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The 360° Curvilinear Perspective: A Hybrid Hypercubic Angular Space Grid Based on the 1968 Barre and Flocon proposal

Abstract

We analyze in detail a specific image of curvilinear perspective developed by Andre Barre and Albert Flocon in 1968 which depicts a square room from its interior by a 360° total perspective. Since its publication, their work has become an important point of reference, but they did not say how it was done. We discuss how this specific case of a pseudo-spherical projection for a hypercube was achieved by hybridized using ellipse curves in one of the spatial directions and a different spherical projection in the other direction. For this analysis we develop the mathematical expressions and study how the ellipsoidal and spherical transformations are hybridized into one solution. Barre and Flocon attempted to use both projections in an angular curvilinear grid as a practical drawing method. One of the main interests of having access to a 360° curvilinear grid arises its ability to act as a drawing guide. We provide an example of its use to demonstrate its practicality.

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Acknowledgements

We wish to thank two anonymous reviewers and Editor-in-Chief Kim Williams for their valuable comments that greatly helped to improve the manuscript. All images are by the authors.

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Correspondence to Julián Santoyo.

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Santoyo, J., Santoyo, M.A. The 360° Curvilinear Perspective: A Hybrid Hypercubic Angular Space Grid Based on the 1968 Barre and Flocon proposal. Nexus Netw J 23, 717–735 (2021). https://doi.org/10.1007/s00004-021-00552-1

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Keywords

  • Curvilinear perspective
  • Grid construction
  • Total perspective
  • Spherical projections
  • Ellipse