A winding machine for winding a fiber texture onto an impregnation mandrel, includes: a take-up mandrel for storing and unwinding a fiber texture, the take-up mandrel having a substantially horizontal axis of rotation; an impregnation mandrel for receiving superposed layers of the fiber texture unwound from the take-up mandrel, the impregnation mandrel having an axis of rotation that is substantially horizontal and parallel to the axis of rotation of the take-up mandrel; a camera directed towards the fiber texture and the impregnation mandrel to examine the passage of warp tracer yarns and weft tracer yarns present in the fiber texture; an image-analysis module for determining the positions of the intersections of warp tracer yarns with the successive weft tracer yarns and comparing these determined positions with corresponding positions for the intersections of reference warp and weft tracer yarns, and determining an offset value for the fiber texture for each of these intersections; electric motors for driving the mandrels in rotation about their respective axes of rotation; and a control unit for controlling the electric motors for driving rotation of the mandrels.