On Nonlinear Perspectives in Science, Art and Nature

Glaeser, Georg

On Nonlinear Perspectives in Science, Art and Nature

Files

123-132.pdf (1.44 MB)

Date

2005

Authors

Glaeser, Georg

Publisher

The Eurographics Association

Abstract

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.

        @inproceedings{10.2312:COMPAESTH/COMPAESTH05/123-132
,
booktitle = {Computational Aesthetics in Graphics, Visualization and Imaging
},
editor = {Laszlo Neumann and Mateu Sbert and Bruce Gooch and Werner Purgathofer
},
title = {{On Nonlinear Perspectives in Science, Art and Nature
}},
author = {Glaeser, Georg
},
year = {2005
},
publisher = {The Eurographics Association
},
ISSN = {1816-0859
},
ISBN = {3-905673-27-4
},
DOI = {10.2312/COMPAESTH/COMPAESTH05/123-132
}
}