3D Axonometric of Technological Systems

Introduction

A 3D Axonometric projection is a type of orthographic projection for creating a pictorial object drawing.
In such a drawing, the object rotates around one or more of its axes to reveal multiple sides.
A conceptual 3D Axonometric of the technological systems required in order to reuse an existing building for agricultural purpose.
It provides further insight into future iterative designs.

“Axonometry” means “to measure along the axes”.
In German literature, axonometry is based on Pohlke’s theorem.
The theorem’s scope of axonometric projection encompasses every type of parallel projection.
Additionally, this includes multi-view projection and also oblique projection.
The term “axonometric” often distinguishes between orthographic views where the principal axes of an object are not orthogonal to the projection plane.
And also orthographic views in which the principal axes of the object are orthogonal to the projection plane.

In multi-view projection these would be auxiliary views and primary views.
Confusingly, the term orthographic projection might be only for the primary views.
Axonometric projection might be synonymous with parallel projection.
Overall an axonometric projection is synonymous with an “auxiliary view” (versus a “primary view”) in an “multi-view orthographic projection”.


With an axonometric projection, the scale of an object does not depend on its location.
In other words, an object in the foreground has the same scale as an object in the background. Consequently, such pictures look distorted, as human vision and photography use perspective projection. Thus, the perceived scale of an object depends on its distance and location from the viewer.


This distortion is the direct result of a presence or absence of foreshortening.
It is especially evident if the object consists of mostly rectangular features.
Despite this limitation, axonometric projection can be useful for purposes of illustration, especially because it allows for simultaneously relaying precise measurements.

The origin of axonometric drawings

Axonometry originated in China. 
Its function in Chinese art was unlike the linear perspective in European art since its perspective was not objective, or looking from the outside.
Instead, its patterns used parallel projections within the painting that allowed the viewer to consider both the space and the ongoing progression of time in one scroll.
According to science author and Medium journalist Jan Krikke, axonometry, and the pictorial grammar that goes with it, had taken on a new significance with the introduction of visual computing and engineering drawing.

Isometry had existed in a rough empirical form for centuries, well before Professor William Farish (1759–1837) of Cambridge University.
He was the first to provide detailed rules for isometric drawing.
Farish published his ideas in the 1822 paper “On Isometric 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 for height, width, and depth applies.

From the middle of the 19th century, according to Jan Krikke (2006) isometry became an “invaluable tool for engineers.
And soon thereafter, axonometry and isometry integrates 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 apply axonometry for their architectural designs.
Hence it resulted in 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 three-dimensional space on a two-dimensional picture plane.
It usually comes as a standard feature of CAD systems and other visual computing tools.

Axonometric Types

The three types of axonometric projection are isometric projection, dimetric projection, and trimetric projection, depending on the exact angle at which the view deviates from the orthogonal. Typically in axonometric drawing, as in other types of pictorials, one axis of space is 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 from foreshortening is uniform, this keeps the proportionality between lengths, and the axes share a common scale.
This eases one’s ability to take measurements directly from the drawing.
Therefore, 120° angles is drawn by only a compass and straightedge.

In dimetric projection, the direction of viewing is such that two of the three axes of space appear equally fore short.
To determine the attendant scale and angles of presentation is to determine the angle of viewing.
The scale of the third direction is determined separately.
Dimensional approximations are common in dimetric drawings.

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.
Dimensional approximations in trimetric drawings are common, and trimetric perspective is seldom in technical drawings.

Limitations

As with other types of parallel projection, objects drawn with axonometric projection do not appear larger or smaller as they lie closer to or farther 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 human vision or 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.

This visual ambiguity has been exploited in op art, as well as “impossible object” drawings.
Though not strictly axonometric, M. C. Escher’s Waterfall (1961) is a well-known image, 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.