Process for grinding the rim of an ophthalmic lens that has two opposite faces, following a predetermined contour corresponding to that of a ring of a spectacle frame in which the lens is intended to be mounted, the contour being delimited on each of the faces by an edge, and the process includes a plotting stage in which the three-dimensional shape of at least one of the edges is plotted. In the plotting stage, the edge is scanned on the illuminated face of lens using a light beam forming a light spot on the face, the successive positions of an image of the light spot are plotted simultaneously on optical reception elements pointing towards the light spot, and the three-dimensional shape of the edge is deduced from the plots made, machining of the lens being carried out according to the plot or plots.