Correction of geometric perceptual distortions in pictures
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A realistic camera model for computer graphics
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiperspective panoramas for cel animation
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Multiple-center-of-projection images
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Ryan: rendering your animation nonlinearly projected
Proceedings of the 3rd international symposium on Non-photorealistic animation and rendering
Nonlinear Perspective Projections and Magic Lenses: 3D View Deformation
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
A framework for multiperspective rendering
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
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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.