Another MC technique, which can be used to calculate the surface rates directly, is ray tracing [10,114]. Ray tracing is a widely applied technique in computer graphics for rendering a scene. A large number of light rays is used to obtain a realistic picture. In recent years, this MC technique has been successfully applied to topography simulation to calculate surface rates [8,64,95]. Especially if the particle trajectories are linear, which is the case for ballistic transport, the same algorithms and techniques can be applied in an analogous manner [A13,A16].
In order to simulate the particle transport and to obtain the surface rates, many particles are launched from the source plane , and their trajectories are calculated. Whenever a particle reaches the surface , it contributes directly to the local surface rates introduced in (2.24). For each surface point , for which the rates should be calculated, a surrounding neighborhood is defined. If the area of that neighborhood, denoted by , is small enough and the surface is smooth, the neighborhood can be assumed to be plane and orthogonal to the surface normal . These neighborhoods of known area are necessary to relate the contribution of a single particle to the rates at point . An incident particle of type with direction and energy striking the neighborhood of point adds
A better strategy is to introduce a volume or weight factor assigned to a particle as proposed in  and which allows to control the number of reemitted particles. Initially, when a particle is launched from the source, its weight factor is set to unity ( ). An incident particle contributes to the local rates according to its current weight factor
The directional and energy distribution of a reemitted particle species obeys
The main computational task of this ray tracing technique is to determine the first surface intersection of rays and to test for intersections with the neighborhoods of all surface points , for which the surface rates should be calculated. The choice of surface representation and of neighborhoods, as well as the corresponding intersection tests are discussed in the following sections.