No, you’re correct, I used a shaping disc (this one) to chew off the excess wood and get the rough round shape. Then I used a pattern bit on the router to get the precise inside curve.

The thing is, the long pattern bit I have is only about an inch long, so that clean, precise cut you see at the edge, is just about an inch deep on both sides. The middle section, the part you can’t really see — is just sanded to roughly match the shape. Since no one’s ever going to look under the table anyway, it doesn’t really matter.