New cubic trigonometric Bézier-like functions with shape parameter: curvature and its spiral segment
type: Item
instance of: scholarly article
title: New cubic trigonometric Bézier-like functions with shape parameter: curvature and its spiral segment
zbMATH Open document ID: 1477.65037
DOI: 10.1155/2021/6330649
author: Abdul Majeed
author: Muhammad Abbas
author: Amna Abdul Sittar
author: Mohsin Kamran
author: Saba Tahseen
author: Homan Emadifar
published in: Journal of Mathematics
publication date: 2021-11-25T00:00:00Z
review text: Summary: This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The \(C^3\) and \(G^3\) continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes' designing.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 7433551
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6330649
OpenAlex ID: W3199608447
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description: scientific article; zbMATH DE number 7433551