# Piegl's algorithm in calculating B-spline basis function

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?

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

• I have NURBS book by Piegl. But I only find the routine to calculate one point on the B-spline curve using recursive formula. Nov 7, 2014 at 2:51
• 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? Nov 12, 2014 at 5:23