## ABSTRACT

CHAPTER 5 COVERS VARIOUS techniques for rendering semitransparentvolume surfaces using an approximation to the Blinn-Phong local surface shading model. Although this model is adequate for shading surfaces, it does not provide suﬃcient lighting characteristics for translucent materials or materials where scattering dominates the visual appearance. Furthermore, the normal required for the Blinn-Phong shading model is derived from the normalized gradient of the scalar ﬁeld. Although this normal is well deﬁned for regions in the volume that have high gradient

magnitudes, this normal is undeﬁned in homogeneous regions, i.e., where the gradient is the zero vector, as seen in Figure 6.1 (left). The use of the normalized gradient is also troublesome in regions with low gradient magnitudes, where noise can signiﬁcantly degrade the gradient computation. In Chapter 10, we discuss volume rendering and transfer function techniques that can be used to directly visualize multivariate data sets. Although a type of derivative measure can be computed for these data sets, it is not suitable for deriving a normal for surface shading.