Rendering - Vector Analysis for Computer Graphics - page 225

n 3

n 2

n l

n r

n 1

n 4

Figure 10.5.

Phong's PhD research improved upon Gouraud's diffuse shading model by interpolating the
two vectors n l and n r rather than the light intensities. Although this increases the processing
time, the specular highlights achieved across a pseudo-smooth object are worth it. Another part
of the extra processing is in normalizing the interpolated normal vector.

10.5 Bump mapping

Irregular surfaces such as bark, or the skin of an orange, have extremely complex surface
geometries and present a real challenge to model within a computer graphic system. But as
we have seen above, cunning schemes can be invented to achieve an acceptable effect, without
expending too much effort, and the same is true for bumpy surfaces.
In 1978 James Blinn published his paper “Simulation of Wrinkled Surfaces” [Blinn, 1978]
and invented bump mapping , which makes a surface appear irregular without involving extra
geometry. Readers are highly recommended to read Mark Kilgard's paper, “A Practical and
Robust Bump-Mapping Technique for Today's GPUs” [Kilgard, 2000], upon which the following
description is based.
Blinn's technique derives a normal vector at a point on a parametric surface, which is then
perturbed using a value from an associated height field (bump map). The surface is then
rendered using the perturbed normals, which modulate the surface light intensities accordingly.
We begin by acknowledging some sort of bivariate vector function P uv that describes a
3D surface, where the parameters uv identify a unique point xyz on the surface. For
example, P uv might describe a plane, cylinder, sphere, toroid, or parametric patch.
From now on, we will reference this function as P and remember that its input parameters
are uv.
By partially differentiating P with respect to u and v, we obtain two vectors P u and P v,
which lie on the tangent plane containing P . By taking their cross product we obtain the surface
normal N at P :

P
u ×

P
v

N = (10.6)

Figure 10.6 illustrates these vectors.