East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

RATIONAL CURVES ARE NOT UNIT SPEED IN THE GENERAL EUCLIDEAN SPACE

  • Lee, Sun-Hong (DEPARTMENT OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
  • Received : 2000.10.06
  • Accepted : 2000.11.26
  • Published : 2010.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.

Keywords

References

  1. L. V. Ahlfors, Complex Analysis, Third Edition, McGraw-Hill Book Co., New York,1979.
  2. R. Dietz, J. Hoschek, and B. Juuttler, An algebraic approach to curves and surfaces on the sphere and on other quadrics, Comput. Aided Geom. Design 10 (1993), 211-229. https://doi.org/10.1016/0167-8396(93)90037-4
  3. R. T. Farouki and T. Sakkalis, Real rational curves are not `unit speed', Comput. Aided Geom. Design 8 (1991), 151-157. https://doi.org/10.1016/0167-8396(91)90040-I
  4. R. T. Farouki and T. Sakkalis, Rational space curves are not \unit speed", Comput. Aided Geom. Design 24(2007), 238-240. https://doi.org/10.1016/j.cagd.2007.01.004
  5. G.-I. Kim, Higher dimensional PH curves, Proc. Japan Acad. 78 (2002), Ser. A., 185-187.
  6. K. K. Kubota, Pythagorean triples in unique factorization domains, Amer. Math.Monthly 79 (1972), 503-505. https://doi.org/10.2307/2317570
  7. S. Lee and G.-I. Kim, Characterization of Minkowski Pythagorean-hodograph curves, J.Appl. Math. & Computing 24 (2007), 521-528.
  8. T. Sakkalis, R. T. Farouki, and L. Vaserstein, Non-existence of rational arc length pa-rameterizations for curves in ${\mathbb{R}^n}$, J. Comput. Appl. Math. 228 (2009), 494-497. https://doi.org/10.1016/j.cam.2008.09.022