What is the Degree of a Bezier Spline?

[Asuralm]

Spline degree??

Dear all:
I have been read a few definition of the degree of a bezier spline. But I still do not understand what's the exact meaning of it. As I understand, if the spline function is n-differentiable then it's of degree n-1. Is this correct? Another way is that if the control point position is determined by n neighbours of the previous level then the spline curve is of degree n-1.

Am I understanding correct?

Could anyone give me some more straight-forward and easy understandable explanations please?

Thanks

 

[HallsofIvy]

If the spline is n-differentiable isn't the degree n+1, not n-1?

I may be thinking of a different "degree". A spline is a piece-wise polynomial such that a certain number of derivatives are continuous. Of course, that depends completely upon the degree of the polynomial since the higher degree gives you more constants to match. A "degree 1" spline is a "broken line" that is continuous but not differentiable at all. A "degree 2" spline is a piecewise quadratic function that is continuous and has continuous derivative at the knots but not second derivative. A "degree-3" (cubic) spline is piecwise cubic, having continuous second derivative at the knots.

 

[Asuralm]

If the spline is n-differentiable isn't the degree n+1, not n-1?

Yes you are right. It's quite helpful. Thank you.

But another problem is what's the relation between the degree of the spline with the subdivision matrix S?