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

Grasshopper
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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.

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Download FroGH:

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

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

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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?

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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.

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

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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 don’t remember)

If you want a deeper understanding of all this you might be interested in this:
https://www.researchgate.net/publication/258840016_Improving_Frenet’s_Frame_Using_Bishop’s_Frame

1 Like
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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

2 Likes
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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?

– Dale

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Thank you! I will try them.

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Hi Quan,

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

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