Abstract
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.
Keywords
Computer aided geometric design (CAGD) curvature Frenet frame field trigonometric Bezier curve trigonometric polynomial
References
- 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.
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- 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.
Abstract
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2022 |
| Published in Issue | Year 2022 Volume: 14 Issue: 1 |