Page 188 - DCAP504_Computer Graphics

Unit 12: Color and Shading Model

A light can reflect in two extreme cases. They are:
1. Diffuse reflection
2. Specular reflection
In diffuse reflection, light energy from the light source gets reflected uniformly in all directions. In
figure 12.6, the small arrows that form a hemisphere represents diffuse reflection. The energy level of
the reflection can be expressed as a function of the incident angle θ between L and surface normal N.
Higher reflection can be achieved through smaller incident angle. The incident angle can be made
smaller by having the reflection proportional to cos(θ).

Figure 12.6: Phong Model

Source: Xiang. Z., Plstock. R. (2006). Computer Graphics. 2nd Edition. Tata McGraw Hill. Pg no. 295
The specular reflection occurs when the surface has the characteristic of a shiny or mirror like surface. If
the surface in figure 12.6 is a perfect mirror then the light rays from the point light source would be
reflected exactly in one direction. A perfect mirror does not exist in reality. So, the Phong model
distributes the reflected energy across a small cone shaped space centered around R. While doing so,
the Phong model distributes more reflection along the direction of R and decreases the reflection energy
quickly as φ increases. The mathematical means for distributing reflected light across a small cone
shaped space centered around R is cos (φ), where k can be used to vary the degree of shininess.
k

k
Did you know? The parameter k in cos (φ) is 1 for a dull surface and 100 for a shiny surface.
Furthermore, the complex inter-object reflection should be considered in some way because many
surfaces we see do not reflect directly by the light source. They are reflected by light that is passing
through the environment. For these kinds of objects there is a need to introduce a directionless ambient
light which illuminates all surfaces in a particular area and gets reflected uniformly in all directions by
each surface.
Thus, according to Phong model, object surfaces might generate a blend of ambient light reflection and
light source dependent diffuse/specular reflection. Mathematically the total reflected energy intensity I
can be written as follows:
k
I=Iaka+Ip (kd cos(θ) + kscos (φ))
where, I a -- the intensity of the ambient light
I p -- the intensity of the point light
0<=k a, k d, k s <=1.0 are reflection co-efficients that represent the ability of a surface to reflect ambient
light in order to create diffuse reflection and to create specular reflection respectively.

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