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Point-based rendering is a compact and efficient means of displaying complex geometry.This article describes an approach to enable flexible point-based rendering, permitting local image refinement, required for example when zooming into very complex scenes, and efficient shadow computations. The method uses a hierarchical packed point representations based on recursive grid data structures. Such compact structures are particularly well adapted to devices with limited memory and display resolution, such as PDA's. Intermediate attributes--such as normals and colors at internal nodes of the hierarchy--are stored, to achieve flexible rendering. The article examines the memory and computation trade-offs involved in the type of structure used, and finds that tri-grids are a suitable compromise for many cases. Implementations of the method on PC and on a PDA are demonstrated for octrees and tri-grids. The PDA version can render objects sampled by 1.3 million points at 2.1 frames per second.