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Show 20 functions, and piecewise Bezier curves by table lookup. 2.6.4 Fast implementation of the recurrence relations The equations for Bi,k are typically specified by the recurrence relation [2) B { 1 Ui :::; u < Ui+l i,t ( u) = 0 otherwise and for r = 2, 3, ... , k. Implementing this relation recursively however, introduces a significant amount of function call overhead. To eliminate this overhead, the equations were reformu-lated as for j = 0 to k - 1 { 1 Ui :::; U < Ui+l blends1 ( u) +- 0 otherwise for level = 2 to k for j = 0 to k - level ni +- i + j blendsj +- _ _.;...u_-.;_jun.u.i _ blends j + Una+ Ievei-l -Uni Bi,k +- blends0 Unj+level-u Uni+leveJ-Una+l blendsi+l The recursive formulation does have one advantage, however. If one considers the 'tree' of values: Bo,t Bo2 ' Bt,I Bo,3 B1,2 Bo,4 B2,1 BI,3 B2,2 B3,t |
