  In this study, by attempting to resolve the angular complication during the
particle generation for the muon tomography applications in the GEANT4
simulations, we exhibit an unconventional methodology that is hinged on the
direction limitation via the vectorial construction from the generation
location to the restriction area rather than using a certain angular
distribution or interval. In other words, we favor a momentum direction that is
determined by a vector constructed between an initial point randomly chosen on
a generative point/plane and a latter point arbitrarily selected on a
restrictive plane of the same dimensions with the basal cross section of the
volume-of-interest (VOI). On account of setting out such a generation scheme,
we optimize the particle loss by keeping an angular disparity that is directly
dependent on the VOI geometry as well as the vertical position of the
restrictive plane for a tomographic system of a finite size. We demonstrate our
strategy for a set of target materials including aluminum, copper, iron, lead,
and uranium with a dimension of 40$\times$10$\times$40 $\rm cm^{3}$ over three
restrictive planes of different positions by using a discrete energy spectrum
between 0.1 and 8 GeV and we compute the scattering angle, the number of
absorption, and the particle loss. Upon our simulation outcomes, we show that
the particle generation by means of restrictive planes is an effective strategy
that is flexible towards a variety of computational objectives in the GEANT4
simulations.
