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 (23, 23'), wherein each layer is formed in a pattern corresponding to a three-dimensional component being manufactured and wherein each layer (23, 23') is formed by dispensing a curable material from a nozzle (5, 5') 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 (23, 23') and/or between forming of at least two adjacent ones of the layers (23, 23') 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 (5, 5') 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 (5, 5') with respect to a tangent plane of the substrate (20, 20") at the center of the region in which the nozzle (5, 5') 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 (23, 23'), wherein each layer is formed in a pattern corresponding to a three-dimensional component being manufactured and wherein each layer (23, 23') is formed by dispensing a curable material from a nozzle (5, 5') 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 (23, 23') and/or between forming of at least two adjacent ones of the layers (23, 23') 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 (5, 5') to the non-planar surface portion,