Game Development Reference
In-Depth Information
CHAPTER 2
■ ■ ■
Some Basic Concepts
A
fter reading Chapter 1, you're probably anxious to incorporate realistic physics into your
game simulations. Before we get into specific physics models to model how airplanes fly or
what happens when a bat hits a baseball, you need to have an understanding of some core
concepts and definitions that will be used throughout the topic. The subjects covered in this
chapter are things that can be used in any physics-based model. A lot of this material may be
familiar to you, but even if you know most of what is here, it's a good idea to refresh your
memory to “set the stage” for the rest of the topic.
Physics models are usually expressed mathematically, and as you probably know mathe-
matics is a language all to itself, full of strange symbols and funny-looking letters. In this chapter,
we'll review some basic math nomenclature, so you won't be confused when you see the symbols
α
later in the topic. This chapter will also present some basic mathematical concepts and
solution techniques that will be used in developing the physics models in subsequent chapters.
Most of the time when you are putting physics into your games, you will be dealing with a
three-dimensional world—how a golf ball flies through the air or how a car drives around a
corner. In this chapter, we will discuss how coordinate reference frames are used to position an
object in space and about the different types of coordinate reference frames. You will see how
certain characteristics, such as velocity, can be expressed three-dimensionally using a mathe-
matical concept known as a
vector
.
Some of the specific subjects we will investigate in this chapter include the following:
or
Σ
•
Systems of units
•
Scientific notation
•
Summation notation
•
Greek letters
•
Coordinate systems and frames of reference
•
Scalars and vectors
•
Matrices and matrix multiplication
•
Rotation matrices
•
Derivatives and differential equations
When you finish this chapter, you will be armed and ready to dive into the wonderful
world of physics, so let's get started.
5
