Abstract: To obtain the profile error of the freeform curves, an efficient evaluation method is brought out which is based on root-finding of polynomial equations and real coded genetic algorithm (RCGA). Firstly, the optimization model for the profile error evaluation was established based on the least squares criterion. Then, the polynomial equations were constructed and the point to curve distance can be obtained effectively by solving the polynomial equations via the Halley iteration. After that, the optimization model was solved by the RCGA and the profile error was obtained. The computation results were also compared with the subdivision method. From the evaluation process, it can be seen that the proposed method is efficient and robust. The computing time is about 5% of that the subdivision method needs under the same condition. Thus, it is more suitable for evaluating the profile error of the freeform curves.

Key words: freeform curves, form error evaluation, point to curve distance, root-finding of polynomial equations, real coded genetic algorithm