Parallel Projections - Transformations and Projections in Computer Graphics - page 56

Because of the temporal approach to scroll art, Chinese (and other Oriental artists)
had to develop a system of perspective with no vanishing points, no explicit light sources,
and no shadows. The result was a special type of parallel perspective, known today as
“Chinese perspective” or axonometric projection. If we imagine the scroll to be the xy
plane and we view it along the z axis, then lines that are parallel to the z axis are drawn
parallel on the scroll instead of converging to a vanishing point.
Approach 2: An orthographic projection of an object shows the details of only
one of its main faces, which is why three or even six projections are needed. Each
projection may be detailed and it may show the true shape of that face with the correct
dimensions, but it shows little or nothing of the rest of the object. Thus, interpreting
and understanding orthographic projections requires experience. Viewing an object
from above, from below, and from four sides tends to confuse an inexperienced person.
Engineers, architects, and designers may be familiar with orthographic projections, but
they have to draw plans that will be viewed and comprehended by their superiors and
customers, and this suggests a projection method that will include some perspective,
will show more than one face of the object, and will also make it easy to compute
dimensions from the drawing. Linear perspective is easy to visualize and understand,
but for engineers and designers it has at least three disadvantages: (1) it is complex
to compute and draw, (2) the relation between dimensions on the diagram and real
dimensions of the object is complex, and (3) distant objects look small. A common
compromise is a drawing in one of the three varieties of axonometric projections.
Axonometric projections show more of the object in each projection but at the
price of having wrong dimensions and angles. An axonometric projection typically
shows three or more faces of the object, but it shrinks some of the dimensions. When
a dimension is measured on the drawing, some computations are needed to convert
it to a true dimension on the object. This is an easy, albeit nontrivial, procedure.
An axonometric projection shows the true shape of a face of the object (with true
dimensions) only if the face happens to be parallel to the projection plane. Otherwise,
theshapeofthefaceisdistortedanditsdimensionsareshrunk.
Before we get to the details, here is a summary of the properties of axonometric
projections:
Axonometric projections are parallel, so a group of parallel lines on the object will
appear parallel in the projection.
There are no vanishing points. Thus, a wide image can be scrolled slowly while dif-
ferent parts of it are observed. At every point, the viewer will see the same perspective.
Distant objects retain their size regardless of their distance from the observer. If
the parameters of the projection are known, then the dimensions of any object, far or
nearby, can be computed from measurements taken on the projection.
There are standards for axonometric projections. A standard may specify the
orientation of the object relative to the observer, which makes it easy for the observer
to compute distances directly from the projection.
To construct an axonometric projection, the object may first have to be rotated to
bring the desired faces toward the projection plane. It is then projected on that plane