Axonometry

Axonometry is a graphical procedure belonging to descriptive geometry that generates a planar image of a three-dimensional object. The term "axonometry" means "to measure along axes", and indicates that the dimensions and scaling of the coordinate axes play a crucial role. The result of an axonometric procedure is a uniformly-scaled parallel projection of the object. In general, the resulting parallel projection is oblique (the rays are not perpendicular to the image plane); but in special cases the result is orthographic (the rays are perpendicular to the image plane), which in this context is called an orthogonal axonometry.

The term axonometry is used both for the graphical procedure described below, as well as the image produced by this procedure.

Axonometry should not be confused with axonometric projection, which in English literature usually refers to orthogonal axonometry.

Pohlke's theorem is the basis for the following procedure to construct a scaled parallel projection of a three-dimensional object:

In order to obtain undistorted results, select the projections of the axes and foreshortenings carefully (see below). In order to produce an orthographic projection, only the projections of the coordinate axes are freely selected; the foreshortenings are fixed (see ).

Notation:

The angles can be chosen so that ${\displaystyle 0^{\circ }<\alpha +\beta <360^{\circ }\ .}$
The forshortenings: ${\displaystyle 0<\;v_{x},\;v_{y},\;v_{z}\ .}$

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