Axonometric projection is a type of parallel projection used for creating a
pictorial drawing of an object, where the object is rotated along one or more
of its axes relative to the plane of projection.
There are four main types of axonometric projection: isometric, dimetric,
trimetric projection, and oblique projection.
"Axonometric" means "to measure along axes". Axonometric projection shows an
image of an object as viewed from a skew direction in order to reveal more than
one side in the same picture. Whereas the term orthographic is sometimes
reserved specifically for depictions of objects where the axis or plane of the
object is parallel with the projection plane, in axonometric projection the
plane or axis of the object is always drawn not parallel to the projection
plane. With axonometric projections the scale
of distant features is the same as for near features, so such pictures will
look distorted, as it is not how our eyes or photography work. This
distortion is especially evident if the object to view is mostly composed of
rectangular features. Despite this limitation, axonometric projection can
be useful for purposes of illustration. History
The concept of an isometric projection had existed in a rough empirical form
for centuries, well before Professor William Farish of Cambridge University
was the first to provide detailed rules for isometric drawing.
Farish published his ideas in the 1822 paper "On Isometrical Perspective", in
which he recognized the "need for accurate technical working drawings free
of optical distortion. This would lead him to formulate isometry. Isometry
means "equal measures" because the same scale is used for height, width, and
depth". From the middle of the 19th century,
according to Jan Krikke isometry became an "invaluable tool for engineers, and
soon thereafter axonometry and isometry were incorporated in the curriculum of
architectural training courses in Europe and the U.S. The popular acceptance of
axonometry came in the 1920s, when modernist architects from the Bauhaus
and De Stijl embraced it". De Stijl architects like Theo van Doesburg used
axonometry for their architectural designs, which caused a sensation when
exhibited in Paris in 1923". Since the 1920s axonometry, or parallel
perspective, has provided an important graphic technique for artists,
architects, and engineers. Like linear perspective, axonometry helps depict 3D
space on the 2D picture plane. It usually comes as a standard feature of
CAD systems and other visual computing tools.
According to Jan Krikke "axonometry originated in China. Its function in
Chinese art was similar to linear perspective in European art. Axonometry,
and the pictorial grammar that goes with it, has taken on a new significance with
the advent of visual computing". Four types
The four types of axonometric projections are isometric projection,
dimetric projection, trimetric projection, and oblique projection,
depending on the exact angle at which the view deviates from the orthogonal.
Typically in axonometric drawing, one axis of space is shown as the vertical.
In isometric projection, the most commonly used form of axonometric
projection in engineering drawing, the direction of viewing is such that the
three axes of space appear equally foreshortened, and there is a common
angle of 120° between them. As the distortion caused by foreshortening is
uniform the proportionality of all sides and lengths are preserved, and the axes
share a common scale. This enables measurements to be read or taken
directly from the drawing. Another advantage is that 120° angles are more
easily constructed using only a compass and straightedge.
In dimetric projection, the direction of viewing is such that two of the three
axes of space appear equally foreshortened, of which the attendant
scale and angles of presentation are determined according to the angle of
viewing; the scale of the third direction is determined separately.
In trimetric projection, the direction of viewing is such that all of the three
axes of space appear unequally foreshortened. The scale along each of
the three axes and the angles among them are determined separately as dictated by
the angle of viewing. In oblique projection, the angles
displayed among the axis, as well as the foreshortening factors are arbitrary.
More precisely, any given set of three coplanar segments originating from the
same point may be construed as forming some oblique perspective of three sides
of a cube. Approximations are common in dimetric
and trimetric drawings. Limitations
As with all types of parallel projection, objects drawn with
axonometric projection do not appear larger or smaller as they extend closer
to or away from the viewer. While advantageous for architectural drawings,
where measurements must be taken directly from the image, the result is a
perceived distortion, since unlike perspective projection, this is not how
photography normally works. It also can easily result in situations where depth
and altitude are difficult to gauge, as is shown in the illustration to the
right. In this isometric drawing, the blue
sphere is two units higher than the red one. However, this difference in
elevation is not apparent if one covers the right half of the picture, as the
boxes are then obscured. This visual ambiguity has been exploited
in op art, including "impossible object" drawings. M. C. Escher's Waterfall is a
well-known example, in which a channel of water seems to travel unaided along a
downward path, only to then paradoxically fall once again as it
returns to its source. The water thus appears to disobey the law of
conservation of energy. References
Further reading Yve-Alain Bois, "Metamorphosis of
Axonometry," Daidalos, no. 1, pp. 41–58