Original scientific paper

Distances and Central Projections

Boris Odehnal orcid.org/0000-0002-7265-5132 ; University of Applied Arts Vienna, Vienna, Austria

Abstract

Given a point P in Euclidean space R^3 we look for all points Q such that the length PQ of the line segments PQ from P to Q equals the length of the central image of the segment. It turns out that for any fixed point P the set of all points Q is a quartic surface Φ. The quartic Φ carries a one-parameter family of circles, has two conical nodes, and intersects the image plane \Pi along a proper line and the three-fold ideal line p of \Pi if we perform the projective closure of the Euclidean three-space. In the following we shall describe and analyze the surface Φ.

Keywords

central projection; distance; principal line; distortion; circular section; quartic surfac; conical node

Hrčak ID:

133844

URI

https://hrcak.srce.hr/133844

Publication date:

30.1.2015.

Article data in other languages: croatian

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