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Item On Shape Design and Optimization of Gerotor Pumps(The Eurographics Association and John Wiley & Sons Ltd., 2024) Pareja-Corcho, Juan C.; Barton, Michael; Pedrera-Busselo, Asier; Mejia-Parra, Daniel; Moreno, Aitor; Posada, Jorge; Hu, Ruizhen; Lefebvre, SylvainA gerotor pump is a two-piece mechanism where two rotational components, interior and exterior, engage each other via a rotational motion to transfer a fluid in a direction parallel to their rotational axes. A natural question arises on what shape of the gerotor is the optimal one in the sense of maximum fluid being pumped for a unit of time, given the constraint of a fixed material needed to manufacture the pump. As there is no closed-formula to answer this question, we propose a new algorithm to design and optimize the shape of gerotor pumps to be as efficient as possible. The proposed algorithm is based on a fast construction of the envelope of the interior component and subsequent optimization. We demonstrate our algorithm on a benchmark gerotor and show that the optimized solution increases the estimated flowrate by 16%. We also use our algorithm to study the effect of the number of teeth on the cavity area of a gerotor.Item Cascading Upper Bounds for Triangle Soup Pompeiu-Hausdorff Distance(The Eurographics Association and John Wiley & Sons Ltd., 2024) Sacht, Leonardo; Jacobson, Alec; Hu, Ruizhen; Lefebvre, SylvainWe propose a new method to accurately approximate the Pompeiu-Hausdorff distance from a triangle soup A to another triangle soup B up to a given tolerance. Based on lower and upper bound computations, we discard triangles from A that do not contain the maximizer of the distance to B and subdivide the others for further processing. In contrast to previous methods, we use four upper bounds instead of only one, three of which newly proposed by us. Many triangles are discarded using the simpler bounds, while the most difficult cases are dealt with by the other bounds. Exhaustive testing determines the best ordering of the four upper bounds. A collection of experiments shows that our method is faster than all previous accurate methods in the literature.