A method of manufacturing a three-dimensional object by means of additive manufacturing, wherein the three-dimensional object comprises a three-dimensional component and the method comprises - providing a substrate (20, 20"), and - successively forming on the substrate (20, 20") a plurality of layers , wherein each layer is formed in a pattern corresponding to a three-dimensional component being manufactured and wherein each layer is formed by dispensing a curable material from a nozzle of a dispensing head (4, 4', 4") and subsequently curing the curable material , wherein - the three-dimensional object is constituted by the combination of the substrate (20, 20") and the three-dimensional component , wherein the substrate (20, 20") has a non-planar surface portion and the three-dimensional component is formed at least in part on the non-planar surface portion in such a manner that it is fixedly secured to the substrate (20, 20"), - during forming of at least one of the layers and/or between forming of at least two adjacent ones of the layers a relative movement between the substrate (20, 20") and the dispensing head (4, 4', 4") is effected such that in a substrate coordinate system the dispensing head (4, 4', 4") moves along a non-linear path over the non-planar surface portion, and - during the relative movement between the substrate (20, 20") and the dispensing head (4, 4', 4") the dispensing head is rotated about a rotation axis to adapt a dispensing direction of the nozzle to the non-planar surface portion, characterized in that during the relative movement between the substrate (20, 20") and the dispensing head (4, 4', 4") an orientation of the nozzle with respect to a tangent plane of the substrate (20, 20") at the center of the region in which the nozzle applies the material is maintained within a predetermined range. - providing a substrate (20, 20"), and - successively forming on the substrate (20, 20") a plurality of layers , wherein each layer is formed in a pattern corresponding to a three-dimensional component being manufactured and wherein each layer is formed by dispensing a curable material from a nozzle of a dispensing head (4, 4', 4") and subsequently curing the curable material , - the three-dimensional object is constituted by the combination of the substrate (20, 20") and the three-dimensional component , wherein the substrate (20, 20") has a non-planar surface portion and the three-dimensional component is formed at least in part on the non-planar surface portion in such a manner that it is fixedly secured to the substrate (20, 20"), - during forming of at least one of the layers and/or between forming of at least two adjacent ones of the layers a relative movement between the substrate (20, 20") and the dispensing head (4, 4', 4") is effected such that in a substrate coordinate system the dispensing head (4, 4', 4") moves along a non-linear path over the non-planar surface portion, and - during the relative movement between the substrate (20, 20") and the dispensing head (4, 4', 4") the dispensing head is rotated about a rotation axis to adapt a dispensing direction of the nozzle to the non-planar surface portion, <EOS>