A meshless hierarchical representation for light transport

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.