Original scientific paper

https://doi.org/10.31896/k.21.3

Generalized Conchoids

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

Abstract

We adapt the classical definition of conchoids as known from the Euclidean plane to geometries that can be modeled within quadrics. Based on a construction by means of cross ratios, a generalized conchoid transformation is obtained. Basic properties of the generalized conchoid transformation are worked out. At hand of some prominent examples - line geometry and sphere geometry - the actions of these conchoid transformations are studied. Linear and also non-linear transformations are presented and relations to well-known transformations are disclosed.

Keywords

conchoid transformation; line geometry; sphere geometry; cross ratio; regulus; Dupin cyclide; Laguerre transformation; equiform transformation; inversion

Hrčak ID:

192227

URI

https://hrcak.srce.hr/192227

Publication date:

9.1.2018.

Article data in other languages: croatian

Visits: 1.760 *