On the Bicubic Bézier Surfaces and Paraboloids in E³

Şeyda Kılıçoglu; Semra Yurttançıkmaz

doi:10.17798/bitlisfen.1735128

On the Bicubic Bézier Surfaces and Paraboloids in E³

Abstract

design (CAD), and animation because they offer a powerful balance of flexibility, smoothness, and control. In addition to being compatible with other surface representations, they have attracted the attention of scientists due to their mathematical strength and understandability, and many studies have been conducted on this subject. In this paper, first we examine the matrix representation of bicubic Bézier surfaces whose control points lie in E³. Second, as examples, we consider elliptic and hyperbolic paraboloids as bicubic Bézier surfaces. Finally, we present a method for determining the control points of a given elliptic paraboloid, hyperbolic paraboloid, and parabolic cylinder as bicubic Bézier surfaces.

Keywords

Ethical Statement

The study is complied with research and publication ethics.

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Details

Primary Language

English

Subjects

Calculus of Variations, Mathematical Aspects of Systems Theory and Control Theory

Journal Section

Research Article

Authors

Şeyda Kılıçoglu
0000-0003-0252-1574
Türkiye

Semra Yurttançıkmaz ^*
0000-0001-6712-3687
Türkiye

Publication Date

December 31, 2025

Submission Date

July 4, 2025

Acceptance Date

December 12, 2025

Published in Issue

Year 2025 Volume: 14 Number: 4

DOI

https://doi.org/10.17798/bitlisfen.1735128

IZ

https://izlik.org/JA22HP55KH

Cite

RIS / Bibtex

APA

Kılıçoglu, Ş., & Yurttançıkmaz, S. (2025). On the Bicubic Bézier Surfaces and Paraboloids in E³. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 14(4), 2357-2373. https://doi.org/10.17798/bitlisfen.1735128

AMA

1.Kılıçoglu Ş, Yurttançıkmaz S. On the Bicubic Bézier Surfaces and Paraboloids in E³. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025;14(4):2357-2373. doi:10.17798/bitlisfen.1735128

Chicago

Kılıçoglu, Şeyda, and Semra Yurttançıkmaz. 2025. “On the Bicubic Bézier Surfaces and Paraboloids in E³”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14 (4): 2357-73. https://doi.org/10.17798/bitlisfen.1735128.

EndNote

Kılıçoglu Ş, Yurttançıkmaz S (December 1, 2025) On the Bicubic Bézier Surfaces and Paraboloids in E³. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14 4 2357–2373.

IEEE

[1]Ş. Kılıçoglu and S. Yurttançıkmaz, “On the Bicubic Bézier Surfaces and Paraboloids in E³”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 4, pp. 2357–2373, Dec. 2025, doi: 10.17798/bitlisfen.1735128.

ISNAD

Kılıçoglu, Şeyda - Yurttançıkmaz, Semra. “On the Bicubic Bézier Surfaces and Paraboloids in E³”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14/4 (December 1, 2025): 2357-2373. https://doi.org/10.17798/bitlisfen.1735128.

JAMA

1.Kılıçoglu Ş, Yurttançıkmaz S. On the Bicubic Bézier Surfaces and Paraboloids in E³. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025;14:2357–2373.

MLA

Kılıçoglu, Şeyda, and Semra Yurttançıkmaz. “On the Bicubic Bézier Surfaces and Paraboloids in E³”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 4, Dec. 2025, pp. 2357-73, doi:10.17798/bitlisfen.1735128.

Vancouver

1.Şeyda Kılıçoglu, Semra Yurttançıkmaz. On the Bicubic Bézier Surfaces and Paraboloids in E³. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025 Dec. 1;14(4):2357-73. doi:10.17798/bitlisfen.1735128