High-precision NURBS interpolation algorithm based on the bisection method

For a high precision Non-Uniform Rational B-Spline (NURBS) interpolator, calculating the parameter of the next path interpolating point is an indispensable step, which affects feedrate fluctuation. This paper presents a new, simple and precise interpolation algorithm for parameter curve which adopts first-order Taylor's expansion, and then make use of the bisection method to achieve accurate path parameters. In the meanwhile, the interpolator is restricted from geometric and kinematical constraints. A simulation study is conducted to demonstrate the advantages of proposed interpolation algorithm compared with other algorithms for the parametric curves represented in the NURBS form.