Splines, how many knots are required?

[sauske]

Hi i would like to get help with these questions.

How many control points d_i are involved when evaluating a cubic B-spline at a single points. The point are deboor.

How many knots are necassart to define a single linear B-spline basis funcion Ni_,2(x)?

Anyone who could kindly explain to me how this works? which formula to use etc?
I need to understand, the answer is not the most important.

Best regards.

 

[Ishuda]

Hi i would like to get help with these questions.

How many control points d_i are involved when evaluating a cubic B-spline at a single points. The point are deboor.

How many knots are necassart to define a single linear B-spline basis funcion Ni_,2(x)?

Anyone who could kindly explain to me how this works? which formula to use etc?
I need to understand, the answer is not the most important.

Best regards.

Working backwards, the number of knots depend on the degree of the B-spline and the continuity (smoothness) requirements. You might look at
https://en.wikipedia.org/wiki/B-spline

 

[sauske]

Working backwards, the number of knots depend on the degree of the B-spline and the continuity (smoothness) requirements. You might look at
https://en.wikipedia.org/wiki/B-spline

thank.
Ive tryied multpl souces, on of them is wiki. But I still dont get it. Can you explain to me maybe?

best regards.

 

[sauske]

Working backwards, the number of knots depend on the degree of the B-spline and the continuity (smoothness) requirements. You might look at
https://en.wikipedia.org/wiki/B-spline

hello.


Thanks for your reply, i tryied to read alot of different sources including wiki. But i still dont get it. Can u might exaplin to me by using the examples above?

 

[stapel]

i tryied to read alot of different sources including wiki. But i still dont get it. Can u might exaplin to me by using the examples above?

We really can't teach courses here. If the worked examples in your textbook, your classroom lectures, and the online sources didn't help, then you may need to consider hiring a qualified local tutor who can work with you, face to face, to figure out where things are going wrong and then provide you with the personal private lessons you have requested.

My best wishes to you in your studies.

 

[Ishuda]

hello.


Thanks for your reply, i tryied to read alot of different sources including wiki. But i still dont get it. Can u might exaplin to me by using the examples above?

As stapel said - we can't really teach courses here. It's been a long time since I looked at splines and even then the control points [de Boor points or B-spline control points] were typically the joints of the spline which is a bit different than the general B-Spline.

As I remember, we generally started with a set of knots (points we want the spline to go through), choose the degree of polynomial n we want to use (typically 3 for cubics) which means then that each de Boor point covered n (3 for cubics) knots.

Again as I remember it, de Boor published some internal papers at GM and later wrote a pretty good book explaining splines from a practical standpoint. You might look the book up it up, it's probably been updated.