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project a non-planar 3D spline

Genius
Genius
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!
4 REPLIES

Re: project a non-planar 3D spline

Siemens Phenom Siemens Phenom
Siemens Phenom

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.

山田
yamada

Re: project a non-planar 3D spline

Genius
Genius

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

Siemens Phenom Siemens Phenom
Siemens Phenom

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.

山田
yamada

Re: project a non-planar 3D spline

Genius
Genius

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