Skip to main content
Log in

A characterization of helical polynomial curves of any degree

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Berger, M.: Geometry. I. Universitext. Springer, Berlin (1987) (Translated from the French by M. Cole and S. Levy)

    Google Scholar 

  2. Beltran, J.V., Monterde, J.: A characterization of quintic helices. J. Comput. Appl. Math. 206, 116–121 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dietz, R., Hoschek, J., Jüttler, B.: An algebraic approach to curves and surfaces on the sphere and on other quadrics. Comput. Aided Geom. Design 10, 211–229 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. Choi, H.I., Lee, D.S., Moon, H.P.: Clifford algebra, spin representation, and rational parametrization of curves and surfaces. Adv. Comput. Math. 17, 5–48 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Farouki, R.T.: Pythagorean-Hodograph Curves. In: Farin, G., Hoschek, J., Kim, M.-S. (eds.) Handbook of Computer Aided Geometric Design, pp. 405–427. North Holland, Amsterdam (2002)

    Chapter  Google Scholar 

  6. Farouki, R.T., Han, Ch.Y., Manni, C., Sestini, A.: Characterization and construction of helical polynomial space curves. J. Comput. Appl. Math. 162, 365–392 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jüttler, B., Mäurer, C.: Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling. Comput. Aided Geom. Design 31, 73–83 (1999)

    MATH  Google Scholar 

  8. Pelosi, F., Farouki, R.T., Manni, C., Sestini, A.: Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics. Adv. Comput. Math. 22, 325–352 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Silvester, J.R.: Geometry. Ancient and Modern. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Monterde.

Additional information

Communicated by Rida Farouki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Monterde, J. A characterization of helical polynomial curves of any degree. Adv Comput Math 30, 61–78 (2009). https://doi.org/10.1007/s10444-008-9063-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-008-9063-x

Keywords

Mathematics Subject Classifications (2000)

Navigation