Analysis of dwell time algorithm based on optimization theory for computer controlled optical surfacing

A mathematical model of the dwell time algorithm based on the optimization theory and matrix equation was established, which aims to minimize the 2-norm or -norm of the residual surface error. In the theory, the dwell time solution meets almost all the requirements of precise computer numerical control (CNC) without any need for extra data processing. Several practical methods were discussed on how to solve the optimization model and obtain an optimal solution. Also analyses of the two algorithms were performed in this paper. The simulations show that both of the two algorithms have high precision. The computation efficiency is crucial for least squares algorithms because it is lower for large computation models. The least squares algorithm is numerically robust, whi