How to get Bishop Frame and Frenet Serret frame of a nurbs curve?

Binormals (22.5 KB)
Binormals V1 without FroGH (19.3 KB)

The GHs above are what I tried so far, for me it is too hard, help!
The first one has a plugin called FroGH, which can return the Frenet Serret frame of a polyline, maybe it can be a reference.

Download FroGH:

Let me shamelessly push this up again, feels like today is my lucky day.

How many people do you think know what a “Bishop Frame” or “Frenet Serret frame” is?

I don’t know what are they exactly either…
But from my very limited experience and all the posts have related keywords, I think they are crucial when animating something moving along a curve in 3D space.
Specially the latter which appears more stable.
Isn’t that pretty important even though GH is not an animation tool?

That may explain the lack of replies, eh? A better explanation is likely to get helpful answers.

And please don’t expect me to look it up or install a plugin to understand your question.

Ha, That is exactly why I posted two GHs up there, thank you for openning it and having a look.

Are you trying to solve a specific problem or is this a theoretical question?
If you are searching a practical solution, PFrame is the answer:
Of each PFrame

  • Z axis is the tangent N
  • X axis is the derivative T
  • Y axis is the cross product B of N and T
    (x and y axes might be the other way around, I don’t remember)

If you want a deeper understanding of all this you might be interested in this:’s_Frame_Using_Bishop’s_Frame

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It occurred to me when I was answering a community question. I used vector math to orient this monkey on the slider. I think if I can get the frames I mentioned in the title(by evaluating a curve), the animation would be much easier and much more accurate on a complex nurbs curve.

I think the bishop frame is crucial when somebody needs to fly a monkey along a trail in the sky.

@Joseph_Oster how can you say it’s not fun, it’s fun, look at the cute monkey.
Honeycam 2023-05-14 09-20-50


Hi @Quan_Li,

RhinoCommon methods such as Curve.CreateRailFrames and Curve. CreatePlanarRailFrames are using in Rhino Sweep1 and ArrayCrv commands. Perhaps this would help?

– Dale

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Thank you! I will try them.

Hi Quan,

Maybe I’m misunderstanding your question but aren’t the Planes depicted in this view what you are after?

Where the planes are all oriented consistently along the evaluated curve?