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Computer-controlled optical surfacing provides superior optical fabrication performance with low-cost mass production over conventional method relying heavily on the skills of optician. However, there are still lots of technical issues to be resolved in computer-controlled optical surfacing, and edge effect has been regarded as one of the most challenging tasks for years due to the unpredictable behaviors of a polishing tool. As a polishing tool approaches the edge of the workpiece, the tool-workpiece contact area decreases and this in turn accompanies the tool-workpiece misfit and non-uniform pressure distribution. Thus, the edge effects should be taken into account in deterministic polishing technique. In this paper, we suggest new edge tool influence functions by modeling the velocity and pressure distribution of a polishing tool with eccentric rotation motion. Here, the finite element analysis was used to accurately predict the non-linear behaviors of a polishing tool at the edge. We verified our proposed method by comparisons with experimental results, and it shows considerable resemblance between them. [ABSTRACT FROM AUTHOR]