Graphics Reference
In-Depth Information
(a)
(b)
(c)
Figure 1.7
Basic types of reflection. (a) Ideal diffuse reflection, from a Lambertian surface, is uniform
in all directions. (b) A perfectly specular (mirror) surface reflects light only in the mirror
direction. (c) Reflection from real surfaces can be quite complex.
All incident light from a particular direction that is not absorbed by the sur-
face is reflected in the specular direction, the direction of mirror reflection. (Unre-
flected light is actually transmitted into the surface according to physical proper-
ties of the materials as described in Section 1.2.6.) Ideal specular reflection does
not fit well into the BRDF framework, because BRDFs normally describe how
incident light is spread out by reflection, and ideal specular reflection exhibits no
such spread. The BRDF of a mirror surface therefore behaves like a Dirac
func-
tion, with the lobes having the shape of infinitely long spikes in the direction of
mirror reflection. In practice, mirror reflection is often handled as a special case
in rendering algorithms.
In reality, perfectly specular surfaces do not actually exist, because surfaces
are neither perfectly smooth nor entirely clean. Roughness causes the reflected
radiance to spread out near the direction of mirror reflection. As the spread in-
creases, the
specularity
of the surface is said to decrease. Highly specular sur-
faces exhibit near mirror reflection, while less specular surfaces appear more dull.
Surfaces of medium to high specularity are sometimes described as
glossy
.Lam-
bertian surfaces can be said to have no specularity; however, perfectly Lamber-
tian surfaces do not exist, either. Real “Lambertian” surfaces normally exhibit
some specularity, and this tends to increase at grazing angles. BRDF models fre-
quently include a mix of Lambertian and specular behavior to better model real
surfaces.
δ
1.2.6 Fresnel Reflectance
Maxwell's equations, which govern the propagation of electromagnetic waves,
determine the behavior of light at a boundary between two spatial regions hav-
ing different physical properties. In this context, a spatial region through which
light travels is called a
medium
. Regarding light as an electromagnetic wave,
Maxwell's equations apply to reflection at a smooth homogeneous surface, such
as a metal surface or a
dielectric
material such as glass or clear plastic. The sur-
