Parallel Projections - Transformations and Projections in Computer Graphics - page 61

As a result, the 27 ◦ standard for axonometric projections (Figure 2.10) makes more
sense. This standard is sometimes also called the 1: 2 isometric projection because it is
based on the ratio h/w =1 / 2.

y

w

45 0

h

x

(b)

(a)

30 0

α

27 0 27 0

Figure 2.10: The 27 ◦ Isometric Projection.

A similar standard is based on the ratio h/w =1,whichleadsto α =45 ◦ .Thiscase
is also known as the military isometric projection. This projection is suitable for appli-
cations where the horizontal faces of the projected object are important. Figure 2.11
shows that the xz plane becomes a regular rhombus in this projection, which makes it
easy to read details and measure distances on this plane.

y

w

45 0

h

x

45 0

α

45 0 45 0

Figure 2.11: The 45 ◦ Isometric Projection.

A Dutch standard for dimetric projections is based on the ratio h/w =0 . 33. It
is known as the 42 ◦ / 7 ◦ standard because it results in angles α and β of these sizes
(Figure 2.12). The z axis (the one that's drawn at 42 ◦ ) is scaled by a factor of 1 / 2.