The use of tetrahedral-based phantoms in conjunction with Monte Carlo dose calculation techniques has shown high capabilities in radiation therapy. However, the generation of a precise dose distribution can be very time-consuming since a fine tetrahedral mesh is required. In this work, we propose a new method that defines the density distribution of patient-specific tetrahedral phantoms, based upon the CT-scans and the direction of the particle beam. The final purpose is to coarsen the tetrahedral mesh to improve computational performance in Monte Carlo simulations while guaranteeing a precise dose distribution in the target volume. Contrarily to the state of the art methods that calculate the density value of a tetrahedron, locally based only on the CT-scans, our approach takes also into account the direction of the beam to minimize the error of the water equivalent thickness of the tetrahedrons before the tumor volume. In this study, the experiments carried out on a multi-layer computational phantom, and a thorax geometry, show that by applying our method on a coarse mesh, we offer a better dose distribution inside the tumor compared to other density mapping methods, in the same level of detail. This is due to the reduction of the water equivalent path length error from 9.65 $mm$ to 0.62 $mm$ in the case the multi-layer phantom, and from 2.42 $mm$ to 0.48 $mm$ for the thorax geometry. Moreover, a similar dose coverage is obtained with refined tetrahedral meshes. As a consequence of the reduction of the number of tetrahedrons, computational time is found to be 25\% shorter than both the refined tetrahedral mesh and the voxel-based structure in most cases. Using a coarse tetrahedral mesh to have accurate dose distributions on a given target is feasible as long as the water equivalent path length in the direction of the beam is respected.