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The B-spline basis function is given by one recursive formula. However,I hope to obtain popular expression: a0x^n + a1x^(n-1) + ... + an. From the answer How to build a recursive spline function in C++, it seems that Piegl's algorithm can do that. Can anyone give more information about the algorithm?

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If you do not have access to the NURBS book by Piegl, then you might look at An Introduction to Polar Forms by Hans-Peter Seidel on pp 38-46 of the 1993 IEEE Computer Graphics & Applications. He diagrams the B-spline computations for the polar form, from which the polynomial coefficient form is a routine conversion.

Let me offer one more reference to an excellent expositor, Phillip J. Schneider, in his paragraph on defining the basis functions. Www.mactech.com/articles/develop/issue_25/schneider.html

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  • $\begingroup$ I have NURBS book by Piegl. But I only find the routine to calculate one point on the B-spline curve using recursive formula. $\endgroup$ – Jogging Song Nov 7 '14 at 2:51
  • $\begingroup$ Is it necessary to convert B-spline curve from recursive form to power basis form? I am to geometric modeling, so I am familiar with the power basis form. Which form does geometric modeling software prefer? $\endgroup$ – Jogging Song Nov 12 '14 at 5:23

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