What is all this G1, G2, G3 stuff?
G1, G2, G3, ..., Gn are commonly used in surface modeling to describe the continuity of two surfaces that meet at an edge.
G1 - positional continuity - means two surfaces that meet along a common edge will have any point along that edge co-resident (they meet at the edge) but they do not have to be tangent/ typically you will have crease where these surfaces meet.
G2 - tangential continuity - means two surfaces will meet at a common edge and the slope of any point along that edge on either surface with be tangent. In other words their first derivatives defining the edge where the surfaces meet will be equal. No crease where the surfaces meet.
G3 - curvature continuity - means two surfaces will meet at a common edge and the rate of change of slope of any point along that edge on either surface will be equal. Or in other words the second derivative of a the function defining a point along the edge where the surfaces meet will be equal. No crease where the surfaces meet and the rate of change in the slope is uniform (think of a spiral vs a circle).
and to G4 would mean the 3rd derivative of a function defining a point along a common edge of two surfaces would be equal and so on. However, although I know packages like alias (formerly studiotools) can handle continuity beyond G3 I have never seen a case where it was used.
This came out exceptionally clean. I'm still trying to figure out how you were able to build and possibly test for G3 continuity building curves in maya. Even modeling the initial surface it's difficult to get the curves just right while matching a reference. Does anyone know a good resource on this? I understand the part where it's being chopped up with trim surfaces, but maya's curve curve tools leave a lot to be desired.