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

Binormals V1.gh (22.5 KB)
Binormals V1 without FroGH plugin.gh (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.

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

How many people do you think know what a â€śBishop Frameâ€ť or â€śFrenet Serret frameâ€ť is?

I donâ€™t know what are they exactly eitherâ€¦
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.
Isnâ€™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 donâ€™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.

hello,
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 donâ€™t remember)

If you want a deeper understanding of all this you might be interested in this:
https://www.researchgate.net/publication/258840016_Improving_Frenetâ€™s_Frame_Using_Bishopâ€™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 itâ€™s not fun, itâ€™s fun, look at the cute monkey.

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Hi @Quan_Li,

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

â€“ Dale

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Thank you! I will try them.

Hi Quan,

Maybe Iâ€™m misunderstanding your question but arenâ€™t the Planes depicted in this view what you are after?

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