Cabinet projection

Cabinet projection

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 such as Paperboy and Pac-Mania.

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.

Mathematical formula

As formula, if the plane facing the viewer is xy, and the receding axis is z, then a point P is project like this:: P egin{pmatrix} x \ y \ z end{pmatrix} = egin{pmatrix}x + 0.5 cdot z cdot cos alpha \ y + 0.5 cdot z cdot sin alpha \ 0 end{pmatrix}Where alpha is the mentioned angle.

The transformation matrix is:: P = egin{bmatrix}1 & 0 & 0.5 cdot cos alpha \0 & 1 & 0.5 cdot sin alpha \0 & 0 & 0end{bmatrix}

References

* [http://www.tpub.com/content/draftsman/14276/css/14276_308.htm 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
*


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