Enhancement of Gielis’ Supershapes in Generating Nature Motifs

  • Rafizah Kechil
  • Noor 'Aina Abdul Razak
  • Siti Asmah Mohamed Department of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Pulau Pinang
  • Fuziatul Norsyiha Ahmad Shukri

Abstract

Nature motifs have played an important role in designing and generating most products such as jewellery, fashion, furniture, textile, or visual arts. The designers may translate their ideas by using the mathematical equations to design the products inspired by the nature motifs. One of the mathematical equations that can be used in creating or designing nature motifs is the Gielis’ Supershape (GS). This formula has been introduced by Johan Gielis, who is the botanist and mathematician. In this paper, we will discuss the nature motif that can be created by using the GS. We also proposed the enhanced GS and do some comparisons. As a result, it shows that the nature shape created by using the enhanced GS is more impressive compared to the shape created using the original GS.

References

[1] S. Pathak, “Biomimicry:(Innovation Inspired by Nature),” Int. J. New Technol. Res., vol. 5, no.
6, pp. 34–38, 2019.
[2] G, Poteraş, György Deák, M. V. Olteanu, I-F. Burlacu, C. Sîrbu,N. Muhammad, and N.A.Mohd
Mortar, “Profiles of blades and paddles for turbines with geometric design inspired by nature,”
in AIP Conference Proceedings, 2020, vol. 2291, no. 1, p. 20016.
[3] K. I. Tsianos and R. Goldman, “Bézier and B-spline curves with knots in the complex plane,”
Fractals, vol. 19, no. 01, pp. 67–86, 2011.
[4] M. Hoffmann and I. Juhász, “On interpolation by spline curves with shape parameters,” in
International Conference on Geometric Modeling and Processing, 2008, pp. 205–214.
[5] H. Hang, X. Yao, Q. Li, and M. Artiles, “Cubic B-Spline curves with shape parameter and their
applications,” Math. Probl. Eng., vol. 2017, 2017.
[6] G. Irving and H. Segerman, “Developing fractal curves,” J. Math. Arts, vol. 7, no. 3–4, pp.
103–121, 2013.
[7] P. do E. Silva, Caroline, J. A. De Souza, and A. Vacavant, “Automated Mathematical Equation
Structure Discovery for Visual Analysis,”,” J. Mach. Learn. Res., vol. 22, pp. 1–25, 2021.
[8] S. K. Mishra, “On estimation of the parameters of gielis superformula from empirical data,”
SSRN Electron. J., 2006.
[9] P. Shi, D. A. Ratkowsky, and J. Gielis, “The generalized Gielis geometric equation and its
application,” Symmetry (Basel)., vol. 12, no. 4, p. 645, 2020.
[10] J. Gielis, D. Caratelli, P. Shi, and P. E. Ricci, “A note on spirals and curvature,” Growth Form,
vol. 1, pp. 1–8, 2020.
[11] M. Matsuura, “Gielis’ superformula and regular polygons,” J. Geom., vol. 106, no. 2, pp. 383–
403, 2015.
[12] J. Gielis, “Natural Polygons and Gielis Transformations,” 2019, p. 53.
[13] J. Gielis, The geometrical beauty of plants. Springer, 2017.
[14] S. Primo, Brandi; Anna, “A MAGIC FORMULA OF NATURE BRANDI Primo (IT), SALVADORI
Anna (IT),” in 17th COnference on Applied Mathematics, 2018, pp. 110–126.
[15] J. A. Norato, “Topology optimization with supershapes,” Struct. Multidiscip. Optim., vol. 58,
no. 2, pp. 415–434, 2018.
Published
2021-05-31
How to Cite
KECHIL, Rafizah et al. Enhancement of Gielis’ Supershapes in Generating Nature Motifs. Mathematical Sciences and Informatics Journal, [S.l.], v. 2, n. 1, p. 49-56, may 2021. ISSN 2735-0703. Available at: <https://myjms.mohe.gov.my/index.php/mij/article/view/12647>. Date accessed: 07 dec. 2022. doi: https://doi.org/10.24191/mij.v2i1.12647.
Section
Articles

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.