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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.

. The figure to the right is an Oblique Projection with an angle of 30° and a ratio of 0.5]]

PRINCIPLE

Like with 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 \alpha 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}


REFERENCES