#### What are knots?

Part of the information needed to define a NURBS curve is a list of numbers called a knot vector and the values of the numbers in this list are called knots.

Imagine a rope. If you hold it at the ends, the rope will sag according to the laws of nature (gravity, the stiffness of the rope, etc.) with a polynomial definition. If you tie it off somewhere along its length (by putting knots in it), there will be a different polynomial definition (sag) for each segment between the knots.

The numbers in the knot vector list must be increasing, but the list can contain duplicates. However, a value can be duplicated at most degree many times. If a value in the knot vector list is duplicated exactly degree many times, it is called a fully multiple knot value.

Examples of valid knot vectors for a degree-3 NURBS curve include:

1, 2, 3, 4, 5, 6 (no fully multiple knot values)

1,1,1,2,3,3,3,4,4,5,6,7,7,7 (here the values 1, 3 and 7 are fully multiple knot values).

-23.456, -3.0, 1.34, 1.34, 99.2, 99.2, 99.2, 100.234, 1.56e45, 1.56e45 (here the value 99.2 is a fully multiple knot value)