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- Anamorfoses e perspectivas curvilíneasPublication . Araújo, AntónioUm texto relativo à construção de perspectivas cilíndricas e esféricas.
- 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.
- Guidelines for drawing immersive panoramas in equirectangular perspectivePublication . Araújo, AntónioVirtual 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.
- 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.
- Explorations in rational drawingPublication . Araújo, AntónioWe discuss the position of the author’s spherical perspective work within a tradition of Rational Drawing, a discipline at the interface of mathematics and the arts.
- Boxing the visual sphere: towards a systematic solution of the cubical perspectivePublication . Araújo, António; Olivero, Lucas; Rossi, AdrianaCubic perspective is an attractive option for drawing VR panoramas, as it carries with it the familiarity of classical perspective and its ease of drawing line segments. Its simplicity is however only apparent as the transition of line images between the various planes of the cube can be baffling to the draughtsman. We argue that the best way to systematize this perspective is to see it fully as a spherical perspective and start by classifying and rendering its geodesics.
- Anamorphosis: optical games with perspective's playful parentPublication . Araújo, AntónioWe 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.
- Cardboarding mixed reality with Dürer MachinesPublication . Araújo, AntónioMixed reality is a direct application of 15 to 17th century principles of anamorphosis. The inherent physicality of anamorphosis, materialized through the Dürer perspective machine makes it an excellent teaching tool for students of digital art interested in mixed reality, whose initial core competencies may be extremely varied. The needs of these students are not met by the mere ephemera of learning how to use a particular piece of software; such knowledge is both transient and limiting of imaginative possibilities. We discuss a didactic strategy of cardboarding, i.e., a process of deliberate rudimentarization, to expose the inner workings of opaque chains of digital processes, to both clarify the elements of these chains and create loci for artistic intervention at their points of connection.
- Spherical perspectivePublication . Araújo, AntónioWe survey the present state of spherical perspective, regarding both mathematical structure and drawing practice, with a view to applications in the visual arts. We define a spherical perspective as the entailment of a conical anamorphosis with a compact flattening of the visual sphere. We examine a general framework for solving spherical perspectives, exemplified with the azimuthal equidistant (“fisheye”) and equirectangular cases. We consider the relation between spherical and curvilinear perspectives. We briefly discuss computer renderings but focus on methods adapted to freehand sketching or technical drawing with simple instruments such as ruler and compass. We discuss how handmade spherical perspective drawings can generate immersive anamorphoses, which can be rendered as virtual reality panoramas, leading to hybrid visual creations that bridge the gap between traditional drawing and digital environments.