We present a GPU based implementation of Reyes-style adaptive surface subdivision, known in Reyes terminology as the Bound/Split and Dice stages. The performance of this task is important for the Reyes pipeline to map efficiently to graphics hardware, but its recursive nature and irregular and unbounded memory requirements present a challenge to an efficient implementation. Our solution begins by characterizing Reyes subdivision as a work queue with irregular computation, targeted to a massively parallel GPU. We propose efficient solutions to these general problems by casting our solution in terms of the fundamental primitives of prefix-sum and reduction, often encountered in parallel and GPGPU environments. Our results indicate that real-time Reyes subdivision can indeed be obtained on today's GPUs. We are able to subdivide a complex model to subpixel accuracy within 15 ms. Our measured performance is several times better than that of Pixar's RenderMan. Our implementation scales well with the input size and depth of subdivision. We also address concerns of memory size and bandwidth, and analyze the feasibility of conventional ideas on screen-space buckets.

We present a strategy for performing view-adaptive, crack-free tessellation of Catmull-Clark subdivision surfaces entirely on programmable graphics hardware. Our scheme extends the concept of breadth-first subdivision, which up to this point has only been applied to parametric patches. While mesh representations designed for a CPU often involve pointer-based structures and irregular per-element storage, neither of these is well-suited to GPU execution. To solve this problem, we use a simple yet effective data structure for representing a subdivision mesh, and design a careful algorithm to update the mesh in a completely parallel manner. We demonstrate that in spite of the complexities of the subdivision procedure, real-time tessellation to pixel-sized primitives can be done. Our implementation does not rely on any approximation of the limit surface, and avoids both subdivision cracks and T-junctions in the subdivided mesh. Using the approach in this paper, we are able to perform real-time subdivision for several static as well as animated models. Rendering performance is scalable for increasingly complex models.

We present a technique for designing memory-bound algorithms with high data reuse on Graphics Processing Units (GPUs) equipped with close-to-ALU software-managed memory. The approach is based on the efficient use of this memory through the implementation of a software-managed cache. We also present an analytical model for performance analysis of such algorithms. We apply this technique to the implementation of the GPU-based solver of the sum-product or marginalize a product of functions (MPF) problem, which arises in a wide variety of real-life applications in artificial intelligence, statistics, image processing, and digital communications. Our motivation to accelerate MPF originated in the context of the analysis of genetic diseases, which in some cases requires years to complete on modern CPUs. Computing MPF is similar to computing the chain matrix product of multi-dimensional matrices, but is more difficult due to a complex data-dependent access pattern, high data reuse, and a low compute-to-memory access ratio. Our GPU-based MPF solver achieves up to 2700-fold speedup on random data and 270-fold on real-life genetic analysis datasets on GeForce 8800GTX GPU from NVIDIA over the optimized CPU version on an Intel 2.4 GHz Core 2 with a 4 MB L2 cache.

We explore software mechanisms for managing irregular tasks on graphics processing units (GPUs). We demonstrate that dynamic scheduling and efficient memory management are critical problems in achieving high efficiency on irregular workloads. We experiment with several task-management techniques, ranging from the use of a single monolithic task queue to distributed queuing with task stealing and donation. On irregular workloads, we show that both centralized and distributed queues have more than 100 times as much idle times as our task-stealing and -donation queues. Our preferred choice is task-donation because of comparable performance to task-stealing while using less memory overhead. To help in this analysis, we use an artificial task-management system that monitors performance and memory usage to quantify the impact of these different techniques. We validate our results by implementing a Reyes renderer with its irregular split-and-dice workload that is able to achieve real-time framerates on a single GPU.

We solve the problem of generating a uniform Poisson-disk sampling that is both maximal and unbiased over bounded non-convex domains. To our knowledge this is the first provably correct algorithm with time and space dependent only on the number of points produced. Our method has two phases, both based on classical dart-throwing. The first phase uses a background grid of square cells to rapidly create an unbiased, near-maximal covering of the domain. The second phase completes the maximal covering by calculating the connected components of the remaining uncovered voids, and by using their geometry to efficiently place unbiased samples that cover them. The second phase converges quickly, overcoming a common difficulty in dart-throwing methods. The deterministic memory is O(n) and the expected running time is O(n log n), where n is the output size, the number of points in the final sample. Our serial implementation verifies that the log n dependence is minor, and nearly O(n) performance for both time and memory is achieved in practice. We also present a parallel implementation on GPUs to demonstrate the parallel-friendly nature of our method, which achieves 2.4x the performance of our serial version.

We provide a simple algorithm and data structures for d-dimensional unbiased maximal Poisson-disk sampling. We use an order of magnitude less memory and time than the alternatives. Our results become more favorable as the dimension increases. This allows us to produce bigger samplings. Domains may be non-convex with holes. The generated point cloud is maximal up to round-off error. The serial algorithm is provably bias-free. For an output sampling of size n in fixed dimension d, we use a linear memory budget and empirical Θ(n) runtime. No known methods scale well with dimension, due to the "curse of dimensionality." The serial algorithm is practical in dimensions up to 5, and has been demonstrated in 6d. We have efficient GPU implementations in 2d and 3d. The algorithm proceeds through a finite sequence of uniform grids. The grids guide the dart throwing and track the remaining disk-free area. The top-level grid provides an efficient way to test if a candidate dart is disk-free. Our uniform grids are like quadtrees, except we delay splits and refine all leaves at once. Since the quadtree is flat it can be represented using very little memory: we just need the indices of the active leaves and a global level. Also it is very simple to sample from leaves with uniform probability. © 2012 The Author(s).

In this work, we introduced k-d darts as a particular type of higherdimensional sampling. We described a k-d dart framework for hyperplanes of general dimension k, and then demonstrated efficiency and accuracy over three applications using k = 1, and accuracy for one application using k = 1. In particular, darts produce accurate estimates of the volume of an object regardless of the dimension, orientation, and aspect ratio of the object. Axis-aligned darts are universally preferable to unaligned ones for sampling square domains, and we expect this to extend to hyperrectangles, such as bounding boxes. Darts also produce accurate mean estimates for function integration. © 2014 ACM 0730-0301/2014/01-ART3 15.00.