Recognition of Paths and Curves in the 2-Dimensional Euclidean Geometry

Authors : İdris ÖREN, Djavvat KHADJİEV

Pages : 116-134

Doi:10.36890/iejg.725297

View : 11 | Download : 4

Publication Date : 2020-10-15

Article Type : Research Paper

Abstract :This paper presents global differential invariants of curves and paths in the 2-dimensional Euclidean geometry for the groups of Euclidean transformations Minsert ignore into journalissuearticles values(2); and special Euclidean transformations $M^{+}insert ignore into journalissuearticles values(2);$. For these groups, analogues of the fundamental theorem for Euclidean curves are obtained in terms of global differential invariants of a path and a curve. Moreover, for given two pathsinsert ignore into journalissuearticles values(or curves); with the common differential G-invariants, evident forms of all Euclidean transformations that maps one of the paths insert ignore into journalissuearticles values(or curves); to the other are found. .
Keywords : Path, invariant, Euclidean geometry