# Transmission / Penetrations Along Rays

The number of transmissions / penetrations are not limited in the rays considered for the computation. The transmission/penetration loss of an object intersecting any ray must be added to the free space loss LFS of this ray:

(1) $\begin{array}{l}{L}_{FS}\text{}=10\mathrm{lg}\frac{{P}_{{t}_{0}}}{{P}_{r}}\text{\hspace{0.17em}}=10\mathrm{lg}{P}_{{t}_{0}}-10\mathrm{lg}{P}_{r}\\ \text{}=20\mathrm{lg}\frac{4\pi r}{{\lambda }_{0}}-10\mathrm{lg}{G}_{t}-10\mathrm{lg}{G}_{r}\end{array}$

An object is defined as a planar polygon. The material properties of the objects can be defined individually.

The determination of the intersection between a ray and an object is explained with a simple example. If more objects must be considered, this analysis must be made for each object individually.

As all objects are planar, they can be represented by their normal vector nW.

Consider the transmission of the ray between the two points P1 and P2. The point Q is computed as the intersection between the line represented by P1 and P2 and the object (described by the normal vector nW and its distance to the origin of the coordinate system). If nW is parallel to the direction from P1 to P2, no transmission / penetration is assumed.

If Q is between the points P1 and P2 and if Q is inside the polygon representing the object, a transmission / penetration occurs and its transmission/penetration loss (material dependent) must be added to the free space loss of the ray between P1 and P2. If Q is outside the polygon or not between P1 and P2, no additional loss due to transmission / penetration must be considered.