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##

10.4 Other Lighting Models

Up to this point we have largely discussed the Phong lighting model.
The diffuse and specular terms for a single light are given by the
following equation:

Section 10.1.1 discusses the use of sphere mapping to
replace the OpenGL per-vertex specular illumination computation with
one performed at each pixel. The specular contribution in the
texture map is computed using the Phong formulation above. However,
the Phong model can be substituted with other bi-directional reflectance
functions to achieve other lighting effects. Since the texture coordinates
are computed with a sphere mapping function, the resulting texture
mapping operation accurately approximates view-dependent specular
reflectance distributions.

One improvement that can be made is to add a *Fresnel* reflection
term,
,[45] to the specular equation:

The Fresnel term specifies the ratio the amount of reflected light to the
amount of transmitted (refracted) light. It is a function of the angle of
incidence,
,
the angle of refraction
and the
material properties of the object (dielectric, metal, etc. as described in
Section 10.8). The effect of the Fresnel term is to
attenuate light as a function of its incident and reflected directions as
well as its wavelength. Light is hardly reflected from dielectrics such as
glass at normal incidence, for example, while being almost totally
reflected at glancing angles. This attenuation is independent of
wavelength. The absorption of metals, on the other hand, can be a function
of the wavelength in, for instance, copper and gold. At glancing angles,
the light color is unaltered in reflection, but at normal incidence the
light is modulated by the color of the metal.

Since the sphere map serves as a table which is indexed by the
the reflection vector, the Fresnel effects can be included in the
environment map by simply computing the specular equation with
the Fresnel term to modulate and shift the color. This can be performed
as a post-processing step on an existing environment map by computing
the Fresnel reflection coefficient at each angle of incidence and
modulating the sphere map.
Reflection, refraction and sphere mapping are discussed in more detail in
Section 11.1. Other bi-directional reflectance
functions can be encoded in a sphere map in a similar fashion.

** Next:** 10.5 Global Illumination
** Up:** 10. Lighting Techniques
** Previous:** 10.3 Gloss Maps
*David Blythe*

*1999-08-06*