Freeform surface localization algorithm based on screw theory

The conventional localization algorithms based on Euler angle are not sufficient in accuracy and efficiency, and singularity often occurs. Furthermore, the present positioning scheme on the basis of screw theory only adapts to simple surfaces. To overcome these shortcomings, a new strategy was proposed to cope with the complex freeform surfaces in this paper from screw theory. Firstly, the complex surfaces were subdivided into pieces of simple patches. The nearest point to each patch from the measured point was found. Then, the nearest point was located using boundary determinant. So efficiency of the localization algorithm was improved. The experimental results indicate that the approach is not only fast but also accurate.