Illumination and shading

Projections, required for displaying a three-dimensional scene on a two-dimensional plane or screen, were discussed in section 5.8. A projection is a special type of mapping from the three-dimensional space to a plane. In this sense, a projection describes only where a point or an object has to be drawn on the projection plane. The determination of visible surfaces in chapter 7 also focussed only on the question which objects should be drawn or projected and which ones are hidden from view by others. The information where an object should be drawn on the projection plane, i.e., which pixels are covered by the object, is not at all sufficient for a realistic representation of a three-dimensional scene. Figure 8.1 shows the projections of a grey sphere and a grey cube, both in two variants. The first variant simply assigns the colour of the sphere and the cube directly to the pixels that are occupied by the corresponding object. This leads to geometric shapes with a homogeneous colour losing almost the complete information about the three-dimensional structure. The projection of the sphere is a grey circle, the cube becomes a grey hexagon.

Taking illumination and light reflections into account leads to different light effects on the surfaces of the three-dimensional objects and to a nonhomogeneous shading of their projections. In this way, even the flat images appear vivid and provide a three-dimensional impression as can be seen in figure 8.1 where the effects of illumination were taken into account for the second sphere and the second cube. Shading refers to rendering an object’s surface with illumination and light reflection effects. This chapter introduces the necessary background and techniques for illumination and shading in computer graphics.