A method of automatically generating a support structure for supporting an object to be fabricated by implementing an additive fabrication method, notably a filament 3D printing method, the object and the support being fabricated simultaneously, characterized in that , the structure being made up of a plurality of horizontal and rectilinear bridges , vertical pillars and inclined connectors , a bottom end of a pillar resting on a bridge, on a base plane or on a point of a surface of the object, and a top end of a pillar bearing a connector, and a bottom end of a connector resting on the top end of a pillar and the top end of a connector corresponding to a point on the surface of the object or to a point to be supported of a bridge, each bridge being supported at least at each of its two end points, either by a connector or by a point of the object, and the pillars may have a zero height, such that a bridge situated above rests directly on a bridge situated below, or a connector bears by its bottom end directly on a bridge, and the connectors may have a zero height, such that a pillar supports a point which is situated directly vertical to the point of the bridge on which the pillar considered bears, the method comprises the steps consisting in: - initializing a set (E) of points to be supported from points on the surface of the object; then, for each direction of a set of horizontal scanning directions, - displacing a scanning plane orthogonally to the current scanning direction; and, when the scanning plane coincides with a point to be supported, creating a possible bridge in the scanning plane supporting the points to be supported of said set of the points to be supported which meet a criterion of distance to the scanning plane; - for each possible bridge created in the scanning in the current scanning direction, computing a value of a cost function for the fabrication of said possible bridge; - selecting a best possible bridge (BPP) out of the possible bridges on the basis of the computed value of the cost function; - subtracting, from the set of the points to be supported, the points supported by the best possible bridge and adding at least the two ends of the best possible bridge to the set of the points to be supported; - placing, in a description file of the support structure, geometrical information relating to the components of the support structure associated with the points supported by the best possible bridge. - initializing a set (E) of points to be supported from points on the surface of the object; - displacing a scanning plane orthogonally to the current scanning direction; and, when the scanning plane coincides with a point to be supported, creating a possible bridge in the scanning plane supporting the points to be supported of said set of the points to be supported which meet a criterion of distance to the scanning plane; - for each possible bridge created in the scanning in the current scanning direction, computing a value of a cost function for the fabrication of said possible bridge; - selecting a best possible bridge (BPP) out of the possible bridges on the basis of the computed value of the cost function; - subtracting, from the set of the points to be supported, the points supported by the best possible bridge and adding at least the two ends of the best possible bridge to the set of the points to be supported; - placing, in a description file of the support structure, geometrical information relating to the components of the support structure associated with the points supported by the best possible bridge. <EOS>