Note: this is joint work with Karan Singh of the University of Toronto.
The human vision system uses linear perspective locally to resolve depth and shape. It is not, however, particularly good at discerning global linear perspective - hence the difficulty in learning to draw in true perspective. Artists have taken advantage of this fact to give the illusion of depth while moving things around on the image plane to produce pleasing 2D compositions. In fact, many artists produce drawings that are perspectively incorrect, but perceptually closer to what the eye actually sees.
The first approaches (1) (2) to non-linear projection essentially allowed each object to have its own camera. Multiperspective projection produces a panorama where the view point is allowed to change.
The most comprehensive system to date is Ryan, which produces non-linear projections by combining two or more camera view points in a reasonable way. This is, in essence, the inverse of a free-form deformation - one can either consider each vertex in the scene to have its own camera, or that the entire scene is deformed, and then rendered with a single projection.
We are currently exploring alternative interfaces to non-linear projection. Although Ryan is very general, it is almost too general, and requires a great deal of hand-placement of cameras.
Our first approach to this problem uses image-space constraints to construct and control the cameras. This is, again, a very general interface, but by defining the cameras in image-space, we make it much easier to ensure that objects end up where we want them in the scene.
On the opposite
end of the generality spectrum is curvi-linear perspective,
which produces a type of perspective distortion characterized by
projecting parallel lines in the model to sinusoids. The interface is
very simple, and since it's implemented in the GPU, fully interactive.
Currently we are exploring other comprehensive interfaces for some common non-linear projections, such as an "inside-out" and "outside-in" projection.
See also camera interpolation and control.
