The calculation is identical for hill shading, and shadows are simply not computed.
Mark's hill shading technique was also used by Schruben (1999) in his relief map of the conterminous United States.
While point source hill shading provides cues to the orientation of a surface, it does not provide visual cues to the relative elevation of the surface.
We present Figure 7(b), a combination of renderings from diffuse illumination and point shadowing using weights of four and one respectively, for visual comparison with Figure 7(d), a combination of renderings from point hill shading and point shadowing in the same ratio.
Horn (1982) pointed out that although most hill shading is based on the Lambertian assumption there is no evidence that this method optimizes perception of surface shape.
Tanaka understood that his illuminated contour map was an approximation of brightness associated with hill shading under the Lambertian assumption; however, no simple method of drawing contours would account for changes in both slope and aspect.
The brightness value for hill shading is (BV = cos([Theta]) *255), which corresponds to the grayness of each illumination vector.
This technique does not offer all the detail of a shaded relief map, as analytical hill shading is applied in a linear versus area-wide fashion.