SGP11: Eurographics Symposium on Geometry Processing

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https://diglib.eg.org/handle/10.2312/436

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Browsing SGP11: Eurographics Symposium on Geometry Processing by Subject "and systems"

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    A Hierarchical Grid Based Framework for Fast Collision Detection
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Fan, Wenshan; Wang, Bin; Paul, Jean-Claude; Sun, Jiaguang; Mario Botsch and Scott Schaefer
    We present a novel hierarchical grid based method for fast collision detection (CD) for deformable models on GPU architecture. A two-level grid is employed to accommodate the non-uniform distribution of practical scene geometry. A bottom-to-top method is implemented to assign the triangles into the hierarchical grid without any iteration while a deferred scheme is introduced to efficiently update the data structure. To address the issue of load balancing, which greatly influences the performance in SIMD parallelism, a propagation scheme which utilizes a parallel scan and a segmented scan is presented, distributing workloads evenly across all concurrent threads. The proposed method supports both discrete collision detection (DCD) and continuous collision detection (CCD) with self-collision. Some typical benchmarks are tested to verify the effectiveness of our method. The results highlight our speedups over prior algorithms on different commodity GPUs.
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    A Multiscale Approach to Optimal Transport
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Mérigot, Quentin; Mario Botsch and Scott Schaefer
    In this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart.
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    On the Shape of a Set of Points and Lines in the Plane
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Kreveld, Marc van; Lankveld, Thijs van; Veltkamp, Remco C.; Mario Botsch and Scott Schaefer
    Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free-form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the guided a-shape: an extension of the well known a-shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided a-shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided a-shape can be constructed in O((n+m) log(n+m)) time, from an input of n points and m guides. We apply guided a-shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided a-shapes of both synthetic and real data and show they are consistently better than a-shapes for this application.