1, -1);
-  _ol_transform_.scale(mapCoordTransform, 2 / mapSize[0], 2 / mapSize[1]);
-  _ol_transform_.translate(mapCoordTransform, 0, mapSize[1]);
-  _ol_transform_.scale(mapCoordTransform, 1, -1);
+  const mapCoordTransform = createTransform();
+  translateTransform(mapCoordTransform, -1, -1);
+  scaleTransform(mapCoordTransform, 2 / mapSize[0], 2 / mapSize[1]);
+  translateTransform(mapCoordTransform, 0, mapSize[1]);
+  scaleTransform(mapCoordTransform, 1, -1);
 
   // the second matrix is the inverse of the projection matrix used in the
   // shader for drawing
-  const projectionMatrixInv = _ol_transform_.invert(this.projectionMatrix.slice());
+  const projectionMatrixInv = invertTransform(this.projectionMatrix.slice());
 
   // the third matrix scales to the image dimensions and flips the y-axis again
-  const transform = _ol_transform_.create();
-  _ol_transform_.translate(transform, 0, imageSize[1]);
-  _ol_transform_.scale(transform, 1, -1);
-  _ol_transform_.scale(transform, imageSize[0] / 2, imageSize[1] / 2);
-  _ol_transform_.translate(transform, 1, 1);
+  const transform = createTransform();
+  translateTransform(transform, 0, imageSize[1]);
+  scaleTransform(transform, 1, -1);
+  scaleTransform(transform, imageSize[0] / 2, imageSize[1] / 2);
+  translateTransform(transform, 1, 1);
 
-  _ol_transform_.multiply(transform, projectionMatrixInv);
-  _ol_transform_.multiply(transform, mapCoordTransform);
+  multiplyTransform(transform, projectionMatrixInv);
+  multiplyTransform(transform, mapCoordTransform);
 
   return transform;
 };
diff --git a/src/ol/renderer/webgl/Layer.js b/src/ol/renderer/webgl/Layer.js
index 391716c135..f79980c35e 100644
--- a/src/ol/renderer/webgl/Layer.js
+++ b/src/ol/renderer/webgl/Layer.js
@@ -8,7 +8,7 @@ import WebGLImmediateRenderer from '../../render/webgl/Immediate.js';
 import LayerRenderer from '../Layer.js';
 import {fragment, vertex} from '../webgl/defaultmapshader.js';
 import Locations from '../webgl/defaultmapshader/Locations.js';
-import _ol_transform_ from '../../transform.js';
+import {create as createTransform} from '../../transform.js';
 import {create, fromTransform} from '../../vec/mat4.js';
 import _ol_webgl_ from '../../webgl.js';
 import WebGLBuffer from '../../webgl/Buffer.js';
@@ -64,13 +64,13 @@ const WebGLLayerRenderer = function(mapRenderer, layer) {
    * @protected
    * @type {ol.Transform}
    */
-  this.texCoordMatrix = _ol_transform_.create();
+  this.texCoordMatrix = createTransform();
 
   /**
    * @protected
    * @type {ol.Transform}
    */
-  this.projectionMatrix = _ol_transform_.create();
+  this.projectionMatrix = createTransform();
 
   /**
    * @type {Array.<number>}
diff --git a/src/ol/renderer/webgl/TileLayer.js b/src/ol/renderer/webgl/TileLayer.js
index 362abab353..373ca0de7d 100644
--- a/src/ol/renderer/webgl/TileLayer.js
+++ b/src/ol/renderer/webgl/TileLayer.js
@@ -16,7 +16,13 @@ import WebGLLayerRenderer from '../webgl/Layer.js';
 import {fragment, vertex} from '../webgl/tilelayershader.js';
 import Locations from '../webgl/tilelayershader/Locations.js';
 import {toSize} from '../../size.js';
-import _ol_transform_ from '../../transform.js';
+import {
+  reset as resetTransform,
+  rotate as rotateTransform,
+  scale as scaleTransform,
+  translate as translateTransform,
+  apply as applyTransform
+} from '../../transform.js';
 import _ol_webgl_ from '../../webgl.js';
 import WebGLBuffer from '../../webgl/Buffer.js';
 
