Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 12

Figure 1.9. Example points labeled with 2D Cartesian coordinates

1.3 3D Cartesian Space

The previous sections have explained how the Cartesian coordinate system
works in 2D. Now it's time to leave the flat 2D world and think about 3D
space.
It might seem at first that 3D space is only “50% more complicated”
than 2D. After all, it's just one more dimension, and we already had two.
Unfortunately, this is not the case. For a variety of reasons, 3D space is more
than incrementally more di cult than 2D space for humans to visualize and
describe. (One possible reason for this di culty could be that our physical
world is 3D, whereas illustrations in topics and on computer screens are
2D.) It is frequently the case that a problem that is “easy” to solve in 2D
is much more di cult or even undefined in 3D. Still, many concepts in
2D do extend directly into 3D, and we frequently use 2D to establish an
understanding of a problem and develop a solution, and then extend that
solution into 3D.
This section extends 2D Cartesian math into 3D. It is divided into four
major subsections.

• Section 1.3.1 begins the extension of 2D into 3D by adding a third

axis. The main concepts introduced are