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 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
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 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}

[edit] References

Potting bench drawn in cabinet view
Potting bench drawn in cabinet view