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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Interpolation of Surfaces with Line of Curvature

Ergin Bayram
Pages
239–246
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

The method is validated with illustrative examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a method to construct parametric surfaces interpolating given finite points and a curve as a line of curvature in 3-dimensional Euclidean space.
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Key Findings & Data:We present an existence theorem of a $C^{0}$-Hermite interpolation of surfaces possessing the given data.
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Conclusion & Impact:The method is validated with illustrative examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$C^{0}$-Hermite interpolation · line of curvature · parametric surface

Abstract

We introduce a method to construct parametric surfaces interpolating given finite points and a curve as a line of curvature in 3-dimensional Euclidean space. We present an existence theorem of a $C^{0}$-Hermite interpolation of surfaces possessing the given data. We show that every parameter curve of a constructed surface is a circular helix if the given curve is a circular helix. The method is validated with illustrative examples.

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Cite This Article

Bayram, E. (2022). Interpolation of Surfaces with Line of Curvature. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 239–246. https://ajindex.com/articles/539595

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