Free-form surface polishing residence time calculation method and system for NURBS (Non-Uniform Rational Breakdown Spectroscopy) curved surface fairing regulation

The invention provides a free-form surface polishing residence time calculation method and system for NURBS curved surface fairing regulation. The method comprises the steps that residence point coordinates and removal amount sampling coordinates are determined, a material removal function matrix is calculated, and the removal amount needed by all points on a workpiece is measured; node vector optimization is realized, edge nodes are added, a weight factor is determined based on material surface type removal optimal fitting, a corresponding NURBS primary function matrix is calculated, and a model is established; solving a least square optimization problem according to the model to obtain a residence time control vertex vector, and calculating a residual error root mean square value and a residence time vector; and the number of nodes is continuously increased through iterative calculation until the root-mean-square value of the residual error meets the convergence threshold value, the target material removal