0

Consider a helical tube with a circular cross section. I already can make a regular helical tube:

what's the equation of helix surface?

Now, instead of a circular cross section, I want to make it have a cross section that is a sine wave imposed over a circle, so that the resulting cross section resembles a flower:

Equation of sine wave around a circle

My two questions are:

  1. How can I parameterize a helical tube that has such a cross section?
  2. Is there a name for this surface?

Thank you very much!

Community
  • 1
Nir
  • 1
  • 1
    If you use the equation in the answer by Jyrki Lahtonen you just need to substitute $a=a_0(1+\sin ku)$. – N74 Apr 08 '17 at 07:56
  • Thank you very much! What is the reasoning behind this substitution? And what can we call this surface? – Nir Apr 08 '17 at 20:12
  • I copy a passage from the cited answer:

    "The key is that we get the desired surface by drawing (3D-)circles with axis direction determined by the direction of the curve, i.e. the tangent. Equivalently, we draw a circle of radius $a$ in the plane spanned by $\vec{n}$ and $\vec{b}$."

    Now we draw your flowered-shaped surface instead of a circle modulating its radius.

     – N74 Apr 08 '17 at 20:32

0 Answers0