Bezier Eğrilerinin Möbius Eğriliği

Öz

Bu çalışmanın amacı Bezier eğrilerinin eğriliğini kullanarak hesapladığım Möbius eğrilerini Bezier eğrilerinin özellikleri araştırılmasından dolayı oarantılı olarak buna karşılık gelen eğriliğin diferensiyellerinin incelenmesidir. Bezier eğrisinin Möbius eğriliği kontrol noktalarında farklı değer alır. Yine açının sabit yada değişken olmasına göre de farklı durumlar söz konusu olduğunda değeri değişebilmektedir.

Anahtar Kelimeler

• Bezier Eğrileri
• Eğrilik
• Möbius Eğriliği

The Möbius Curvature of Bezier Curves

Abstract

The aim of this study is to observe the Möbius curvature is computed by me as using curvature of Bezier curve is therefore proportional to the differentials of the curvature also correspond to a such as survey properties of Bezier curves. The Möbius curvature of Bezier curve has different value according to the control points. Also when the different cases may ocur, it has different values according to the angle is constant or not.

Keywords

• Bezier curves
• Curvature
• Möbius Curvature.

References

1. Erkan, E., Yüce, S. (2018). Serret Frenet Frame and Curvatures of Bezier Curves. Mathematics, 6(321), 2-20.
2. Hasan, Z. A., Yahya, Z. R., Rusdi, N. A. and Roslan, N. (2018). Curve Construction in Different Cubic Funtions using Differential Evolution. Mucet 2017, MATEC Web of Conferences 150, 06030.
3. Marsland, S., Mclachlan, R. I. (2016). Möbius Invariants of Shapes and Images. Symmetry, Integrability and Geometry: Methods and Applications, 12, 080, 29 pages.
4. Roslan, N., Yahya, Z. R. (2015). Different Mutatition Strategies for Reconstruction of Japanese Character. Acceptance for Malaysian Technical Universities Confererence on Engineering and Technology, (MUCET 2015) Johor Bharu, 11-13 October 2015.
5. Rusdi, N. A., Yahya, Z. R. (2015). Reconstruction of Arabic Font with Quartic Bezier Curve. Sains Malaysiana 44, 1209-1216.
6. Rusdi, N. A., Yahya, Z. R. (2014). Reconstruction of Generic Shape with Cubic Bezier least Square Method. International Conference on Mathematics Engineering and Industrial Applications, ICOMEIA 2014, AIP Publishing 1660, 0500004.
7. Rusdi, N. A., Yahya, Z. R. (2014). Reconstruction of Arabic Font using Artificial Bee Colony Algorithm, Acceptance for Malaysian Technical Universities Confererence on Engineering and Technology, (MUCET 2015).
8. Patterson, B. C. (1928). The different invariants of inversive Geometry. Amer. J. Math. 50, 553-568.

9. Samanci, H. K., Çelik, S. and İncesu, M. (2015). The Bishop Frame of Bezier Curves. Life Science Journal, 12 (6).
10. Yan, L. L., Liang J. F. (2011). An Extension of the Bezier Model. Applied mathematics and Computation, Vol: 18, No:6, 2863-2879.
11. Forrest, A. R. (1968). Curves and Surfaces for Computer Aided Design. Ph. D. Thesis, University of Cambridge.