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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)256-263
Number of pages8
JournalComputer-Aided Design and Applications
Volume15
Issue number2
DOIs
Publication statusPublished - Mar 4 2018

Fingerprint

Plane Curve
Fairness
Splines
Shear deformation
Polynomials
Metric
Curve
Invariant
Geometry
Curvature
Monotonic
Curve Complex
B-spline Curve
Similarity
Shear Deformation
Control Points
Integrand
Energy
Symmetry
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics

Cite this

Miura, K. T., Suzuki, S., Gobithaasan, R. U., Usuki, S., Inoguchi, J. I., Sato, M., ... Shimizu, Y. (2018). Fairness metric of plane curves defined with similarity geometry invariants. Computer-Aided Design and Applications, 15(2), 256-263. https://doi.org/10.1080/16864360.2017.1375677

Fairness metric of plane curves defined with similarity geometry invariants. / Miura, Kenjiro T.; Suzuki, Sho; Gobithaasan, R. U.; Usuki, Shin; Inoguchi, Jun ichi; Sato, Masayuki; Kajiwara, Kenji; Shimizu, Yasuhiro.

In: Computer-Aided Design and Applications, Vol. 15, No. 2, 04.03.2018, p. 256-263.

Research output: Contribution to journalArticle

Miura, KT, Suzuki, S, Gobithaasan, RU, Usuki, S, Inoguchi, JI, Sato, M, Kajiwara, K & Shimizu, Y 2018, 'Fairness metric of plane curves defined with similarity geometry invariants', Computer-Aided Design and Applications, vol. 15, no. 2, pp. 256-263. https://doi.org/10.1080/16864360.2017.1375677
Miura, Kenjiro T. ; Suzuki, Sho ; Gobithaasan, R. U. ; Usuki, Shin ; Inoguchi, Jun ichi ; Sato, Masayuki ; Kajiwara, Kenji ; Shimizu, Yasuhiro. / Fairness metric of plane curves defined with similarity geometry invariants. In: Computer-Aided Design and Applications. 2018 ; Vol. 15, No. 2. pp. 256-263.
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