Summed Area Tables for Cube Maps.

The original Summed Area Table (SAT) structure is designed for handling 2D rectangular data. Due to the nature of spherical functions, the SAT structure cannot handle cube maps directly. This paper proposes a new SAT structure for cube maps and develops the corresponding lookup algorithm. Our formulation starts by considering a cube map as part of an auxiliary 3D function defined in a 3D rectangular space. We interpret the 2D integration process over the cube map surface as a 3D integration over the auxiliary 3D function. One may suggest that we can create a 3D SAT for this auxiliary function, and then use the 3D SAT to achieve the 3D integration. However, it is not practical to generate or store this special 3D SAT directly. This 3D SAT has some nice properties that allow us to store it in a storage-friendly data structure, namely Summed Area Cube Map (SACM). A SACM can be stored in a standard cube map texture. The lookup algorithm of our SACM structure can be implemented efficiently on current graphics hardware. In addition, the SACM structure inherits the favorable properties of the original SAT structure.