# What is the offset curve of a 2D slice of the 3D offset of a twisted swept figure

I have a simple 2D shape as below helically swept.

I then do an offset in 3D from the surface. to get

if I take a 2D cross section I then get

As you can see the offset curve of the 2D section is a non constant offset from the original shape.

My question is. Is there a simple relation/or algorithm to figure out the 2D offset curve given

• the original curve ( piecewise linear or spline )
• the 3d constant offset
• the helix lead ( the length over which it turns 360 degrees )

I Think the solution is

Tangent to point on 2D primary curve

t0


Tangent to helix that point on 2D primary curve makes as it is swept

t1


Normal to 3d surface is

normal = t0 x t1


The offset vector in 3D is the unit normal times the offset

offsetVector = unitNormal * offset


2D offset is the projection of the offsetVector onto the XY plane.

I think this is right. Can somebody confirm?

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