Surface surveying device, in particular profiler or 3D scanner, for determining a multiplicity of 3D coordinates of measurement points on a surface, comprising • a scanning unit for optically scanning the surface, said scanning unit comprising o a transmission unit for emitting optical, coherent and collimated measurement radiation, in particular laser radiation, o a deflection apparatus for scanning guidance of the measurement radiation over the surface in at least one deflection direction, o means for registering the relative deflection direction in each case, and o a detector for detecting the measurement radiation reflected by a respective measurement point, • means for determining a position and orientation of the scanning unit, • a carrier for carrying the scanning unit and at least part of the means for determining a position and orientation, • a control and evaluation unit with a surface surveying functionality for controlling the scanning unit and for determining the 3D coordinates of the measurement points on the basis of the respective deflection direction and a distance value derived by means of detected measurement radiation, whereby the carrier is embodied as an unmanned aerial vehicle (3a-3c) which is capable of hovering and comprises a lead, the latter being connected at one end thereof to the aerial vehicle (3a-3c) and being able to be held at the other end by a user, wherein • the lead is provided for guiding the aerial vehicle (3a-3c) in the air by the user and • the position of the aerial vehicle (3a-3c) in the air is predetermined by the effective length of the lead, said length, in particular, being changeable by the user, and • the lead is electrically conductive and serves for ∘ energy supply and/or o control and/or data signal transmission to and/or from parts of the surface surveying device situated in the air, in particular of the aerial vehicle (3a-3c) and/or of the scanning unit, characterized in that the control and evaluation unit has a gesture control functionality such that control commands are output to the aerial vehicle (3b, 3c) and/or the scanning unit on the basis of recorded movement images of hand movements of the user, in particular wherein the carrier has a camera for recording the movement images. • a scanning unit for optically scanning the surface, said scanning unit comprising o a transmission unit for emitting optical, coherent and collimated measurement radiation, in particular laser radiation, o a deflection apparatus for scanning guidance of the measurement radiation over the surface in at least one deflection direction, o means for registering the relative deflection direction in each case, and o a detector for detecting the measurement radiation reflected by a respective measurement point, o a transmission unit for emitting optical, coherent and collimated measurement radiation, in particular laser radiation, o a deflection apparatus for scanning guidance of the measurement radiation over the surface in at least one deflection direction, o means for registering the relative deflection direction in each case, and o a detector for detecting the measurement radiation reflected by a respective measurement point, • means for determining a position and orientation of the scanning unit, • a carrier for carrying the scanning unit and at least part of the means for determining a position and orientation, • a control and evaluation unit with a surface surveying functionality for controlling the scanning unit and for determining the 3D coordinates of the measurement points on the basis of the respective deflection direction and a distance value derived by means of detected measurement radiation, whereby the carrier is embodied as an unmanned aerial vehicle (3a-3c) which is capable of hovering and comprises a lead, the latter being connected at one end thereof to the aerial vehicle (3a-3c) and being able to be held at the other end by a user, wherein • the lead is provided for guiding the aerial vehicle (3a-3c) in the air by the user and • the position of the aerial vehicle (3a-3c) in the air is predetermined by the effective length of the lead, said length, in particular, being changeable by the user, and • the lead is electrically conductive and serves for ∘ energy supply and/or o control and/or data signal transmission to and/or from parts of the surface surveying device situated in the air, in particular of the aerial vehicle (3a-3c) and/or of the scanning unit, ∘ energy supply and/or o control and/or data signal transmission to and/or from parts of the surface surveying device situated in the air, in particular of the aerial vehicle (3a-3c) and/or of the scanning unit,