Hi everyone,

Here is a 3d curve I drew, with its curvature vectors (unitized for illustration) alongside. As you can see we encounter several “discontinuities” of these vectors (abrupt angle shifting in various spots). I’d like to obtain the same curve, but whith these vectors forming a “continuity”.

Now, I know this problem has already been addressed several times here and that it can occur with connected curves (case here btw), but also “mysteriously” (the mystery laying in the Frenet-Serret frame computing algorithm: aka Tangent and perpendicular frame).

The thing is I use this Frenet frame to compute some dynamic simulation in grasshopper (with Anemone for the recursive part, fyi). It’s all about the trajectory of a point particle alongside a 3d curve, in simple gravity field (so, basically a rollercoaster).

Thus, each computed frenet frame is dependent on the previous one.

So I cannot simply rotate the frame manually in a discrete division of the curve, because said division is computed through the recursion.

Is there a way to obtain the same curve but with continuous torsion?

I’ve already tried :

- Rebuild command,
- Extract vertices and redraw a curve with these,
- Offset a little the curve in order to get a “cleaner” one,

But all of these don’t seem to work.

A big thank you if you can help me,

Regards.

Frenet shifting along curve.gh (13.9 KB)