4.6 Shading

Shading is essential to put object borders in contrast and to make the image look three dimensional. The normalized version of the gradient vector, the surface normal, is used in the shading equation. Shading is computed for each sample, however, this technique is purely for visual purposes since it is assumed that each voxel has an uninterrupted view of the light source (even when buried in the middle of a volume), which it is not physically realistic.

For example, the Phong shading model with depth clueing can be used to produce a satisfactory illusion of smooth surfaces at reasonable cost (Pho75). The colour $c(\vec x)$ at sample point $\vec x$, is given by the Phong equation :

$c(\vec x) = c_a k_a + \frac{c_p}{k_1+k_2 d(\vec x)}(k_d(\vec n.\vec l) + k_s(\vec r. \vec v)^p )$

where

$$\begin{array}{ll} \mbox{$ c_a$} & \mbox{= colour of ambient l... ...$ \vec r = -\vec l + 2(\vec l . \vec n)\vec n$.}\\ \end{array}$$

The Phong reflection model considers the reflection from a surface to consist of three components : ambient light, diffuse component and specular component. The ambient term is a constant and simulates global and indirect illumination, where as the diffuse and specular components are dependent of the view, light directions and normals at the surface.