diff --git a/modules/juce_graphics/geometry/juce_AffineTransform.h b/modules/juce_graphics/geometry/juce_AffineTransform.h
index 70937aeb81..dfc3a29c17 100644
--- a/modules/juce_graphics/geometry/juce_AffineTransform.h
+++ b/modules/juce_graphics/geometry/juce_AffineTransform.h
@@ -127,10 +127,24 @@ public:
     AffineTransform translated (float deltaX,
                                 float deltaY) const noexcept;
 
+    /** Returns a new transform which is the same as this one followed by a translation. */
+    template <typename PointType>
+    AffineTransform translated (PointType delta) const noexcept
+    {
+        return translated ((float) delta.x, (float) delta.y);
+    }
+
     /** Returns a new transform which is a translation. */
     static AffineTransform translation (float deltaX,
                                         float deltaY) noexcept;
 
+    /** Returns a new transform which is a translation. */
+    template <typename PointType>
+    static AffineTransform translation (PointType delta) noexcept
+    {
+        return translation ((float) delta.x, (float) delta.y);
+    }
+
     /** Returns a copy of this transform with the specified translation matrix values. */
     AffineTransform withAbsoluteTranslation (float translationX,
                                              float translationY) const noexcept;
diff --git a/modules/juce_graphics/geometry/juce_Rectangle.h b/modules/juce_graphics/geometry/juce_Rectangle.h
index 04adce4e17..640a50cdfd 100644
--- a/modules/juce_graphics/geometry/juce_Rectangle.h
+++ b/modules/juce_graphics/geometry/juce_Rectangle.h
@@ -711,7 +711,6 @@ public:
     }
 
     /** Casts this rectangle to a Rectangle<float>.
-        Obviously this is mainly useful for rectangles that use integer types.
         @see getSmallestIntegerContainer
     */
     Rectangle<float> toFloat() const noexcept
@@ -721,7 +720,6 @@ public:
     }
 
     /** Casts this rectangle to a Rectangle<double>.
-        Obviously this is mainly useful for rectangles that use integer types.
         @see getSmallestIntegerContainer
     */
     Rectangle<double> toDouble() const noexcept
@@ -730,6 +728,18 @@ public:
                                   static_cast<double> (w),     static_cast<double> (h));
     }
 
+    /** Casts this rectangle to a Rectangle with the given type.
+        If the target type is a conversion from float to int, then the conversion
+        will be done using getSmallestIntegerContainer().
+    */
+    template <typename TargetType>
+    Rectangle<TargetType> toType() const noexcept
+    {
+        Rectangle<TargetType> r;
+        copyWithRounding (r);
+        return r;
+    }
+
     /** Returns the smallest Rectangle that can contain a set of points. */
     static Rectangle findAreaContainingPoints (const Point<ValueType>* const points, const int numPoints) noexcept
     {
diff --git a/modules/juce_graphics/geometry/juce_RectangleList.h b/modules/juce_graphics/geometry/juce_RectangleList.h
index 9bcb2056ee..92c183cf64 100644
--- a/modules/juce_graphics/geometry/juce_RectangleList.h
+++ b/modules/juce_graphics/geometry/juce_RectangleList.h
@@ -343,7 +343,8 @@ public:
 
         @see getIntersectionWith
     */
-    bool clipTo (const RectangleList& other)
+    template <typename OtherValueType>
+    bool clipTo (const RectangleList<OtherValueType>& other)
     {
         if (rects.size() == 0)
             return false;
@@ -354,12 +355,12 @@ public:
         {
             const RectangleType& rect = rects.getReference (j);
 
-            for (int i = other.rects.size(); --i >= 0;)
+            for (const Rectangle<OtherValueType>* r = other.begin(), * const e = other.end(); r != e; ++r)
             {
-                RectangleType r (other.rects.getReference (i));
+                RectangleType clipped (r->template toType<ValueType>());
 
-                if (rect.intersectRectangle (r))
-                    result.rects.add (r);
+                if (rect.intersectRectangle (clipped))
+                    result.rects.add (clipped);
             }
         }