Efficient HPR-Based Rendering of Point Clouds

Recently, Katz et al. have shown how visibility information for a point cloud may be estimated by the so-called HPR operator. In a nutshell, the operator consists of a simple transformation of the cloud followed by a convex hull computation. Since convex hulls take O(n log n) time to compute in the worst case, this method has been considered impractical for real-time rendering of medium to large point clouds. In this paper, we describe a GPU implementation of an approximate convex-hull algorithm that runs in O(n+k) time, where k is a parameter of the method. Experiments show that the method is suitable for real-time rendering and partial reconstruction of point clouds with millions of points.