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Publications

Anamorphosis: optical games with perspective's playful parent

Publication . Araújo, António

We explore conical anamorphosis in several variations and discuss its various constructions, both physical and diagrammatic. While exploring its playful aspect as a form of optical illusion, we argue against the prevalent perception of anamorphosis as a mere amusing derivative of perspective and defend the exact opposite view - that perspective is the derived concept, consisting of plane anamorphosis under arbitrary limitations and ad-hoc alterations. We show how to define vanishing points in the context of anamorphosis in a way that is valid for all anamorphs of the same set. We make brief observations regarding curvilinear perspectives, binocular anamorphoses, and color anamorphoses.

2017Conference object

Open access

Guidelines for drawing immersive panoramas in equirectangular perspective

Publication . Araújo, António

Virtual Reality (VR) Panoramas work by interactively creating immersive anamorphoses from spherical perspectives. These panoramas are usually photographic but a growing number of artists are making hand-drawn equirectangular perspectives in order to visualize them as VR panoramas. This is a practice with both artistic and didactic interest. However, these drawings are usually done by trial-and-error, with ad-hoc measurements and interpolation of precomputed grids, a process with considerable limitations.We develop in this work the analytic tools for plotting great circles, straight line images and their vanishing points, and then provide guidelines for achieving these constructions in good approximation without computer calculations, through descriptive geometry diagrams that can be executed using only ruler, compass, and protractor.

2017-09Conference object

Open access

Drawing equirectangular VR panoramas with ruler, compass, and protractor

Publication . Araújo, António

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.

2018-04Journal article

Open access

Let's Sketch in 360º: spherical perspectives for virtual reality panoramas

Publication . Araújo, António

In this workshop we will learn how to draw a 360-degree view of our environment using spherical perspective, and how to visualize these drawings as immersive panoramas by uploading them to virtual reality platforms that provide an interactive visualization of a 3D reconstruction of the original scene. We shall show how to construct these drawing in a simple way, using ruler and compass constructions, facilitated by adequate gridding that takes advantage of the symmetry groups of these spherical perspectives. We will consider two spherical perspectives: equirectangular and azimuthal equidistant, with a focus on the former due to its seamless integration with visualization software readily available on social networks. We will stress the relationship between these panoramas and the notion of spherical anamorphosis.

2018Conference object

Open access

Ruler, compass, and nail: constructing a total spherical perspective

Publication . Araújo, António

We obtain a construction of a total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360-degree field of view. Since the 1960s, several generalizations of this perspective have been proposed, but they were either works of a computational nature, inadequate for drawing with simple instruments, or lacked a general method for solving all vanishing points. We establish a general setup for anamorphosis and central perspective, define the total spherical perspective within this framework, study its topology, and show how to solve it with simple instruments. We consider its uses both in freehand drawing and in computer visualization, and its relation with the problem of reflection on a sphere.

2018-06-26Journal article

Open access