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Year 2022, Volume: 71 Issue: 1, 133 - 152, 30.03.2022
https://doi.org/10.31801/cfsuasmas.895598

Abstract

References

  • Marsh, D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
  • Derivatives of a Bezier Curve, https://pages.mtu.edu/ 126 shene/COURSES/cs3621/NOTES/spline /Bezier/bezier-der.html
  • Erkan, E., Yüce, S., Some notes on geometry of Bezier curves in Euclidean 4-space, Journal of Engineering Technology and Applied Sciences, 5(3) (2020), 93-101. https://doi.org/10.30931/jetas.837921
  • Taş, F., İlarslan, K., A new approach to design the ruled surface, International Journal of Geometric Methods in Modern Physics, 16(6) (2019), 1950093. https://doi.org/10.1142/S0219887819500932
  • Farin, G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • Hagen, H., Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3) (1986), 629-638. https://doi.org/10.1216/RMJ-1986-16-3-629
  • Zhang, J. W. C., Jieqing, F., Bezier curves and surfaces, Graphical Models and Image Processing, 61(1) (1999), 2-15.
  • Incesu, M., LS (3)-equivalence conditions of control points and application to spatial Bezier curves and surfaces, AIMS Mathematics, 5(2) (2020) 1216-1246. https://doi.org/10.3934/math.2020084
  • Incesu, M., Gursoy, O., LS (2)-Equivalence conditions of control points and application to planar Bezier curves, New Trends in Mathematical Sciences, 5(3) (2017), 70-84. https://doi.org/10.20852/ntmsci.2017.186
  • Michael, S., Bezier Curves and Srfaces, Lecture 8, Floater Oslo, 2003.
  • Kılıçoğlu, Ş., Şenyurt, S., On the cubic Bezier curves in E3, Ordu University Journal of Science and Technology, 9(2) (2019) 83-97.
  • Kılıçoğlu, S., Şenyurt, S., On the involute of the cubic Bezier curve by using matrix representation in E3, European Journal of Pure and Applied Mathematics, 13 (2020), 216-226.https://doi.org/10.29020/nybg.ejpam.v13i2.3648

On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$

Year 2022, Volume: 71 Issue: 1, 133 - 152, 30.03.2022
https://doi.org/10.31801/cfsuasmas.895598

Abstract

Using the matrix representation form, the first, second, third, fourth, and fifth derivatives of 5th order Bezier curves are examined based on the control points in E3E3. In addition to this, each derivative of 5th order Bezier curves is given by their control points. Further, a simple way has been given to find the control points of a Bezier curves and its derivatives by using matrix notations. An example has also been provided and the corresponding figures which are drawn by Geogebra v5 have been presented in the end.

References

  • Marsh, D., Applied Geometry for Computer Graphics and CAD, Springer Science and Business Media, 2006.
  • Derivatives of a Bezier Curve, https://pages.mtu.edu/ 126 shene/COURSES/cs3621/NOTES/spline /Bezier/bezier-der.html
  • Erkan, E., Yüce, S., Some notes on geometry of Bezier curves in Euclidean 4-space, Journal of Engineering Technology and Applied Sciences, 5(3) (2020), 93-101. https://doi.org/10.30931/jetas.837921
  • Taş, F., İlarslan, K., A new approach to design the ruled surface, International Journal of Geometric Methods in Modern Physics, 16(6) (2019), 1950093. https://doi.org/10.1142/S0219887819500932
  • Farin, G., Curves and Surfaces for Computer-Aided Geometric Design, Academic Press, 1996.
  • Hagen, H., Bezier-curves with curvature and torsion continuity, Rocky Mountain J. Math., 16(3) (1986), 629-638. https://doi.org/10.1216/RMJ-1986-16-3-629
  • Zhang, J. W. C., Jieqing, F., Bezier curves and surfaces, Graphical Models and Image Processing, 61(1) (1999), 2-15.
  • Incesu, M., LS (3)-equivalence conditions of control points and application to spatial Bezier curves and surfaces, AIMS Mathematics, 5(2) (2020) 1216-1246. https://doi.org/10.3934/math.2020084
  • Incesu, M., Gursoy, O., LS (2)-Equivalence conditions of control points and application to planar Bezier curves, New Trends in Mathematical Sciences, 5(3) (2017), 70-84. https://doi.org/10.20852/ntmsci.2017.186
  • Michael, S., Bezier Curves and Srfaces, Lecture 8, Floater Oslo, 2003.
  • Kılıçoğlu, Ş., Şenyurt, S., On the cubic Bezier curves in E3, Ordu University Journal of Science and Technology, 9(2) (2019) 83-97.
  • Kılıçoğlu, S., Şenyurt, S., On the involute of the cubic Bezier curve by using matrix representation in E3, European Journal of Pure and Applied Mathematics, 13 (2020), 216-226.https://doi.org/10.29020/nybg.ejpam.v13i2.3648
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Şeyda Kılıçoglu 0000-0001-8535-944X

Süleyman Şenyurt 0000-0003-1097-5541

Publication Date March 30, 2022
Submission Date March 12, 2021
Acceptance Date August 5, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

APA Kılıçoglu, Ş., & Şenyurt, S. (2022). On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 133-152. https://doi.org/10.31801/cfsuasmas.895598
AMA Kılıçoglu Ş, Şenyurt S. On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):133-152. doi:10.31801/cfsuasmas.895598
Chicago Kılıçoglu, Şeyda, and Süleyman Şenyurt. “On the Matrix Representation of 5th Order Bezier Curve and Derivatives in E$^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 133-52. https://doi.org/10.31801/cfsuasmas.895598.
EndNote Kılıçoglu Ş, Şenyurt S (March 1, 2022) On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 133–152.
IEEE Ş. Kılıçoglu and S. Şenyurt, “On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 133–152, 2022, doi: 10.31801/cfsuasmas.895598.
ISNAD Kılıçoglu, Şeyda - Şenyurt, Süleyman. “On the Matrix Representation of 5th Order Bezier Curve and Derivatives in E$^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 133-152. https://doi.org/10.31801/cfsuasmas.895598.
JAMA Kılıçoglu Ş, Şenyurt S. On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:133–152.
MLA Kılıçoglu, Şeyda and Süleyman Şenyurt. “On the Matrix Representation of 5th Order Bezier Curve and Derivatives in E$^{3}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 133-52, doi:10.31801/cfsuasmas.895598.
Vancouver Kılıçoglu Ş, Şenyurt S. On the matrix representation of 5th order Bezier curve and derivatives in E$^{3}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):133-52.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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