Tracing Ray Differentials

Homan Igehy, Stanford University

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.

Download paper:

Read the addendum:

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.


Copyright Notice (from ACM):
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.