Multiple Coordinate Spaces - 3D Math Primer for Graphics and Game Development - page 84

Figure 3.1
Camera space using left-handed
conventions

Note carefully the differences between camera space, which is a 3D
space, and screen space, which is a 2D space. The mapping of camera-
space coordinates to screen-space coordinates involves an operation known
as projection. We'll discuss camera space in more detail, and this conver-
sion process in particular, when we talk about coordinate spaces used in
rendering in Section 10.3.

3.2.4 Upright Space

Sometimes the right terminology is the key to unlocking a better under-
standing of a subject. Don Knuth coined the phrase “name and conquer”
to refer to the common and important practice in mathematics and com-
puter science of giving a name to a concept that is used frequently. The
goal is to avoid repeating the details of this idea each time it is invoked,
resulting in a reduction of clutter and an easier time focusing on the larger
issue, for which the thing being named is only one part. It has been our
experience that to conquer coordinate space transformations, when com-
municating either to human beings via words or to computers via code, it
is helpful to associate with each object a new coordinate space, which we
call the upright coordinate space of the object. An object's upright space
is, in a certain sense, “halfway” between world space and its object space.
The axes of upright space are parallel with the axes of world space, but
the origin of upright space is coincident with the origin of object space.
Figure 3.2 illustrates this principle in 2D. (Notice that we have made an
arbitrary choice to place the origin between the robot's feet, rather than at
her center of mass.)