Linear-Time Algorithm for Computing the Bernstein–Bézier Coefficients of B-spline Basis Functions

A new differential-recurrence relation for the B-spline functions of same degree is proved. From this relation, a recursive method computing coefficients m in Bernstein–Bézier form derived. Its complexity proportional to number case coincident boundary knots. This means that, asymptotically, algorithm optimal. In other cases, increased by at most O(m3). When basis are known, it possible compute any function linear time with respect its performing geometric proposed recently authors. scales well when evaluating curve multiple points, e.g., order render it, since one only needs find each knot span once. many curves points (as rendering tensor product surfaces), such approach has lower computational than using de Boor–Cox algorithm. The numerical tests show that efficient. problem finding power can be solved similarly.