Poopćene konhoide

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.Prilagođavamo klasičnu definiciju konhoida iz euklidske ravnine geometrijama definiranim kvadrikama. Postiže se poopćena konhoidna transformacija koja se temelji na konstrukciji pomoću dvoomjera. Proučavaju se osnovna svojstva ovakve transformacije. Djelovanje poopćene konhoidne transformacije se proučava na nekim istaknutim primjerima kao što su pravčasta i sferna geometrija. Prikazuju se linearne i nelinearne transformacije te su opisane veze s dobro poznatim transformacijama