Let's take another look at the sundial, below. The left side is the front view; the right side is the side view. In the side view, the headrest of the sofa is seen through one of the sundial hour panels. This is the view from ground level. The sofa's cylindrical headrest is seen edge-on as a dark circle through the middle of one of the panels.

Now look at the set of images below. Each one shows the view of the sofa from the Sun's position at the indicated time. From the Sun's point of view, the ring of panels is seen almost edge-on (in the top-half of each image, in front of the sofa back). You can see that the panels provide shade for the back of the sofa throughout the day.