Axonometric projection

Part of a series on:

Graphical projection

Planar Parallel projection Orthographic projection Multiviews Plan, or floor plan Section Elevation Auxiliary view Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection Perspective projection Linear perspective One-point perspective Two-point perspective Three-point perspective Zero-point perspective Curvilinear perspective Reverse perspective

Other 3D projection Stereographic projection Anamorphic projection

Views Bird's-eye view/Aerial view Detail view 3/4 perspective Exploded view drawing Fisheye Fixed 3D Panorama Top-down perspective Worm's-eye view Zoom

Topics Computer graphics Computer-aided design Descriptive geometry Engineering drawing Foreshortening Map projection Projective geometry Technical drawing Vanishing point Video games with isometric graphics

v • d • e

Axonometric projection is a type of parallel projection used to create a pictorial drawing of an object, where the object is rotated along one or more of its axes relative to the plane of projection.^[1] Axonometric projection is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane.^[2]

There are three main types of axonometric projection: isometric, dimetric, and trimetric projection.

Overview

"Axonometric" means "to measure along axes".^[3] Axonometric projection shows an image of an object as viewed from a skew direction in order to reveal more than one side in the same picture.

Because with axonometric projections the scale of distant features is the same as for near features, such pictures will look distorted, as it is not how our eyes or photography work. This distortion is especially evident if the object to view is mostly composed of rectangular features. Despite this limitation, axonometric projection can be useful for purposes of illustration.^[4]

Three types of axonometric projections

Three views of a wooden cabinet.

The three types of axonometric projections are isometric projection, dimetric projection, and trimetric projection. Typically in axonometric drawing, one axis of space is shown as the vertical.

• In isometric projection the direction of viewing is such that the three axes of space appear equally foreshortened, of which the displayed angles among them and also the scale of foreshortening are universally known. However in creating a final, isometric instrument drawing, in most cases a full-size scale, i.e., without using a foreshortening factor, is employed to good effect because the resultant distortion is difficult to perceive.

Example of a dimetric axonometric drawing from a US Patent (1874)

• In dimetric projection, the direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale of the third direction (vertical) is determined separately. Approximations are common in Dimetric drawings.

• In trimetric projection, the direction of viewing is such that all of the three axes of space appear unequally foreshortened. The scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing. Approximations in trimetric drawings are common.

References

Further reading

• Yve-Alain Bois, "Metamorphosis of Axonometry," Daidalos, no. 1 (1981), pp. 41–58

Wikimedia Commons has media related to: Axonometric projection