Cabinet projection

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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.

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

Contents

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 \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}

See also

References

Potting bench drawn in cabinet view
Retrieved from "http://en.wikipedia.org/wiki/Cabinet_projection"

This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.