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.
Highlights
1.1 PREVIOUS WORKThis work intends to settle equirectangular spherical perspective as a proper perspective, by providing clear and complete rules to solve all lines and vanishing points, and a method for drawing them with simple tools
Equirectangular perspective has, some important advantages: it is the standard input for VR panorama rendering engines, so it skips a conversion step that tends to generate troublesome artefacts; its coordinates correspond to the natural angles that one measures in surveying; it renders onto a rectangle rather than a disc, which accords well both with image files and with the usual shape of drawing pads, sketchbooks and picture frames; and, as we shall see, it has many of the useful features of cylindrical perspective with the advantage of covering the whole field of view
How well does this perspective measure up against the alternatives? Its greatest failing is the awkwardness of line plots for high φ0, but outdoor sketching can focus on eyeballing shapes and measuring angles, and accurate plotting done later back in the studio; or some smart gridding can be called upon, using the symmetries pointed out above
Summary
This work intends to settle equirectangular spherical perspective as a proper perspective, by providing clear and complete rules to solve all lines and vanishing points, and a method for drawing them with simple tools. It aims to bridge the gap between traditional and digital drawing, in the creation of immersive VR panoramas. This is a revision and expansion of previous results I presented in a recent conference paper (Araújo, 2017)
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