If you wish your B-spline to start and end at your first and last control points,
you need an open uniform knot vector. You see below (n=3, k=4) B-spline with the
[0, 0, 0, 0, 1, 1, 1, 1] knot vector (really [0.0, 0.001, 0.002,
0.003, 1, 1.001, 1.002, 1.003] is used).
An order k open uniform B-spline with n + 1 = k control
points is the Bezier curve of order k (you see cubic Bezier spline
under the first B-spline curve).
At last you can compare quadratic, cubic B-splines and Bezier curve
of degree n = 7
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updated 8 August 2001