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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

Partial regularity of the solutions to a turbulent problem in porous media

Publication . de Oliveira, H. B.; Paiva, A.

A one-equation turbulent model that is being used with success in the applications to model turbulent flows through porous media is studied in this work. We consider the classical Navier-Stokes equations, with feedback forces fields, coupled with the equation for the turbulent kinetic energy (TKE) through the turbulence production term and through the turbulent and the diffusion viscosities. Under suitable growth conditions on the feedback functions involved in the model, we prove the local higher integrability of the gradient solutions to the steady version of this problem.

2019-09Journal article

Restricted

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

Kelvin-Voigt equations perturbed by anisotropic relaxation, diffusion and damping

Publication . Antontsev, S. N.; de Oliveira, H.B.; Khompysh, Kh.

The purpose of this work is the analysis of the existence and uniqueness of weak solutions to a Kelvin-Voigt problem wherein the viscous and relaxation parts of the stress tensor are given by distinct power-laws. We assume that the viscous and relaxation terms may be fully anisotropic and that the momentum equation is perturbed by a damping term which may also be fully anisotropic. In the particular case of considering this problem with a linear and isotropic relaxation term, we prove the existence of global and local weak solutions. The uniqueness of weak solutions is established in this case as well. For the full anisotropic problem, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients must interact in order to be established global and local in time a priori estimates. (C) 2019 Elsevier Inc. All rights reserved.

2019-05Journal article

Restricted

Topologia, anamorfose, e o bestiário das perspectivas curvilíneas

Publication . Araújo, António Bandeira

Faz-se uma breve digressão pelo catálogo das perspectivas curvilíneas centrais, descrevendo algumas das suas propriedades topológicas, geométricas, e ópticas, enfatizando a sua ligação com o conceito fundamental de anamorfose com vista a esclarecer alguns equívocos clássicos relativos à posição fundamental ocupada pela perspectiva clássica.

2016-09Journal article

Open Access