Nonuniform B-splines

We have seen, that uniform B-splines are used to build closed curves. You need an open uniform knot vector, if you wish your B-spline to start and end at your first and last control points. You see below (n=3 k=4) B-spline with the [0 0 0 0 1 1 1 1] knot vector (really [.0 .001 .002 .003 1 1.001 1.002 1.003] are used as I was lazy to make an accurate applet :)

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 in the right applet).
At last you can compare quadratic, cubic B-splines and Bezier curve of degree n = 7

You can play with control points and knots to see how they influence on the curves shapes (e.g. multiple control points and knots).
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updated 8 August 2001