This article discusses imaging of three-dimensional objects. For an abstract mathematical discussion, see Projection (linear algebra).

Oblique projection is a simple type of graphical projection used for producing pictorial, two-dimensional images of three-dimensional objects. Graphical projection is a Protocol by which an image of an imaginary three-dimensional object is projected onto a planar surface without the aid of mathematical calculation An image (from Latin imago) or picture is an artifact usually two-dimensional that has a similar appearance to some subject &mdashusually

Oblique projection with foreshortening by half, seen from the side. Graphical projection is a Protocol by which an image of an imaginary three-dimensional object is projected onto a planar surface without the aid of mathematical calculation Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two-dimensional projection plane Perspective (from Latin perspicere to see through in the graphic arts such as drawing is an approximate representation on a flat surface (such as paper of an image as it is perceived Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D A plan is an Orthographic projection of a 3-dimensional object from the position of a horizontal plane through the object A floor plan ( floorplan) in Architecture and Building engineering is a Diagram, usually to scale, of the relationships between rooms In Geometry, a cross section is the intersection of a body in 2-dimensional space with a line or of a body in 3-dimensional space with a plane etc An elevation is an Orthographic projection of a 3-dimensional object from the position of a horizontal plane beside an object An auxiliary view is an angle at which one can view an object that is not one of the primary views for an Orthographic projection. Axonometric projection ("to measure along axes" is a technique used in orthographic pictorials Isometric projection is a form of Graphical projection —more specifically an Axonometric projection. Dimetric projection is a form of Axonometric projection, in which its direction of viewing is such that two of the three axes of space appear equally foreshortened of which Trimetric projection is a form of Axonometric projection, where the direction of viewing is such that all of the three axes of space appear unequally foreshortened The cavalier perspective, also called cavalier projection or high view point, is a way to represent a three dimensional object on a flat drawing and more specifically Cabinet projection or sometimes cabinet perspective is a type of Oblique projection. 3D projection is any method of mapping three-dimensional points to a two-dimensional plane Owned by Atlassian Software Systems, FishEye is a Revision control browser and search engine Stereoscopy, stereoscopic imaging or 3-D (three-dimensional imaging is any technique capable of recording three-dimensional visual Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image A map projection is any method of representing the Surface of a sphere or other shape on a plane. A bird's-eye view is a View of an object from above as though the observer were a Bird, often used in the making of Blueprints, Floor plans Top-down perspective, also sometimes referred to as bird's-eye view, overhead view or helicopter view, A worm's-eye view is a View of an object from below as though the observer were a Worm.

Definition and method

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. Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D 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). Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and 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 less than 1, 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'. One way to draw using an oblique view is to draw the side of the object you are looking at in two dimensions, i. e. flat, and then draw the other sides at an angle of 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.

Oblique pictorial

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 Pohlke's theorem, from the German mathematician Pohlke, who published it in the early 19th century. ^[1]

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 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.

Cavalier projection is the name of such a projection, where the length along the z axis remains unscaled. The cavalier perspective, also called cavalier projection or high view point, is a way to represent a three dimensional object on a flat drawing and more specifically ^[2]

Cabinet projection, popular in furniture illustrations, is an example of such a technique, wherein the receding axis is scaled to half-size. Cabinet projection or sometimes cabinet perspective is a type of Oblique projection. ^[2]

Examples

Besides technical drawing and illustrations, computer games (especially from the era before the advent of 3D games) also often use a form of oblique projection. Examples of such games include Ultima VII, EarthBound, and Paperboy. Ultima VII is the seventh of the Ultima series of Computer role-playing games The game was released in two parts Ultima VII The EarthBound, known in Japan as, is a role-playing Video game designed by Shigesato Itoi for the Super Nintendo Entertainment Paperboy is a 1984 Arcade game by Atari Games. The players take the role of a Paperboy who delivers Newspapers along a

References

1. ^ Weisstein, Eric W. "Pohlke's Theorem." From MathWorld--A Wolfram Web Resource.
2. ^ ^{a b} Parallel Projections from PlaneView3D Online

Further reading

Foley, James (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406.  

See also

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