Abstract: In order to describe the optical properties or a charged particle beam reali-stically, the random sampling of initial conditions of particles in ray-tracing isdiscussed in the paper. The emission surface of particles may be a plane. acylindrical surface or a spherical surface. The distribution functions may beexpressed analytically or numerically. Next, in order to analyse the properties ofthe charged particle beam systematically by use of the results from ray-tracingefficiently, the graphic processing and analysing of particle trajectories are alsodiscussed, including the spline function fitting of trajectories. the graphic draftingof trajectories and beam envelopes, the determining of image dimensions and thecorresponding positions, and also the graphic drafting of particle distributionson arbitrary cross sections.