extract control points of curve with spline

I almost studied whole matlab help and mathwork posts about spline.

But, nobody wants to extract control points out of a given curve!!!

every body goes in opposit direction, they have the knots then they produce the curve but I want control points based on the curve?

[John D'Errico]

I want world peace. But that does not mean I can HAVE world peace. I want a Lamborghini for Xmas. Yeah, right. Not gonna happen either.

Answer 1

[Matt J]

But, nobody wants to extract minimum number of control points out of a given curve!!!

There is no minimum number unless the given curve is already a piecewise polynomial, in which case, the number of knots is known immediately from the given form of the piecewise polynomial.

If the given curve is not a piecewise polynomial, it can only be approximated by one. The accuracy of the approximation always improves with additional knots, so there is no "minimum" that can be defined.

[Mehri Mehrnia]

Thank you for the answer.

with optimizing the least square, this problem can be solved. a solution more similiar to spapi(k,x,y) is helpful for me.

[Matt J]

If you claim to know the solution, what is your question?

[Mehri Mehrnia]

I'm not sure and I do not know how to use it.

Answer 2

[Bruno Luong]

Calm down, if you have 1D data, this FEX function provides to compule the spline with reduced knots to approximate the data.

There is no such thing as minimum since its always a compromise between approxmation error and number of knots as soon as you appriximate a function with non-zero fourth derivative (virtually every function infact)

[Mehri Mehrnia]

I've just edited the question and remove the min part as confused every one.