A process for the additive manufacture of a part within a machine, the machine including a working surface, a device for spreading the powder layer along at least one longitudinal horizontal direction, at least one injector of powder over the working surface, the injector being movable with respect to the working surface along at least one transverse horizontal direction, and a system for regulating the amount of powder dispensed by the injector, the process including the following stages: moving the injector along a trajectory comprising at least one component parallel to the transverse horizontal direction; and regulating the amount of powder dispensed by the injector at any point of the trajectory of the injector.