SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5)

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https://diglib.eg.org/handle/10.2312/14332

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Browsing SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5) by Subject "Computer Graphics [I.3.5]"

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    Discrete Line Congruences for Shading and Lighting
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Wang, Jun; Jiang, Caigui; Bompas, Philippe; Wallner, Johannes; Pottmann, Hellmut; Yaron Lipman and Hao Zhang
    Two-parameter families of straight lines (line congruences) are implicitly present in graphics and geometry processing in several important ways including lighting and shape analysis. In this paper we make them accessible to optimization and geometric computing, by introducing a general discrete version of congruences based on piecewise-linear correspondences between triangle meshes. Our applications of congruences are based on the extraction of a so-called torsion-free support structure, which is a procedure analogous to remeshing a surface along its principal curvature lines. A particular application of such structures are freeform shading and lighting systems for architecture. We combine interactive design of such systems with global optimization in order to satisfy geometric constraints. In this way we explore a new area where architecture can greatly benefit from graphics.
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    Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Larsson, Thomas; Källberg, Linus; Yaron Lipman and Hao Zhang
    In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1:001-approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.
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    Watertight Scenes from Urban LiDAR and Planar Surfaces
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Kreveld, Marc van; Lankveld, Thijs van; Veltkamp, Remco C.; Yaron Lipman and Hao Zhang
    The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scene's surfaces. Related work generally either approximates the data with the risk of over-smoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. We present a method that combines these polygons into a watertight model. The polygon-based shape is closed with free-form meshes based on visibility information. To achieve this, we divide 3-space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graph-cut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modeler's description of urban scenes using simple boxes.