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 "Curve"

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    CubeCover - Parameterization of 3D Volumes
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Nieser, Matthias; Reitebuch, Ulrich; Polthier, Konrad; Mario Botsch and Scott Schaefer
    Despite the success of quad-based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CUBECOVER is a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field. The input of CUBECOVER is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. CUBECOVER has similarities to the QUADCOVER algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space.
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    Rational Bi-cubic G2 Splines for Design with Basic Shapes
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Karciauskas, Kestutis; Peters, Jörg; Mario Botsch and Scott Schaefer
    The paper develops a rational bi-cubic G<sup>2</sup> (curvature continuous) analogue of the non-uniform polynomial C<sup>2</sup> cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic shapes.
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    Surface Patches from Unorganized Space Curves
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Abbasinejad, Fatemeh; Joshi, Pushkar; Amenta, Nina; Mario Botsch and Scott Schaefer
    Recent 3D sketch tools produce networks of three-space curves that suggest the contours of shapes. The shapes may be non-manifold, closed three-dimensional, open two-dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise-smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi-automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [BBS08], our system allows the user to build the desired surface with just a few mouse-clicks.