Detector geometry and simulation results can be viewed as a 3D picture using the event display. In order to be able to see particles' trajectories, one has to set fEventDisplay=kTRUE; in the r3bsim.C macro.
To start the event display, from the macros/r3b/ directory:
In order to display trajectories: click on "FairEventManager", then on tab "Info" and button "Update".
The hierarchy of geometry volumes can be viewed in "Scenes" --> "Geometry scene" --> "cave_1".