Abstract
In this paper, we define and investigate the properties of null Bézier curves in Minkowski 3-space. The method applied is a theoretical literature study, applying the definitions of Bézier curves and the geometric framework of null curves in semi-Riemannian geometry. We establish several fundamental characteristics of these curves, including the causal nature of their tangent vectors at endpoints and their Frenet frame apparatus when parametrized by pseudo-arc length. Furthermore, we define the concept of a null Bertrand pair for such curves and prove that if a null Bézier curve of degree n≥3 admits a Bertrand mate, then both curves are necessarily helices. Finally, we provide a conclusive parametric representation of any null Bézier curve in terms of a single non-constant function. This representation offers a powerful tool for explicitly constructing null Bézier curves within this geometric setting.
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Publication Info
- Year
- 2025
- Type
- article
- Volume
- 11
- Issue
- 2
- Pages
- 113-121
- Citations
- 0
- Access
- Closed
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Cite This
Arfah Arfah
(2025).
Null Bézier Curves in Minkowski 3-Space.
Journal Of Natural Sciences And Mathematics Research
, 11
(2)
, 113-121.
https://doi.org/10.21580/jnsmr.v11i2.25323
Identifiers
- DOI
- 10.21580/jnsmr.v11i2.25323