Modifying the shape of FB-spline curves

  • Miklós Hoffmann
  • Imre Juhász


FB-spline curves are the unification of recently developed trigonometric CB-spline and hyperbolic HB-spline curves, including the classical B-spline curves. These generalized curves overcome some restrictions of B-spline curves and allow to design some important curves like helix, cycloids or catenary. Their properties, however, have been studied only theoretically. In this paper practical shape modification algorithms of FB-spline curves are discussed, including the geometrical effects of the alteration of shape parameters, which are essential from the users’ point of view.


FB-spline curve C-curves H-curves Shape modification 

Mathematics Subject Classification (2000)



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  1. 1.
    Chen, Q., Wang, G.: A class of Bézier-like curves. Comput. Aided Geom. Des. 20, 29–39 (2003) CrossRefzbMATHGoogle Scholar
  2. 2.
    Hoffmann, M., Li, Y., Wang, G.: Paths of C-Bézier and C-B-spline curves. Comput. Aided Geom. Des. 23, 463–475 (2006) CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Juhász, I.: On the singularity of a class of parametric curves. Comput. Aided Geom. Des. 23, 146–156 (2006) CrossRefzbMATHGoogle Scholar
  4. 4.
    Li, Y., Wang, G.: Two kinds of B-basis of the algebraic hyperbolic space. J. Zheijang Univ. Sci. 6, 750–759 (2005) CrossRefGoogle Scholar
  5. 5.
    Lü, Y., Wang, G., Yang, X.: Uniform hyperbolic polynomial B-spline curves. Comput. Aided Geom. Des. 19, 379–393 (2002) CrossRefGoogle Scholar
  6. 6.
    Mainar, E., Pena, J.M.: A basis of C-Bézier splines with optimal properties. Comput. Aided Geom. Des. 19, 291–295 (2002) CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Mainar, E., Pena, J.M., Sanchez-Reyes, J.: Shape preserving alternatives to the rational Bézier model. Comput. Aided Geom. Des. 18, 37–60 (2001) CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Morin, G., Warren, J., Weimer, H.: A subdivision scheme for surface of revolution. Comput. Aided Geom. Des. 18, 483–502 (2001) CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Pottmann, H.: The geometry of Tchebycheffian splines. Comput. Aided Geom. Des. 10, 181–210 (1993) CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Pottmann, H., Wagner, M.: Helix splines as an example of affine Tchebycheffian splines. Adv. Comput. Math. 2, 123–142 (1994) CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Wang, G., Chen, Q., Zhou, M.: NUAT B-spline curves. Comput. Aided Geom. Des. 21, 193–205 (2004) CrossRefMathSciNetGoogle Scholar
  12. 12.
    Yang, Q., Wang, G.: Inflection points and singularities on C-curves. Comput. Aided Geom. Des. 21, 207–213 (2004) CrossRefzbMATHGoogle Scholar
  13. 13.
    Zhang, J.W.: C-curves, an extension of cubic curves. Comput. Aided Geom. Des. 13, 199–217 (1996) CrossRefzbMATHGoogle Scholar
  14. 14.
    Zhang, J.W.: Two different forms of CB-splines. Comput. Aided Geom. Des. 14, 31–41 (1997) CrossRefzbMATHGoogle Scholar
  15. 15.
    Zhang, J.W.: C-Bézier curves and surfaces. Graph. Models Image Process. 61, 2–15 (1999) CrossRefzbMATHGoogle Scholar
  16. 16.
    Zhang, J.W., Krause, F.-L.: Extend cubic uniform B-splines by unified trigonometric and hyperbolic basis. Graph. Models 67, 100–119 (2005) CrossRefzbMATHGoogle Scholar
  17. 17.
    Zhang, J.W., Krause, F.-L., Zhang, H.: Unifying C-curves and H-curves by extending the calculation to complex numbers. Comput. Aided Geom. Des. 22, 865–883 (2005) CrossRefMathSciNetzbMATHGoogle Scholar

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© KSCAM and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceKároly Eszterházy UniversityEgerHungary
  2. 2.Department of Descriptive GeometryUniversity of MiskolcMiskolc–EgyetemvárosHungary

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