The problems of the trajectories constructing for field electrons and emission images simulation are considered. As an approximation of the emitter shape an explicitly and implicitly defined surfaces are selected. Hyperboloidal, ellipsoidal and paraboloidal models are studied. Also an equipotential surface of the charged sphere-on-orthogonal-cone system is used. A simple solution of the field distribution problem is allowed to formulate the Cauchy problem for the motion equations. The shape of the anode (the projector microscope screen) can be selected in any desired form. Achieving a screen by electrons is performed with dense output technique in numerical approach to the solution. The distribution of the work function on the cathode surface is obtained. The trajectories for the projection of the field emission activity as the image are used.