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

Year 2020, Volume: 13 Issue: 2, 116 - 134, 15.10.2020

İdris Ören , Djavvat Khadjiev

https://doi.org/10.36890/iejg.725297

Abstract

This paper presents global differential invariants of curves and paths in the 2-dimensional Euclidean geometry for the groups of Euclidean transformations M(2) and special Euclidean transformations $M^{+}(2)$. 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 paths(or curves) with the common differential G-invariants, evident forms of all Euclidean transformations that maps one of the paths (or curves) to the other are found. .

Keywords

Path, invariant, Euclidean geometry

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