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03-30-2018 12:40 AM - edited 03-30-2018 12:42 AM

I often try to project a non-planar **3D spline** to **a plane or a sketch**, and find that both the **poles** and the **knots** can also be projected precisely to the resulting 2D spline. I like this matching relationship.

But I have some concern about the reliability of the supposed projecting relationship between functional points on the 3D spline and those on the 2D spline.

Hope to have your comments. Thanks!

Solved! Go to Solution.

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- spline

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04-01-2018 02:47 AM - edited 04-01-2018 02:48 AM

Suppose you have a spline **S** with poles **P1, ..., Pn**. And suppose** T** is any affine transformation. Then the transformed spline **T(S)** has poles** T(P1), ..., T(Pn)** and the same knots as the original spline **S**. In other words, you can transform a spline just by transforming its poles and keeping the same knots.

Affine transformations include translations, rotations, scaling (uniform or non-uniform), skewing, and projections along a vector onto a plane.

This doesn't include the **Toward Point** and **Angle to Vector** options of projection -- those are not affine transformations.

yamada

Re: project a non-planar 3D spline

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04-01-2018 05:54 AM

Hi @Yamada Thanks for explaining the underlying math!

Hope you would not mind two more questions:

**Q1.** Is there any easy way to **skew a spline**? Currenly I build sophisticated constraints in sketch to do this job. It's really a painful process.

**Q2.** NX generates knots automatically in a multi-segment spline. For example a 2-segment spline has a knot between the start and the end and generally % parameter of the knot is not 50%. Is there any easy principle for judging **% parameter of knots in a spline**?

Thanks!

Re: project a non-planar 3D spline

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04-01-2018 08:13 AM

Can you ask new questions, please. No-one will be able to find the questions (or the answers) if we hide them here as part of a "project a spline" topic. I will be happy to answer them both. But, tomorrow, maybe.

yamada

Re: project a non-planar 3D spline

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04-01-2018 08:42 AM - edited 04-01-2018 08:49 AM

Hi @Yamada Sure. Just do the answer when you can find some time. Thank you!

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