I'm into oval shapes these days, and worked up one in an open segmented version. The trick was to keep the segments the same size all around the circumference while using my usual wedge method for this type of bowl.
Here's a picture of the bowl and what the rings looked like from the underside, once cut. I sanded the remainder of the wedges from the center so I could use it for the base. An alternative would have been just to use another thin piece of wood.
Same technique as I've been using, but the different shape gives it a totally new look.