Capture region that geometry crosses during transformation

Hello, I’m wondering if someone can point me in the right direction to capture the entire region that a simple geometry crosses as it goes through a finite rotation and transformation.

Specifically I would like to be able to have a single geometry that represents the entire region passed by the geometry in it’s full range of motion. I am including the grasshopper file that includes the full motion and a photo which is simply several baked step along that path of motion that represents what that shape should look like as those steps approach infinity.

LemansSwing(simple).gh (14.7 KB)
Shelf moving through range of swing.pdf (16.8 KB)

Thanks for any help or direction you may have,

Here are a few photos for to better explain the problem:

The second screenshot shows roughly the shape of the single curve I am hoping to achieve.

Hello
I think you can elevate curve profile depending on the angle, then record positions using a data recorder then loft the curves
then project on a plane


Region union seems best.

LemansSwing(simple).gh (18.2 KB)

See this link it could also helps

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Thank you for the solution Laurent - I am going to explore it to try and fully understand the approach!