Adam,
Perhaps I should have made clear that I was speaking of convex Newport shells. My cartoon may have been a little bit much of a simplification but it falls out of the carving procedure I was taught which involves cutting Vees between each ray as a carving step even though they do not appear as Vees, but flats, at the conclusion.
Start by roughing out the outline of the entire carving, and than reserve the area surrounded by the scroll and containing the splayed hollowed leaves in the center by depth cutting its perimeter with gouges of suitable radii to obtain the eliptical outline, and back cutting inward along the area of the rays of the shell.
Next, carve and plane the S-shaped surface of the entire ray area to smooth contours that are constant depths circumferentially, but vary in profile radially to suit the shape of the eventual rays. I believe this step is critically important to getting nice uniform ray/flutes to the shell.
Only after this surface is nicely faired do you come back and cut the varying curved Vee grooves between each ray that devolve to straight lnes in plan view at the end of the fan, round the convex rays to become tangent to the Vees already cut, and then cut the concave rays , leaving some of the edge of the Vee standing as a sharp ridge separating the rays.
I believe this general method was laid out by Al Breed in an article in Fine Woodworking
about ten years ago; if I am mistaken, or misunderstood - my apologies.
I find carving shells somewhat nerve wracking because of the investment in time which is at risk until the very last cuts in the splayed hollow leaves are complete - because they tend to chip easily due to the variations in carving relative to the grain.
Karl