TY - JOUR

T1 - Fairness metric of plane curves defined with similarity geometry invariants

AU - Miura, Kenjiro T.

AU - Suzuki, Sho

AU - Gobithaasan, R. U.

AU - Usuki, Shin

AU - Inoguchi, Jun ichi

AU - Sato, Masayuki

AU - Kajiwara, Kenji

AU - Shimizu, Yasuhiro

N1 - Funding Information:
This work was supported in part by JSPS Grant-in-Aid for Scientific Research (B) Grant Number 25289021, JSPS Grant-in-Aid for Challenging Exploratory Research Grant Number 26630038, JST RISTEX Service Science, Solutions and Foundation Integrated Research Program, ImPACT Program of the Council for Science, Technology and Innovation, the joint research program “Differential Geometry and Discrete Differential Geometry for Industrial Design” of Institute of Mathematics for Industry, Kyushu University and FRGS grant (FRGS: 59431) provided by University Malaysia Terengganu and Ministry of Education, Malaysia. We would like to express our deepest gratitude to Prof. Hiroyuki Ochiai at Kyushu University, Prof. Nozomu Matsuura at Fukuoka University and Prof. Sampei Hirose at Shibaura Institute of Technology.
Publisher Copyright:
© 2017 CAD Solutions, LLC.

PY - 2018/3/4

Y1 - 2018/3/4

N2 - 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.

AB - 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.

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U2 - 10.1080/16864360.2017.1375677

DO - 10.1080/16864360.2017.1375677

M3 - Article

AN - SCOPUS:85032488083

VL - 15

SP - 256

EP - 263

JO - Computer-Aided Design and Applications

JF - Computer-Aided Design and Applications

SN - 1686-4360

IS - 2

ER -