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2.2 Photometric image formation 59

0.5 0.5
Ambient Ambient
Diffuse Diffuse
0.4 0.4
Exp=10 Exp=10
Exp=100 Exp=100
0.3 Exp=1000 0.3 Exp=1000
0.2 0.2
0.1 0.1

0.0 0.0
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
(a) (b)

Figure 2.18 Cross-section through a Phong shading model BRDF for a fixed incident illumination direction:
(a) component values as a function of angle away from surface normal; (b) polar plot. The value of the Phong
exponent k e is indicated by the “Exp” labels and the light source is at an angle of 30 away from the normal.
◦

blue sky. In the Phong model, the ambient term does not depend on surface orientation, but
depends on the color of both the ambient illumination L a (λ) and the object k a (λ),

f a (λ)= k a (λ)L a (λ). (2.92)
Putting all of these terms together, we arrive at the Phong shading model,

+
L r (ˆv r ; λ)= k a (λ)L a (λ)+ k d (λ) L i (λ)[ˆv i · ˆn] + k s (λ) L i (λ)(ˆv r · ˆs i ) . (2.93)
k e
i i
Figure 2.18 shows a typical set of Phong shading model components as a function of the
angle away from the surface normal (in a plane containing both the lighting direction and the
viewer).
Typically, the ambient and diffuse reflection color distributions k a (λ) and k d (λ) are the
same, since they are both due to sub-surface scattering (body reflection) inside the surface
material (Shafer 1985). The specular reflection distribution k s (λ) is often uniform (white),
since it is caused by interface reflections that do not change the light color. (The exception
to this are metallic materials, such as copper, as opposed to the more common dielectric
materials, such as plastics.)
The ambient illumination L a (λ) often has a different color cast from the direct light
sources L i (λ), e.g., it may be blue for a sunny outdoor scene or yellow for an interior lit
with candles or incandescent lights. (The presence of ambient sky illumination in shadowed
areas is what often causes shadows to appear bluer than the corresponding lit portions of a
scene). Note also that the diffuse component of the Phong model (or of any shading model)
depends on the angle of the incoming light source ˆv i , while the specular component depends
on the relative angle between the viewer v r and the specular reflection direction ˆs i (which
itself depends on the incoming light direction ˆv i and the surface normal ˆn).
The Phong shading model has been superseded in terms of physical accuracy by a number
of more recently developed models in computer graphics, including the model developed by
Cook and Torrance (1982) based on the original micro-facet model of Torrance and Sparrow
(1967). Until recently, most computer graphics hardware implemented the Phong model but
the recent advent of programmable pixel shaders makes the use of more complex models
feasible.