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Anamorphosis Reformed: From Optical Illusions to Immersive Perspectives

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Handbook of the Mathematics of the Arts and Sciences

Abstract

We discuss a definition of conical anamorphosis that sets it at the foundation of both classical and curvilinear perspectives. In this view, anamorphosis is an equivalence relation between three-dimensional objects, which includes two-dimensional representatives, not necessarily flat. Vanishing points are defined in a canonical way that is maximally symmetric, with exactly two vanishing points for every line. The definition of the vanishing set works at the level of anamorphosis, before perspective is defined, with no need for a projection surface. Finally, perspective is defined as a flat representation of the visual data in the anamorphosis. This schema applies to both linear and curvilinear perspectives and is naturally adapted to immersive perspectives, such as the spherical perspectives. Mathematically, the view here presented is that the sphere and not the projective plane is the natural manifold of visual data up to anamorphic equivalence. We consider how this notion of anamorphosis may help to dispel some long-standing philosophical misconceptions regarding the nature of perspective.

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Acknowledgements

A. B. Araújo was funded by FCT Portuguese national funds through project UIDB/Multi/04019/2020

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Authors and Affiliations

  1. CIAC-UAb, Center for Research in Arts and Communication, Universidade Aberta, R. Escola Politécnica, Lisbon, Portugal

    António B. Araújo

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  1. António B. Araújo
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Correspondence to António B. Araújo .

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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Montana, Missoula, MT, USA

    Bharath Sriraman

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  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  2. Department of Mathematics Education, College of Education, Seoul National University, Seoul, South Korea

    Kyeong-Hwa Lee

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Araújo, A.B. (2020). Anamorphosis Reformed: From Optical Illusions to Immersive Perspectives. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_101-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_101-1

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