Abstract: Based on the non-uniform rational B-spline (NURBS) curve theory, the general rule of how the knot vector affects the shape of the NURBS curve is put forward. The local support property on how a knot affects the NURBS curve is demonstrated. The quantitative computation formula on how a knot affects the NURBS curve is obtained. An experiment performed on the example in computer aided geometric design (CAGD) proves that it is possible that the NURBS curve can be modified locally and be designed interactively by modifying a single knot. And another experiment performed on the measurement of the edge of the vane of the aero-engine compressor proves that the fitting model with the minimum errors can be achieved by the knot factor method (KFM) that is based on the rule. Both experiments prove that the rule proposed here is correct, practical and feasible.

Key words: Knot vector, B-spline base function, Knot factor, Non-uniform rational B-spline(NURBS)