where ti+k-i-ti (6.30) P(t) This algorithm is shown graphically in Figure 6.5. An example of the evaluation of a point on an cubic(k=4, I= 3)B-spline curve is shown in Figure 6.6 P3 4+ Figure 6.6: Evaluation of a point on a B-spline curve with the de boor algorithm The algorithm shown in Figure 6.5 also permits the splitting of the segment into segments of the same order left polygon PoPI P2 P3 ight polygo P3P3P3P3where, α j i = u − ti ti+k−j − ti (6.30) ⇒ P k−1 k−1 = P(t) This algorithm is shown graphically in Figure 6.5. An example of the evaluation of a point on an cubic (k = 4, l = 3) B-spline curve is shown in Figure 6.6. P1 1 P2 2 P3 3 P3 2 P3 1 P3 0 P2 0 P1 0 P2 1 P0 0 t0 =t1 =t2 =t3 u t4 t5 t6 Figure 6.6: Evaluation of a point on a B-spline curve with the de Boor algorithm. The algorithm shown in Figure 6.5 also permits the splitting of the segment into two smaller segments of the same order: left polygon: P 0 0 P 1 1 P 2 2 P 3 3 right polygon: P 3 3 P 2 3 P 1 3 P 0 3 13