Oblique projection
Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional (2D) images of three-dimensional (3D) objects.
The cavalier projection was used by French military artists in the 18th century to depict fortifications.
are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space.
For this reason oblique is rarely used by professional designers or engineers.
In an oblique pictorial drawing, the angles displayed among the axis, as well as the foreshortening factors (scale) 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.
[2] The resulting distortions make the technique unsuitable for formal, working drawings.
Doing so creates a true shape image of the chosen plane.
This specific category of oblique projections, whereby lengths along the directions
are drawn at angle using a reduction factor is very much in use for industrial drawings.
On the flat drawing, two axes, x and z on the figure, are perpendicular and the length on these axes are drawn with a 1:1 scale; it is thus similar to the dimetric projections, although it is not an axonometric projection, as the third axis, here y, is drawn in diagonal, making an arbitrary angle with the x″ axis, usually 30 or 45°.
It is thus often used when a figure must be drawn by hand, e.g. on a black board (lesson, oral examination).
Some also explain the name by the fact that it was the way a rider could see a small object on the ground from his horseback.
[8] The term cabinet projection stems from its use in illustrations by the furniture industry.
As a formula, if the plane facing the viewer is xy, and the receding axis is z, then a point P is projected like this: Where
The transformation matrix is: Alternatively one could remove one third from the leading arm projected off the starting face, thus giving the same result.
