On the Bicubic Bézier Surfaces and Paraboloids in E³

Year 2025, Volume: 14 Issue: 4, 2357 - 2373, 31.12.2025

Şeyda Kılıçoglu , Semra Yurttançıkmaz

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

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

Bicubic Bézier surfaces , Control points , Matrix representation , Elliptic paraboloid , Hiperbolic paraboloid , Parabolic cylinder

Ethical Statement

The study is complied with research and publication ethics.

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