Short-characteristics method illustrated with an example of a 3D irregularly spaced Cartesian grid. We consider all quantities in the observer’s frame. They are defined in the vertices of the cells (grid points). (O,x,y,z) is an example of a coordinate system with the unit vectors (e_x,e_y,e_z). The specific intensity is calculated in the current point M_c, for a radiation propagating from the upwind end point M_u to the downwind end point M_d. The direction n of the ray is defined by the polar angle θ and the azimuthal angle ϕ. The short-characteristic is defined by the line joining M_u and M_c. The transfer equation is solved in its integral form along this short-characteristic. The cells around point M_c are marked with the following indices: i, i+1 in x-direction, j, j+1 in y-direction, and k, k+1 in z-direction.