Cabinet projection

From Wikipedia, the free encyclopedia

Views
Graphical projections Planar projection Perspective projection Parallel projection Orthographic projection Multiviews Plan, or floor plan Section Elevation Auxiliary view Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier perspective Cabinet projection 3D projection Fisheye Stereoscopic Projection Anamorphic projection Map projection
Other views Bird's-eye view/Aerial view Top-down perspective Worm's-eye view
This box: view • talk • edit

Cabinet projection or sometimes cabinet perspective is a type of oblique projection. The term stems from the use for illustrations in furniture industry. This projection has been used in early video games like Paperboy.

The figures to the left are orthographic projections. The figure to the right is an oblique projection with an angle of 30° and a ratio of 0.5

[edit] Principle

Like Cavalier perspective, cabinet projection is an oblique projection, where one face of the projected object is parallel to the viewing plane, and the third axis is projected as going off in an angle (typical 30° or 45°). Unlike Cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half.

[edit] Mathematical formula

As formula, if the plane facing the viewer is $x y$ , and the receding axis is $z$ , then a point $P$ is project like this:

$P \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} x + 0.5 \cdot z \cdot cos \alpha \\ y + 0.5 \cdot z \cdot sin \alpha \\ 0 \end{pmatrix}$

Where $α$ is the mentioned angle.

The transformation matrix is:

$P = \begin{bmatrix} 1 & 0 & 0.5 \cdot \cos \alpha \\ 0 & 1 & 0.5 \cdot \sin \alpha \\ 0 & 0 & 0 \end{bmatrix}$

[edit] References

Potting bench drawn in cabinet view

Illustrator Draftsman 3 & 2 - Volume 2 Standard Practices and Theory, page 68 from http://www.tpub.com
Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, ACM Computing Surveys (CSUR), v.10 n.4, p.465-502, Dec. 1978
Foley, James (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406.