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Journal for Geometry and Graphics 08 (2004), No. 2, 215--224
Copyright Heldermann Verlag 2004

On Arne Dür's Equation Concerning Central Axonometries

Hellmuth Stachel
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Vienna, Austria

It is a classical Descriptive Geometry problem in the Euclidean n-space to characterize the central projections among collinear transformations with rank deficiency. Recently A. Dür [Journal for Geometry and Graphics 7 (2003) 137--143] presented for n = 3 a characterization in form of an equation in complex coordinates -- the central axonometric counterpart of the Gauss equation for orthogonal axonometries. Here two new proofs for Dür's equation are given combined with equivalent statements. And its n-dimensional generalization is addressed which characterizes two-dimensional orthogonal central views among central axonometries.

Keywords: Central projection, central axonometry.

MSC: 51N05

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