The original question about the 3-point spline curve monsters was formulated too late in the evening after a long day of work and the answer should really have been obvious.
I increasingly find myself confronted with modeling problems and almost exclusively when working with surfaces in Fusion 360. To find a solution for a given problem I then have to determine if this is a limit in my understanding or a limit in available tools or a technical limit in what can be accomplished with a given software. The latter one would be the kernel.
Thus I am very interested in what is going on under the hood. So if the kernel can handle 5 and higher degrees of NURBS then that leaves 2 areas where I need t look for "solutions". Available tools and my own limitations.
Here is one such model, which seems simple but attempting to have somewhat decent curvature continuity (G2) or at the very least tangency (G1) across the main surfaces proved to be a challenge.
I was helping another user with this model. The main problem as so often was that Fusion 360 refused to shell part of the object, the high curvature area where the wing joins the fuselage. The reason was improper modeling techniques such as missing tangency and curvature continuity constraints in sketches and in lofts.
I fixed most of these but also backed myself into a corner again in that same area having to fill a 5-sided area. I resorted to using a 5-sided patch and the curvature at the boundary is not great, but I was able to "shell" the object by individually offsetting and trimming surfaces.


While still less than ideal from a surfacing standpoint, nicely looking functional models can be created. This user 3D prints quite sophisticated models and wins competitions with his creations and I was happy to be able to help him.
This next image was my own project. The object I was really interested in was not the actual bicycle lamp. I needed an adapter in order to be able to attach it to my recumbent. Or perhaps better put, I did not like the adapter it came with when I purchased it. I'll leave it for the participants in this thread to figure out what kind of weird bicycle I ride 😉




With these images, I hope to highlight what I generally consider to be a modeling challenge. There is no way to model these objects solely with solid modeling techniques. Technical surfacing, on the other hand, requires quite a bit of knowledge of how NURBS surfaces work, so in essence, the original question was driven not by any specific modeling challenge but to gain a little bit of knowledge to help meet future challenges.
Oh, and this "thing" was also 3D printed at Shapeways looks and works great.