Fairness metric of plane curves defined with similarity geometry invariants

Kenjiro T. Miura, Sho Suzuki, R. U. Gobithaasan, Shin Usuki, Jun ichi Inoguchi, Masayuki Sato, Kenji Kajiwara, Yasuhiro Shimizu

研究成果: Contribution to journalArticle査読

4 被引用数 (Scopus)


A curve is considered fair if it consists of continuous and few monotonic curvature segments. Polynomial curves such as Bézier and B-spline curves have complex curvature function, hence the curvature profile may oscillate easily with a little tweak of control points. Thus, bending energy and shear deformation energy are common fairness metrics used to produce curves with monotonic curvature profiles. The fairness metrics are used not just to evaluate the quality of curves, but it also aids in reaching to the final design. In this paper, we propose two types of fairness metric functionals to fair plane curves defined by the similarity geometry invariants, i.e. similarity curvature and its reciprocal to extend a variety of aesthetic fairing metrics. We illustrate numerical examples to show how log-aesthetic curves change depending on σ and G1 constraints. We extend LAC by modifying the integrand of the functionals and obtain quasi aesthetic curves. We also propose σ-curve to introduce symmetry concept for the log-aesthetic curve.

ジャーナルComputer-Aided Design and Applications
出版ステータス出版済み - 3 4 2018

All Science Journal Classification (ASJC) codes

  • 計算力学
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 計算数学


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