This is my "specialty." I can't even count how many I've carved--hundreds. I used to draw a D-shape on the top and arcs on the side, but after doing it so many times, I didn't need a template and could just see the 3-D shape in my head. It occurred to me that some luthiers approach things very scientifically, always going with the measurement, relying on the ruler. That's not a bad thing--if you tried to do everything by eye you'd end up with a really interesting and likely non-functional instrument.
But as an artist and a painter, I view carving as sculpting. You have to see the thing as a three-dimensional, "living" object that fits like a piece in a larger puzzle or finger of a hand, hand of an arm, arm of a body.
So even a little thing like a nut is a sculpture. If you draw a face by tracing lines you may never come to recognize the face while you're too busy measuring the lines. Da Vinci could have sculpted or painted bodies based completely on proportions, which he did as a starting point, but he gave much credit to also bringing life to the personality of the person being sculpted.
All these little parts come together to create a body, a violin, that has a personality and a spirit of its own. Nothing in my head is just a measurement or just a tracing of a template. There must always be more to it than that if lutherie is to be an art form, which I believe it is.