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a) 8D Delaunay graph (b) 100D global optimization (c) 8D rendering (d) 23D motion planning Fig. 1. Spoke-dart sampling for high-dimensional applications: Delaunay graph construction, optimization, rendering, and motion planning.Blue noise sampling has proved useful for many graphics applications, but remains under-explored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples, and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution, and the adaptability of the intermediate processes of our method, are useful in these applications.

Figure 1: A sifted point cloud (right) retains much of the visual quality of the original (left), but using fewer points. 113k points were reduced by 16% in 19 seconds. Sifted disks are maximal and satisfy the same sizing function as the original. AbstractWe introduce the Sifted Disk technique for locally resampling a point cloud in order to reduce the number of points. Two neighboring points are removed and we attempt to find a single random point that is sufficient to replace them both. The resampling respects the original sizing function; In that sense it is not a coarsening. The angle and edge length guarantees of a Delaunay triangulation of the points are preserved. The sifted point cloud is still suitable for texture synthesis because the Fourier spectrum is largely unchanged. We provide an efficient algorithm, and demonstrate that sifting uniform Maximal Poisson-disk Sampling (MPS) and Delaunay Refinement (DR) points reduces the number of points by about 25%, and achieves a density about 1/3 more than the theoretical minimum. We show two-dimensional stippling and meshing applications to demonstrate the significance of the concept.

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We engineer a GPU implementation of a B-Tree that supports concurrent queries (point, range, and successor) and updates (insertions and deletions). Our B-tree outperforms the state of the art, a GPU log-structured merge tree (LSM) and a GPU sorted array. In particular, point and range queries are significantly faster than in a GPU LSM (the GPU LSM does not implement successor queries). Furthermore, B-Tree insertions are also faster than LSM and sorted array insertions unless insertions come in batches of more than roughly 100k. Because we cache the upper levels of the tree, we achieve lookup throughput that exceeds the DRAM bandwidth of the GPU. We demonstrate that the key limiter of performance on a GPU is contention and describe the design choices that allow us to achieve this high performance.