The transient electromagnetic field produced by a current pulse moving along a polygonal line is considered theoretically. The algorithm that calculates the field components is based on Borisov et al.'s space-time representation of a transient field due to a straight line radiator. The scalar wave equation is solved explicitly. The dependence of the magnetic field on the radiator parameters, length of the radiating segments, duration of the current pulse, and the velocities of the wavefronts are discussed. The space-time field structure calculations for specific current waveforms of finite duration are carried out using both PC algorithms and analytical integration.