@@ -355,21 +361,21 @@ WebGLTileLayerRenderer.prototype.prepareFrame = function(frameState, layerState,
   this.scheduleExpireCache(frameState, tileSource);
 
   const texCoordMatrix = this.texCoordMatrix;
-  _ol_transform_.reset(texCoordMatrix);
-  _ol_transform_.translate(texCoordMatrix,
+  resetTransform(texCoordMatrix);
+  translateTransform(texCoordMatrix,
     (Math.round(center[0] / tileResolution) * tileResolution - framebufferExtent[0]) /
           (framebufferExtent[2] - framebufferExtent[0]),
     (Math.round(center[1] / tileResolution) * tileResolution - framebufferExtent[1]) /
           (framebufferExtent[3] - framebufferExtent[1]));
   if (viewState.rotation !== 0) {
-    _ol_transform_.rotate(texCoordMatrix, viewState.rotation);
+    rotateTransform(texCoordMatrix, viewState.rotation);
   }
-  _ol_transform_.scale(texCoordMatrix,
+  scaleTransform(texCoordMatrix,
     frameState.size[0] * viewState.resolution /
           (framebufferExtent[2] - framebufferExtent[0]),
     frameState.size[1] * viewState.resolution /
           (framebufferExtent[3] - framebufferExtent[1]));
-  _ol_transform_.translate(texCoordMatrix, -0.5, -0.5);
+  translateTransform(texCoordMatrix, -0.5, -0.5);
 
   return true;
 };
@@ -387,7 +393,7 @@ WebGLTileLayerRenderer.prototype.forEachLayerAtPixel = function(pixel, frameStat
     pixel[0] / frameState.size[0],
     (frameState.size[1] - pixel[1]) / frameState.size[1]];
 
-  const pixelOnFrameBufferScaled = _ol_transform_.apply(
+  const pixelOnFrameBufferScaled = applyTransform(
     this.texCoordMatrix, pixelOnMapScaled.slice());
   const pixelOnFrameBuffer = [
     pixelOnFrameBufferScaled[0] * this.framebufferDimension,
diff --git a/src/ol/renderer/webgl/VectorLayer.js b/src/ol/renderer/webgl/VectorLayer.js
index f39c854035..fc32b07afd 100644
--- a/src/ol/renderer/webgl/VectorLayer.js
+++ b/src/ol/renderer/webgl/VectorLayer.js
@@ -9,7 +9,7 @@ import WebGLReplayGroup from '../../render/webgl/ReplayGroup.js';
 import RendererType from '../Type.js';
 import {defaultOrder as defaultRenderOrder, getTolerance as getRenderTolerance, getSquaredTolerance as getSquaredRenderTolerance, renderFeature} from '../vector.js';
 import WebGLLayerRenderer from '../webgl/Layer.js';
-import _ol_transform_ from '../../transform.js';
+import {apply as applyTransform} from '../../transform.js';
 
 /**
  * @constructor
@@ -186,7 +186,7 @@ WebGLVectorLayerRenderer.prototype.hasFeatureAtCoordinate = function(coordinate,
  * @inheritDoc
  */
 WebGLVectorLayerRenderer.prototype.forEachLayerAtPixel = function(pixel, frameState, callback, thisArg) {
-  const coordinate = _ol_transform_.apply(
+  const coordinate = applyTransform(
     frameState.pixelToCoordinateTransform, pixel.slice());
   const hasFeature = this.hasFeatureAtCoordinate(coordinate, frameState);
 
diff --git a/src/ol/source/Raster.js b/src/ol/source/Raster.js
index c7440b691f..bc2543184d 100644
--- a/src/ol/source/Raster.js
+++ b/src/ol/source/Raster.js
@@ -19,7 +19,7 @@ import ImageSource from '../source/Image.js';
 import RasterOperationType from '../source/RasterOperationType.js';
 import SourceState from '../source/State.js';
 import TileSource from '../source/Tile.js';
-import _ol_transform_ from '../transform.js';
+import {create as createTransform} from '../transform.js';
 
