Game Development Reference
In-Depth Information
The idea of a solid area is probably new to some readers, but we can
easily understand the idea by comparing it to angles in the plane. A “reg-
ular” angle is measured (in radians) based on the length of its projection
onto the unit circle. In the same way, a solid angle measures the area as
projected onto the unit sphere surrounding the point. The SI unit for solid
angle is the steradian, abbreviated “sr.” The complete sphere has 4π sr; a
hemisphere encompasses 2π sr.
By measuring the radiance per unit solid an-
gle, we can express the intensity of light at a
certain point as a function that varies based
upon the direction of incidence. We are very
close to having the unit of measurement that de-
scribes the intensity of a ray. There is just one
slight catch, illustrated by Figure 10.1, which
is a close-up of a very thin pencil of light rays
striking a surface. On the top, the rays strike
the surface perpendicularly, and on the bottom,
light rays of the same strength strike a different
surface at an angle. The key point is that the
area of the top surface is smaller than the area
of the bottom surface; therefore, the irradiance
on the top surface is larger than the irradiance
on the bottom surface, despite the fact that the
two surfaces are being illuminated by the “same
number” of identical light rays. This basic phe-
nomenon, that the angle of the surface causes
incident light rays to be spread out and thus
contribute less irradiance, is known as Lambert's
law. We have more to say about Lambert's law
in Section 10.6.3, but for now, the key idea is
that the contribution of a bundle of light to the
irradiance at a surface depends on the angle of
that surface.
Due to Lambert's law, the unit we use in graphics to measure the
strength of a ray, radiance, is defined as the radiant flux per unit pro-
jected area, per unit solid angle. To measure a projected area, we take
the actual surface area and project it onto the plane perpendicular to the
ray. (In Figure 10.1, imagine taking the bottom surface and projecting it
upwards onto the top surface). Essentially this counteracts Lambert's law.
Table 10.1 summarizes the most important radiometric terms.
Whereas radiometry takes the perspective of physics by measuring the
raw energy of the light, the field of photometry weighs that same light using
the human eye. For each of the corresponding radiometric terms, there is
Figure 10.1
The two surfaces are receiving
identical bundles of light, but
the surface on the bottom has a
larger area, and thus has a
lower irradiance.
Search WWH ::




Custom Search