- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 560246, 15 pages
Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics
Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, Republic of Korea
Received 17 January 2012; Accepted 11 February 2012
Academic Editor: Saminathan Ponnusamy
Copyright © 2012 Sunhong Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. T. Farouki and T. Sakkalis, “Pythagorean hodographs,” Journal of Research and Development, vol. 34, no. 5, pp. 736–752, 1990.
- R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, vol. 1 of Geometry and Computing, Springer, Berlin, Germany, 2008.
- R. T. Farouki and C. A. Neff, “Hermite interpolation by Pythagorean hodograph quintics,” Mathematics of Computation, vol. 64, no. 212, pp. 1589–1609, 1995.
- G. Albrecht and R. T. Farouki, “Construction of Pythagorean-hodograph interpolating splines by the homotopy method,” Advances in Computational Mathematics, vol. 5, no. 4, pp. 417–442, 1996.
- B. Jüttler, “Hermite interpolation by Pythagorean hodograph curves of degree seven,” Mathematics of Computation, vol. 70, no. 235, pp. 1089–1111, 2001.
- B. Jüttler and C. Mäurer, “Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling,” Computer-Aided Design, vol. 31, pp. 73–83, 1999.
- R. T. Farouki, M. al-Kandari, and T. Sakkalis, “Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves,” Advances in Computational Mathematics, vol. 17, no. 4, pp. 369–383, 2002.
- F. Pelosi, R. T. Farouki, C. Manni, and A. Sestini, “Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics,” Advances in Computational Mathematics, vol. 22, no. 4, pp. 325–352, 2005.
- Z. Šír, B. Bastl, and M. Lávička, “Hermite interpolation by hypocycloids and epicycloids with rational offsets,” Computer Aided Geometric Design, vol. 27, no. 5, pp. 405–417, 2010.
- A. I. Kurnosenko, “Two-point Hermite interpolation with spirals by inversion of hyperbola,” Computer Aided Geometric Design, vol. 27, no. 6, pp. 474–481, 2010.
- M. Bartoň, B. Jüttler, and W. Wang, “Construction of rational curves with rational. Rotation-minimizing frames via Möbius transformations,” in Mathematical Methods for Curves and Surfaces, Lecture Notes in Computer Science, pp. 15–25, Springer, Berlin, Germany, 2010.
- K. Ueda, “Spherical Pythagorean-hodograph curves,” in Mathematical Methods for Curves and Surfaces, II (Lillehammer, 1997), Innovations in Applied Mathematics, pp. 485–492, Vanderbilt University Press, Nashville, Tenn, USA, 1998.
- L. V. Ahlfors, Complex Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, NY, USA, Third edition, 1978.
- R. T. Farouki, “The conformal map of the hodograph plane,” Computer Aided Geometric Design, vol. 11, no. 4, pp. 363–390, 1994.
- H. Pottmann, “Rational curves and surfaces with rational offsets,” Computer Aided Geometric Design, vol. 12, no. 2, pp. 175–192, 1995.
- J.-C. Fiorot and Th. Gensane, “Characterizations of the set of rational parametric curves with rational offsets,” in Curves and Surfaces in Geometric Design, P. J. Laurent, A. Le Mehaute, and L. L. Schumaker, Eds., pp. 153–160, A K Peters, Wellesley, Mass, USA, 1994.
- H. Pottmann, “Applications of the dual Bézier representation of rational curves and surfaces,” in Curves and Surfaces in Geometric Design (Chamonix-Mont-Blanc, 1993), P. J. Laurent, A. Le Mehaute, and L. L. Schumaker, Eds., pp. 377–384, A K Peters, Wellesley, Mass, USA, 1994.
- H. Pottmann, “Curve design with rational Pythagorean-hodograph curves,” Advances in Computational Mathematics, vol. 3, no. 1-2, pp. 147–170, 1995.
- K. K. Kubota, “Pythagorean triples in unique factorization domains,” The American Mathematical Monthly, vol. 79, pp. 503–505, 1972.