 
 /**
@@ -128,14 +128,14 @@ const RasterSource = function(options) {
    */
   this.frameState_ = {
     animate: false,
-    coordinateToPixelTransform: _ol_transform_.create(),
+    coordinateToPixelTransform: createTransform(),
     extent: null,
     focus: null,
     index: 0,
     layerStates: layerStates,
     layerStatesArray: layerStatesArray,
     pixelRatio: 1,
-    pixelToCoordinateTransform: _ol_transform_.create(),
+    pixelToCoordinateTransform: createTransform(),
     postRenderFunctions: [],
     size: [0, 0],
     skippedFeatureUids: {},
diff --git a/src/ol/transform.js b/src/ol/transform.js
index e8cda64521..968b1c4c10 100644
--- a/src/ol/transform.js
+++ b/src/ol/transform.js
@@ -2,7 +2,6 @@
  * @module ol/transform
  */
 import {assert} from './asserts.js';
-const _ol_transform_ = {};
 
 
 /**
@@ -22,16 +21,16 @@ const _ol_transform_ = {};
  * @private
  * @type {ol.Transform}
  */
-_ol_transform_.tmp_ = new Array(6);
+const tmp_ = new Array(6);
 
 
 /**
  * Create an identity transform.
  * @return {!ol.Transform} Identity transform.
  */
-_ol_transform_.create = function() {
+export function create() {
   return [1, 0, 0, 1, 0, 0];
-};
+}
 
 
 /**
@@ -39,9 +38,9 @@ _ol_transform_.create = function() {
  * @param {!ol.Transform} transform Transform.
  * @return {!ol.Transform} Transform.
  */
-_ol_transform_.reset = function(transform) {
-  return _ol_transform_.set(transform, 1, 0, 0, 1, 0, 0);
-};
+export function reset(transform) {
+  return set(transform, 1, 0, 0, 1, 0, 0);
+}
 
 
 /**
@@ -51,7 +50,7 @@ _ol_transform_.reset = function(transform) {
  * @param {!ol.Transform} transform2 Transform parameters of matrix 2.
  * @return {!ol.Transform} transform1 multiplied with transform2.
  */
-_ol_transform_.multiply = function(transform1, transform2) {
+export function multiply(transform1, transform2) {
   const a1 = transform1[0];
   const b1 = transform1[1];
   const c1 = transform1[2];
@@ -73,7 +72,7 @@ _ol_transform_.multiply = function(transform1, transform2) {
   transform1[5] = b1 * e2 + d1 * f2 + f1;
 
   return transform1;
-};
+}
 
 /**
  * Set the transform components a-f on a given transform.
@@ -86,7 +85,7 @@ _ol_transform_.multiply = function(transform1, transform2) {
  * @param {number} f The f component of the transform.
  * @return {!ol.Transform} Matrix with transform applied.
  */
-_ol_transform_.set = function(transform, a, b, c, d, e, f) {
+export function set(transform, a, b, c, d, e, f) {
   transform[0] = a;
   transform[1] = b;
   transform[2] = c;
@@ -94,7 +93,7 @@ _ol_transform_.set = function(transform, a, b, c, d, e, f) {
   transform[4] = e;
   transform[5] = f;
   return transform;
-};
+}
 
 
 /**
@@ -103,7 +102,7 @@ _ol_transform_.set = function(transform, a, b, c, d, e, f) {
  * @param {!ol.Transform} transform2 Matrix to set transform from.
  * @return {!ol.Transform} transform1 with transform from transform2 applied.
  */
-_ol_transform_.setFromArray = function(transform1, transform2) {
+export function setFromArray(transform1, transform2) {
   transform1[0] = transform2[0];
   transform1[1] = transform2[1];
   transform1[2] = transform2[2];
@@ -111,7 +110,7 @@ _ol_transform_.setFromArray = function(transform1, transform2) {
   transform1[4] = transform2[4];
   transform1[5] = transform2[5];
   return transform1;
-};
+}
 
