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- Using off-the-shelf AR and VR software for teaching immersive perspectives to 9th grade studentsPublication . Flores, Manuel; Araújo, AntónioRecent research has argued that an immersive reformulation of the concepts of anamorphosis and perspective can have beneficial effects on the teaching of these concepts to young students, and a didactic itinerary for Portuguese 9th grade students has been proposed and executed along these lines. A part of this reformulation is an integration with VR and AR visualizations which was implemented with off-the-shelf software. We report on both the advantages and limitations of these off-the-shelf platforms and propose adaptations and alternatives that might improve the didactic experience.
- Ruler, compass, and nail: constructing a total spherical perspectivePublication . Araújo, AntónioWe 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.
- Applications of anamorphosis and mixed reality in a classroom settingPublication . Flores, Manuel; Araújo, AntónioWe report on a novel use of handmade anamorphoses in connection with Mixed Reality in a classroom setting involving Portuguese 9th grade visual education students. This is based on a conceptual reformulation of anamorphosis that makes it intrinsically immersive and connects it naturally with digital visualizations. We propose that this is a useful device for motivating the study of perspective and descriptive geometry for young students.
- Drawn onto a skybox: an invitation to collaborative immersive drawing using the spheri platformPublication . Araújo, António; Olivero, Lucas FabianWe describe an installation that invites the audience to collaborate on the performance of immersive drawings that will be visualized on-the-fly using the custom hardware-software platform Spheri. These drawings are made on a flat surface using traditional physical materials and following a modular tracing process that helps the user conform to the rules of cubical spherical perspective. Concurrently with the drawing performance, the Spheri platform captures the drawing and converts it into an immersive VR visualization on-the-fly, while tracking the drawing motion and choosing the camera viewpoint accordingly. The installation explores the new media of immersive handmade perspectives as well as new forms of intuitive and performative visualization. Countering the expectations of digital media as instruments for efficiency and ease of production, it aims instead at leading the user into slow and pondered geometrical thinking through handmade immersive drawing.
- Workshop - Drawing equirectangular perspectives for VR panoramas with Eq A Sketch 360Publication . Araújo, AntónioIn this workshop we will explore the construction of immersive environments in equirectangular perspective using the Eq A Sketch 360 software. Eq A Sketch 360 is a serious toy for spherical perspective drawing. It has two innovative features: a sliding geodesic grid and an equirectangular snap-to ruler. These tools turn equirectangular drawing into a proper perspective, where all lines and vanishing points may be drawn by hand, to create immersive environments from either observation or imagination. This contrasts with previous methods of equirectangular drawing, that either avoided perspective altogether by drawing directly in VR view, or were limited to fixed grid methods with ad-hoc estimation of measurements. Eq A Sketch both forces and helps the user to learn spherical perspective. We will show how to draw by hand with perfect control of proportions and bearings, to make standalone designs or constructions that can be mixed with 360-degree photography.
- Anamorphosis reformed: from optical illusions to immersive perspectivesPublication . Araújo, AntónioWe 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.
- Enhancing the teaching of spherical perspective with spheriPublication . Olivero, Lucas Fabian; Araújo, AntónioSpherical perspectives and the practice of immersive drawing are going through a period of rapid development along with a concurrent growth of interest in their applications to various fields. The teaching of new practitioners must often be done in short workshops lateral to established curricula, which is a challenge due to the complexity of the subject. We present a digital tool for performative immersive drawing that can be instrumental in enabling a quick and informative transmission of the principles of immersive drawing to a student audience.
- Drawing equirectangular VR panoramas with ruler, compass, and protractorPublication . Araújo, AntónioThis 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.
- A geometria (descritiva) da anamorfose e das perspectivas curvilíneasPublication . Araújo, AntónioA anamorfose, enquanto artifício mimético, é o conceito fundamental que sustenta a perspectiva clássica e as perspectivas curvilíneas centrais. Enquanto conceito transversal merece uma plataforma, que presentemente não ocupa, no ensino das perspectivas, da geometria descritiva, e da realidade mista em computação gráfica e arte digital. Nesta palestra damos um panorama de vários trabalhos recentes do presente autor que pretendem contribuir para a criação de tal plataforma.