Graphics Programs Reference
In-Depth Information
The main advantage of orthographic projections is the ease of measuring dimen-
sions. The projection of a segment of length l on the object is a segment of length l
(or of a length related to l in a simple way) on the projection plane. This helps in
manufacturing an object directly from a drawing and is the main reason orthographic
projections are used in technical drawing.
Figure 2.5 shows a side view and the top view of a thin hexagon. It is easy to
see that a segment of length l on side a becomes a segment of the same length on the
projection, while a segment of length l on side b becomes a segment of length l cos β on
the projection (where β = 270
α ).
Top view
Side view
a
α
b
b
l
l
a
l
l cos β
Figure 2.5: Segments on the Sides of a Hexagon.
I feel like I am diagonally parked in a parallel universe.
—Unknown
2.2 Axonometric Projections
The term axonometric is derived from the Greek αξων or αξoναζ (axon, axis) and
μτρoν (metron, a measure). We approach this type of parallel projections from two
points of view.
Approach 1: Linear perspective, the topic of Chapter 3, was developed in the West
during the Renaissance and is based on geometric optics. The observer is considered
a point that receives straight rays of light and senses only the color, the intensity, and
the direction of a ray but not the distance it has traveled. Oriental art, in contrast, has
developed in a different direction and has adopted a different system of perspective, one
that is suitable for scroll paintings.
A Chinese scroll painting is normally executed on a horizontal rectangle about
40 cm high and several meters long. The painting is viewed slowly from right to left
while unrolling the scroll, and it tells a story in time. As the eye moves to the left, we
see later occurrences of the same scene, not new views. We can call this approach to
art “narrative,” in contrast to Western art, which is situational. Figure C.4 (page 236)
is an example of this type of art. It is a 33-foot-long scroll titled A City of Cathay that
was painted by artists of the Qing court (1662-1795).
 
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