A device suitable forsupplying grinding fluid to an apparatus for generating curved surfaces by means of a rotating grindstone, and which supplies grinding fluid to the grinding point under the optimum conditions following up the grinding point moves. Being provided with a means of turning the nozzles, which spout grinding fluid onto the grinding point from a fixed direction, about the axis of the grindstone, it is able to constantly ensure a sufficient supply of grinding fluid to the grinding point by controlling this rotation so that the nozzles are always pointing in a fixed direction relative to the grinding point so that the tendency of clogging and wear of the grindstone is suppressed. It is thus able to improve the accuracy and quality of the surface of the object being ground.