Shade is defined as reduced reflection depending on the angle between the terrain surface and the incident light such as the sun.
The effect of hill shading is based on the assumption that the terrain is Lambertian surface as explained in 3-7.
Shadow is projected areas that the incident light cannot reach because of visual hindrance of objects on terrain relief as shown in Figure 3.20.
Computation of Hill Shading
Hill shading = |cos q
| = |nxsx + nysy+ nzsz |£
1.0
Where q : angle between surface normal vector and incident light vector (see Figure 3.19) normal vector of terrain surface
Shadow Algorithm
Usually the incident light is regarded as the sun with the solar zenith angle (90-b)
and the azimuth angle measured from the south, positive to the east.
The shadow algorithm to determine whether the central point z (see Figure 3.15 (a) is sun lit or is in sun shadow is given as follows;
Step 1: According to the sun azimuth with respect to the eight zones as shown in Figure 3.22 (a), the resultant height H with the weight p at the corner points and (1-p) at the side points is computed for comparing the height from the central point Z5 (see Figure 3.22 (b)).
H = pZm + (1-p)Zn p, m and n are given in Figure 3.22 (a).
Step 2: If the following equation is true, the central point is in shadow (see Figure 3.22 (c))
Step 3: If the central point is assigned to be in shadow, Z5 is replaced by the following value and repeat the above procedures to other neighboring points.