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Axonometry

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One of the methods of mapping three-dimensional figures into a plane. An axonometry consists in projecting the figure, after an orthogonal Cartesian coordinate system and a coordinate plane into which the figure will be projected have been chosen, on the chosen plane for the diagram (figure). Depending on the mode of the projection, the axonometry may be parallel or central. If the direction of the parallel projection into the chosen plane is perpendicular to this plane, the axonometry is said to be normal or orthogonal; otherwise it is said to be skew. The parameters of an orthogonal axonometry are the cosines of the angles between the coordinate axes and the chosen plane, and are sometimes called distortion indices. If two distortion indices are equal, the axonometry is called a dimetry, and if three distortion indices are equal, an isometry; if all distortion indices are different, it is called a trimetry. The principal theorem on axonometries is the Pohlke–Schwartz theorem: Any tetrahedron can be projected to an arbitrarily given plane tetragon.

References

[1] E.A. Glazunov, N.F. Chetverukhin, "Axonometry" , Moscow (1953) (In Russian)
How to Cite This Entry:
Axonometry. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Axonometry&oldid=11620
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098