shear & reflection

Shading
For the most part, interactive computer graphics systems are polygon processors. From the hardware perspective, systems are optimized for passing polygons down the pipeline. Performance is measured in terms of polygons per second, a measurement that always includes lighting and shading. From the application perspective, a large class of CAD applications have the user design polygonal meshes. Even if the software supports curved surfaces, these surfaces are rendered as polygonal meshes that approximate the surface.

Because a polygon has the same normal for the entire surface, normals only need be computed once. Often normals are stored in an application data structure. Further efficiencies can be obtained for many special conditions such as a distant light source, and we must also be careful to avoid visual artifacts. We will investigate two methods for shading a polygonal mesh : flat shading, and smooth or interpolative (Gouraud) shading.
Flat Shading :
The three vectors need for shading ( L, n, and v ) can vary as we move from point to point on a surface. For a flat polygon, however, n is constant. If we assume a distant viewer, v is constant over the polygon. Finally, if the light source is distant, L is constant. Here distant could be interpreted in the strict sense of meaning that the source is at infinity.

If the three vectors are constant, then the shading calculation needs to be carried out only once for each polygon, and each point on the polygon is assigned the same shade. This technique is known as flat, or constant, shading. In OpenGL, we specify flat shading as follows :