Situation normal [Gourand and Phong shading]

Two of the most famous graphics techniques, derived from shading algorithms by Henri Gouraud and Bui Tuong Phong, have been implemented in hardware and software worldwide. Both methods use various hacks to smooth out the shading of a polygonal surface. So rather than looking like an assembly of flat slabs, a smooth-shaded model seems smoother. The sharp creases between polygons are gone, replaced by a continuous change in tone or color. But if the original polygons aren't being rendered directly, then the shading doesn't correspond to the original model. What model does it correspond to? In other words, what is the smooth surface which, when rendered accurately, has the same appearance as a Phong shaded polygonal model? Phong normal interpolation is the process of computing a point's surface normal by linear interpolation of the components of two normals at either end of a line containing that point. This normal may then be used as part of a shading equation that takes into account specular highlights in an empirical manner, Phong illumination. Throughout this article, I deal only with perfectly diffuse surfaces lit by a single light source, so Phong illumination isn't part of the discussion. We assume that the light source is conveniently located at infinity. Gourand shading means the process of interpolating a color component to find intermediate color values across a polygon. Phong shading means interpolating surface normals to find intermediate normals that we can then evaluate with respect to the light source to find a color for that point.