Косоаксонометрическая проекция и её разновидности

Type of technical drawing
the imaging of 3D objects

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 objects are not in perspective and so do not correspond to any view of an object that can be obtained in practice, but the technique yields somewhat convincing and useful results. 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 1st or 2nd centuries to the 18th century, especially to depict rectilinear objects such as houses. Various graphical projection techniques can be used in computer graphics, including in Computer Aided Design (CAD), computer games, computer generated animations, and special effects used in movies.

In cavalier projection (sometimes cavalier perspective or high view point) a point of the object is represented by three coordinates, x, y and z. On the drawing, it is represented by only two coordinates, x″ and y″. 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°. The length of the third axis is not scaled. It is very easy to draw, especially with pen and paper. It is thus often used when a figure must be drawn by hand, e. g. on a black board (lesson, oral examination). The representation was initially used for military fortifications. In French, the "cavalier" (literally rider, horseman, see Cavalry) is an artificial hill behind the walls that allows sighting of the enemy above the walls. The cavalier perspective was the way the things were seen from this high point. 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.

The term cabinet projection stems from its use in illustrations by the furniture industry. Like cavalier perspective, one face of the projected object is parallel to the viewing plane, and the third axis is projected as going off at an angle (typically or about ~63.4°). Unlike cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half.

In the military projection, the angles of the x and z axis and y and z axis are at 45°, meaning that the angle between the x axis and the y axis is 90°. That is, the xy plane is not skewed. It is rotated over 45°, though.

Besides technical drawing and illustrations, video games (especially those preceding the advent of 3D games) also often use a form of oblique projection. Examples include SimCity, Ultima VII, Ultima Online, EarthBound, Paperboy and, more recently, Tibia.