Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

HIGHER DIMENSIONAL MINKOWSKI PYTHAGOREAN HODOGRAPH CURVES

  • Kim, Gwang-Il (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University) ;
  • Lee, Sun-Hong (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University)
  • Published : 2004.01.01

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Abstract

Rational parameterization of curves and surfaces is one of the main topics in computer-aided geometric design because of their computational advantages. Pythagorean hodograph (PH) curves and Minkowski Pythagorean hodograph (MPH) curves have attracted many researcher's interest because they provide for rational representation of their offset curves in Euclidean space and Minkowski space, respectively. In [10], Kim presented the characterization of the PH curves in the Euclidean space and analyzed the relation between the class of PH curves and the class of rational curves. In this paper, we extend the characterization of PH curves in [10] into that of MPH curves in the general Minkowski space and consider some generalized MPH curves satisfying this characterization.

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References

  1. Adv. Comput. Math. v.5 Construction of $C^2$ Pythagorean hodograph interpolation splines by the homotopy method G. Albrecht;R. T. Farouki
  2. Adv. Comput. Math. v.17 Clifford algebra, spin representation, and rational parameterization of curves and surfaces H. I. Choi;D. S. Lee;H. P. Moon
  3. Pacific J. Math. v.181 no.1 Mathematical theory of medial axis transform H. I. Choi;S. W. Choi;H. P. Moon
  4. Comput. Aided Geom. Design v.10 An algebraic approach to curves and surfaces on the sphere and on other quadrics R. Dietz;J. Hoschek;B. Juttler
  5. Geometry Processing for Design and Manufacturing Pythagorean hodograph curves in practical use R. T. Farouki
  6. Comput. Aided Geom. Design v.11 The conformal maps $z{\to}z^2$ of the hodograph plane R. T. Farouki
  7. Math. Comput. v.64 Hermite interpolating by Pythagorean hodograph quintics R. T. Farouki;C. A. Neff
  8. IBM J. Res. Development v.34 Pythagorean hodographs R. T. Farouki;T. Sakkalis
  9. Adv. Comput. Math. v.2 Pythagorean-hodograph space curves R. T. Farouki;T. Sakkalis
  10. Proc. Japan Acad. v.78 Higher dimensional PH curves G. -I. Kim
  11. Comput. Aided Geom. Design v.16 Minkowski Pythagorean hodographs H. P. Moon
  12. J. Symbolic Comput. v.23 Computing rational parametrizations of canal surfaces M. Peternell;H. Pottman