diff --git a/modules/juce_graphics/geometry/juce_Parallelogram.h b/modules/juce_graphics/geometry/juce_Parallelogram.h
new file mode 100644
index 0000000000..7e7fcd86c8
--- /dev/null
+++ b/modules/juce_graphics/geometry/juce_Parallelogram.h
@@ -0,0 +1,192 @@
+/*
+  ==============================================================================
+
+   This file is part of the JUCE library.
+   Copyright (c) 2017 - ROLI Ltd.
+
+   JUCE is an open source library subject to commercial or open-source
+   licensing.
+
+   By using JUCE, you agree to the terms of both the JUCE 5 End-User License
+   Agreement and JUCE 5 Privacy Policy (both updated and effective as of the
+   27th April 2017).
+
+   End User License Agreement: www.juce.com/juce-5-licence
+   Privacy Policy: www.juce.com/juce-5-privacy-policy
+
+   Or: You may also use this code under the terms of the GPL v3 (see
+   www.gnu.org/licenses).
+
+   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
+   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
+   DISCLAIMED.
+
+  ==============================================================================
+*/
+
+namespace juce
+{
+
+//==============================================================================
+/**
+    Represents a parallelogram that is defined by 3 points.
+    @see Rectangle, Point, Line
+*/
+template <typename ValueType>
+class Parallelogram
+{
+public:
+    //==============================================================================
+    /** Creates a parallelogram with zero size at the origin.
+    */
+    Parallelogram() noexcept
+    {
+    }
+
+    /** Creates a copy of another parallelogram. */
+    Parallelogram (const Parallelogram& other) noexcept
+       : topLeft (other.topLeft), topRight (other.topRight), bottomLeft (other.bottomLeft)
+    {
+    }
+
+    /** Creates a parallelogram based on 3 points. */
+    Parallelogram (Point<ValueType> topLeftPosition,
+                   Point<ValueType> topRightPosition,
+                   Point<ValueType> bottomLeftPosition) noexcept
+       : topLeft (topLeftPosition), topRight (topRightPosition), bottomLeft (bottomLeftPosition)
+    {
+    }
+
+    /** Creates a parallelogram from a rectangle. */
+    Parallelogram (Rectangle<ValueType> rectangle) noexcept
+       : topLeft (rectangle.getTopLeft()),
+         topRight (rectangle.getTopRight()),
+         bottomLeft (rectangle.getBottomLeft())
+    {
+    }
+
+    Parallelogram& operator= (const Parallelogram& other) noexcept
+    {
+        topLeft = other.topLeft;
+        topRight = other.topRight;
+        bottomLeft = other.bottomLeft;
+        return *this;
+    }
+
+    /** Destructor. */
+    ~Parallelogram() noexcept {}
+
+    //==============================================================================
+    /** Returns true if the parallelogram has a width or height of more than zero. */
+    bool isEmpty() const noexcept                                   { return topLeft != topRight || topLeft != bottomLeft; }
+
+    /** Returns true if the parallelogram's coordinates are all finite numbers, i.e. not NaN or infinity. */
+    inline bool isFinite() const noexcept                           { return topLeft.isFinite() && topRight.isFinite() && bottomLeft.isFinite(); }
+
+    /** Returns the width of the parallelogram (i.e. the straight-line distance between the top-left and top-right. */
+    inline ValueType getWidth() const noexcept                      { return Line<ValueType> (topLeft, topRight).getLength(); }
+
+    /** Returns the height of the parallelogram (i.e. the straight-line distance between the top-left and bottom-left. */
+    inline ValueType getHeight() const noexcept                     { return Line<ValueType> (topLeft, bottomLeft).getLength(); }
+
+    //==============================================================================
+    /** Returns the parallelogram's top-left position as a Point. */
+    Point<ValueType> getTopLeft() const noexcept                    { return topLeft; }
+
+    /** Returns the parallelogram's top-right position as a Point. */
+    Point<ValueType> getTopRight() const noexcept                   { return topRight; }
+
+    /** Returns the parallelogram's bottom-left position as a Point. */
