
Notes for February 13 class  Phong shading
Phong model for specular reflection
The first really interesting model for surface reflection was developed by BuiTong Phong in 1973.
Before that, computer graphics surfaces were rendered using only diffuse lambert reflection.
Phong's was the first model that accounted for specular highlights.
The Phong model begins by defining a reflection vector R, which is a reflection of the
direction to the light source L about the surface normal N.
As we showed in class, and as you can see from the diagram on the right,
it is given by:
R = 2 (N • L) N  L




Once R has been defined, then the Phong model
approximates the specular component of surface reflectance
as:
s_{rgb} max(0, E • R)^{p} )
where s_{rgb} is the color of specular reflection, p is a specular power,
and E is the direction to the eye (in our case, E = W, the
reverse of the ray direction).
The larger the specular power p, the "shinier" the surface will appear.
We can have more than one light.
To get the complete Phong reflectance, we sum over the lights in the scene:
a_{rgb} +
∑_{i}
lightColor_{i}
(
d_{rgb} max(0, N • L_{i}) +
s_{rgb} max(0, E • R) ^{p}
)
where
a_{rgb},
d_{rgb} and
s_{rgb}
are the ambient, diffuse and specular color,
respectively, and p is the specular power.
Mirror reflection
You can also implement mirror reflection by
mixing in the result of forming a reflection ray (V',W'):
W' = reflect W about N
V' = S + ε W'
where S is the point on the sphere surface
and ε is a small positive number
such as 0.001.




Homework (due before class on Tuesday Feb 20)
 Implement the Phong reflectance model.

Using your ray tracing code from last class,
and using the sample code included in these course notes,
incorporate Phong shading.
In this version of the library code,
I have included the noise function.
Feel to use noise anywhere in your code,
as we did in class, to create interesting
textures and shading effects.
You should do this with the x,y,z,r that define each sphere.
Feel free to play with light color,
as well as the properties that control surface material:
ambient color, diffuse color, specular color and specular power.

If you haven't done so yet, implement multiple spheres.
At each pixel, your ray tracer should render the nearest sphere (if any).
 Extra credit:

Implement mirror reflection,
so that one sphere can be seen
as a mirror reflection in another.

Try using noise to modify normal vector N.
That can look especially cool when combined with mirror reflection.

See whether you can figure out how to make a different material
for each sphere in the scene.
 See if you can make something cool and fun, try to make it animated.
