Physically-Based Shading Models in Film and Game Production——SIGGRAPH 2010 Course Notes
http://renderwonk.com/publications/s2010-shading-course/hoffman/s2010_physically_based_shading_hoffman_a_notes.pdf
background: physically-based shading
in this section of the course notes, we will go over the fundamentals behind physically-based shading models, starting with a qualitative description of the underlying physics, followed by a quantitative description of the relevant mathematical models, and finally discussing how these mathematical models can be implemented for shading.
The Physics of Shading
The physical phenomena underlying shading are those related to the interaction of light with matter.
To understand these phenomena, it helps to have a basic understanding of the nature of light.
Light is an electromagnetic transverse wave, which means that it oscillates in directions perpendicular
to its propagation (see Figure 1).
Since light is a wave, it is characterized by its wavelength—the distance from peak to peak. Electromagnetic
wavelengths cover a very wide range but only a tiny part of this range (about 400 to 700
nanometers) is visible to humans and thus of interest for shading (see Figure 2).
The effect matter has on light is defined by a property called the refractive index. The refractive
index is a complex number; its real part measures how the matter affects the speed of light (slowing
it down relative to its speed in a vacuum) and the imaginary part determines whether the light is
absorbed (converted to other forms of energy) as it propagates. The refractive index may vary as a
function of light wavelength.
implementing shading
in the previous section, we saw the mathematical models that are typically employed to describe surface shading. in this section, we will discuss how such models are implemented in film and game production renderers.
General Lighting
In the most general case, the BRDF must be integrated against incoming light from all different
directions. This includes not only primary light sources (with area) but also skylight and accurate
reflections of other objects in the scene. To fully solve this, global illumination algorithms are required.
Detailed descriptions of these algorithms are outside the domain of this talk; more details can be found
in various references ([18, 11]), as well as Adam Martinez’s talk in this course, Faster Photorealism in
Wonderland: Physically-Based Shading and Lighting at Sony Pictures Imageworks.
Punctual Light Sources 精准光源
a far mor restricted, but common production lighting environment is comprised of one or more punctual light sources. these are the classic computer graphics point, directional, and spot lights (more complex variants are also used[4]). since they are inifinitely small and infinitely bright, they are not physically realizable or realistic, but they do produce reasonable results in many cases and are computationally convenient. punctual light sources are parameterized by the light color Clight and the light direction Lc. for artist convenience, Clight does not correspond to a direct radiometric measure of the light’s intensity; it is specified as the color a white Lambertian surface would have when illuminated by the light from a direction parallel to the surface normal (Lc=n). like other color quantities we have seen, Clight is spectral (RGB)——valued, but unlike them its range is unbounded.
the primary advantage of punctual light sources is that they greatly simplify the reflection equation (Equation 1),
as we will show here. we will start by defining a tiny area light source centered on Lc, with a small angular extent ε. this tiny area light illuminates a shaded surface point with the incoming radiance function Ltiny(l). the incoming radiance function has the following two properties: