30-Issue 5

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https://diglib.eg.org/handle/10.2312/165

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Browsing 30-Issue 5 by Subject "Computer Graphics [I.3.5]"

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    Functional Webs for Freeform Architecture
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Deng, B.; Pottmann, Helmut; Wallner, Johannes; Mario Botsch and Scott Schaefer
    Rationalization and construction-aware design dominate the issue of realizability of freeform architecture. The former means the decomposition of an intended shape into parts which are sufficiently simple and efficient to manufacture; the latter refers to a design procedure which already incorporates rationalization. Recent contributions to this topic have been concerned mostly with small-scale parts, for instance with planar faces of meshes. The present paper deals with another important aspect, namely long-range parts and supporting structures. It turns out that from the pure geometry viewpoint this means studying families of curves which cover surfaces in certain well-defined ways. Depending on the application one has in mind, different combinatorial arrangements of curves are required. We here restrict ourselves to so-called hexagonal webs which correspond to a triangular or tri-hex decomposition of a surface. The individual curve may have certain special properties, like being planar, being a geodesic, or being part of a circle. Each of these properties is motivated by manufacturability considerations and imposes constraints on the shape of the surface. We investigate the available degrees of freedom, show numerical methods of optimization, and demonstrate the effectivity of our approach and the variability of construction solutions derived from webs by means of actual architectural designs.
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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.