A Meshless Hierarchical
Representation for Light Transport

Jaakko Lehtinen, Matthias Zwicker, Emmanuel Turquin,
Janne Kontkanen, Frédo Durand, François Sillion, Timo Aila
ACM Transactions in Graphics 27(3) (Proc. SIGGRAPH 2008).


We introduce a meshless hierarchical representation for solving light transport problems. Precomputed radiance transfer (PRT) and finite elements require a discrete representation of illumination over the scene. Non-hierarchical approaches such as per-vertex values are simple to implement, but lead to long precomputation. Hierarchical bases like wavelets lead to dramatic acceleration, but in their basic form they work well only on flat or smooth surfaces. We introduce a hierarchical function basis induced by scattered data approximation. It is decoupled from the geometric representation, allowing the hierarchical representation of illumination on complex objects. We present simple data structures and algorithms for constructing and evaluating the basis functions. Due to its hierarchical nature, our representation adapts to the complexity of the illumination, and can be queried at different scales. We demonstrate the power of the new basis in a novel precomputed direct-to-indirect light transport algorithm that greatly increases the complexity of scenes that can be handled by PRT approaches.


The authors thank Michael Doggett, Michael Garland, Nicolas Holzschuch, Tomas Akenine-Möller, Andy Nealen, Sylvain Paris, Jussi Räsänen, and Lauri Savioja for feedback; Stephen Duck for the Great Hall scene; DreamWorks Animation for the Jade Palace model; Eric Tabellion and Andrew Pearce for help with the Jade Palace model; the Stanford Computer Graphics Laboratory for the David model; Marko Dabrovic (www.rna.hr) for the Sponza Atrium model. This research was supported by the National Technology Agency of Finland, Anima Vitae, AMD Research Finland, NVIDIA Helsinki, Remedy Entertainment, the Academy of Finland (Grant 108 222), the INRIA Associate Research Team ARTIS/ MIT, and NSF CAREER 044756. Jaakko Lehtinen acknowledges an NVIDIA Fellowship. Frédo Durand acknowledges a Microsoft Research New Faculty Fellowship and a Sloan Fellowship.


More Applications

The basis can be applied in a wide variety of situations. For two further examples, you can also take a look at an earlier version of this work.
Jaakko Lehtinen, Oct 4 2008