Fast Non-Linear Projections using Graphics Hardware
Linear perspective projections are used extensively in graphics.
They provide a non-distorted view, with simple computations that
map easily to hardware. Non-linear projections, such as the view
given by a fish-eye lens are also used, either for artistic reasons or in
order to provide a larger field of view, e.g. to approximate environment
reflections or omnidirectional shadow maps. As the computations
related to non-linear projections are more involved, they are
harder to implement, especially in hardware, and have found little
use so far in practical applications. In this paper, we apply existing
methods for non-linear projections [Lloyd et al. 2006; Hou et al.
2006; Fournier 2005] to a specific class: non-linear projections with
a single center of projection, radial symmetry and convexity. This
class includes, but is not limited to, paraboloid projections, hemispherical
projections and fish-eye lenses. We show that, for this
class, the projection of a 3D triangle is a single curved triangle, and
we give a mathematical analysis of the curved edges of the triangle;
this analysis allows us to reduce the computations involved, and
to provide a faster implementation. The overhead for non-linearity
is bearable and can be balanced with the fact that a single nonlinear
projection can replaces as many as five linear projections (in
a hemicube), with less discontinuities and a smaller memory cost,
thus making non-linear projections a practical alternative.
Images and movies
See also
BibTex references
@InProceedings\{GHFP08, author = "Gascuel, Jean-Dominique and Holzschuch, Nicolas and Fournier, Gabriel and Peroche, Bernard", title = "Fast Non-Linear Projections using Graphics Hardware", booktitle = "ACM Symposium on Interactive 3D Graphics and Games", month = "feb", year = "2008", keywords = "games \& GPUs, graphics hardware", url = "http://maverick.inria.fr/Publications/2008/GHFP08" }