Notes on where I went and the obstacle faced.
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Instead of using multiple planes, I created the fan pattern and the 3D path in one sketch, with parametrically rising 3D lines as one can see.
Then connected the points at the top, but for some reason Fusion 360 doesn't like me sweeping with a spline as the path. (Will see the video again - because I think it did exactly that). Why is my 'OK' disabled?
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Edit: Got further in the above situation by selecting Path + Guide Surface (using a temporary extruded cylinder face) - that works!
But that outcome wasn't quite smooth and I disliked that one needs to tune the splines by hand (two of them!).
Here is a way that doesn't involve spline tuning.
1. Create "step" points in a 3D sketch as shown above (but no need to connect them by spline).
2. Surface > Loft them together. I left the topmost (0 step) out.
3. At this point, I extruded a solid body to the surface. Needed to Surface > Modify > Extend the surface since their outlines were the same and "Extrude To" didn't like it.
4. Mirrorred the body
5. Joined the gap (by Solid > Revolve)
6. Smoothened the top (Fillet)
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This is still not mathematically ideal since not all surface lines are radial-from-center-and-horizontal (in lack of better terms) but this is good enough. The non-radialness comes from the use of Fillet and can thus be done differently, if someone wants a "horizontal" body (ie. where the highest peak doesn't lean downwards, as it does in the picture).
Hint: Inspect > Isocurve analysis > Type: U may be useful in seeing the forms.
DISCLAIMER:
I needed to struggle with the Fustion 360 Forums as well. Ran out of time editing the above post. That's why the duplicate. I got what I wanted - thanks for the help.
Asko Kauppi
IT guy into Cleantech.