Ray Casting and Rasterization - Computer Graphics: Principles and Practice - page 413

Listing 15.17: The single-bounce shading code.

1 void shade( const Scene & scene, const Triangle &T, const Point3 &P,

const Vector3 &n, const Vector3 & w_o, Radiance3 & L_o) {

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L_o = Color3 (0.0f, 0.0f, 0.0f);

// For each direction (to a light source)
for ( unsigned int i = 0; i < scene.lightArray.size(); ++i) {
const Light & light = scene.lightArray[i];

const Vector3 & offset = light.position - P;
const float distanceToLight = offset.length();
const Vector3 & w_i = offset / distanceToLight;

if (visible(P, w_i, distanceToLight, scene)) {
const Radiance3 & L_i = light.power / (4 * PI * square(distanceToLight));

// Scatter the light
L_o +=
L_i *
T.bsdf(n).evaluateFiniteScatteringDensity(w_i, w_o) *
max(0.0, dot(w_i, n));

}

}

}

of the angle between w_i and n to account for the projected area over which
incident radiance is distributed (by the Tilting principle).

15.4.6 Lambertian Scattering
The simplest implementation of the BSDF assumes a surface appears to
be the same brightness independent of the viewer's orientation. That is,
evaluateFiniteScatteringDensity returns a constant. This is called Lam-
bertian reflectance, and it is a good model for matte surfaces such as paper and
flat wall paint. It is also trivial to implement. Listing 15.18 gives the implementa-
tion (see Section 14.9.1 for a little more detail and Chapter 29 for a lot more). It
has a single member, lambertian , that is the “color” of the surface. For energy
conservation, this value should have all fields on the range [ 0, 1 ] .

Listing 15.18: Lambertian BSDF implementation, following Listing 14.6.

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class BSDF {
public :
Color3 k_L;

/ ** Returns f = L_o / (L_i * w_i.dot(n)) assuming
incident and outgoing directions are both in the
positive hemisphere above the normal * /
Color3 evaluateFiniteScatteringDensity
( const Vector3 & w_i, const Vector3 & w_o) const {
return k_L / PI;

}

};

Figure 15.7 shows our triangle scene rendered with the Lambertian
BSDF using k_L=Color3(0.0f, 0.0f, 0.8f) . Because our triangle's vertex

Figure 15.7: A green Lambertian
triangle.