There is no managed way to do the outline. However, GDI+ does have an function called GdipWindingModeOutline that can do exactly this.
Here is the MSDN reference
This code does the trick:
// Declaration required for interop
[DllImport(@"gdiplus.dll")]
public static extern int GdipWindingModeOutline( HandleRef path, IntPtr matrix, float flatness );
void someControl_Paint(object sender, PaintEventArgs e)
{
// Create a path and add some rectangles to it
GraphicsPath path = new GraphicsPath();
path.AddRectangles(rectangles.ToArray());
// Create a handle that the unmanaged code requires. nativePath private unfortunately
HandleRef handle = new HandleRef(path, (IntPtr)path.GetType().GetField("nativePath", BindingFlags.NonPublic | BindingFlags.Instance).GetValue(path));
// Change path so it only contains the outline
GdipWindingModeOutline(handle, IntPtr.Zero, 0.25F);
using (Pen outlinePen = new Pen(Color.FromArgb(255, Color.Red), 2))
{
g.DrawPath(outlinePen, path);
}
}