Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 369

Perspective projection Orthographic projection

Figure 10.6
Perspective versus orthographic projection

in terms of two angles, we give two sizes: the physical width and height of
the box.
The zoom value has a different meaning in orthographic projection com-
pared to perspective. It is related to the physical size of the frustum box:

Converting between
zoom and frustum size in
orthographic projection

zoom = 2/size, size = 2/zoom.

As with perspective projections, there are two different zoom values, one
for x and one for y, and their ratio must be coordinated with the aspect ratio
of the rendering window in order to avoid producing a “squashed” image.
We developed Equation (10.5) with perspective projection in mind, but this
formula also governs the proper relationship for orthographic projection.

10.3 Coordinate Spaces

This section reviews several important coordinate spaces related to 3D view-
ing. Unfortunately, terminology is not consistent in the literature on the
subject, even though the concepts are. Here, we discuss the coordinate
spaces in the order they are encountered as geometry flows through the
graphics pipeline.

10.3.1 Model, World, and Camera Space
The geometry of an object is initially described in object space, which is
a coordinate space local to the object being described (see Section 3.2.2).