Real-Time Rendering, Third Edition, 3rd Edition

i

i

i

i

i

i

i

i

Chapter 7

Advanced Shading

“Let the form of an object be what it may, light, shade, and

perspective will always make it beautiful.”

—John Constable

The Gouraud shading model was invented in 1971 [435]. Phong’s specu-

lar highlighting equation was introduced around 1975 [1014]. The concept

of applying textures to surfaces was presented a year later by Blinn and

Newell [96]. As part of the standard fixed-function pipeline, these algo-

rithms were the mainstay of graphics accelerators for years. The advent of

programmable shaders has vastly increased the available options—modern

GPUs can evaluate (almost) arbitrary shading models. This moves the

focus from “what is possible?” to “what are the best choices for this ap-

plication?”

An understanding of the underlying physical and psychological princi-

ples pertinent to rendering is important in navigating these choices. The

previous chapters presented the technologies for controlling the graphics

pipeline and the basic theory behind their use. In this chapter some of

the scientific underpinnings of rendering are discussed. Radiometry is pre-

sented first, as this is the core field concerned with the physical transmission

of light. Our perception of color is a purely psychological phenomenon, and

is discussed in the section on colorimetry. A shading model is comprised of

two main parts: the light source and the material model. Sections on both

describe the various options that are available. The final sections detail

methods for the efficient implementation of shading models.

The options covered in this chapter are limited by one basic assumption.

Each light source is assumed to illuminate a surface location from one

direction only—area, ambient, and environment lighting are not covered.

Chapter 8 will describe the theory and practice necessary for the use of

more general types of illumination.

201

i

i

i

i

i

i

i

i

202 7. Advanced Shading

7.1 Radiometry

The explanation of the example shading model in Chapter 5 included a

brief discussion of some concepts from radiometry. Here we will go over

those concepts in more depth, and introduce some new ones.

Radiometry deals with the measurement of electromagnetic radiation.

Such radiation consists of a flow of photons, which behave as either par-

ticles or waves, depending on circumstance. Using the mental model of

photons as particles works well for the most part. Although some physical

phenomena cannot be modeled without accounting for the wave properties

of photons,

1

these are usually ignored by even high-quality batch rendering

systems [1089].

One wave-related property of photons that cannot be disregarded is

the fact that each has an associated frequency or wavelength.

2

This is

an important property, because the energy of each photon is proportional

to its frequency, which affects interactions between photons and matter.

Most importantly, it affects the interaction of photons with sensors such

as the rods and cones in the human eye. Different frequencies of photons

are perceived as light of different colors (or not perceived at all, if they

are outside the limited range of human vision). The relationships between

a photon’s wavelength λ (in meters), frequency ν (in Hertz, or cycles per

second) and energy Q (in joules) are

ν =

c

λ

,

λ =

c

ν

,

Q = hν,

(7.1)

where c is the speed of light (2.998 ×10

8

meters/second) and h is Planck’s

constant (6.62620 × 10

−34

joule-seconds).

Electromagnetic radiation exists in a range of frequencies and energies,

from ELF (extremely low frequency) radio waves to gamma rays. Photons

with wavelengths between roughly 380 to 780 nanometers are perceptible to

the human eye, so only this range, the visible spectrum, is typically used for

rendering. Figure 7.1 shows the colors perceived for monochromatic (single-

wavelength) light throughout the visible spectrum. Recall that photon

energy is proportional to frequency: “bluer” photons are more energetic;

“redder” photons are less energetic.

In this section, we will discuss the various radiometric units and their

relationships. They units are summarized in Table 7.1.

1

These phenomena include polarization, interference, and diffraction.

2

Quantum theory shows that each photon actually has a range of associated frequen-

cies, but this fact can be ignored for rendering.