+    Point<ValueType> getBottomLeft() const noexcept                 { return bottomLeft; }
+
+    /** Returns the parallelogram's bottom-right position as a Point. */
+    Point<ValueType> getBottomRight() const noexcept                { return topRight + (bottomLeft - topLeft); }
+
+    //==============================================================================
+    /** Returns true if the two parallelograms are identical. */
+    bool operator== (const Parallelogram& other) const noexcept     { return topLeft == other.topLeft && topRight == other.topRight && bottomLeft == other.bottomLeft; }
+
+    /** Returns true if the two parallelograms are not identical. */
+    bool operator!= (const Parallelogram& other) const noexcept     { return ! operator== (other); }
+
+    //==============================================================================
+    /** Returns a parallelogram which is the same as this one moved by a given amount. */
+    Parallelogram operator+ (Point<ValueType> deltaPosition) const noexcept
+    {
+        auto p = *this;
+        p += deltaPosition;
+        return p;
+    }
+
+    /** Moves this parallelogram by a given amount. */
+    Parallelogram& operator+= (Point<ValueType> deltaPosition) noexcept
+    {
+        topLeft += deltaPosition;
+        topRight += deltaPosition;
+        bottomLeft += deltaPosition;
+        return *this;
+    }
+
+    /** Returns a parallelogram which is the same as this one moved by a given amount. */
+    Parallelogram operator- (Point<ValueType> deltaPosition) const noexcept
+    {
+        return operator+ (-deltaPosition);
+    }
+
+    /** Moves this parallelogram by a given amount. */
+    Parallelogram& operator-= (Point<ValueType> deltaPosition) noexcept
+    {
+        return operator-= (-deltaPosition);
+    }
+
+    /** Returns a parallelogram that has been scaled by the given amount, centred around the origin. */
+    template <typename PointOrScalarType>
+    Parallelogram operator* (PointOrScalarType scaleFactor) const noexcept
+    {
+        auto p = *this;
+        p *= scaleFactor;
+        return p;
+    }
+
+    /** Scales this parallelogram by the given amount, centred around the origin. */
+    template <typename PointOrScalarType>
+    Parallelogram operator*= (PointOrScalarType scaleFactor) noexcept
+    {
+        topLeft *= scaleFactor;
+        topRight *= scaleFactor;
+        bottomLeft *= scaleFactor;
+        return *this;
+    }
+
+    //==============================================================================
+    /** Returns a point within this parallelogram, specified as proportional coordinates.
+        The relative X and Y values should be between 0 and 1, where 0 is the left or
+        top of this parallelogram, and 1 is the right or bottom. (Out-of-bounds values
+        will return a point outside the parallelogram).
+    */
+    Point<ValueType> getRelativePoint (Point<ValueType> relativePosition) const noexcept
+    {
+        return topLeft
+                + (topRight - topLeft) * relativePosition.x
+                + (bottomLeft - topLeft) * relativePosition.y;
+    }
+
+    /** Returns a transformed verstion of the parallelogram. */
+    Parallelogram transformedBy (const AffineTransform& transform) const noexcept
+    {
+        auto p = *this;
+        transform.transformPoints (p.topLeft, p.topRight, p.bottomLeft);
+        return p;
+    }
+
+    /** Returns the smallest rectangle that encloses this parallelogram. */
+    Rectangle<ValueType> getBoundingBox() const noexcept
+    {
+        const Point<ValueType> points[] = { topLeft, topRight, bottomLeft, getBottomRight() };
+        return Rectangle<ValueType>::findAreaContainingPoints (points, 4);
+    }
+
+    Point<ValueType> topLeft, topRight, bottomLeft;
+};
+
+} // namespace juce
diff --git a/modules/juce_graphics/juce_graphics.h b/modules/juce_graphics/juce_graphics.h
index 6953c238e7..358500276a 100644
--- a/modules/juce_graphics/juce_graphics.h
+++ b/modules/juce_graphics/juce_graphics.h
@@ -105,6 +105,7 @@ namespace juce
 #include "geometry/juce_Point.h"
 #include "geometry/juce_Line.h"
 #include "geometry/juce_Rectangle.h"
+#include "geometry/juce_Parallelogram.h"
 #include "placement/juce_Justification.h"
 #include "geometry/juce_Path.h"
 #include "geometry/juce_RectangleList.h"