Geodesic
On Arne Dür's Equation Concerning Central Axonometries
Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 215-224
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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.
Classification : 51N05
Mots-clés : Central projection, central axonometry 
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     title = {On {Arne} {D\"ur's} {Equation} {Concerning} {Central} {Axonometries}},
     journal = {Journal for geometry and graphics},
     pages = {215--224},
     year = {2004},
     volume = {8},
     number = {2},
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H. Stachel. On Arne Dür's Equation Concerning Central Axonometries. Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 215-224. http://geodesic.mathdoc.fr/item/JGG_2004_8_2_JGG_2004_8_2_a8/