Analysis and Optimisation Strategy on Influence of Knot Vector to NURBS Curve

This study investigates the variation in the NURBS shape caused by knot vectors produced by various algorithms to minimise the influence of knot vectors on the NURBS interpolation. The differences in shape variations of NURBS curves computed by knot vectors generated by the Hartley–Judd, Riesenfeld and Rogers algorithms are compared and analysed; an error function is defined to analyse the mathematical features of the differences caused by the three calculations and a weighted average calculation method beyond the classical algorithm is proposed. Additionally, the study introduces a combinatorial algorithm for optimising the computing process and increasing computing efficiency. The experimental results show that the new method produces a more accurate NURBS curve than the classical method does, making it more suitable for CNC interpolation.