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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.22 No.1

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Isogonal and isotomic conjugates of quadratic rational Bezier curves

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.1, pp.25-34
https://doi.org/10.7468/jksmeb.2015.22.1.25
Yun, Chan Ran
Ahn, Young Joon
Yun,, C. R. , & Ahn,, Y. J. (2015). Isogonal and isotomic conjugates of quadratic rational Bezier curves. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(1), 25-34, https://doi.org/10.7468/jksmeb.2015.22.1.25

Abstract

In this paper we characterize the isogonal and isotomic conjugates of conic. Every conic can be expressed by a quadratic rational B<TEX>$\acute{e}$</TEX>zier curve having control polygon <TEX>$b_0b_1b_2$</TEX> with weight w > 0. We show that the isotomic conjugate of parabola and hyperbola with respect to <TEX>${\Delta}b_0b_1b_2$</TEX> is ellipse, and that the isotomic conjugate of ellipse with the weight <TEX>$w={\frac{1}{2}}$</TEX> is identical. We also find all cases of the isogonal conjugate of conic with respect to <TEX>${\Delta}b_0b_1b_2$</TEX>. Our characterizations are derived easily due to the expression of conic by the quadratic rational B<TEX>$\acute{e}$</TEX>ezier curve in standard form.

keywords
isogonal conjugate, isotomic conjugate, conic, quadratic rational B<tex> $\acute{e}$</tex>zier curve, ellipse, parabola, hyperbola

Reference

1.

Ahn, Y.J.;Kim, H.O.;. (1998). Curvatures of the quadratic rational B&#xE9;zier curves. Comp. Math. Appl., 36, 71-83.

2.

Akopyan, A.V.;. (2012). Conjugation of lines with respect to a triangle. J. Classical Geometry, 1, 23-31.

3.

Farin, G.;. Curves and Surfaces for CAGD.

4.

Goddijn, A.;van Lamoen, F.;. (2005). Triangle-Conic Porism (57-61). Forum Geom..

5.

Guinand, A.P.;. (1975). Graves triads in the geometry of the triangle. Journal of Geometry, 6, 131-142. 10.1007/BF01920045.

6.

Guinand, A.P.;. (2002). Conjugacies in the plane of a triangle. Aequationes Mathematicae, 63, 158-167. 10.1007/s00010-002-8014-8.

7.

Pamfilos, P.;. (2012). On tripolars and parabolas (287-300). Forum Geom..

8.

Sastry, K.R.S.;. (2004). Triangles with special isotomic conjugate pairs (73-80). Forum Geom..

9.

Yiu, P.;. (2001). Introduction to the Geometry of the Triangle . Florida Atlantic University Lecture Notes.

10.

Yun, C.R.;. Isogonal and isotomic conjugates of quadratic rational B&#xE9;zier curve. MS Thesis.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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