Parallel projection
The projection is called orthographic if the rays are perpendicular (orthogonal) to the image plane, and oblique or skew if they are not.
Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the center or viewpoint, as this point is moved towards infinity.
Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between the lens and the focal point in photography) or "zoom".
The term orthographic is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are also parallel with the projection plane (or the paper on which the orthographic or parallel projection is drawn).
However, when the principal planes or axes of an object are not parallel with the projection plane, but are rather tilted to some degree to reveal multiple sides of the object, they are called auxiliary views or pictorials.
A typical (but non-obligatory) characteristic of multiview orthographic projections is that one axis of space usually is displayed as vertical.
Because of its simplicity, oblique projection is used exclusively for pictorial purposes rather than for formal, working drawings.
In an oblique pictorial drawing, the displayed angles separating the coordinate axes as well as the foreshortening factors (scaling) are arbitrary.
From this analytic representation of a parallel projection one can deduce most of the properties stated in the previous sections.
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.
[4] 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.
[4][3][5][6] The concept of isometry had existed in a rough empirical form for centuries, well before Professor William Farish (1759–1837) of Cambridge University was the first to provide detailed rules for isometric drawing.
[7][8] 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.
Isometry means "equal measures" because the same scale is used for height, width, and depth".
[9] From the middle of the 19th century, according to Jan Krikke (2006)[9] 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".
[9] De Stijl architects like Theo van Doesburg used axonometry for their architectural designs, which caused a sensation when exhibited in Paris in 1923".
[9] 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.
[4] Objects drawn with parallel 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 parallel, 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.
