Graphics Reference
In-Depth Information
when the incoming and outgoing directions are mirror reflections of each other,
and zero elsewhere.
As described in Chapter 1, perfectly diffuse and perfect mirror surfaces do
not really exist. Surfaces that are nearly Lambertian exhibit some directional
dependence, just as some of the light reflected off a mirror deviates slightly from
the ideal direction of reflection. For a general surface, the
specular direction
is
defined as the direction that light would be reflected if the surface were a perfect
mirror; in polar coordinates, the specular direction of
.
The
specularity
of a surface depends on how broadly reflected light is distributed
around the specular direction. At medium angles of incidence, the light reflected
from typical specular surfaces is greatest at the specular direction, and falls off
quickly as the outgoing vector moves away from the specular direction. The rate
of this “falloff” is one measure of the specularity of a surface: shiny surfaces
have a sharp falloff away from the specular direction; the falloff is more gradual
for more dull surfaces.
(
θ
i
,
φ
i
)
is simply
(
θ
i
,
φ
i
±
π
)
The Phong model.
Around 1973, Bui Tuong Phong proposed a simple model
for specular falloff using an integer power of the cosine of the angle
that the
outgoing direction vector makes with the specular direction [Phong 75]. The pur-
pose was to add realism to renderings of 3D models. CG rendering was still
in its infancy at the time. Scanline rendering of polygons was the predominant
method (if not the only method) for rendering 3D surfaces. Henri Gouraud had
developed the now ubiquitous technique of computing the lighting at the ver-
tices of a polygon mesh, and continuously interpolating the computed vertex col-
ors across a polygon during scanline rendering [Gouraud 71].
3
Phong extended
this method to interpolate vertex normals, so that an approximate surface normal
was available at each point on the polygon during scanline rendering. The ob-
ject was usually assumed to be illuminated by a single directional light source.
To render a point, the specular direction is computed according to the interpo-
lated surface normal, and the specular deviation angle
α
between the reflected
light direction and the direction to the eye is used to compute the specular falloff
(
Figure 8.2
)
. The term
Phong shading
is often used to refer to the method of
interpolating vertex normals as well as the cosine falloff model.
Figure 8.2 illustrates the angles used in Phong's reflection model. In the con-
text of simple specular BRDF models, the incident direction is the direction of the
α
3
At the time, frame buffers had yet to be realized; scanline rendering was usually done by rendering
each individual pixel onto photosensitive film. A basic film recorder places a flat cathode ray tube
(CRT) ) screen against the film, and exposes a single pixel by illuminating the corresponding point on
the screen for a fixed exposure time. Early rendering algorithms had to be sure not to record a pixel
more than once, or it would appear twice as bright.
