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Spline degree?

  1. Aug 7, 2007 #1
    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?

  2. jcsd
  3. Aug 7, 2007 #2


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    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.
  4. Aug 7, 2007 #3
    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?
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