# Matrix Row-Column Sampling for the Many-Light Problem

## Milos Hasan, Fabio Pellacini, Kavita Bala

*Proceedings of SIGGRAPH 2007* (SIGGRAPH 2007, *ACM Transactions on Graphics, Volume 26, Number 3*)

**Abstract:**
Rendering complex scenes with indirect illumination, high dynamic range
environment lighting, and many direct light sources remains a challenging
problem. Prior work has shown that all these effects can be approximated by
many point lights. This paper presents a scalable solution to the many-light
problem suitable for a GPU implementation. We view the problem as a large
matrix of samplelight interactions; the ideal final image is the sum of the
matrix columns. We propose an algorithm for approximating this sum by sampling
entire rows and columns of the matrix on the GPU using shadow mapping. The key
observation is that the inherent structure of the transfer matrix can be
revealed by sampling just a small number of rows and columns. Our prototype
implementation can compute the light transfer within a few seconds for scenes
with indirect and environment illumination, area lights, complex geometry and
arbitrary shaders. We believe this approach can be very useful for rapid
previewing in applications like cinematic and architectural lighting design.

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**Acknowledgments: National Science Foundation (NSF),
Intel Corporation, NVidia for equipment donations.**