Professional paper

Perspective Collineation and Osculating Circle of Conic in PE-plane and I-plane

Ana Sliepčević ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Ivana Božić ; Department of Civil Engineering, Polytechnic of Zagreb, Zagreb, Croatia

Abstract

All perspective collineations in a real affine plane are classified according to a constant cross-ratio and the position of the center and axis. A special attention will be given to the conditions which basic elements of perspective collineation have to fulfill in order to obtain the touch or osculation or hyperosculation of two conics. On the affine models of an isotropic and pseudo-Euclidean plane the osculating circle of a conic is constructed by using perspective collineations.

Keywords

perspective collineation; homology; elation; constant cross-ratio; conic; osculating circle

Hrčak ID:

77101

URI

https://hrcak.srce.hr/77101

Publication date:

29.12.2011.

Article data in other languages: croatian

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