Game Development Reference

In-Depth Information

2

T
HE
M
ATHEMATICS

OF
P
ARTICLES

dimensional mathematics. In particular it looks at vector mathematics and

vector calculus—the fundamental building blocks on which all our physics code will

be built. I'll avoid some of the harder topics we'll only need later. Matrices and quater-

nions, for example, will not be needed until chapter 9, so I'll postpone reviewing them

until that point.

Before we look at simulating the physics of particles, this chapter reviews three-

2.1

V
ECTORS

Most of the mathematics we are taught at school deals with single number—numbers

to represent the number of apples we have or the time it takes for a train to make a

journey, or the numerical representation ofafraction.Wecanwritealgebraicequa-

tions that tell us the value of one number in terms of others. If
x

y
2

=

and
y

=

3, then

we know
x

9. This kind of single number on its own is called a “scalar value.”

Mathematically a vector is an element of a vector space: a structure that displays

certain mathematical properties for addition and multiplication. For our purposes

the only vector spaces we're interested in are regular (called Euclidean) 2D and 3D

spaces. In this case the vector represents a position in those spaces.

Vectors are usually represented as an ordered list of numbers that can be treated

in a similar way to a single number in an algebraic equation. If
y
is a vector (let's say

it contains the numbers 2 and 3), and if
x

=

2
y
, then
x
will also be a vector of two

numbers, in this case 4 and 6. Vectors can undergo the same mathematical operations

15

=