Skip to main content
SpringerLink
Log in

A Note About Generalized Forms of the Gielis Formula

  • Conference paper
  • First Online:
Modeling in Mathematics

Part of the book series: Atlantis Transactions in Geometry ((ATLANTIS,volume 2))

Abstract

We generalize the Gielis Superformula by extending the R. Chacón approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 149.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J. Gielis, A generic geometric transformation that unifies a wide range of natural and abstract shapes. Am. J. Bot. 90, 333–338 (2003)

    Article  Google Scholar 

  2. J. Gielis, S. Haesen, L. Verstraelen, Universal shapes: from the supereggs of Piet Hein to the cosmic egg of Georges Lemaître. Kragujevac J. Math. 28, 55–67 (2005)

    Google Scholar 

  3. M. Koiso, B. Palmer, Rolling constructions for anisotropic Delaunay surfaces. Pacific J. Math. 2, 345–378 (2008)

    Google Scholar 

  4. D. Caratelli, P. Natalini, P.E. Ricci, Fourier solution of the wave equation for a star-like-shaped vibrating membrane. Comput. Math. Appl. 59, 176–184 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Matsuura, Gielis’ superformula and regular polygons. J. Geom. 106(2), 383–403 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Chacón, Modeling natural shapes with a simple nonlinear algorithm. Int. J. Bifurc. Chaos 16, 2365–2368 (2006)

    Article  Google Scholar 

  7. V.I. Arnold, O.A. Oleinik, Topology of real algebraic manifolds. Moscow Univ. Bull. 34, 5–17 (1979)

    MATH  Google Scholar 

  8. J. Gielis, D. Caratelli, P.E. Ricci, T. Gerats, The common descent of biological shape description and special functions (submitted)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Bioengineering Sciences, University of Antwerp, Groenenborgerlaan, 171, 2020, Antwerp, Belgium

    Johan Gielis

  2. Dipartimento di Matematica e Fisica, Università Degli Studi Roma Tre, Largo San Leonardo Murialdo, 1, 00146, Rome, Italy

    Pierpaolo Natalini

  3. International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186, Rome, Italy

    Paolo Emilio Ricci

Authors
  1. Johan Gielis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierpaolo Natalini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Emilio Ricci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paolo Emilio Ricci .

Editor information

Editors and Affiliations

  1. Bio-Engineering Sciences, University of Antwerp, Antwerp, Belgium

    Johan Gielis

  2. International Telematic University UniNettuno, Roma, Italy

    Paolo Emilio Ricci

  3. Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Ilia Tavkhelidze

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Atlantis Press and the author(s)

About this paper

Cite this paper

Gielis, J., Natalini, P., Ricci, P.E. (2017). A Note About Generalized Forms of the Gielis Formula. In: Gielis, J., Ricci , P., Tavkhelidze, I. (eds) Modeling in Mathematics . Atlantis Transactions in Geometry, vol 2. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-261-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation