41-Issue 6

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https://diglib.eg.org/handle/10.2312/2633218

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Browsing 41-Issue 6 by Subject "computational geometry"

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    Computing Schematic Layouts for Spatial Hypergraphs on Concentric Circles and Grids
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Bekos, M.A.; Dekker, D.J.C.; Frank, F.; Meulemans, W.; Rodgers, P.; Schulz, A.; Wessel, S.; Hauser, Helwig and Alliez, Pierre
    Set systems can be visualized in various ways. An important distinction between techniques is whether the elements have a spatial location that is to be used for the visualization; for example, the elements are cities on a map. Strictly adhering to such location may severely limit the visualization and force overlay, intersections and other forms of clutter. On the other hand, completely ignoring the spatial dimension omits information and may hide spatial patterns in the data. We study layouts for set systems (or hypergraphs) in which spatial locations are displaced onto concentric circles or a grid, to obtain schematic set visualizations. We investigate the tractability of the underlying algorithmic problems adopting different optimization criteria (e.g. crossings or bends) for the layout structure, also known as the support of the hypergraph. Furthermore, we describe a simulated‐annealing approach to heuristically optimize a combination of such criteria. Using this method in computational experiments, we explore the trade‐offs and dependencies between criteria for computing high‐quality schematic set visualizations.
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    Delaunay Painting: Perceptual Image Colouring from Raster Contours with Gaps
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Parakkat, Amal Dev; Memari, Pooran; Cani, Marie‐Paule; Hauser, Helwig and Alliez, Pierre
    We introduce Delaunay Painting, a novel and easy‐to‐use method to flat‐colour contour‐sketches with gaps. Starting from a Delaunay triangulation of the input contours, triangles are iteratively filled with the appropriate colours, thanks to the dynamic update of flow values calculated from colour hints. Aesthetic finish is then achieved, through energy minimisation of contour‐curves and further heuristics enforcing the appropriate sharp corners. To be more efficient, the user can also make use of our colour diffusion framework, which automatically extends colouring to small, internal regions such as those delimited by hatches. The resulting method robustly handles input contours with strong gaps. As an interactive tool, it minimizes user's efforts and enables any colouring strategy, as the result does not depend on the order of interactions. We also provide an automatized version of the colouring strategy for quick segmentation of contours images, that we illustrate with applications to medical imaging and sketch segmentation.
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    Transforming an Adjacency Graph into Dimensioned Floorplan Layouts
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Bisht, Sumit; Shekhawat, Krishnendra; Upasani, Nitant; Jain, Rahil N.; Tiwaskar, Riddhesh Jayesh; Hebbar, Chinmay; Hauser, Helwig and Alliez, Pierre
    In recent times, researchers have proposed several approaches for building floorplans using parametric/generative design, shape grammars, machine learning, AI, . This paper aims to demonstrate a mathematical approach for the automated generation of floorplan layouts. Mathematical formulations warrant the fulfilment of all input user constraints, unlike the learning‐based methods present in the literature. Moreover, the algorithms illustrated in this paper are robust, scalable and highly efficient, generating thousands of floorplans in a few milliseconds.We present G2PLAN, a software based on graph‐theoretic and linear optimization techniques, that generates all topologically distinct floorplans with different boundary rooms in linear time for given adjacency and dimensional constraints. G2PLAN builds on the work of GPLAN and offers solutions to a wider range of adjacency relations (one‐connected, non‐triangulated graphs) and better dimensioning customizability. It also generates a catalogue of dimensionless as well as dimensioned floorplans satisfying user requirements.