Game Engine Architecture

428 10. The Rendering Engine

z the viewing direction vector V = [ Vx Vy Vz ], which extends from the

refl ection point to the virtual camera’s focal point (i.e., the negation of

the camera’s world-space “front” vector);

z the ambient light intensity for the three color channels,

A = [ AR AG AB ];

z the surface normal N = [ Nx Ny Nz ] at the point the light ray impinges

on the surface;

z the surface refl ectance properties, which are

□ the ambient refl ectivity kA,

□ the diff use refl ectivity kD,

□ the specular refl ectivity kS,

□ and a specular “glossiness” exponent α;

z and, for each light source i,

□ the light’s color and intensity Ci = [ CRi CGi CBi ],

□ the direction vector Li from the refl ection point to the light source.

In the Phong model, the intensity I of light refl ected from a point can be ex-

pressed with the following vector equation:

A D( )( ) ,i Si i

i

I= +kk kA∑⎣⎦⎡⎤NL⋅+R V⋅α C

where the sum is taken over all lights i aff ecting the point in question. This can

be broken into three scalar equations, one for each color channel:

( )( ) ,

( )( ) ,

( )( ).

R A R D i S i Ri

i

G A G D i S i Gi

B A B D i S i Bi

I kA k k C

I kA k k C

I kA k k C

α

α

α

= +⎡⎤⎣⎦⋅+ ⋅

= + ⎡⎤⎣⎦⋅+ ⋅

= + ⎡⎤⎣⎦⋅+ ⋅

∑

∑

∑

NL R V

NL R V

NL R V

i

i

Figure 10.23. Ambient, diffuse and specular terms are summed to calculate Phong

refl ection.