Isoparametric Curve of Quadratic F-Bézier Curve

  • Received : 2013.01.02
  • Accepted : 2013.03.25
  • Published : 2013.03.30


In this thesis, we consider isoparametric curves of quadratic F-B$\acute{e}$zier curves. F-B$\acute{e}$zier curves unify C-B$\acute{e}$zier curves whose basis is {sint, cos t, t, 1} and H-B$\acute{e}$zier curves whose basis is {sinht, cosh t, t,1}. Thus F-B$\acute{e}$zier curves are more useful in Geometric Modeling or CAGD(Computer Aided Geometric Design). We derive the relation between the quadratic F-B$\acute{e}$zier curves and the quadratic rational B$\acute{e}$zier curves. We also obtain the geometric properties of isoparametric curve of the quadratic F-B$\acute{e}$zier curves at both end points and prove the continuity of the isoparametric curve.


Supported by : Chosun University


  1. H. Pottmann, "The geometry of Tchebycheffian spines", Comput. Aided Geom. D., Vol. 10, pp. 181-210, 1993.
  2. J. Zhang, "C-curves: An extension of cubic curves", Comput. Aided Geom. D., Vol. 13, pp. 199-217, 1996.
  3. J. Zhang, "Two different forms of C-B-splines", Comput. Aided Geom. D., Vol. 14, pp. 31-41, 1997,
  4. J. W. Zhang, "C-Bezier curves and surfaces", Graph. Models Image Process, Vol. 61, pp. 2-15, 1999.
  5. E. Mainar, J. Pena, and J. Sanchez-Reyes, "Shape preseving alternatives to the raional Bezier model", Comput. Aided Geom. D., Vol. 18, pp. 37-60, 2001.
  6. Q. Chen and G. Wang, "A class of Bezier-like curves", Comput. Aided Geom. D., Vol. 20, pp. 29-39, 2003.
  7. Y. Lu, G. Wang, and X. Yang, "Uniform hyperbolic polynomial B-spline curves", Comput. Aided Geom. D., Vol. 19, pp. 379-393, 2002.
  8. J. W. Zhang and F.-L. Krause, "Extend cubic uniform B-splines by unified trigonometric and hyberolic basis", Graph. Models, Vol. 67, pp. 100-119, 2005.
  9. J. Zhang, F.-L. Krause, and H. Zhang, "Unifying C-curves and H-curves by extending the calculation to complex numbers", Comput. Aided Geom. D., Vol. 22, pp. 865-883, 2005.
  10. G. Farin, "Curves and surfaces for Computer Aided Geometric Design: A particle code", fifth ed. Academic Press, London, 2001.
  11. M. Floater, "An $O(h^{2n})$ Hermite approximation for conic sections", Comput. Aided Geom. D., Vol. 14, pp. 135-151, 1997.
  12. H. Y. Park, "Properties of isoparametric curve of quadratic F-Bezier curve", M.S. thesis, Chosun University, 2012.