Oblique projection

Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional images of three-dimensional objects. The objects are not in perspective, so they do not correspond to any view of an object that can be obtained in practice, but the technique does yield somewhat convincing and useful images. Oblique projection is commonly used in technical drawing. The cavalier projection was used by French military artists in the 18th century to depict fortifications. Oblique projection was used almost universally by Chinese artists from the first or second centuries to the 18th century, especially when depicting rectilinear objects such as houses. Oblique projection is a type of parallel projection: In both oblique projection and orthographic 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 ) {displaystyle (x,y,z)} on the x y {displaystyle xy} -plane gives ( x + a z , y + b z , 0 ) {displaystyle (x+az,y+bz,0)} . The constants a {displaystyle a} and b {displaystyle b} uniquely specify a parallel projection. When a = b = 0 {displaystyle a=b=0} , the projection is said to be 'orthographic' or 'orthogonal'. Otherwise, it is 'oblique'. The constants a {displaystyle a} and b {displaystyle 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.