What Kind Of A Bezier Curve Is This?

[spinecad]

What kind of Bezier curve is such as the attached image that has 7 points?

[SEANT]

It could be a degree 6 Bezier curve, but more likely is a degree 3 NURBS curve.

[SEANT]

Definitely a degree 3 NURBS.

[spinecad]

Can anyone please make an illustration of weight and knot of a curve?

[ReMark]

What course are you taking?

 

Knot insertion: http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS-knot-insert.html

[spinecad]

What course are you taking?

 

I am learning NURBS theory.

 

I am reading my book, it has relation with knot and weight.

[spinecad]

So the spline with control vertex in AutoCAD 2012 is a NURBS curve?

[SEANT]

Yes, that is correct.

[spinecad]

For the given NURBS curve as attached image where b0, b1, b2, b3, b4, b5, and b6 are the control points, which one is called by the knot vector?

[SEANT]

The Knot Vector is somewhat of a "behind the scenes" component of a spline. Used only for the mathematical basis function. If the spline you have illustrated above was created with the CV option of the SPLINE command then the Knot vector will be:

0,0,0,0,1,2,3,4,4,4,4

 

The Fit Point option of the SPLINE command will create varying Knot Vectors depending on the setting for the Knot Parameterization. The default Knot = Chord would create a Knot Vector:

0,0,0,0,Length(b0 to b1), Length(b0 to b1 + b1 to b2), Length(b0 to b1 + b1 to b2 + b2 to b3)), etc. The last four entries would be the length of the entire b0 to b6 polyline repeated four times.

 

Edit:

I included a couple of additional knots that are not required.

Edited March 24, 2013 by SEANT

[spinecad]

The Knot Vector is somewhat of a "behind the scenes" component of a spline. Used only for the mathematical basis function. If the spline you have illustrated above was created with the CV option of the SPLINE command then the Knot vector will be:

0,0,0,0,1,2,3,4,5,6,6,6,6

 

What is this order of the numbers means?

 

0,0,0,0,1,2,3,4,5,6,6,6,6

 

It doesn't looks like a coordinate to me.

[SEANT]

Weight are fairly straightforward.* Experiment by changing the weight in the Properties Panel to see how they affect the spline.

 

While manipulating splines in the drawing editor, Knots and Knot Vectors don't really come into play much. Knot play a much larger role when working with spline in the computer programming phase.

 

Knot features are probably the most visually evident when several splines are combined with the JOIN command. If the "joined" spline has a kink, that is indication of a recurring knot value at that point in the knot vector.

 

I posted a routine here that creates a circular spline by varying the weights and knot vector of a NURBS curve.

http://www.cadtutor.net/forum/showthread.php?32338-Splined-Circles

 

*Saddly, AutoCAD has a bug that makes manipulating spline via dragging a weighted control vertex quite difficult.

[SEANT]

It is not a coordinate. I would not attach much concern to Knots and Knot Vectors until you start working with splines via programming (Autolisp, ObjectARX)

[spinecad]

NURBS curve.

[spinecad]

I am learning the theory of the NURBS curve by a book.

 

However, there is something I don't understand.

 

What is the basic equation of the NURBS curve?

 

At I read in my book, the NURBS curve containing several symbols.

 

Control points are symbolized as b.

Degree is symbolized as d.

What is the meaning of k symbol?

 

Can you show me an example finding the NURBS curve such as my #5 post in below link?

 

http://www.cadtutor.net/forum/showth...d=1#post528446

 

Thank you

[SEANT]

NURBS is an acronym standing for the term Non-Uniform, Rational B-Spline (Basis Spline). I don't have to show you anything - you showed yourself an example of a NURBS curve.

 

NURBS are the most generalized super set; Bezier and B-Splines are specialized subsets of NURBS. The curve you show above is an example of all three.

 

Without a doubt, the math behind nurbs creation, interrogation, and manipulation is quite intense. The link that ReMark showed is one page of very good course notes. See if it helps.

http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/

 

Ask here if you have specific questions - though you may want to avoid asking about a "k symbol" unless it can be shown in full context.

[SLW210]

I combined your related threads into one thread and moved them to the AutoCAD 2D Drafting, Object Properties & Interface forum.

[spinecad]

I need a picture of the knot vector of a NURBS curve.

 

How to define a knot vector?

 

How suppose I to understand of a knot vector if it be explained such as #10 post?

 

Confuse.

[SEANT]

What is your ultimate goal? If it is to be an awesome NURBS/Freeform modeler then the Knot issue is irrelevant. If your intention is to become a computer programmer – with an emphasis on NURBS development – then look at the link I put in post # 16 – especially the section on B-Splines. It gives a pretty good explanation on how the procedure works.

Edited March 26, 2013 by SEANT

[spinecad]

Could you send me en example of NURBS curve?

 

Also, could you tell me how to define to knot sequence?