Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 5

The First Law of Computer Graphics

If it looks right, it is right.

We will be doing a lot of trigonometry in this topic. Trigonometry
involves real numbers such as π, and real-valued functions such as sine and
cosine (which we'll get to later). Real numbers are a convenient fiction,
so we will continue to use them. How do you know this is true? Because,
Descartes notwithstanding, we told you so, because it would be nice, and
because it makes sense.

1.2 2D Cartesian Space

You probably have used 2D Cartesian coordinate systems even if you have
never heard the term “Cartesian” before. “Cartesian” is mostly just a fancy
word for “rectangular.” If you have ever looked at the floor plans of a house,
used a street map, seen a football 1 game, or played chess, you have some
exposure to 2D Cartesian coordinate spaces.
This section introduces 2D Cartesian mathematics, the mathematics of
flat surfaces. It is divided into three main subsections.

• Section 1.2.1 provides a gentle introduction to the concept of 2D

Cartesian space by imagining a fictional city called Cartesia.

• Section 1.2.2 generalizes this concept to arbitrary or abstract 2D

Cartesian spaces. The main concepts introduced are

◦ the origin

◦ the x- and y-axes

◦ orienting the axes in 2D

• Section 1.2.3 describes how to specify the location of a point in the

2D plane using Cartesian (x,y) coordinates.

1 This sentence works no matter which sport you think we are referring to with the
word “football.” Well, OK, it works a little better with American football because of
the clearly marked yard lines.