diff --git a/engine/core/painting/Point.dart b/engine/core/painting/Point.dart
index 856f3360fdfc0c2addab930972c4bea341c6920b..82d2875e3b82c72a145429c439229f2d92c3839d 100644
--- a/engine/core/painting/Point.dart
+++ b/engine/core/painting/Point.dart
@@ -4,9 +4,22 @@
 
 part of dart.sky;
 
+/// Holds 2 floating-point coordinates.
 class Point {
   double x;
   double y;
 
   Point(this.x, this.y);
+
+  bool operator ==(other) {
+    if (!(other is Point)) return false;
+    return x == other.x && y == other.y;
+  }
+  int get hashCode {
+    int result = 373;
+    result = 37 * result + x.hashCode;
+    result = 37 * result + y.hashCode;
+    return result;
+  }
+  String toString() => "Point($x, $y)";
 }
diff --git a/engine/core/painting/Rect.dart b/engine/core/painting/Rect.dart
index a54f7aeaf9cbeffd2f17600846bb8cf9268ba14e..4c958fdbcfe0c7a940cfd16c4874285218aa2fe9 100644
--- a/engine/core/painting/Rect.dart
+++ b/engine/core/painting/Rect.dart
@@ -4,29 +4,26 @@
 
 part of dart.sky;
 
+/// Holds 4 floating-point coordinates for a rectangle.
 class Rect {
-  Float32List _value;
+  final Float32List _value = new Float32List(4);
   double get left => _value[0];
   double get top => _value[1];
   double get right => _value[2];
   double get bottom => _value[3];
 
-  Rect() : new Float32List(4);
+  Rect();
 
   Rect.fromPointAndSize(Point point, Size size) {
-    _value = new Float32List(4)
-        ..[0] = point.x
-        ..[1] = point.y
-        ..[2] = point.x + size.width
-        ..[3] = point.y + size.height;
+    _value
+      ..[0] = point.x
+      ..[1] = point.y
+      ..[2] = point.x + size.width
+      ..[3] = point.y + size.height;
   }
 
   Rect.fromLTRB(double left, double top, double right, double bottom) {
-    _value = new Float32List(4)
-        ..[0] = left
-        ..[1] = top
-        ..[2] = right
-        ..[3] = bottom;
+    setLTRB(left, top, right, bottom);
   }
 
   Point get upperLeft => new Point(left, top);
@@ -36,13 +33,26 @@ class Rect {
 
   // Rects are inclusive of the top and left edges but exclusive of the bottom
   // right edges.
-  bool contains(Point point) => point.x >= left && point.x < right
-                             && point.y >= top && point.y < bottom;
+  bool contains(Point point) =>
+      point.x >= left && point.x < right && point.y >= top && point.y < bottom;
 
   void setLTRB(double left, double top, double right, double bottom) {
-    _value[0] = left
-        ..[1] = top
-        ..[2] = right
-        ..[3] = bottom;
+    _value
+      ..[0] = left
+      ..[1] = top
+      ..[2] = right
+      ..[3] = bottom;
   }
+
+  bool operator ==(other) {
+    if (!(other is Rect)) return false;
+    for (var i = 0; i < 4; ++i) {
+      if (_value[i] != other._value[i]) return false;
+    }
+    return true;
+  }
+  int get hashCode {
+    return _value.fold(373, (value, item) => (37 * value + item.hashCode));
+  }
+  String toString() => "Rect.LTRB($left, $top, $right, $bottom)";
 }
diff --git a/engine/core/painting/Size.dart b/engine/core/painting/Size.dart
index cf41608b8a9936efb4b5dee1837fd8d2d0d40457..5697086c319c9361d59a5c736e3956d5e571b96e 100644
--- a/engine/core/painting/Size.dart
+++ b/engine/core/painting/Size.dart
@@ -4,9 +4,22 @@
 
 part of dart.sky;
 
+/// Holds a 2D floating-point size.
 class Size {
   double width;
   double height;
 
-  Point(this.width, this.height);
+  Size(this.width, this.height);
+
+  bool operator ==(other) {
+    if (!(other is Size)) return false;
+    return width == other.width && height == other.height;
+  }
+  int get hashCode {
+    int result = 373;
+    result = 37 * result + width.hashCode;
+    result = 37 * result + height.hashCode;
+    return result;
+  }
+  String toString() => "Size($width, $height)";
 }