Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

enter image description here

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

enter image description here

if I take a 2D cross section I then get

enter image description here

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?

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.