| Oblique Projection |
Article Index for Oblique |
Website Links For Oblique |
Information AboutOblique Projection |
| CATEGORIES ABOUT OBLIQUE PROJECTION | |
| perspective projection | |
| technical drawing | |
| descriptive geometry | |
|
Oblique projection is a simple type of Graphical Projection used for producing pictorial, two-dimensional Images of three-dimensional objects. WHAT IT IS ''Oblique projection'' is a type of angle to produce the projected image, as opposed to the perpendicular angle used in orthographic projection. Mathematically , the ''parallel projection'' of the point on the -plane gives . The constants and uniquely specify a parallel projection. When , the projection is said to be ''orthographic'' or ''orthogonal''. Otherwise, it is ''oblique''. The constants and 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'. 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. Weisstein, Eric W. "Pohlke's Theorem." From MathWorld--A Wolfram Web Resource. 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 and are preserved, but lengths along direction 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 axis remains unscaled. Parallel Projections from ''PlaneView3D Online'' '' Cabinet Projection '', popular in furniture illustrations, is an example of such a technique, wherein the receding axis is scaled to half-size. 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. One example of such a game is Ultima VII . REFERENCES FURTHER READING 1 SEE ALSO |
|
|