 
 /**
@@ -123,13 +122,13 @@ _ol_transform_.setFromArray = function(transform1, transform2) {
  * @return {ol.Coordinate|ol.Pixel} return coordinate so that operations can be
  *     chained together.
  */
-_ol_transform_.apply = function(transform, coordinate) {
+export function apply(transform, coordinate) {
   const x = coordinate[0];
   const y = coordinate[1];
   coordinate[0] = transform[0] * x + transform[2] * y + transform[4];
   coordinate[1] = transform[1] * x + transform[3] * y + transform[5];
   return coordinate;
-};
+}
 
 
 /**
@@ -138,12 +137,11 @@ _ol_transform_.apply = function(transform, coordinate) {
  * @param {number} angle Angle in radians.
  * @return {!ol.Transform} The rotated transform.
  */
-_ol_transform_.rotate = function(transform, angle) {
+export function rotate(transform, angle) {
   const cos = Math.cos(angle);
   const sin = Math.sin(angle);
-  return _ol_transform_.multiply(transform,
-    _ol_transform_.set(_ol_transform_.tmp_, cos, sin, -sin, cos, 0, 0));
-};
+  return multiply(transform, set(tmp_, cos, sin, -sin, cos, 0, 0));
+}
 
 
 /**
@@ -153,10 +151,9 @@ _ol_transform_.rotate = function(transform, angle) {
  * @param {number} y Scale factor y.
  * @return {!ol.Transform} The scaled transform.
  */
-_ol_transform_.scale = function(transform, x, y) {
-  return _ol_transform_.multiply(transform,
-    _ol_transform_.set(_ol_transform_.tmp_, x, 0, 0, y, 0, 0));
-};
+export function scale(transform, x, y) {
+  return multiply(transform, set(tmp_, x, 0, 0, y, 0, 0));
+}
 
 
 /**
@@ -166,10 +163,9 @@ _ol_transform_.scale = function(transform, x, y) {
  * @param {number} dy Translation y.
  * @return {!ol.Transform} The translated transform.
  */
-_ol_transform_.translate = function(transform, dx, dy) {
-  return _ol_transform_.multiply(transform,
-    _ol_transform_.set(_ol_transform_.tmp_, 1, 0, 0, 1, dx, dy));
-};
+export function translate(transform, dx, dy) {
+  return multiply(transform, set(tmp_, 1, 0, 0, 1, dx, dy));
+}
 
 
 /**
@@ -185,7 +181,7 @@ _ol_transform_.translate = function(transform, dx, dy) {
  * @param {number} dy2 Final translation y.
  * @return {!ol.Transform} The composite transform.
  */
-_ol_transform_.compose = function(transform, dx1, dy1, sx, sy, angle, dx2, dy2) {
+export function compose(transform, dx1, dy1, sx, sy, angle, dx2, dy2) {
   const sin = Math.sin(angle);
   const cos = Math.cos(angle);
   transform[0] = sx * cos;
@@ -195,7 +191,7 @@ _ol_transform_.compose = function(transform, dx1, dy1, sx, sy, angle, dx2, dy2)
   transform[4] = dx2 * sx * cos - dy2 * sx * sin + dx1;
   transform[5] = dx2 * sy * sin + dy2 * sy * cos + dy1;
   return transform;
-};
+}
 
 
 /**
@@ -203,8 +199,8 @@ _ol_transform_.compose = function(transform, dx1, dy1, sx, sy, angle, dx2, dy2)
  * @param {!ol.Transform} transform Transform.
  * @return {!ol.Transform} Inverse of the transform.
  */
-_ol_transform_.invert = function(transform) {
-  const det = _ol_transform_.determinant(transform);
+export function invert(transform) {
+  const det = determinant(transform);
   assert(det !== 0, 32); // Transformation matrix cannot be inverted
 
   const a = transform[0];
@@ -222,7 +218,7 @@ _ol_transform_.invert = function(transform) {
   transform[5] = -(a * f - b * e) / det;
 
