Drawing Equirectangular VR Panoramas with Ruler, Compass, and Protractor

DOI: https://doi.org/10.7559/citarj.v10i1.471
Keywords: Visual arts, immersive art, immersive panoramas, VR panoramas, equirectangular perspective, spherical perspective, perspective, drawing, descriptive geometry, digital art, ruler and compass, social networks

Abstract

This work presents a method for drawing Virtual Reality panoramas by ruler and compass operations. VR panoramas are immersive anamorphoses rendered from equirectangular spherical perspective data. This data is usually photographic, but some artists are creating hand-drawn equirectangular perspectives to be visualized in VR. This practice, that lies interestingly at the interface between analog and digital drawing, is hindered by a lack of method, as these drawings are usually done by trial-and-error, with ad-hoc measurements and interpolation of pre-computed grids, a process with considerable artistic limitations. I develop here the analytic tools for plotting all great circles, line images and their vanishing points, and then show how to achieve these constructions through descriptive geometry diagrams that can be executed using only ruler, compass, and protractor. Approximations of line images by circular arcs and sinusoids are shown to have acceptable errors for low values of angular elevation. The symmetries of the perspective are studied and their uses for improving gridding methods are discussed.

Author Biography

António Bandeira Araújo, Department of Science and Technology, Universidade Aberta, Portugal
António Bandeira Araújo is a geometer and draughtsman. He holds a degree in physics and a Ph.D. in mathematics. He had training in drawing, painting, and scientific illustration, and has published illustration work. His main interest lies in the interactions between mathematics and the visual arts, both classical and digital. He lectures at Universidade Aberta in Portugal and is a member of CIAC-UAb (Centro de Investigação em Artes e Comunicação) and CMAF-CIO (Centro de Matemática, Aplicações Fundamentais e Investigação Operacional).

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Equirectangular perspective of a stairwell
Published
2018-04-03
Issue
Vol 10 No 1 (2018): Volume 10 - Number 1, 2018
Section
Articles

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