VISUALIZATION OF 3D GRAY-TONE IMAGES - Fundamentals of Three-Dimensional Digital Image Processing - page 222

I = intensity of reflected light at a point P,
I i = intensity of incident light at a point P,
δ = angle between the direction of reflection and the direction to a viewpoint,
α = angle of incidence,
k α = specular reflection index at a point P (function of α ),
n = parameter representing the extent of expansion of reflected light around
the exact reflection direction.
In either (1) and (2), a density value (brightness) at a point P on a
2D image plane H P is determined by the intensity of reflected light given
above. This process of giving light and dark appropriately to a surface is
called shading . The shading in the context of this chapter is simply a tool for
rendering an object surface in such a way that the 3D shape of an object is
perceived easily. Parameters in equations given above are suitably selected in
consideration of easiness in understanding the shape of an object.
In computer graphics, in particular in photorealistic rendering, we intend
to generate an image that looks like real objects or real scenes or an image that
gives as an impression as similar to the real phenomena as possible. Models
and parameters are selected considering physical properties of real light and
material. We shall leave details of such sophisticated rendering techniques to
other topics on graphics [Foley84, Watt98].
It should be noticed that the intensity of light reflected by a surface at a
point P on a 2D image strongly depends on the normal vector at a point P
on a surface of a 3D object. This suggests that the brightness of a 2D image
may be calculated using Eqs. 7.7 7.9 if the surface normal is given at each

point, even if details of an object are not described exactly.

∼

7.6.2 Smooth shading

The following problems may occur in applying methods explained above to
surfaces of objects generated by a polygon model.

(i) Normal vectors are not defined uniquely on a vertex and on an edge.
(ii) Normal vectors change rapidly on both sides of an edge. As a result, an
abrupt change in brightness levels arises in the vicinity of edges. Spurious
edges or artifacts that look like fold lines may be seen even on a smooth
plane surface. On a rendered image, a border or an edge between two
adjacent faces of a polygon is enhanced too much. The Mach effect of the
human vision system emphasizes this phenomenon furthermore, and as a
result the image quality deteriorates significantly.

These problems are overcome by interpolating brightness values or only
normal vectors appropriately and smoothing changes in them. This is called
smooth shading . We will introduce examples below (Fig. 7.9).