Tracing Ray Differentials
Appears in the Computer Graphics (SIGGRAPH '99 Proceedings)
Antialiasing of ray traced images is typically performed by super-sampling
the image plane. While this type of filtering works well
for many algorithms, it is much more efficient to perform filtering
locally on a surface for algorithms such as texture mapping. In
order to perform this type of filtering, one must not only trace the
ray passing through the pixel, but also have some approximation
of the distance to neighboring rays hitting the surface (i.e., a ray’s
footprint). In this paper, we present a fast, simple, robust scheme
for tracking such a quantity based on ray differentials, derivatives
of the ray with respect to the image plane.
In the paper, equation (12) is derived for a planar surface, and it is
stated without proof that this is valid for arbitrary surfaces. The addendum proves this statement.
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