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diff --git a/ui/gfx/geometry/axis_transform2d.h b/ui/gfx/geometry/axis_transform2d.h
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+++ b/ui/gfx/geometry/axis_transform2d.h
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+// Copyright (c) 2017 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef UI_GFX_GEOMETRY_AXIS_TRANSFORM2D_H_
+#define UI_GFX_GEOMETRY_AXIS_TRANSFORM2D_H_
+
+#include "ui/gfx/geometry/rect_f.h"
+#include "ui/gfx/geometry/vector2d_f.h"
+#include "ui/gfx/gfx_export.h"
+
+namespace gfx {
+
+// This class implements the subset of 2D linear transforms that only
+// translation and uniform scaling are allowed.
+// Internally this is stored as a scalar pre-scale factor, and a vector
+// for post-translation. The class constructor and member accessor follows
+// the same convention.
+class GFX_EXPORT AxisTransform2d {
+ public:
+  constexpr AxisTransform2d() = default;
+  constexpr AxisTransform2d(float scale, const Vector2dF& translation)
+      : scale_(scale), translation_(translation) {}
+
+  bool operator==(const AxisTransform2d& other) const {
+    return scale_ == other.scale_ && translation_ == other.translation_;
+  }
+  bool operator!=(const AxisTransform2d& other) const {
+    return !(*this == other);
+  }
+
+  void PreScale(float scale) { scale_ *= scale; }
+  void PostScale(float scale) {
+    scale_ *= scale;
+    translation_.Scale(scale);
+  }
+  void PreTranslate(const Vector2dF& translation) {
+    translation_ += ScaleVector2d(translation, scale_);
+  }
+  void PostTranslate(const Vector2dF& translation) {
+    translation_ += translation;
+  }
+
+  void PreConcat(const AxisTransform2d& pre) {
+    PreTranslate(pre.translation_);
+    PreScale(pre.scale_);
+  }
+  void PostConcat(const AxisTransform2d& post) {
+    PostScale(post.scale_);
+    PostTranslate(post.translation_);
+  }
+
+  void Invert() {
+    DCHECK(scale_);
+    scale_ = 1.f / scale_;
+    translation_.Scale(-scale_);
+  }
+
+  PointF MapPoint(const PointF& p) const {
+    return ScalePoint(p, scale_) + translation_;
+  }
+  PointF InverseMapPoint(const PointF& p) const {
+    return ScalePoint(p - translation_, 1.f / scale_);
+  }
+
+  RectF MapRect(const RectF& r) const {
+    DCHECK(scale_ >= 0.f);
+    return ScaleRect(r, scale_) + translation_;
+  }
+  RectF InverseMapRect(const RectF& r) const {
+    DCHECK(scale_ > 0.f);
+    return ScaleRect(r - translation_, 1.f / scale_);
+  }
+
+  float scale() const { return scale_; }
+  const Vector2dF& translation() const { return translation_; }
+
+  std::string ToString() const;
+
+ private:
+  // Scale is applied before translation, i.e.
+  // this->Transform(p) == scale_ * p + translation_
+  float scale_ = 1.f;
+  Vector2dF translation_;
+};
+
+static inline AxisTransform2d PreScaleAxisTransform2d(const AxisTransform2d& t,
+                                                      float scale) {
+  AxisTransform2d result(t);
+  result.PreScale(scale);
+  return result;
+}
+
+static inline AxisTransform2d PostScaleAxisTransform2d(const AxisTransform2d& t,
+                                                       float scale) {
+  AxisTransform2d result(t);
+  result.PostScale(scale);
+  return result;
+}
+
+static inline AxisTransform2d PreTranslateAxisTransform2d(
+    const AxisTransform2d& t,
+    const Vector2dF& translation) {
+  AxisTransform2d result(t);
+  result.PreTranslate(translation);
+  return result;
+}
+
+static inline AxisTransform2d PostTranslateAxisTransform2d(
+    const AxisTransform2d& t,
+    const Vector2dF& translation) {
+  AxisTransform2d result(t);
+  result.PostTranslate(translation);
+  return result;
+}
+
+static inline AxisTransform2d ConcatAxisTransform2d(
+    const AxisTransform2d& post,
+    const AxisTransform2d& pre) {
+  AxisTransform2d result(post);
+  result.PreConcat(pre);
+  return result;
+}
+
+static inline AxisTransform2d InvertAxisTransform2d(const AxisTransform2d& t) {
+  AxisTransform2d result = t;
+  result.Invert();
+  return result;
+}
+
+// This is declared here for use in gtest-based unit tests but is defined in
+// the //ui/gfx:test_support target. Depend on that to use this in your unit
+// test. This should not be used in production code - call ToString() instead.
+void PrintTo(const AxisTransform2d&, ::std::ostream* os);
+
+}  // namespace gfx
+
+#endif  // UI_GFX_GEOMETRY_AXIS_TRANSFORM2D_H_