   return transform;
-};
+}
 
 
 /**
@@ -230,7 +226,6 @@ _ol_transform_.invert = function(transform) {
  * @param {!ol.Transform} mat Matrix.
  * @return {number} Determinant.
  */
-_ol_transform_.determinant = function(mat) {
+export function determinant(mat) {
   return mat[0] * mat[3] - mat[1] * mat[2];
-};
-export default _ol_transform_;
+}
diff --git a/test/spec/ol/render.test.js b/test/spec/ol/render.test.js
index 1c1a55ddeb..8ab353c2e1 100644
--- a/test/spec/ol/render.test.js
+++ b/test/spec/ol/render.test.js
@@ -2,7 +2,7 @@ import {equals} from '../../../src/ol/array.js';
 import {DEVICE_PIXEL_RATIO} from '../../../src/ol/has.js';
 import {toContext} from '../../../src/ol/render.js';
 import CanvasImmediateRenderer from '../../../src/ol/render/canvas/Immediate.js';
-import _ol_transform_ from '../../../src/ol/transform.js';
+import {scale as scaleTransform, create as createTransform} from '../../../src/ol/transform.js';
 
 
 describe('ol.render', function() {
@@ -27,7 +27,7 @@ describe('ol.render', function() {
         [0, 0, size[0] * pixelRatio, size[1] * pixelRatio]);
       expect(canvas.style.width).to.be(size[0] + 'px');
       expect(canvas.style.height).to.be(size[1] + 'px');
-      const transform = _ol_transform_.scale(_ol_transform_.create(),
+      const transform = scaleTransform(createTransform(),
         pixelRatio, pixelRatio);
       expect(equals(render.transform_, transform)).to.be.ok();
     });
diff --git a/test/spec/ol/renderer/canvas/intermediatecanvas.test.js b/test/spec/ol/renderer/canvas/intermediatecanvas.test.js
index 77b6a3b631..a4496cff34 100644
--- a/test/spec/ol/renderer/canvas/intermediatecanvas.test.js
+++ b/test/spec/ol/renderer/canvas/intermediatecanvas.test.js
@@ -1,4 +1,4 @@
-import _ol_transform_ from '../../../../../src/ol/transform.js';
+import {create as createTransform} from '../../../../../src/ol/transform.js';
 import ImageLayer from '../../../../../src/ol/layer/Image.js';
 import MapRenderer from '../../../../../src/ol/renderer/Map.js';
 import IntermediateCanvasRenderer from '../../../../../src/ol/renderer/canvas/IntermediateCanvas.js';
@@ -27,11 +27,11 @@ describe('ol.renderer.canvas.IntermediateCanvas', function() {
         },
         size: [10, 10],
         pixelRatio: 1,
-        coordinateToPixelTransform: _ol_transform_.create(),
-        pixelToCoordinateTransform: _ol_transform_.create()
+        coordinateToPixelTransform: createTransform(),
+        pixelToCoordinateTransform: createTransform()
       };
       renderer.getImageTransform = function() {
-        return _ol_transform_.create();
+        return createTransform();
       };
       MapRenderer.prototype.calculateMatrices2D(frameState);
       layerState = layer.getLayerState();
diff --git a/test/spec/ol/renderer/canvas/replay.test.js b/test/spec/ol/renderer/canvas/replay.test.js
index e732121c3b..337a5fadc0 100644
--- a/test/spec/ol/renderer/canvas/replay.test.js
+++ b/test/spec/ol/renderer/canvas/replay.test.js
@@ -15,7 +15,7 @@ import {renderFeature} from '../../../../../src/ol/renderer/vector.js';
 import Fill from '../../../../../src/ol/style/Fill.js';
 import Stroke from '../../../../../src/ol/style/Stroke.js';
 import Style from '../../../../../src/ol/style/Style.js';
-import _ol_transform_ from '../../../../../src/ol/transform.js';
+import {create as createTransform, scale as scaleTransform} from '../../../../../src/ol/transform.js';
 
 describe('ol.render.canvas.ReplayGroup', function() {
 
@@ -27,7 +27,7 @@ describe('ol.render.canvas.ReplayGroup', function() {
     let fill0, fill1, style1, style2;
 
