Research Article
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Year 2020, Volume: 69 Issue: 2, 1377 - 1388, 31.12.2020

İdris Ören Muhsin İncesu

https://doi.org/10.31801/cfsuasmas.692608
Cited By: 1

Abstract

References

  • Zhang, C. , Du, S., Liu, J.,Li, Y., Xue,J., Liu, Y., Robust iterative closest point algorithm with bounded rotation angle for 2D registration, Neurocomputing, 195(2016),172-180.
  • Besl, P. J., McKay, N. D., A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2) (1992), 239-256.
  • Du, S., Zheng, N., Ying, S., Liu, J., Affine iterative closest point algorithm for point set registration, Pattern Recognition Letters, 31(2010),791-799.
  • Chen, H., Zhang, X., Du, S., Wu, Z., Zheng, N., A Correntropy-based affine iterative closest point algorithm for robust point set registration, IEEE/CAA J. Autom. Sin., 6 (4) (2019), 981-991.
  • Weiss, I., Geometric invariants and object recognition, J. Math. Imaging Vision, 10 (3) (1993), 201-231 .
  • Sanchez-Reyes, J., Complex rational Bézier curves, Comput. Aided Geom. Design, 26(8) (2009), 865-876.
  • Tsianos, K. I., Goldman, R., Bézier and B-spline curves with knots in the complex plane, Fractals, 19(1) (2011), 67-86.
  • Ait-Haddou, R., Herzog, W., Nomura, T., Complex Bézier curves and the geometry of polygons, Comput. Aided Geom. Design, 27(7) (2010), 525-537.
  • Ören, İ., On the control invariants of planar Bézier curves for the groups M(2) and SM(2), Turk. J. Math. Comput. Sci.,10 (2018), 74-81.
  • Khadjiev, D., Ören, İ., Pekşen,Ö., Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space, Int. J. Geom. Methods Mod. Phys., 15(6)(2018), 1-28.
  • Alcazar, J. G., Hermoso, C., Muntingh, G., Detecting similarity of rational plane curves, J. Comput. Appl. Math., 269 (2014), 1-13.
  • Alcazar, J. G., Hermoso, C,, Muntingh, G., Similarity detection of rational space curves, J. Symbolic Comput., 85 (2018), 4-24.
  • Alcazar, J. G., Gema, M. Diaz-Toca, Hermoso, C., On the problem of detecting when two implicit plane algebraic curves are similar, Internat. J. Algebra Comput, 29 (5) (2019),775-793.
  • Hauer, M., Jüttler, B., Detecting affine equivalences of planar rational curves, EuroCG 2016, Lugano, Switzerland, March 30-April 1, 2016.
  • Ören, İ., Equivalence conditions of two Bézier curves in the Euclidean geometry, Iran J Sci Technol Trans Sci, 42(3) (2016),1563-1577.
  • Reyes, J. S., Detecting symmetries in polynomial Bézier curves,J. Comput. Appl. Math., 288 (2015), 274-283.
  • Mozo-Fernandez, J., Munuera, C., Recognition of polynomial plane curves under affine transformations, AAECC, 13 (2002), 121-136.
  • Gürsoy, O., İncesu, ., LS(2)-Equivalence conditions of control points and application to planar Bézier curves, New Trends in Mathematical Science, 3 (2017), 70-84.
  • Bez, H.E., Generalized invariant-geometry conditions for the rational Bézier paths, Int J Comput Math, 87 (2010), 793-811 .
  • Encheva, R. P., Georgiev, G. H., Similar Frenet curves, Result. Math, 55 (2009), 359-372.
  • Khadjiev, D., Ören, İ., Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat., 27(2) (2019), 37-65.
  • Marsh, D., Applied Geometry For Computer Graphics and CAD, Springer-Verlag, London,1999.
  • Berger, M., Geometry I, Springer-Verlag, Berlin, Heidelberg, 1987.

Recognition of complex polynomial Bezier curves under similarity transformations

Year 2020, Volume: 69 Issue: 2, 1377 - 1388, 31.12.2020

İdris Ören Muhsin İncesu

https://doi.org/10.31801/cfsuasmas.692608
Cited By: 1

Abstract

In this paper, similarity groups in the complex plane C, polynomial curves
and complex Bezier curves in C are introduced. Global similarity invariants of polynomial
curves and complex Bezier curves in C are given in terms of complex functions.
The problem of similarity of two polynomial curves in C are solved. Moreover,
in case two polynomial curve (complex Bezier curve) are similar for the similarity
group, a general form of all similarity transformations, carrying one curve into the
other curve, are obtained.

