Nurbs Curve - Knot Vectors

Would anyone be willing to explain the Knot Vector in the Nurbs Curve component. I understand it should look something like 0,0,0,1,1,1,4,4,666. But I am unable to understand what these numbers represent and how to control a curve with them. I have read the following link (http://www.rhino3d.com/nurbs.htm) but am having difficulty understanding how to implement the use of the Knot Vector.

The source of my difficulties may also be because of trouble with the syntax of the Knot Vector. I am unable to feed the component with the proper data so the component never turns "grey" it is always either "red" or "orange". If I understood the syntax issues I might be able to experiment with different configurations of the Knot Vector to explore how the knot vector operates.

Thank you in advance for any explanation or syntax you can offer to clear this up for me. I attached files fyi.

Stan Carroll

Attachments:

knot vector help.3dm, 29 KB
knot vector help.ghx, 45 KB

Replies to This Discussion

Permalink Reply by Danny Boyes on September 12, 2010 at 2:42pm

I've just worked this out have a look at this:
http://www.grasshopper3d.com/forum/topics/grasshopper-070053-availa...

Permalink Reply by David Rutten on September 12, 2010 at 4:35pm

I added a Knot Vector component that creates a valid knot vector based on Point Count, Degree and Periodic state. Though I suspect making a periodic curve from scratch is still quite beyond most users.

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Stan Carroll on September 12, 2010 at 5:56pm

Perfect, Thank you David. Keep up the great work!!

Stan Carroll

Permalink Reply by Stan Carroll on September 12, 2010 at 6:01pm

Thanks Danny, nice approach.

I am glad to see that David is offering the new component to aid in knot development. I still don't get how the knots affect the curve. Hopefully as soon as we get Davids new knot vector component experimentation will reveal the knot vector's effect on the curve.

Stan Carroll

Permalink Reply by Jon Mirtschin on September 12, 2010 at 10:14pm

http://www.grasshopper3d.com/profiles/blogs/essential-mathematics-s...

Knot Vectors can be used to introduce discontinuities into curves/surfaces. I assume you've read the above reference by Rajaa? p32 has a small discussion and diagram.

Permalink Reply by Stan Carroll on September 12, 2010 at 11:56pm

It has been a while since I read Rajaa's primer. I will revisit. Thank you Jon.

Stan Carroll

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