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Thickness design for ambiguous cylinder illusion

  • Kokichi SugiharaEmail author
Original Paper Area 3
  • 136 Downloads

Abstract

This paper proposes methods for giving as uniform a thickness as possible to a class of illusion solids called ambiguous cylinders. Ambiguous cylinders are solids that have two quite different appearances when seen from two specific viewpoints, and thus create the impression of impossible objects. In order to realize them as physical objects, we have to give them thickness. However, it is impossible to give a completely uniform thickness despite this being desirable. Instead we have to content ourselves with second-best methods. For this purpose, this paper proposes three alternative strategies for creating objects as uniform as possible. Each strategy has its own merits and demerits, and hence users can choose their method according to their priorities for the visual effects which they want to emphasize.

Keywords

Optical illusion Impossible object Anomalous cylinder Ambiguous object Uniform thickness 

Mathematics Subject Classification

00A66 

Notes

Acknowledgements

Funding was provided by Japan Society for the Promotion of Science (Grant Nos. 15K12067, 16H01728).

References

  1. 1.
    Farin, G.: Curves and Surfaces for CAGD: A Practical Guide, 4th edn. Academic Press, San Diego (1988)zbMATHGoogle Scholar
  2. 2.
    Farouki, R.T., Neff, C.A.: Analytic properties of plane offset curves. Comput. Aided Geom. Des. 7, 83–99 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gregory, R.L.: The Intelligent Eye. Weidenfeld & Nicolson, London (1970)Google Scholar
  4. 4.
    Gomes, J., Darsa, L., Costa, B., Velho, L.: Wrapping and Morphing of Graphical Objects. Morgan Kaufmann Publisher Inc., San Francisco (1999)Google Scholar
  5. 5.
    Hoschek, J.: Offset curves in the plane. Comput. Aided Des. 17, 77–82 (1985)CrossRefGoogle Scholar
  6. 6.
    Hundert, E.M.: Lessons from an Optical Illusion. Harvard University Press, Cambridge (1995)Google Scholar
  7. 7.
    Ninio, J.: The Science of Illusions. Cornell University Press, Ithaca (2001)Google Scholar
  8. 8.
    Penrose, L.S., Penrose, R.: Impossible objects: a special type of visual illusion. Br. J. Psychol. 49, 31–33 (1958)CrossRefGoogle Scholar
  9. 9.
    Perkins, D.N.: Visual discrimination between rectangular and nonrectangular parallelepipeds. Percept. Psychophys. 12, 396–400 (1972)CrossRefGoogle Scholar
  10. 10.
    Robinson, J.O.: The Psychology of Visual Illusion. Dover Publications Inc, Mineola (1998)Google Scholar
  11. 11.
    Seckel, A.: The Ultimate Book of Optical Illusions. Sterling, New York (2005)Google Scholar
  12. 12.
    Sugihara, K.: Machine Interpretation of Line Drawings. The MIT Press, Cambridge (1986)Google Scholar
  13. 13.
    Sugihara, K.: Three-dimensional realization of anomalous pictures—an application of picture interpretation theory to toy design. Pattern Recognit. 30, 1061–1067 (1997)CrossRefGoogle Scholar
  14. 14.
    Sugihara, K.: Design of solids for antigravity motion illusion. Comput. Geom. Theory Appl. 47, 675–682 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Sugihara, K.: Ambiguous cylinders: a new class of impossible objects. Comput. Aided Draft. Des. Manuf. 25(3), 19–25 (2015)Google Scholar
  16. 16.
    Sugihara, K.: A new type of impossible objects that become partly invisible in a mirror. Jpn. J. Ind. Appl. Math. 33, 525–535 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Wade, N.J., Hughes, P.: Fooling the eyes: Trompe l’œil and reverse perspective. Perception 28, 1115–1119 (1999)CrossRefGoogle Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan KK 2017

Authors and Affiliations

  1. 1.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityTokyoJapan

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