Figure 1: With the eight seeds (highlighted and shown in different colors) in a 64×64 grid on the leftmost picture, the progress of each round of the jump flooding algorithm is shown in the other six pictures, with the rightmost being the computed Voronoi diagram. AbstractThis paper studies jump flooding as an algorithmic paradigm in the general purpose computation with GPU. As an example application of jump flooding, the paper discusses a constant time algorithm on GPU to compute an approximation to the Voronoi diagram of a given set of seeds in a 2D grid. The errors due to the differences between the approximation and the actual Voronoi diagram are hardly noticeable to the naked eye in all our experiments. The same approach can also compute in constant time an approximation to the distance transform of a set of seeds in a 2D grid. In practice, such constant time algorithm is useful to many interactive applications involving, for example, rendering and image processing. Besides the experimental evidences, this paper also confirms quantitatively the effectiveness of jump flooding by analyzing the occurrences of errors. The analysis is a showcase of insights to the jump flooding paradigm, and may be of independent interests to other applications of jump flooding.

Testing autonomous driving algorithms on real autonomous vehicles is extremely costly and many researchers and developers in the field cannot afford a real car and the corresponding sensors. Although several free and open-source autonomous driving stacks, such as Autoware and Apollo are available, choices of open-source simulators to use with them are limited. In this paper, we introduce the LGSVL Simulator which is a high fidelity simulator for autonomous driving.The simulator engine provides end-to-end, full-stack simulation which is ready to be hooked up to Autoware and Apollo. In addition, simulator tools are provided with the core simulation engine which allow users to easily customize sensors, create new types of controllable objects, replace some modules in the core simulator, and create digital twins of particular environments.

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This paper presents a novel approach to compute, for a given point set S in R 2 , its Delaunay triangulation T (S). Though prior work mentions the possibility of using the graphics processing unit (GPU) to compute Delaunay triangulations, no known implementation and performance have been reported. Our work uncovers various challenges in the use of GPU for such a purpose. In practice, our approach exploits the GPU to assist in the computation of a triangulation T ′ of S that is a good approximation to T (S). From that, the approach employs the CPU to transform T ′ to T (S). As a major part of the total work is done by the GPU with parallel computing capability, it is a fast and practical approach, particularly for a large number of points (millions with the current state-of-the-art GPU). For such cases, our current implementation can run up to 53% faster on a Core2 Duo machine when compared to Triangle, the well-known fastest Delaunay triangulation implementation.

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The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework -the CVT in universal covering space. The novel spherical and hyperbolic CVT energy functions are defined, and the relationship between minimizing the energy and the CVT is proved. We also show by our experimental results that both spherical and hyperbolic CVTs have the similar property as their Euclidean counterpart where the sites are uniformly distributed with respect to given density values. As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus>1) surfaces.