Nonuniform B-splines

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