A Cubic Bézier Model with Shape Parameters

Juncheng Li

doi:doi:10.11648/j.acm.20140306.19

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A Cubic Bézier Model with Shape Parameters

Juncheng Li

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

Received: 16 December 2014 Accepted: 28 December 2014 Published: 8 January 2015

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Abstract

A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.19
Page(s)	343-348
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Cubic Bézier Curve, Cubic Polynomial, Shape Parameter, Shape Adjustment

References

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[3]	J. W. Zhang, F. L. Krause and H. Y. Zhang. “Unifying C-curves and H-curves by extending the calculation to complex numbers”, Computer Aided Geometric Design, vol. 22, no. 9, pp. 865-883, 2005.
[4]	X.-A. Han, Y. C. Ma and X. L. Huang, “The cubic trigonometric Bézier curve with two shape parameters”, Applied Mathematical Letters, vol. 22, no. 2, pp. 226-231, 2009.
[5]	J. C. Li, D. B. Zhao, B. J. Li and G. H. Chen, “A family of quasi-cubic trigonometric curves”, Journal of Information and Computational Science, vol. 7, no. 13, pp. 2847-2854, 2010.
[6]	X. L. Han and Y. P. Zhu, “Curve construction based on five trigonometric blending functions”, BIT Numerical Mathematics, vol. 52, no. 4, pp. 953-979, 2012.
[7]	J. C. Li, “A class of cubic trigonometric Bézier curve with a shape parameter”, Journal of Information and Computational Science, vol. 10, no.10, pp. 3071-3078, 2013.
[8]	U. Bashir, M. Abbsa and J. M.Ali, “The G2 and C2 rational quadratic trigonometric Bézier curve with two shape parameters with applications”, Applied Mathematics and Computation, vol. 219. no. 20, pp. 10183-10197, 2013.
[9]	W. T. Wang and G. Z. Wang, “Bézier curves with shape parameters”, Journal of Zhejiang University SCIENCE A, vol. 6, no. 6, pp. 497-501, 2005.
[10]	X.-A. Han, Y. C. Ma and X. L.Huang, “A novel generalization of Bézier curve and surface”, Journal of Computational and Applied Mathematics, vol. 217, no. 1, pp. 180-193, 2008.
[11]	L. Q. Yang and X M. Zeng, “Bézier curves and surfaces with shape parameters”, International Journal of Computer Mathematics, vol. 86, no. 7, pp. 1253-1263, 2009.
[12]	L. L. Yan and Q. F. Liang, “An extension of the Bézier model”, Applied Mathematics and Computation, vol. 218, no. 6, pp. 2863-2879, 2011.
[13]	J. Chen and G. J. Wang, “A new type of the generalized Bézier curves”, Applied Mathematics: A Journal of Chinese Universities, vol. 26, no. 1, pp. 47–56, 2011.
[14]	Y. P. Zhu and X. L. Han, “A class of αβγ-Bernstein-Bézier basis functions over triangular domain”, Applied Mathematics and Computation, vol. 220, no. 17, pp. 446-454, 2013.
[15]	T. N. Xiang, Z. Liu, W. F. Wang and P. Jiang, “A novel extension of Bézier curves and surfaces of the same degree”, Journal of Information and Computational Science, vol. 7, no. 10, pp. 2080-2089, 2010.

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APA Style

Juncheng Li. (2015). A Cubic Bézier Model with Shape Parameters. Applied and Computational Mathematics, 3(6), 343-348. https://doi.org/10.11648/j.acm.20140306.19

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ACS Style

Juncheng Li. A Cubic Bézier Model with Shape Parameters. Appl. Comput. Math. 2015, 3(6), 343-348. doi: 10.11648/j.acm.20140306.19

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AMA Style

Juncheng Li. A Cubic Bézier Model with Shape Parameters. Appl Comput Math. 2015;3(6):343-348. doi: 10.11648/j.acm.20140306.19

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@article{10.11648/j.acm.20140306.19,
  author = {Juncheng Li},
  title = {A Cubic Bézier Model with Shape Parameters},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {343-348},
  doi = {10.11648/j.acm.20140306.19},
  url = {https://doi.org/10.11648/j.acm.20140306.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.19},
  abstract = {A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.},
 year = {2015}
}

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TY  - JOUR
T1  - A Cubic Bézier Model with Shape Parameters
AU  - Juncheng Li
Y1  - 2015/01/08
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20140306.19
DO  - 10.11648/j.acm.20140306.19
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 343
EP  - 348
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.19
AB  - A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.
VL  - 3
IS  - 6
ER  -

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Author Information

Juncheng Li

Department of Mathematics, Hunan University of Humanities, Science and Technology, Loudi, China

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APA Style

Juncheng Li. (2015). A Cubic Bézier Model with Shape Parameters. Applied and Computational Mathematics, 3(6), 343-348. https://doi.org/10.11648/j.acm.20140306.19

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ACS Style

Juncheng Li. A Cubic Bézier Model with Shape Parameters. Appl. Comput. Math. 2015, 3(6), 343-348. doi: 10.11648/j.acm.20140306.19

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AMA Style

Juncheng Li. A Cubic Bézier Model with Shape Parameters. Appl Comput Math. 2015;3(6):343-348. doi: 10.11648/j.acm.20140306.19

Copy | Download

@article{10.11648/j.acm.20140306.19,
  author = {Juncheng Li},
  title = {A Cubic Bézier Model with Shape Parameters},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {343-348},
  doi = {10.11648/j.acm.20140306.19},
  url = {https://doi.org/10.11648/j.acm.20140306.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.19},
  abstract = {A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A Cubic Bézier Model with Shape Parameters
AU  - Juncheng Li
Y1  - 2015/01/08
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20140306.19
DO  - 10.11648/j.acm.20140306.19
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 343
EP  - 348
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.19
AB  - A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.
VL  - 3
IS  - 6
ER  -

Copy | Download