distance between two Shapes/Areas in Java?

Question

If I have two java.awt.geom.Area's made out of the union of various simple Shapes (Polygons and Ellipses), is there a method out there to find the distance (i.e. closest distance) between the two Areas?

To clarify: suppose I have two arbitrary Areas, each of which is created from the union of shapes of any sort:

//Define the first area
Area a = new Area(new Ellipse2D.Double(50, 50, 100, 100));
a.add(new Area(new Rectangle2D.Double(100, 100, 100, 100)));

//Define the second area
Area b = new Area(new Ellipse2D.Double(200, 300, 100, 100));
b.add(new Area(new Ellipse2D.Double(250, 250, 100, 100)));

What I want is a method getDistance(Area a, Area b) that gives me a double representing the shortest distance between any point in Area a and any point in Area b. Here's an image of the above two Areas with a line in blue indicating the distance I'm interested in:

Is there a method out there to do this? If not, how might I implement one?

Answer 1

There doesn't seem to be a method that does that exactly; however, using PathIterators, you should be able to compare point to point along the outline of the shapes and find the distance manually.

http://docs.oracle.com/javase/6/docs/api/java/awt/geom/PathIterator.html

This Wikipedia article describes how you could efficiently implement this to avoid the quadratic obvious implementation.