Knot vector rules

The number of knots in the knot vector is always equal to the number of control points plus the order of the curve. A linear curve has at least four knot vectors. A quadratic curve has 6 knot vectors, and a cubic curve has eight knot vectors.

The values in the knot vector must be in ascending order. A knot vector with the following eight values [ 0 0 0 1 2 3 3 3 ] is a valid cubic knot vector, but a knot vector with these values [ 0 0 0 2 1 3 3 3 ] is not. The magnitude of the knots makes no difference. The ratios of the values to each other is the significant factor. The knot vectors [ 0 0 0 1 2 2 2 ], [ 100 100 100 200 300 300 300 ], and [0.5 0.5 0.5 0 0.5 0.5 0.5 ] produce the same curve. In general, integer sequences starting at zero help to keep things simple.


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