Browsing by Author "Bukenberger, Dennis R."

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    At‐Most‐Hexa Meshes
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2022) Bukenberger, Dennis R.; Tarini, Marco; Lensch, Hendrik P. A.; Hauser, Helwig and Alliez, Pierre
    Volumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. Still, their construction bears several additional challenges compared to boundary‐based representations. Tetrahedral meshes and (pure) hex‐meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hex‐meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. Hex‐dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. In this work, we introduce a strict subset of general hex‐dominant meshes, which we term ‘at‐most‐hexa meshes’, in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. We exemplify the ease of construction of at‐most‐hexa meshes by proposing a frugal and straightforward method to generate high‐quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre‐computations and can start directly from surfaces or samples. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We introduce specialized operations on the three‐dimensional graph structure to enforce consistency during the relaxation. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes.
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    Constructing L∞ Voronoi Diagrams in 2D and 3D
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Bukenberger, Dennis R.; Buchin, Kevin; Botsch, Mario; Campen, Marcel; Spagnuolo, Michela
    Voronoi diagrams and their computation are well known in the Euclidean L2 space. They are easy to sample and render in generalized Lp spaces but nontrivial to construct geometrically. Especially the limit of this norm with p -> ∞ lends itself to many quad- and hex-meshing related applications as the level-set in this space is a hypercube. Many application scenarios circumvent the actual computation of L∞ diagrams altogether as known concepts for these diagrams are limited to 2D, uniformly weighted and axis-aligned sites. Our novel algorithm allows for the construction of generalized L∞ Voronoi diagrams. Although parts of the developed concept theoretically extend to higher dimensions it is herein presented and evaluated for the 2D and 3D case. It further supports individually oriented sites and allows for generating weighted diagrams with anisotropic weight vectors for individual sites. The algorithm is designed around individual sites, and initializes their cells with a simple meshed representation of a site's level-set. Hyperplanes between adjacent cells cut the initialization geometry into convex polyhedra. Non-cell geometry is filtered out based on the L∞ Voronoi criterion, leaving only the non-convex cell geometry. Eventually we conclude with discussions on the algorithms complexity, numerical precision and analyze the applicability of our generalized L∞ diagrams for the construction of Centroidal Voronoi Tessellations (CVT) using Lloyd's algorithm.
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    Stereo‐Consistent Contours in Object Space
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Bukenberger, Dennis R.; Schwarz, Katharina; Lensch, Hendrik P. A.; Chen, Min and Benes, Bedrich
    Notebook scribbles, art or technical illustrations—line drawings are a simplistic method to visually communicate information. Automated line drawings often originate from virtual 3D models, but one cannot trivially experience their three‐dimensionality. This paper introduces a novel concept to produce stereo‐consistent line drawings of virtual 3D objects. Some contour lines do not only depend on an objects geometry, but also on the position of the observer. To accomplish consistency between multiple view positions, our approach exploits geometrical characteristics of 3D surfaces in object space. Established techniques for stereo‐consistent line drawings operate on rendered pixel images. In contrast, our pipeline operates in object space using vector geometry, which yields many advantages: The position of the final viewpoint(s) is flexible within a certain window even after the contour generation, e.g. a stereoscopic image pair is only one possible application. Such windows can be concatenated to simulate contours observed from an arbitrary camera path. Various types of popular contour generators can be handled equivalently, occlusions are natively supported and stylization based on geometry characteristics is also easily possible.Notebook scribbles, art or technical illustrations—line drawings are a simplistic method to visually communicate information. Automated line drawings often originate from virtual 3D models, but one cannot trivially experience their three‐dimensionality. This paper introduces a novel concept to produce stereo‐consistent line drawings of virtual 3D objects. Some contour lines do not only depend on an objects geometry, but also on the position of the observer. To accomplish consistency between multiple view positions, our approach exploits geometrical characteristics of 3D surfaces in object space. Established techniques for stereo‐consistent line drawings operate on rendered pixel images. In contrast, our pipeline operates in object space using vector geometry, which yields many advantages: The position of the final viewpoint(s) is flexible within a certain window even after the contour generation, e.g. a stereoscopic image pair is only one possible application.