#EggsAndDarts
To transfer the egg and dart in https://pixelfed.social/p/Splines/797038670230603707 to the #doublyCurved surface of an #ovolo is a multistep process.
There are 24 eggs and darts around the entire Ovolo. So each egg and dart nominally occupies 360°/24 = 15°.
#Revolve arc AD in https://pixelfed.social/p/Splines/792124787573855518 about the #columnAxis to get the virtual surface. Points A and D are same in both figures. Then use cutting planes as described in https://pixelfed.social/p/Splines/790645054230337543 to get a wedge-shaped segment whose angle is 15° and one side of which is marked with A and D.
This is a doubly curved surface. Unlike a cylinder, where one side is straight while the other is curved, the surface of an Ovolo is curved in both horizontal and vertical directions.
To transfer the egg and dart to a doubly curved surface, we need a new operation called #UnrollSurface, which unrolls the wedge shape into a flat surface whose top-left corner is marked Q. Note the top is wider than the bottom.
Place the flattened wedge between the rim and the flat slab and align the top of the flat portion of the slab with the center of the top edge of the flattened wedge. Temporarily move the dart to align its center too, but only move it in the horizontal direction
If the flattened wedge were flexible and if the eggs and darts were flexible, we could flip all of these over, flex and squeeze the solid shapes, and line up Q with D so that the rim and dart appear "outside" the original wedge while the slab remains "inside" (or toward the center of the Ovolo).
Fortunately, in a #CAD tools, solids don't always have to be treated as rigid. Now we will use another new operation called #FlowOnSurface to flow the egg and dart on the wedge.
We then slice off the top of the egg and dart at the location PQ in https://pixelfed.social/p/Splines/796958366767133979.
Finally, we separate the dart, which we had aligned with the egg to minimize distortion