160 4. 3D Math for Games

`“A” axes, while the vector PB gives the position of that same point relative to a`

diff erent set of axes “B.”

In physics, a set of coordinate axes represents a frame of reference, so

we sometimes refer to a set of axes as a coordinate frame (or just a frame).

People in the game industry also use the term coordinate space (or simply

space) to refer to a set of coordinate axes. In the following sections, we’ll look

at a few of the most common coordinate spaces used in games and computer

graphics.

`4.3.9.1. Model Space`

When a triangle mesh is created in a tool such as Maya or 3DStudioMAX, the

positions of the triangles’ vertices are specifi ed relative to a Cartesian coordi-

nate system which we call model space (also known as object space or local space).

The model space origin is usually placed at a central location within the object,

such as at its center of mass, or on the ground between the feet of a humanoid

or animal character.

Most game objects have an inherent directionality. For example, an air-

plane has a nose, a tail fi n, and wings that correspond to the front, up, and

left /right directions. The model space axes are usually aligned to these natural

directions on the model, and they’re given intuitive names to indicate their

directionality as illustrated in Figure 4.17.

`z Front. This name is given to the axis that points in the direction that the`

object naturally travels or faces. In this book, we’ll use the symbol F to

refer to a unit basis vector along the front axis.

z Up. This name is given to the axis that points towards the top of the

object. The unit basis vector along this axis will be denoted U.

z Left or right. The name “left ” or “right” is given to the axis that points

toward the left or right side of the object. Which name is chosen de-

pends on whether your game engine uses left -handed or right-handed

`xA`

`yA xB`

`yB`

`PA= (2 , 3)`

`PB= (1, 5)`

`Figure 4.16. Position vectors for the point P relative to different coordinate axes.`