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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 10 - Sayı: 10

On the Control Invariants of Planar Bezier Curves for the Groups ´ M(2) and S M(2)

İDRİS ÖREN
Pages
74–81
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Similar results are given for plane polynomial curves.

📌 3 Key Takeaways

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Objective & Hypothesis:Let G = M(2) be the group generated by all orthogonal transformations and translations of the 2-dimensional Euclidean space E2 or G = S M(2) be the subgroup of M(2) generated by rotations and translations ofE2.
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Key Findings & Data:In this paper, global G-invariants of plane Bezier curves in ´ E2 are introduced.
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Conclusion & Impact:Similar results are given for plane polynomial curves.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

Let G = M(2) be the group generated by all orthogonal transformations and translations of the 2-dimensional Euclidean space E2 or G = S M(2) be the subgroup of M(2) generated by rotations and translations ofE2. In this paper, global G-invariants of plane Bezier curves in ´ E2 are introduced. Using complex numbers and theglobal G-invariants of a plane Bezier curves, for given two plane B ´ ezier curves ´ x(t) and y(t), evident forms of alltransformations g ∈ G, carrying x(t) to y(t), are obtained. Similar results are given for plane polynomial curves.

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Cite This Article

ÖREN, İ. (2018). On the Control Invariants of Planar Bezier Curves for the Groups ´ M(2) and S M(2). Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 74–81. https://ajindex.com/articles/374710

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