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In an eyeglass lens grinding apparatus for grinding a periphery of a lens, a lens holding system holds a lens while clamping the lens. A data input system inputs shape data of an eyeglass frame to which the lens is fitted, and layout data of the lens with respect to the eyeglass frame. An edge-position-data calculating system obtains edge position data of the lens after layout, on the basis of the data inputted by the data input system. A first measuring system measures an edge position of the lens before processing that is held by the lens holding system, on the basis of the edge position data obtained by the edge-position-data calculating system. A second measuring system measures an edge position of the lens after rough grinding, on the basis of the edge position data. A chamfering-process-data calculating system obtains chamfering process data for processing a corner portion of an edge of the lens after finish processing, on the basis of a result of measurement by the second measuring system. A chamfering process system having a chamfering grinding wheel processes the corner portion of the edge of the lens after the finish processing. A chamfering-process controlling system controls the chamfering process system on the basis of the chamfering process data obtained by the chamfering-process-data calculating system.
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