Family of Surfaces with a Common Special Polynomial Curves
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, cilt.43, 2025 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 43
- Basım Tarihi: 2025
- Doi Numarası: 10.5269/bspm.70672
- Dergi Adı: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
Polynomial curves play an important role in statistics, mathematics, engineering, computer science, and many other fields. It is widely used to model and analyze data. By using it to best simulate data points, it is possible to gain better insights and predictions on data sets. In engineering applications, it is used to model material properties, vibration analysis, temperature changes and similar factors. Computer graphics and animations are frequently used to represent the surfaces of objects, especially in 3D modeling and animation software for rendering surfaces and objects. In this paper, we establish the necessary and sufficient conditions to parameterize a surface family on which the polynomial curve of any given curve lies as an isogeodesic, isoasymptotic and curvature line in E3. We also extend this idea on ruled surfaces. Finally, we present some examples and picture the corresponding surfaces.