For the estimation of the degree of shading of diffuse irradiance, the object polygon is considered as being projected on a hemisphere. The objects represented by the object polygon block the diffuse irradiation that passes through the object polygon on the hemisphere. As a simple example, Figure 2.23 shows a polygon with four points, with two of them on the horizontal ground plane. The two remaining points define the polygon clearly.

y(a) = m • a + n describes the connecting line of the points pj and p2 for ax*a2 as well as y1 >0 and y2 > 0. The parameters m and n of this line are:

Assuming an isotropic intensity distribution, the diffuse irradiance Ediff,hor,Ai through the area Ai on a horizontal surface becomes:

Figure 2.23 Two Points, the Horizontal Meridian and Two Polar Meridians

Define the Polygon Area

Figure 2.23 Two Points, the Horizontal Meridian and Two Polar Meridians

### Define the Polygon Area

The parameter Le iso is the isotropic radiant intensity, that falls out of the equation when calculating the degree of diffuse shading. When using the anisotropic distribution, the integral also includes the angle-dependent radiant intensity Le. However, only numerical methods are able to solve this integral. When simulating tilted planes, the angle of incidence 0, according to Equation (2.24), must be considered. Therefore, a complex analytical solution also exists (Quaschning and Hanitsch, 1998).

The diffuse irradiance Ediff,P through the polygon surface of an object polygon with n polygon points p1 = (a1, yx) to p = (a, y) can be calculated by:

IPi-Pm!

Finally, the degree of shading of diffuse irradiance 5diff hor for a horizontal surface is the ratio of the diffuse irradiance reduction and the total diffuse irradiance. For an isotropic radiant intensity distribution, the shading becomes:

JJilTjmr,l>

ibH.kw

The degree of diffuse irradiance for a tilted surface is calculated analogously:

If the object polygon is transparent, the shading degree S must be weighted additionally with the transmittance t.