Knot multiplicity at the ends, order or degree?

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  07 July 2012
Knot multiplicity at the ends, order or degree?


In "The NURBS Book" by Piegl and Tiller they use the order as multiplicity at the ends of the knot vector. Reading the explanation it seems consistent with the rest of the theory, e.g a degree 3 B-spline basis function, N_{0,3}(u), will be spread out on four knot spans involving five knots, for example U= [0,0,0,0,1, ...].

In a lot of other literature (more recent, e.g Farin), the multiplicity of the end knots is the degree. Why?
(Different algorithms of course, but how and why?)

Preferably I would like to find some (the) publication which led to the paradigm shift, if there ever was one.

Last edited by linsnos : 07 July 2012 at 09:16 AM.
  07 July 2012
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