Ultrathin Pt wires have been successfully assembled and welded together by Joule heating into complex forms, like 2D and 3D structures. A parameter for successful welding which governs melting phenomenon at the contact points of two wires has been proposed for the straight line (1D) welding. The applicability of the parameter is verified for 2D and 3D welding. In this report, melting and solidification at the contact portion of ultrathin wires occurred under a constant current supply without controlling the time for heat input. Joule heat welding method is found to be suitable in fabrication of 3D structures in NEMS/MEMS.