Vectors - 3D Math Primer for Graphics and Game Development - page 31

Chapter 2

Vectors

Yellow fever vaccine should be administered
10 to 12 days before exposure to the vector.
— The United States Dispensatory (1978)

Vectors are the formal mathematical entities we use to do 2D and 3D
math. The word vector has two distinct but related meanings. Mathe-
matics topics, especially those on linear algebra, tend to focus on a rather
abstract definition, caring about the numbers in a vector but not necessar-
ily about the context or actual meaning of those numbers. Physics topics,
on the other hand, tend towards an interpretation that treats a vector as a
geometric entity to the extent that they avoid any mention of the coordi-
nates used to measure the vector, when possible. It's no wonder that you
can sometimes find people from these two disciplines correcting one another
on the finer points of “how vectors really work.” Of course the reality is
that they are both right, 1 and to be proficient with 3D math, we need to
understand both interpretations of vectors and how the two interpretations
are related.
This chapter introduces the concept of vectors. It is divided into the
following sections.

• Section 2.1 covers some of the basic mathematical properties of vec-

tors.

• Section 2.2 gives a high-level introduction to the geometric properties

of vectors.

• Section 2.3 connects the mathematical definition with the geometric

one and discusses how vectors work within the framework of Cartesian
coordinates.

1 But the perspective taken by physics textbooks is probably the one that's more
appropriate for video game programming, at least in the beginning.

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