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. .
📌 3 Key Takeaways
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Objective & Hypothesis: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 $M^{+}(2)$.
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Key Findings & Data: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.
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Conclusion & Impact: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. .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Path · invariant · Euclidean geometry
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. .
Ören, İ., Khadjiev, D. (2020). Recognition of Paths and Curves in the 2-Dimensional Euclidean Geometry. International Electronic Journal of Geometry, Volume: 13 Issue: 2. https://doi.org/10.36890/iejg.725297
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