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Graphical projections Orthographic projection Plan, or floor plan view Section Elevation Axonometric projection Isometric projection Dimetric projection Trimetric projection Axiometric projection Oblique projection, and Perspective projection Cavalier perspective Cabinet perspective Top-down perspective Other views Aerial view Bird's-eye view Map projection Planform Worm's-eye view  This box: view • talk • edit

Oblique projection is a simple type of graphical projection used for producing pictorial, two-dimensional images of three-dimensional objects.

Oblique projection is a type of parallel projection. Thus, it projects an image by intersecting parallel rays (projectors) from the three-dimensional source object with the drawing surface (projection plane). In both oblique projection and orthographic projection (the other type of parallel projection), parallel lines of the source object produce parallel lines in the projected image. The projectors in oblique projection intersect the projection plane at an oblique angle to produce the projected image, as opposed to the perpendicular angle used in orthographic projection.

Mathematically, the parallel projection of the point (x,y,z) on the xy-plane gives (x + az,y + bz,0). The constants a and b uniquely specify a parallel projection. When a = b = 0, the projection is said to be orthographic or orthogonal. Otherwise, it is oblique. The constants a and b are not necessarily inferior to unity, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space. In a general oblique projection, spheres of the space are projected as ellipses on the drawing plane, and not as circles as you would expect them from an orthogonal projection.

Oblique drawing is also the crudest '3D' drawing method but the easiest to master. Oblique is not really a '3D' system but a 2 dimensional view of an object with 'forced depth'. When using oblique the side of the object you are looking at is drawn in two dimensions, i.e. flat. The other sides are drawn in at 45 degrees but instead of drawing the sides full size they are only drawn with half the depth creating 'forced depth' adding an element of realism to the object. Even with this 'forced depth', oblique drawings look very unconvincing to the eye. For this reason oblique is rarely used by professional designer and engineers.

Synonymous : In mathematics books, it seems we also find skew projection to mean the same thing.

In an oblique pictorial drawing, the angles displayed among the axes, 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. This result is known as Polke's theorem, from the German mathematician Pohlke, who published it in the early 19th century.

The resulting distortions make the technique unsuitable for formal, working drawings. Nevertheless, the distortions are partially overcome by aligning one plane of the image parallel to the plane of projection. Doing so creates a true shape (isometric) image of the chosen plane. This specific category of oblique projections, whereby lengths along the directions x and y are preserved, but lengths along direction z are drawn at angle using a reduction factor is very much in use for industrial drawings.

Cabinet Projection, popular in furniture illustrations, is an example of such a technique, wherein the receding axis is scaled to half-size and drawn at an angle of 45-degrees.

• Plans (drawings)
• Projection (linear algebra)
• Projection operator
• Parallel (geometry)