     beforeEach(function() {
-      transform = _ol_transform_.create();
+      transform = createTransform();
       replay = new CanvasReplayGroup(1, [-180, -90, 180, 90], 1, 1, false);
       feature0 = new Feature(new Polygon(
         [[[-90, 0], [-45, 45], [0, 0], [1, 1], [0, -45], [-90, 0]]]));
@@ -92,7 +92,7 @@ describe('ol.render.canvas.ReplayGroup', function() {
       replay.replay(context, transform, 0, {});
       expect(lineToCount).to.be(4);
       lineToCount = 0;
-      _ol_transform_.scale(transform, 0.25, 0.25);
+      scaleTransform(transform, 0.25, 0.25);
       replay.replay(context, transform, 0, {});
       expect(lineToCount).to.be(3);
     });
@@ -249,7 +249,7 @@ describe('ol.render.canvas.ReplayGroup', function() {
       renderFeature(replay, polygon, style, 1);
       renderFeature(replay, multipolygon, style, 1);
       renderFeature(replay, geometrycollection, style, 1);
-      _ol_transform_.scale(transform, 0.1, 0.1);
+      scaleTransform(transform, 0.1, 0.1);
       replay.replay(context, transform, 0, {});
       expect(calls.length).to.be(9);
       expect(calls[0].geometry).to.be(point.getGeometry());
diff --git a/test/spec/ol/renderer/canvas/tilelayer.test.js b/test/spec/ol/renderer/canvas/tilelayer.test.js
index 6fe530c08d..21ba13e2f0 100644
--- a/test/spec/ol/renderer/canvas/tilelayer.test.js
+++ b/test/spec/ol/renderer/canvas/tilelayer.test.js
@@ -6,7 +6,7 @@ import MapRenderer from '../../../../../src/ol/renderer/Map.js';
 import CanvasTileLayerRenderer from '../../../../../src/ol/renderer/canvas/TileLayer.js';
 import TileWMS from '../../../../../src/ol/source/TileWMS.js';
 import XYZ from '../../../../../src/ol/source/XYZ.js';
-import _ol_transform_ from '../../../../../src/ol/transform.js';
+import {create as createTransform} from '../../../../../src/ol/transform.js';
 
 
 describe('ol.renderer.canvas.TileLayer', function() {
@@ -89,13 +89,13 @@ describe('ol.renderer.canvas.TileLayer', function() {
         extent: [0, 0, 20, 10],
         size: [20, 10],
         pixelRatio: 2,
-        coordinateToPixelTransform: _ol_transform_.create(),
-        pixelToCoordinateTransform: _ol_transform_.create(),
+        coordinateToPixelTransform: createTransform(),
+        pixelToCoordinateTransform: createTransform(),
         usedTiles: {},
         wantedTiles: {}
       };
       renderer.getImageTransform = function() {
-        return _ol_transform_.create();
+        return createTransform();
       };
       MapRenderer.prototype.calculateMatrices2D(frameState);
       const layerState = layer.getLayerState();
diff --git a/test/spec/ol/renderer/webgl/imagelayer.test.js b/test/spec/ol/renderer/webgl/imagelayer.test.js
index f741ad4191..ccfc693c64 100644
--- a/test/spec/ol/renderer/webgl/imagelayer.test.js
+++ b/test/spec/ol/renderer/webgl/imagelayer.test.js
@@ -1,4 +1,4 @@
-import _ol_transform_ from '../../../../../src/ol/transform.js';
+import {apply as applyTransform} from '../../../../../src/ol/transform.js';
 import Map from '../../../../../src/ol/Map.js';
 import ImageLayer from '../../../../../src/ol/layer/Image.js';
 import ImageSource from '../../../../../src/ol/source/Image.js';
@@ -52,23 +52,23 @@ describe('ol.renderer.webgl.ImageLayer', function() {
         pixelRatio, viewCenter, viewResolution, viewRotation, imageExtent);
       const matrix = renderer.getProjectionMatrix();
 
-      let output = _ol_transform_.apply(matrix, [-1, -1]);
+      let output = applyTransform(matrix, [-1, -1]);
       expect(output[0]).to.eql(-6);
       expect(output[1]).to.eql(-6);
 
