Parallel Projections - Transformations and Projections in Computer Graphics - page 52

2
Parallel Projections

There are several variants of parallel projections, but they are all based on the following
principle: Select a direction v and construct a ray that starts at a general point P on
the object and goes in the direction v .Thepoint P ∗ where this ray intercepts the
projection plane becomes the projection of P . The process is repeated for all the points
on the object, creating a set of parallel rays, which is why this class of projections is
called parallel. Figure 2.1 illustrates the principle of parallel projections. In Figure 2.1a
the rays are perpendicular to the projection plane and in Figure 2.1b they strike at a
different angle. This is why the latter method is called oblique projection (Section 2.3).
Figure 2.1c shows a different interpretation of parallel projections. Because the
rays are parallel, we can imagine that they originate at a centerofprojection located
at infinity. This interpretation unifies parallel and perspective projections and is in
accordance with the general rule of projections (page 2) which distinguishes between
parallel and perspective projections by the location of the center of projection.
The three types of parallel projections are orthographic, axonometric, and oblique.

∞

(a) (b) (c)

Figure 2.1: Parallel Projections.