Bibliographic Details
| Title: |
Bezier Curves and Surfaces with the Generalized α -Bernstein Operator. |
| Authors: |
Canlı, Davut1 (AUTHOR) davutcanli@odu.edu.tr, Şenyurt, Süleyman1 (AUTHOR) |
| Source: |
Symmetry (20738994). Feb2025, Vol. 17 Issue 2, p187. 24p. |
| Subject Terms: |
*COMPUTER-aided design, *ALGORITHMS, *ENGINEERING, *DEFINITIONS, *CLASSIFICATION |
| Abstract: |
In the field of Computer-Aided Geometric Design (CAGD), a proper model can be achieved depending on certain characteristics of the predefined blending basis functions. The presence of these characteristics ensures the geometric properties necessary for a decent design. The objective of this study, therefore, is to examine the generalized α -Bernstein operator in the context of its potential classification as a novel blending type basis for the construction of Bézier-like curves and surfaces. First, a recursive definition of this basis is provided, along with its unique representation in terms of that for the classical Bernstein operator. Next, following these representations, the characteristics of the basis are discussed, and one shape parameter for α -Bezier curves is defined. In addition, by utilizing the recursive definition of the basis, a de Casteljau-like algorithm is provided such that a subdivision schema can be applied to the construction of the new α -Bezier curves. The parametric continuity constraints for C 0 , C 1 , and C 2 are also established to join two α -Bezier curves. Finally, a set of cross-sectional engineering surfaces is designed to indicate that the generalized α -Bernstein operator, as a basis, is efficient and easy to implement for forming shape-adjustable designs. [ABSTRACT FROM AUTHOR] |
|
Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Academic Search Complete |
|
Full text is not displayed to guests. |
Login for full access.
|
