Abstract: A Meshless Hierarchical Representation for Light Transport
We introduce a meshless hierarchical representation for solving
light transport problems. Precomputed radiance transfer (PRT) and
Þnite 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. Hier-
archical bases like wavelets lead to dramatic acceleration, but in
their basic form they work well only on ßat 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 con-
structing and evaluating the basis functions. Due to its hierarchical
nature, our representation adapts to the complexity of the illumi-
nation, 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.