A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications
Joint Authors
Maqsood, Sidra
Hu, Gang
Ramli, Ahmad Lutfi Amri
Miura, Kenjiro T.
Abbas, Muhammad
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-05-25
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper.
These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well.
The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces.
This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values.
These GT-Bézier curves meet the conditions required for parametric continuity (C0, C1, C2, and C3) as well as for geometric continuity (G0, G1, and G2).
Furthermore, some curve and surface design applications have been discussed.
The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bézier curves and surfaces which make them a treasured way for the project of curve and surface modeling.
American Psychological Association (APA)
Maqsood, Sidra& Abbas, Muhammad& Hu, Gang& Ramli, Ahmad Lutfi Amri& Miura, Kenjiro T.. 2020. A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1194890
Modern Language Association (MLA)
Maqsood, Sidra…[et al.]. A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications. Mathematical Problems in Engineering No. 2020 (2020), pp.1-25.
https://search.emarefa.net/detail/BIM-1194890
American Medical Association (AMA)
Maqsood, Sidra& Abbas, Muhammad& Hu, Gang& Ramli, Ahmad Lutfi Amri& Miura, Kenjiro T.. A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-25.
https://search.emarefa.net/detail/BIM-1194890
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194890