-      output = _ol_transform_.apply(matrix, [1, -1]);
+      output = applyTransform(matrix, [1, -1]);
       expect(output[0]).to.eql(2);
       expect(output[1]).to.eql(-6);
 
-      output = _ol_transform_.apply(matrix, [-1, 1]);
+      output = applyTransform(matrix, [-1, 1]);
       expect(output[0]).to.eql(-6);
       expect(output[1]).to.eql(6);
 
-      output = _ol_transform_.apply(matrix, [1, 1]);
+      output = applyTransform(matrix, [1, 1]);
       expect(output[0]).to.eql(2);
       expect(output[1]).to.eql(6);
 
-      output = _ol_transform_.apply(matrix, [0, 0]);
+      output = applyTransform(matrix, [0, 0]);
       expect(output[0]).to.eql(-2);
       expect(output[1]).to.eql(0);
     });
diff --git a/test/spec/ol/transform.test.js b/test/spec/ol/transform.test.js
index bd0f6b8aab..13b5d91846 100644
--- a/test/spec/ol/transform.test.js
+++ b/test/spec/ol/transform.test.js
@@ -1,4 +1,16 @@
-import _ol_transform_ from '../../../src/ol/transform.js';
+import {
+  create,
+  reset,
+  set,
+  setFromArray,
+  translate,
+  scale,
+  rotate,
+  multiply,
+  compose,
+  invert,
+  apply
+} from '../../../src/ol/transform.js';
 
 
 describe('ol.transform', function() {
@@ -9,71 +21,71 @@ describe('ol.transform', function() {
     });
   }
 
-  describe('ol.transform.create()', function() {
+  describe('create()', function() {
     it('creates an identity transform', function() {
-      expect(_ol_transform_.create()).to.eql([1, 0, 0, 1, 0, 0]);
+      expect(create()).to.eql([1, 0, 0, 1, 0, 0]);
     });
   });
 
-  describe('ol.transform.reset()', function() {
+  describe('reset()', function() {
     it('resets tansform to an identity transform', function() {
       const transform = [1, 2, 3, 4, 5, 6];
-      expect(_ol_transform_.reset(transform)).to.eql([1, 0, 0, 1, 0, 0]);
+      expect(reset(transform)).to.eql([1, 0, 0, 1, 0, 0]);
       expect(transform).to.eql([1, 0, 0, 1, 0, 0]);
     });
   });
 
-  describe('ol.transform.set()', function() {
+  describe('set()', function() {
     it('sets the given values', function() {
-      const transform = _ol_transform_.create();
-      expect(_ol_transform_.set(transform, 1, 2, 3, 4, 5, 6)).to.eql([1, 2, 3, 4, 5, 6]);
+      const transform = create();
+      expect(set(transform, 1, 2, 3, 4, 5, 6)).to.eql([1, 2, 3, 4, 5, 6]);
       expect(transform).to.eql([1, 2, 3, 4, 5, 6]);
     });
   });
 
-  describe('ol.transform.setFromArray()', function() {
+  describe('setFromArray()', function() {
     it('sets values of 2nd transform on 1st transform', function() {
-      const transform1 = _ol_transform_.create();
+      const transform1 = create();
       const transform2 = [1, 2, 3, 4, 5, 6];
-      expect(_ol_transform_.setFromArray(transform1, transform2)).to.eql(transform2);
+      expect(setFromArray(transform1, transform2)).to.eql(transform2);
       expect(transform1).to.eql(transform2);
     });
   });
 
-  describe('ol.transform.translate()', function() {
+  describe('translate()', function() {
     it('applies translation to a transform', function() {
-      const transform = _ol_transform_.create();
-      expect(_ol_transform_.translate(transform, 3, 4)).to.eql([1, 0, 0, 1, 3, 4]);
+      const transform = create();
+      expect(translate(transform, 3, 4)).to.eql([1, 0, 0, 1, 3, 4]);
       expect(transform).to.eql([1, 0, 0, 1, 3, 4]);
     });
   });
 
