2023年7月25日
Log-Aesthetic Curves: Similarity Geometry, Integrable Discretization and Variational Principles
Computer Aided Geometric Design
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- 巻
- 105
- 号
- 開始ページ
- 102233
- 終了ページ
- 102233
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.cagd.2023.102233
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize them as invariant curves under the integrable flow on plane curves which is governed by the Burgers equation. We propose a variational principle for these curves, leading to the stationary Burgers equation as the Euler-Lagrange equation. As an application of the formulation developed here, we propose a discretization of these curves and the associated variational principle which preserves the underlying integrable structure. We finally present algorithms for the generation of discrete log-aesthetic curves for given G1 data based on the similarity geometry. Our method is able to generate S-shaped discrete curves with an inflection as well as C-shaped curves according to the boundary condition. The resulting discrete curves are regarded as self-adaptive discretization and thus high-quality even with a small number of points.
- リンク情報
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- DOI
- https://doi.org/10.1016/j.cagd.2023.102233
- 共同研究・競争的資金等の研究課題
- 設計の新パラダイムを拓く新しい離散的な曲面の幾何学
- 共同研究・競争的資金等の研究課題
- 幾何形状を記述する可積分系の理論の深化
- 共同研究・競争的資金等の研究課題
- トリム曲面接続の理論解析と計測点群データからの高品質トリム曲面の生成
- 共同研究・競争的資金等の研究課題
- 離散可積分幾何の深化と展開
- URL
- http://arxiv.org/abs/1808.03104 本文へのリンクあり
- ID情報
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- DOI : 10.1016/j.cagd.2023.102233
- ISSN : 0167-8396