On Nonlinear Perspectives in Science, Art and Nature

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Georg Glaeser: On Nonlinear Perspectives in Science, Art and Nature. In: László Neumann, Mateu Sbert, Bruce Gooch, Werner Purgathofer (Eds.): Eurographics Workshop on Computational Aesthetics. 2005. 123-132




Classic perspectives, i.e., central projections onto a plane, are extremely common in our days. Photos, movies, computer generated animations almost exclusively use this technique. They are linear since straight lines in space appear as straight lines in the image. Nevertheless, humans and animals of all kind have a more complicated method to develop images in their brains. They measure angles, not lengths. Together with nonlinear projections onto curved surfaces, impressions are transformed into spatial imagination. When it comes to 2D-reproduction of such processes, we need nonlinear perspectives in 2-space. They usually look like fisheye-images, i.e., projections of space onto a plane via a not symmetric, extremely refracting spherical lens. Similar distortions occur when we look out of still water or into reflecting spheres. In fine Arts, the angle measuring was intuitively applied by artists. In geometry, the inversion at a circle (sphere), several models of non-Euclidean geometries and the stereographic projection onto the plane or mappings of the sphere respectively lead to comparable results. We call the latter transformations "secondary" nonlinear perspectives. Finally, realtime algorithms are presented that transform primary nonlinear perspectives like special refractions into classic perspectives. Therefore, we work with Taylor series (or, if possible, with accurate formulas) and – for speed reasons – with precalculated tables.

Extended Abstract


author = {Glaeser, Georg},
title = {On Nonlinear Perspectives in Science, Art and Nature},
booktitle = {Proceedings of the First Eurographics Conference on Computational Aesthetics in Graphics, Visualization and Imaging},
series = {Computational Aesthetics'05},
year = {2005},
isbn = {3-905673-27-4},
location = {Girona, Spain},
pages = {123--132},
numpages = {10},
url = {http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/123-132 http://de.evo-art.org/index.php?title=On_Nonlinear_Perspectives_in_Science,_Art_and_Nature },
doi = {10.2312/COMPAESTH/COMPAESTH05/123-132},
acmid = {2381237},
publisher = {Eurographics Association},
address = {Aire-la-Ville, Switzerland, Switzerland},

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