Keywords

Bezier curve Invariant similarity

References

  • Zhang, C. , Du, S., Liu, J.,Li, Y., Xue,J., Liu, Y., Robust iterative closest point algorithm with bounded rotation angle for 2D registration, Neurocomputing, 195(2016),172-180.
  • Besl, P. J., McKay, N. D., A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2) (1992), 239-256.
  • Du, S., Zheng, N., Ying, S., Liu, J., Affine iterative closest point algorithm for point set registration, Pattern Recognition Letters, 31(2010),791-799.
  • Chen, H., Zhang, X., Du, S., Wu, Z., Zheng, N., A Correntropy-based affine iterative closest point algorithm for robust point set registration, IEEE/CAA J. Autom. Sin., 6 (4) (2019), 981-991.
  • Weiss, I., Geometric invariants and object recognition, J. Math. Imaging Vision, 10 (3) (1993), 201-231 .
  • Sanchez-Reyes, J., Complex rational Bézier curves, Comput. Aided Geom. Design, 26(8) (2009), 865-876.
  • Tsianos, K. I., Goldman, R., Bézier and B-spline curves with knots in the complex plane, Fractals, 19(1) (2011), 67-86.
  • Ait-Haddou, R., Herzog, W., Nomura, T., Complex Bézier curves and the geometry of polygons, Comput. Aided Geom. Design, 27(7) (2010), 525-537.
  • Ören, İ., On the control invariants of planar Bézier curves for the groups M(2) and SM(2), Turk. J. Math. Comput. Sci.,10 (2018), 74-81.
  • Khadjiev, D., Ören, İ., Pekşen,Ö., Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space, Int. J. Geom. Methods Mod. Phys., 15(6)(2018), 1-28.
  • Alcazar, J. G., Hermoso, C., Muntingh, G., Detecting similarity of rational plane curves, J. Comput. Appl. Math., 269 (2014), 1-13.
  • Alcazar, J. G., Hermoso, C,, Muntingh, G., Similarity detection of rational space curves, J. Symbolic Comput., 85 (2018), 4-24.
  • Alcazar, J. G., Gema, M. Diaz-Toca, Hermoso, C., On the problem of detecting when two implicit plane algebraic curves are similar, Internat. J. Algebra Comput, 29 (5) (2019),775-793.
  • Hauer, M., Jüttler, B., Detecting affine equivalences of planar rational curves, EuroCG 2016, Lugano, Switzerland, March 30-April 1, 2016.
  • Ören, İ., Equivalence conditions of two Bézier curves in the Euclidean geometry, Iran J Sci Technol Trans Sci, 42(3) (2016),1563-1577.
  • Reyes, J. S., Detecting symmetries in polynomial Bézier curves,J. Comput. Appl. Math., 288 (2015), 274-283.
  • Mozo-Fernandez, J., Munuera, C., Recognition of polynomial plane curves under affine transformations, AAECC, 13 (2002), 121-136.
  • Gürsoy, O., İncesu, ., LS(2)-Equivalence conditions of control points and application to planar Bézier curves, New Trends in Mathematical Science, 3 (2017), 70-84.
  • Bez, H.E., Generalized invariant-geometry conditions for the rational Bézier paths, Int J Comput Math, 87 (2010), 793-811 .
  • Encheva, R. P., Georgiev, G. H., Similar Frenet curves, Result. Math, 55 (2009), 359-372.
  • Khadjiev, D., Ören, İ., Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat., 27(2) (2019), 37-65.
  • Marsh, D., Applied Geometry For Computer Graphics and CAD, Springer-Verlag, London,1999.
  • Berger, M., Geometry I, Springer-Verlag, Berlin, Heidelberg, 1987.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

İdris Ören 0000-0003-2716-3945

Muhsin İncesu 0000-0003-2515-9627

Publication Date December 31, 2020
Submission Date February 21, 2020
Acceptance Date September 22, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Ören, İ., & İncesu, M. (2020). Recognition of complex polynomial Bezier curves under similarity transformations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1377-1388. https://doi.org/10.31801/cfsuasmas.692608
AMA Ören İ, İncesu M. Recognition of complex polynomial Bezier curves under similarity transformations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1377-1388. doi:10.31801/cfsuasmas.692608
Chicago Ören, İdris, and Muhsin İncesu. “Recognition of Complex Polynomial Bezier Curves under Similarity Transformations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1377-88. https://doi.org/10.31801/cfsuasmas.692608.
EndNote Ören İ, İncesu M (December 1, 2020) Recognition of complex polynomial Bezier curves under similarity transformations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1377–1388.
IEEE İ. Ören and M. İncesu, “Recognition of complex polynomial Bezier curves under similarity transformations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1377–1388, 2020, doi: 10.31801/cfsuasmas.692608.
ISNAD Ören, İdris - İncesu, Muhsin. “Recognition of Complex Polynomial Bezier Curves under Similarity Transformations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1377-1388. https://doi.org/10.31801/cfsuasmas.692608.
JAMA Ören İ, İncesu M. Recognition of complex polynomial Bezier curves under similarity transformations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1377–1388.
MLA Ören, İdris and Muhsin İncesu. “Recognition of Complex Polynomial Bezier Curves under Similarity Transformations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1377-88, doi:10.31801/cfsuasmas.692608.
Vancouver Ören İ, İncesu M. Recognition of complex polynomial Bezier curves under similarity transformations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1377-88.

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