Parallel Projections - Transformations and Projections in Computer Graphics - page 54

and T y project points orthographically on the yz and the xz planes, respectively.

⎛ ⎞ ⎛ ⎞ ⎛ ⎞

000
010
001

100
000
001

100
010
000

⎝ ⎠ , T y = ⎝ ⎠ , T z = ⎝ ⎠ .

T x = (2.1)

The object of Figure 2.2 has two properties that make it especially easy to project.
It is similar to a cube, and its edges are aligned with the coordinate axes. In general, if
the main edges of the object are not aligned with the coordinate axes, its orthographic
projections along the axes may look unfamiliar and confusing, and it is preferable to
rotate the object, if at all possible, and align it before it is projected. If the object is
not cubical, the best option is to select on the object three axes that are judged the
“main” ones and align them with the coordinate axes. The object is then surrounded
by a bounding box (Figure 2.3) and the box is projected. Once this is done, the object
is transferred into the projected bounding box in a process similar to that described in
Section 3.3. If the object is so complex that it is impossible to find three such axes, then
the designer should consider projecting several sectional views of the object or using a
nonorthographic projection.

Figure 2.3: Orthographic Projection of a Curved Object.

Exercise 2.1: Try to interpret the three orthographic projections of Figure 2.4.

(a) (b) (c)

Figure 2.4: Three Orthographic Projections for Exercise 2.1.