The Approximation of Generalized Log-Aesthetic Curves with <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </math> Cubic Trigonometric Bézier Function-Reference-Cited by-同舟云学术

The Approximation of Generalized Log-Aesthetic Curves with $G^{2}$ Cubic Trigonometric Bézier Function

Published:2023-09-07 Issue: Volume:2023 Page:1-18
ISSN:2314-4785
Container-title:Journal of Mathematics
language:en
Short-container-title:Journal of Mathematics

Author:

Albayari Diya’ J.¹²,Gobithaasan R. U.³⁴^ORCID,Miura Kenjiro T.⁵^ORCID

Affiliation:

1. Mathematics Department, Arab Evangelical Episcopal Church Council (Ahliyyah & Mutran), Amman 11181, Jordan

2. Mathematics Department, Ibn Rushd National Academy, Amman 17126, Jordan

3. Special Interest Group on Modelling & Data Analytics, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

4. School of Mathematics Sciences, Universiti Sains Malaysia, Gelugor 11800, Penang, Malaysia

5. Graduate School of Science & Technology, Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu, Shizuoka 432-8561, Japan

Abstract

One of the requirements of curves in computer-aided design (CAD) is a curve with monotonic curvature profiles. Generalized log-aesthetic curves (GLACs) comprise a family of aesthetic curves which possesses a monotonic curvature profile. However, we cannot directly implement GLAC in CAD systems since it is in the form of a transcendental form. In this paper, we used cubic trigonometric Bézier (T-Bézier) curves with two shape parameters to approximate GLAC with G2 continuity. The final approximation formula inherits the shape parameters of GLAC whereas T-Béziers’ shape parameters are utilized to satisfy G2 constraints. Numerical results indicate that the proposed algorithm is capable of approximating GLAC within the given tolerance in (at least) two iterations.

Funder

Japan Science and Technology Agency

Publisher

Hindawi Limited

Subject

General Mathematics

Link

http://downloads.hindawi.com/journals/jmath/2023/7457223.pdf

Reference25 articles.

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