Grasshopper

algorithmic modeling for Rhino

How the arc can be  rotated  around  its start and end point by using  vector?

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I think I see where you're going with this?

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Oh.  I thought that 'EdgeSrf' with only two edges was too simple but didn't see the flaw until I baked it...  "Easy fix" to get a flat lofted result by dividing the 'IntCrv' and making straight lines to the center-top, but boring.  Lacking the saddle effect.

Can this arc be created by using  ax2   parabola or any other  formula ?

yes

 Parabola has been created but it cannot be rotated such polygon around the center point.

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Oh yes it can!  To build on the earlier code in this thread, you need to create your parabola in the same frame of reference as the 'Arc' and 'IntCrv' examples.

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In this code you posted, parabols rotate such poligon.gh, if you had connected the 'Range' output to Y instead of X on 'Pt', the parabola would at least be oriented properly for the polar array...

The benefit of using the polygon edges as the basis instead of the polar array is that the parabola ends touch as you want.

Thanks 

Poligon is better than polar array in this form. How can the poligon and parabole corner points be moved to Z direction to obtain the image form attached ?

Looks like you have mucked up the algorithm so the curves don't meet at the polygon vertices anymore!?  That's going backwards...  And moving anything in the Z direction is about as simple as it gets!

It appears you didn't learn much from my code examples.  Too bad.

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