-  describe('ol.transform.scale()', function() {
+  describe('scale()', function() {
     it('applies scaling to a transform', function() {
-      const transform = _ol_transform_.create();
-      expect(_ol_transform_.scale(transform, 3, 4)).to.eql([3, 0, 0, 4, 0, 0]);
+      const transform = create();
+      expect(scale(transform, 3, 4)).to.eql([3, 0, 0, 4, 0, 0]);
       expect(transform).to.eql([3, 0, 0, 4, 0, 0]);
     });
   });
 
-  describe('ol.transform.rotate()', function() {
+  describe('rotate()', function() {
     it('applies rotation to a transform', function() {
-      const transform = _ol_transform_.create();
-      assertRoughlyEqual(_ol_transform_.rotate(transform, Math.PI / 2), [0, 1, -1, 0, 0, 0]);
+      const transform = create();
+      assertRoughlyEqual(rotate(transform, Math.PI / 2), [0, 1, -1, 0, 0, 0]);
       assertRoughlyEqual(transform, [0, 1, -1, 0, 0, 0]);
     });
   });
 
-  describe('ol.transform.multiply()', function() {
+  describe('multiply()', function() {
     it('multiplies two transforms', function() {
       const transform1 = [1, 2, 1, 2, 1, 2];
       const transform2 = [1, 2, 1, 2, 1, 2];
-      expect(_ol_transform_.multiply(transform1, transform2)).to.eql([3, 6, 3, 6, 4, 8]);
+      expect(multiply(transform1, transform2)).to.eql([3, 6, 3, 6, 4, 8]);
       expect(transform1).to.eql([3, 6, 3, 6, 4, 8]);
     });
   });
 
-  describe('ol.transform.compose()', function() {
+  describe('compose()', function() {
     it('composes a translate, scale, rotate, translate transform', function() {
       const dx1 = 3;
       const dy1 = 4;
@@ -83,36 +95,36 @@ describe('ol.transform', function() {
       const dx2 = -dx1 / 2;
       const dy2 = -dy1 / 2;
 
-      const expected = _ol_transform_.create();
-      _ol_transform_.translate(expected, dx1, dy1);
-      _ol_transform_.scale(expected, sx, sy);
-      _ol_transform_.rotate(expected, angle);
-      _ol_transform_.translate(expected, dx2, dy2);
+      const expected = create();
+      translate(expected, dx1, dy1);
+      scale(expected, sx, sy);
+      rotate(expected, angle);
+      translate(expected, dx2, dy2);
 
-      const composed = _ol_transform_.create();
-      const composedReturn = _ol_transform_.compose(composed, dx1, dy1, sx, sy, angle, dx2, dy2);
+      const composed = create();
+      const composedReturn = compose(composed, dx1, dy1, sx, sy, angle, dx2, dy2);
       expect(composed).to.equal(composedReturn);
       expect(composed).to.eql(expected);
     });
   });
 
-  describe('ol.transform.invert()', function() {
+  describe('invert()', function() {
     it('inverts a transform', function() {
       let transform = [1, 0, 1, 0, 1, 0];
       expect(function() {
-        _ol_transform_.invert(transform);
+        invert(transform);
       }).to.throwException();
       transform = [1, 1, 1, 2, 2, 0];
-      expect(_ol_transform_.invert(transform)).to.eql([2, -1, -1, 1, -4, 2]);
+      expect(invert(transform)).to.eql([2, -1, -1, 1, -4, 2]);
       expect(transform).to.eql([2, -1, -1, 1, -4, 2]);
     });
   });
 
-  describe('ol.transform.apply()', function() {
+  describe('apply()', function() {
     it('applies a transform to a 2d vector', function() {
-      const transform = _ol_transform_.translate(_ol_transform_.create(), 2, 3);
+      const transform = translate(create(), 2, 3);
       const point = [1, 2];
-      expect(_ol_transform_.apply(transform, point)).to.eql([3, 5]);
+      expect(apply(transform, point)).to.eql([3, 5]);
       expect(point).to.eql([3, 5]);
     });
   });