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Comparison of Gouraud and Phong Shading
Phong shading requires more calculations, but produces better results for specular reflection than Gouraud shading in the form of more realistic highlights. Consider the specular reflection term in Eq. (3.4) :
cos^{n} (s)
If n is large (the surface is a good smooth reflector) and one vertex has a very small value of s (it is reflecting the light ray in the direction of the observer) whilst the rest of the vertices have large values of s - a highlight occurs somewhere on our polygon. With Gouraud shading, nowhere on the polygon can have a brighter colour (i.e. higher value) than a vertex so unless the highlight occurs on or near a vertex, it will be missed out altogether. When it is near a vertex, its effect is spread over the whole polygon. With Phong shading however, an internal point may indeed have a higher value than a vertex and the highlight will occur tightly focused in the (approximately) correct position.
[(a+b)/(c+d)^(e+f)]+(g+h)/i
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