Öz
The geometry of curves and surfaces plays a very important role in computer-aided geometric design (CAGD). The goal of this paper is to construct the Frenet frames of trigonometric B\'ezier curves in Euclidean $ 2 $ and $ 3- $space. Especially, the curvatures of these curves are investigated at the beginning and the ending points.
Anahtar Kelimeler
Computer aided geometric design (CAGD) curvature Frenet frame field trigonometric Bezier curve trigonometric polynomial
Kaynakça
- Ammad, M., Misro, M.Y., Construction of local shape adjustable surfaces using quintic trigonometric B\'ezier curve, Symmetry, 12(2020), 1205.
- Bashir, U., Abas, M., Awang, M., Ali, J., The quadratic trigonometric B\'ezier curve with single shape parameter, J. Basic Appl. Sci. Res., 2(2012), 2541-2546.
- Dube, M., Sharma, R., Quartic trignometric B\'ezier curve with a shape parameter, Int. J. Math. Comput. Appl. Res., 3(2013), 89-96.
- Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
- Han, X.A., Ma, Y.C., Huang, X.L., The cubic trigonometric B\'ezier curve with two shape parameters, Applied Mathematics Letters, 22(2009), 226-231.
- Han, X.A., Huang, X.L., Ma, Y.C., Shape analysis of cubic trigonometric B\'ezier curves with a shape parameter, Appl. Math. Comput., 217(2010), 2527-2533.
- Misro, M., Ramli, A., Ali, J., Quintic trigonometric B\'ezier curve with two shape parameters, Sains Malaysiana, 46(2017), 825-831.
- O'Neill, B., Elemantary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
- Sharma, R., Quartic trigonometric B\'ezier curves and surfaces with shape parameter, Int. J. Innov. Res. Comput. Commun. Eng., 3297(2016), 7712–7717.
- Sun, X., Ji, X., Parametric model for kitchen product based on cubic T-Bézier curves with symmetry, Symmetry, 12(2020), 505.
Öz
Kaynakça
- Ammad, M., Misro, M.Y., Construction of local shape adjustable surfaces using quintic trigonometric B\'ezier curve, Symmetry, 12(2020), 1205.
- Bashir, U., Abas, M., Awang, M., Ali, J., The quadratic trigonometric B\'ezier curve with single shape parameter, J. Basic Appl. Sci. Res., 2(2012), 2541-2546.
- Dube, M., Sharma, R., Quartic trignometric B\'ezier curve with a shape parameter, Int. J. Math. Comput. Appl. Res., 3(2013), 89-96.
- Gray, A., Abbena, E., Salamon, S., Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
- Han, X.A., Ma, Y.C., Huang, X.L., The cubic trigonometric B\'ezier curve with two shape parameters, Applied Mathematics Letters, 22(2009), 226-231.
- Han, X.A., Huang, X.L., Ma, Y.C., Shape analysis of cubic trigonometric B\'ezier curves with a shape parameter, Appl. Math. Comput., 217(2010), 2527-2533.
- Misro, M., Ramli, A., Ali, J., Quintic trigonometric B\'ezier curve with two shape parameters, Sains Malaysiana, 46(2017), 825-831.
- O'Neill, B., Elemantary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
- Sharma, R., Quartic trigonometric B\'ezier curves and surfaces with shape parameter, Int. J. Innov. Res. Comput. Commun. Eng., 3297(2016), 7712–7717.
- Sun, X., Ji, X., Parametric model for kitchen product based on cubic T-Bézier curves with symmetry, Symmetry, 12(2020), 505.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 14 Sayı: 1 |