A method for finishing a shape of a component by machining, in which one area is produced by smelting with a thickened portion forming a first surface with a surrounding profile and a theoretical profile defined by a second surface, the method including: defining, on the second surface, a grid forming nodes and squares; defining each point over which the machining tool is to pass according to weighting coefficients equal to weight to be given to the nodes of the square in which the tool is located, to be the barycenter of assigned nodes of the coefficients; measuring, for each node located outside an outer limit, the delta between the first surface at the node and the theoretical position of the node; calculating deltas for each node within the outer limit by interpolation from already known deltas; using the weighting coefficients, defining the delta to be applied at each point.