Research on the Algorithm of NURBS Curve Bidirectional Optimization Interpolation with S-type Acceleration and Deceleration Control

Abstract

There is no precise analytical relationship between the curve length and the parameter of non-uniform rational B-splines(NURBS).Furthermore,the feedrate is always subject to the non-linearly varying curvature.Accordingly,it is hard to precisely determine the deceleration point when interpolating NURBS curves with S-type acceleration and deceleration(ACC/DEC).The traditional algorithms usually flow only one direction along the curve,not only neglecting that feedrate is always constrained by curvature,but also having complex ACC/DEC classification and computing equations.Therefore,a new interpolation algorithm which is independent of precise calculating of curve length and based on synchronously positive and reverse acceleration is proposed on the condition of unknown moving distance.The proposed algorithm determines the maximum feedrate and the meet point of positive and reverse interpolation of each NURBS segment dynamically and in real time.Consequently,the optimal interpolation that satisfies all the feedrate conditions everywhere is realized.Solving high order equations and fussy classification of ACC/DEC modes is avoided and the velocities at the extreme curvature points and end points are guaranteed to map the determined values exactly by the proposed algorithm.Two interpolation examples are presented to verify its simplicity,efficiency,good adaptability and the ability to meet the requirements of both high speed and high accuracy of computer numerical control.